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Brad Dennis Capstone Project

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					Using Alternative Assessment Methods to Alleviate Math Test Anxiety




                        A Capstone Project
                 Submitted in Partial Fulfillment of
                the Requirements for the Degree of
              Master of Arts in Teaching: Mathematics




                       Bradley Lloyd Dennis




         Department of Mathematics and Computer Science
                  College of Arts and Sciences




                        Graduate School
                      Minot State University
                      Minot, North Dakota




                          Summer 2012
                                                                     ii

                            This capstone project was submitted by

                                    Bradley Lloyd Dennis



Graduate Committee:



Dr. Kodwo Annan, Chairperson



Dr. Laurie Geller



Dr. Ryan Winburn



Dean of Graduate School



Dr. Linda Cresap


Date of defense: July 5, 2012
                                                                                                   iii

                                            Abstract

Math test anxiety causes a gap between a student’s understanding and test achievement. This was

a concern for me as a classroom teacher as it decreased the validity of my tests as assessment

tools, and worse, it created contempt toward math. If I could alleviate some of this anxiety

toward math tests I could consequently produce more accurate test scores and better student

sentiment. After researching different methods of reducing test anxiety, I used cheat sheets and

the allowance of hints on tests as alternative assessment techniques in my classroom. These

assessment techniques gave students a safety net should they freeze up from test anxiety and also

gave me additional assessment tools as a math teacher.
                                                                                                iv

                                       Acknowledgements

       First, I would like to thank my mom and dad for instilling in me the values of hard work

and perseverance, along with many others. These qualities have molded me into the person I am

today. Thank you for being such outstanding parents.

       Thank you to the staff at Minot State University, especially Dr. Kodwo Annan for his

diligence as my Capstone advisor, and Dr. Laurie Geller for her extensive help throughout my

time at MSU. Your knowledge and insight were essential in the completion of this project.

       Thanks to my friends and colleagues Sue Forster and Steve Schultz for being my

sounding boards. I admire you both on personal and professional levels. Sue, it has been a

pleasure and an honor having the room next to yours for the last five years; you are the

measuring stick by which I compare all high school math teachers.

       Finally, I would like to thank those students at Bismarck High School who were my

inspiration for this project. Your dedication to learning and persistence when faced with

difficulty inspired me to be a better teacher. On the occasions I see these individuals after

graduation, I am never surprised these aforementioned qualities have led to your success.
                                                                                                                                                     v

                                                            Table of Contents

                                                                                                                                               Page

Abstract .......................................................................................................................................... iii

Acknowledgements ........................................................................................................................ iv

List of Tables ............................................................................................................................... viii

List of Figures ................................................................................................................................ ix

Chapter One: Introduction ...............................................................................................................1

           Motivation for the Project ....................................................................................................2

           Background on the Problem.................................................................................................2

           Statement of the Problem .....................................................................................................3

           Statement of Purpose ...........................................................................................................4

           Research Questions/Hypotheses ..........................................................................................4

           Summary ..............................................................................................................................4

Chapter Two: Review of Literature .................................................................................................5

           Teacher/Classroom ..............................................................................................................6

           Student’s Lack of Test Preparation Strategies .....................................................................7

           Student’s Worry ...................................................................................................................8

           Fear Appeals ........................................................................................................................9

           Distractions ..........................................................................................................................9

           Traditional vs. Dynamic Testing........................................................................................10

           Collaborative Assessment ..................................................................................................10

           Cheat Sheets .......................................................................................................................11

           Distraction Avoidance .......................................................................................................12
                                                                                                                                                  vi

           Summary ............................................................................................................................12

Chapter Three: Research Design and Method ...............................................................................14

           Setting ................................................................................................................................14

           Intervention/Innovation......................................................................................................14

           Design ................................................................................................................................15

           Description of Methods......................................................................................................16

           Expected Results ................................................................................................................18

           Timeline for the Study .......................................................................................................18

           Summary ............................................................................................................................18

Chapter Four: Data Analysis and Interpretation of Results ...........................................................20

           Data Analysis .....................................................................................................................20

           Interpretation of Results .....................................................................................................30

           Summary ............................................................................................................................31

Chapter Five: Conclusions, Action Plan, Reflections, and Recommendations .............................32

           Conclusions ........................................................................................................................32

           Action Plan.........................................................................................................................33

           Reflections and Recommendations for Other Teachers.....................................................33

           Summary ............................................................................................................................35

References ......................................................................................................................................37

Appendices .....................................................................................................................................40

           Appendix A: Cheat Sheet Requirements ...........................................................................41

           Appendix B: Geometry Preliminary Survey ......................................................................42

           Appendix C: Geometry Post Test Survey: Cheat Sheets ...................................................43
                                                                                                                      vii

Appendix D: Geometry Post Test Survey: Hints ...............................................................44

Appendix E: IRB Approval Form ......................................................................................45

Appendix F: Principal Consent Form ................................................................................46

Appendix G: Research Participant Assent Form ...............................................................47

Appendix H: Parent/Guardian Research Consent Form ....................................................49

Appendix I: Chapter Seven Test ........................................................................................51

Appendix J: Chapter Eight Test .........................................................................................55

Appendix K: Chapter Nine Test ........................................................................................59

Appendix L: Chapter Ten Test ..........................................................................................64
                                                                                                                               viii

                                                      List of Tables

Table                                                                                                                       Page

1.      Preliminary Survey Results................................................................................................21

2.      Chapter 7 Survey Results After Using Cheat Sheets .........................................................23

3.      Chapter 8 Survey Results After Using Cheat Sheets .........................................................25

4.      Chapter 9 Survey Results After Using Hints .....................................................................27

5.      Chapter 10 Survey Results After Using Hints ...................................................................28

6.      Comparison of Student Sentiment for Each Survey ..........................................................30
                                                                                                                                          ix

                                                          List of Figures

Figure                                                                                                                               Page

1.       Student response to a question on the preliminary survey. ................................................22

2.       Student response to a question on the chapter seven post-test survey after

         using cheat sheets. ..............................................................................................................24

3.       Student response to a question on the chapter eight post-test survey after

         using cheat sheets. ..............................................................................................................26

4.       Student response to a question on the chapter nine tests survey using hints. ....................27

5.       Student response to a question on the chapter ten post-test survey using hints. ................29
                                          Chapter One

                                           Introduction

       I have been a math teacher for seven years, during which time I have administered and

corrected hundreds of tests and quizzes. As simplistic as it may be, the majority of my students

who prepared themselves appropriately for tests performed well and those who did not

performed poorly. While I have had those gifted few students who seem to effortlessly ace every

exam with little thought to preparation, most students needed several hours of practice,

questioning, and studying to perform well on a math test. I enjoyed helping students individually

to understand concepts taught in class and with their test preparations as it gave me feedback on

their triumphs and struggles in learning the material.

       While much of this interaction was during class, there were many other chances for

student contact. During tutoring there were far fewer students, an environment that gave shy

students less apprehension in asking questions. Before and after football and wrestling practice,

along with bus rides and hotel stays, there was an opportunity to help my athletes and

statisticians when they needed it. Sometimes the only time needed was in the hall between

classes. All of these different relations allowed me to better understand my students, and I

believe they better understood me as well.

       After these interactions I would form an idea of how well I thought these students should

do on my test. While my impressions of answered questions and completed homework indicated

those students understood the concepts, this was not a true assumption. The day of the test would

arrive and without fail I would have tests that would have me at a loss. “Suzy” left questions

blank she had answered without pause just the day before. “Jordan” averaged an A on his

homework for the chapter but got a C on the test. I couldn’t understand why this happened.
                                                                                                     2

        Not only was it disheartening for students who worked so hard when they received their

tests back, it was discomforting for me as well. What was causing this difference between my

perception of student ability and their actual test score? I would wait for a personal opportunity

to ask them what they thought was going on; thinking there had to be something I was missing.

While their demeanor ranged from mad to embarrassed (which was hard for me to witness),

when I asked them what had happened, the answer usually boiled down to one basic thing… they

failed to recall what they knew just the day before. Many of these students blamed anxieties for

their troubles as well.

Motivation for the Project

        This presented me with a problem. As a classroom teacher, I expect my students to learn

math and be ready for the next level of math, be it high school, college, or the job market.

Testing is the primary tool I use when determining whether a student has mastered concepts or

not. Intuitively, performing well on a test demonstrates student understanding, while poor

performance implies insufficient knowledge of the content. This black and white view does not

tell the whole story however if a student’s test anxiety impedes their ability to process and recall

information for a test. Alarmed with this inconsistency, I wanted to change it: this became the

goal of my research project. I was also interested in determining if those students who showed a

lack of motivation had similar anxieties of testing poorly.

Background on the Problem

        It has been my observation that many people have no problem expressing they are bad at

math. In the classroom, the students often give the excuse “I hate math” or “I am just not good at

math.” At parent teacher conferences, it is often the case where the parents insist they are of no

help to their student when it comes to math. Both parents and students often give the excuse, “I
                                                                                                     3

hate math” or “I am/was not good at math.” Chinn (2009) stated, “It appears to be socially

acceptable to admit to having low abilities with numbers, a situation that lowers anxiety in

adults” (p. 61). On the flip side of the coin, I have never overheard anyone saying, “It’s no big

deal that ‘Little Johnny’ isn’t doing well in English, I can’t read either.” I wondered if this

dislike of mathematics arose not from their inability to use math, but from their anxiety and/or

poor performance on math tests.

       Walker (1975) defined anxiety as a reaction people have to a situation where they believe

their well-being is endangered or threatened in some way. Anxiety related to mathematics is not

uncommon. The combination of having only one correct answer often combined with the added

stress of time constraints also leads to a negative outlook on mathematics (Chinn, 2009). It

makes sense that a student who gave an honest effort to prepare but came up short will be

anxious about performing poorly on the next test. The problem for me then became finding a

way to make the student sufficiently comfortable in what has become an uncomfortable situation.

The benefits of success here were twofold: students would feel less stress during the test and the

test would produce a more accurate depiction of student knowledge. After researching possible

many possible avenues, I decided to examine the alternative assessment methods of using cheat

sheets and hints in my classroom. Hints are a type of dynamic assessment method that allows

students to ask a hint on a question in exchange for losing a point, while cheat sheets are a

limited set of self-prepared notes the students may use during the exam. It was my hope that

these methods would reduce math test anxiety in my students.

Statement of the Problem

       Testing is needed to assess students and will inevitably cause some stress in my students.

Conversely, testing a student who is overloaded with anxiety levels causing their minds to be
                                                                                                   4

overridden by worry is counterproductive. If teachers are to help anxious students successfully

take math tests, it is important to seek a remedy to reduce their anxiety.

Statement of Purpose

       The purpose of my action research project was to implement and compare the

effectiveness of hints and cheat sheets at reducing test anxiety in my geometry students.

Different approaches were needed in an attempt to assist a range of students and their levels of

anxiety. In doing so, I hoped my tests would produce more accurate assessments results of

student performance.

Research Questions/Hypotheses

       Do cheat sheets and hints reduce math test anxiety in my geometry students? If so, to

what degree are these interventions effective and which method do students prefer? Will test

scores improve through the use of these methods?

Summary

       This chapter addressed my initial concerns with math test anxiety. Math test anxiety can

result in inaccurate test scores due to students’ inability to recall what they have learned. A

combination of discomfort with mathematics and apprehension when taking tests can lead to an

uncomfortable situation in a math classroom. The intent of my action research project was to

determine if I could reduce the amount of anxiety my students experienced through alternative

assessment techniques. In Chapter Two, research pertaining to test anxiety in mathematics is

discussed.
                                           Chapter Two

                                       Review of Literature

       The implications of test anxiety are far-reaching when considering how frequently tests

are administered throughout primary, secondary, and post-secondary settings. A student’s

educational career is determined in large part by his or her performance on tests. Therefore,

when an individual experiences test anxiety, the results can be dramatic.

       The purpose of my project was to implement and compare the effectiveness of hints and

cheat sheets at reducing test anxiety in my geometry students. Many ways to alleviate test

anxiety through use of different testing strategies exist, along with research on elements that

contribute to test anxiety. Much of the research was related to unique test anxieties associated

with mathematics, as this was my discipline of expertise as well as the environment in which

strategies were put into practice.

       Wigfield and Meece (1988) studied math test anxiety on students from elementary to

secondary schools and observed that test anxiety was highest in ninth grade and lowest among

sixth graders. They concluded that strategies to build anxious students’ confidence in their math

ability are necessary to improve test scores. They also suggested that math anxious students may

need trainings in order to reduce their fear and dread in math tests.

       Numerous factors interacted when determining if a student has experienced anxiety on

tests or in mathematics (Brady & Bowd, 2005; Putwain, 2007; Woodard, 2004). It was nearly

impossible for one to consider all environmental, dispositional, and situational factors (Baloglu

& Kocak, 2006) attributed to every student in a single classroom. While studies indicated that

many factors contribute to math test anxiety, they frequently mentioned the effect of teacher’s
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role, tests associated with the classroom setting, students as individuals, and types of tests as

significant.

Teacher/Classroom

        The traditional mathematics classroom has created feelings of discomfort for many

students (Baloglu & Kocak, 2006; Brady & Bowd, 2005; Woodard, 2004). Thoughts of

memorizing formulas and algorithms, rigorous proofs, the “kill and drill” approach to learning

math facts, and other less than favorable factors may have contributed to anxiety (Brady & Boyd,

2005). Often times a math teacher has been thought of as a hostile, or at best insensitive,

individual (Brady & Boyd, 2005) whose attitude creates anxiety in itself (Baloglu & Kocak,

2006). Much of this perception probably has stemmed from the habitual pursuit of a singular

correct answer in the primary grades (Brady & Boyd, 2005). Poor teaching strategies have

developed negative feelings toward mathematics when a student is repeatedly told they are

incorrect in their calculations. The combination of these factors compounds the problem, which

made math class feel more like entering a dragon’s lair even if their perceptions were more

imagined than real.

        As with any curricular area, ineffective teaching methods in the mathematics classroom

have led to student anxieties (Baloglu & Kocak, 2006; Woodard, 2004). These anxieties start at a

young age for several reasons. Brady and Boyd (2005) found instructors at the elementary level

who had elevated measures of anxiety “spend less time planning mathematics lessons and using

mathematics instruction time for non-mathematics related activities more often than their less

math-anxious colleagues” (p. 39). Unfortunately, the instructor’s anxieties often translated to

anxieties for their students (Vinson, 2001). These problems were not confined to just the

elementary level, as both elementary and secondary teachers of mathematics may have relatively
                                                                                                     7

weak academic backgrounds (Brady & Bowd, 2005).

       Recognizing poor mathematics instruction as detrimental and contributing to

mathematics anxiety (Brady & Bowd, 2005) has improved methods of instruction by alleviating

the causes of math anxiety. Rachal, Daigle, and Rachal (2007) found “many students do not

develop effective learning strategies unless they receive explicit instruction and the opportunity

to apply these skills” (p. 191). Without the “know how” students struggled when attempting to

study for tests. Alerting students to these methods may have helped reduce their anxieties.

       Math instructors could have developed helpful pedagogic strategies; these included

communicating passion in their subject area, conveying clear objectives, and giving feedback

(Woodard, 2004). Childs (2009) found teachers who encouraged a positive attitude in regards to

testing itself and who viewed exam days as celebratory dates recorded positive results in their

classroom. According to Woodward (2004), teachers reduced stress when awarding credit for

procedure when grading instead of focusing only on the answer. Alternative assessment

techniques such as “oral questioning, observation, demonstration, discussion, journal writing and

retesting” (Woodard, 2004, Recommendations section, para. 1) may have produced a more

accurate picture of student knowledge.

Student’s Lack of Test Preparation Strategies

       According to Covington and Omelich (as cited in Veenman, Kerseboom, & Imthorn,

2000), “Learning must be present in order to be interfered with” (p. 392). While one may have

been quick to dismiss the student who was not taking notes in class or otherwise had not

appeared to be making use of their time as lazy, there were reasons for inattentiveness. This

apparent negligence was often because students had not developed good learning strategies, not

only in mathematics but throughout the curriculum. The assumption is that students were
                                                                                                    8

developing cognitive and behavioral skills on their own at some time in their academic career

(Rachal et al., 2007). These skills include the metacognitive skills of “task orientation, planning,

monitoring, checking, and recapitulation” that were considered prerequisites to effective learning

(Veenman et al., 2000). Many students have been found to be deficient in these areas of

cognition, which can be attributed to two factors. In the first case, they lacked the self-knowledge

of their own learning strategies. In other words, these students did not figure out how best they

learn as individuals. Consequently, those students who had poor study skills often experienced

failure and as a result developed test anxieties (Veenman et al., 2000).

       According to Doron, Stephan, Boiche, and Le Scanff (2009), individuals who viewed

ability as stable or constant often displayed behavioral disengagement. These students considered

ability to be predetermined and fixed, and thus felt they had no control over their performance on

exams. These beliefs were reinforced by students experiencing repeated failures in the past. Not

surprisingly, the study found those individuals with a belief in ability to change (improve)

accurately predicted the use of positive strategies for learning to adapt to examination demands.

Student’s Worry

       Despite their efforts, some students with good study skills suffer from math test anxiety.

These are students who performed well when given an informal assessment the day before a test,

but froze up when the test was placed in front of them. According to Rodger, Murray, and

Cummings (2007), “Proneness for high-anxious people leaves them susceptible to tension and

nervous reaction in a wide range of evaluative situations, including a test or exam” (p. 92).

Individuals who had task irrelevant negative self-thoughts experienced a component of anxiety

referred to as “worry” (Chinn, 2009; Doron et al., 2009; Miejer, 2001; Putwain, 2007; Putwain &

Symes, 2011; Veenman et al., 2000). Not only were these thoughts distracting, they worsened
                                                                                                       9

the confidence level of the student taking the test, which inhibited their test taking ability. Poor

performance on previous tests was an example of these thoughts (Putwain, 2007). Feelings about

previous experiences distracted from the test being taken. Failure to answer questions invoked

more anxiety as the test taker’s threat perception increased (Rodger et al., 2007). In essence,

when worry goes unchecked it can have a compounding affect.

       In contrast, students who had a positive attitude toward mathematics were found to have

less anxiety on math tests (Dodeen & Darabi, 2009). As mentioned previously, students did

better when teachers showed tests in a positive light (Childs, 2009). Recent research has shown

mathematics anxiety can be forecasted by a student’s predisposition toward test anxiety (Cates &

Rhymer, 2003; Kesici & Erdogan, 2009). Observing a student’s learning strategies and

motivational beliefs predicted success or failure in mathematics.

Fear Appeals

       It has been a commonly used practice for teachers to motivate students by putting added

stress on the importance of a test and the implications of performing well on it (Putwain &

Symes, 2011). While fear-based emphasis may be beneficial in other areas, it is better left out of

the test setting. As discussed by Putwain and Symes (2011), these fear appeals can actually be

detrimental to student learning. Some students perceive fear appeals as threatening, producing

worry and apprehension that invokes poor test performance (Putwain & Roberts, 2009).

Repeated use can result in a test taker disregarding importance of the exam entirely, something

similar to “the teacher who cried wolf.”

Distractions

       Working memory is an integral part of taking mathematics tests (Beilock & Carr, 2005).

As previously discussed, test anxiety contributes to distractibility in testing situations which
                                                                                                       10

exhausts a portion of working memory during a test. Therefore outside distractions are especially

detrimental to students experiencing anxiety as compared to those who are not highly anxious

(Parks-Stamm, Gollwitzer, & Oettingen, 2010). While temptation-inhibiting strategies are

discussed later, it can be stated here that any efforts to eliminate distractions from the test taking

environment would appear beneficial.

Traditional vs. Dynamic Testing

       Traditional testing techniques do not allow an individual to draw conclusions based on

their mistakes, unlike many typical day-to-day situations (Miejer, 2001). For example, when one

is trained in on a job, in many instances an individual is supervised in training before being left

alone to do a task independently. In contrast, students in most math classes take an entire test

independent of outside influences before they hand in the test and are later given feedback.

Miejer (2001) stated these “static” testing conditions are associated with higher levels of test

anxiety.

       In Miejer’s (2001) article, “Learning Potential and Anxious Tendency,” he described a

dynamic testing method, in which students were allowed hints and were graded in response to

the number of hints needed to attain the correct answer. In this alternative assessment method,

some credibility was given to the hypothesis that conventional testing techniques are biased

against those experiencing anxious tendencies. This bias can be lessened, to an extent, by

offering help to students during a test while maintaining the validity of the test itself. While this

strategy may have its merits, difficulties may arise for a teacher trying to attempt this in a large

classroom. Miejer’s (2001) study utilized computers to alleviate this problem.

Collaborative Assessment

       Many studies have shown collaborative assessment to decrease the level of test anxiety
                                                                                                    11

experienced by students (Ioannou & Artino, 2010). Ioannaou and Artino (2010) found

collaborative assessment was “more enjoyable and generally less stressful than a regular test,”

(p. 195) supported by the fact several of the students in the study admitted to having studied less

than usual. Individuals whose anxieties make it difficult to retrieve learned information may find

it easier to recall when they can discuss questions and answers with others (Breedlove, Burkett &

Winfield, 2004). In addition, it should be noted this study found no significant difference in

scores between students taking a test collaboratively and those testing individually.

Cheat Sheets

       Erbe (2007) discussed how using cheat sheets can reduce test anxiety in students. Most

people know cheat sheets as a piece of paper on which notes, examples, formulas, definitions,

etc. are written to use on a test. Without the use of a cheat sheet, this material must be

memorized.

       Memorization of one form or another has been previously mentioned as source of anxiety

on math tests (Brady & Boyd, 2005). However, Bloom and Krathwohl (1956) found recall is a

low level skill in the cognitive domain, which presents a paradox of sorts; aspects students

stressed over most are the least important in regards to learning. Erbe (2007) added these facts

and formulas are the easiest to find in a “real life problem-solving situation” (p. 96); meaning,

the failure to remember formulas did not prevent the attainment of an answer for a resourceful

individual. Teachers, and thus students, focused studying on higher level problems instead of

memorizing facts and formulas.

       Cheat sheets included other benefits; they have been shown to increase test scores

(Skidmore & Aagaard, 2004) and facilitate deeper learning. As with many classroom teachers,

Erbe (2007) found, “Students loved …cheat sheets. They found, however, that they rarely
                                                                                                      12

needed them” (p. 97). This implies sufficient learning took place from the preparation of the

cheat sheet.

Distraction Avoidance

       Parks-Stamm et al. (2010) stressed developing a strategy to maintain focus on the test.

The goal was to maintain focus without creating distracting thoughts of test stress. Of the two

strategies tested, the technique of “temptation-inhibiting implementation intentions” (p. 30) was

found most effective as test anxiety increased. Instead of trying to maintain focus on the task

(test) when presented with a distraction, the method focused attention away from the task. This

technique dismissed the distraction (e.g. “If my neighbors are distracting, I will not pay attention

to them”). Subjects in the same study who attempted to avoid distraction by focusing harder on a

task (e.g. “If my neighbor is distracting, I will focus harder on my test”) were less effective when

experiencing high levels of test anxiety. In other words, it was better to recognize a distraction

and dismiss it, rather than project the anxious energy back into the test.

Summary

       Test anxiety and math anxiety were prevalent and had numerous causes. Poor

pedagogical practices on the part of the instructor have led to students who are turned off from

mathematics, situations, or both. Failure on the students’ part to adequately prepare for a test or

lack of test preparation strategies put them at a disadvantage, creating anxieties during the test.

Highly anxious students had distracting thoughts about their impending failure and were more

easily distracted by their environment, thus depleting working memory needed in testing

situations. Traditional testing practices do not model real world situations, where collaboration,

learning, and problem solving are stressed.
                                                                                                  13

       There have been several attempts to look at new methods of testing more beneficial and

less stressful than those used by mainstream teachers. These tests more closely model real world

situations where adaptability, resourcefulness, and collaboration are as important as knowledge

and memory. In the next chapter, I discussed how I incorporated a few of these ideas into

practice, attempting to alleviate test anxiety and obtain a better picture of student knowledge

from assessment.
                                            Chapter Three

                                    Research Design and Method

          The focus of this project was to implement and compare the effectiveness of hints and

cheat sheets at reducing test anxiety in my geometry students. A cheat sheet is a hand written set

of notes a student creates as an aid in remembering information from the instructional unit being

assessed. Hints are used to prompt a student that is stuck on a problem in hopes that the student

will then be able to complete the problem. This chapter explains who was part of the study, how

I incorporated each intervention, and the strategy used to analyze the data.

Setting

          At the time of this study, I taught high school mathematics in a Midwestern state. The

population of the high school was about 1,400 students in grades 10-12. The school was one of

two public high schools in the city, along with an alternative high school and two private high

schools that also existed. I taught two sections of Geometry, which I used to conduct my

research. The initial sample size for each class was 17 and 13 students, which was average for

the school but slightly less in comparison to previous years. The two geometry classes consisted

of 9 females, 8 males and 8 females, 5 males, respectively. Two students were dropped during

the project; one because of a change in schedule and the other for lack of attendance.

Intervention/Innovation

          I required students to use cheat sheets on Geometry tests for the first two tests of the

semester. My primary goal was to alleviate test anxiety, but I also hoped to improve the test

preparation strategies of my students. The requirements of the cheat sheet (see Appendix A)

were distributed more than one week before the first test of the third quarter. I required each

student produce a cheat sheet at the beginning of class the day before the test. A prior
                                                                                                    15

arrangement with another teacher allowed me to make copies of the sheets and return them to the

students before the end of the class. The original cheat sheets were also collected when the test

was handed in to compare with the copied versions of the cheat sheets. This was used to

determine how much was added to each cheat sheet the night before test. Students were awarded

points for completion based on the copied version, and the original was used to award bonus

points. The purpose of awarding bonus points in this manner was to encourage students to start

preparing for the test days in advance instead of the night before test.

         I used hints to alleviate anxiety on the third and fourth tests of the semester. Hints allow

students to ask for help to assist them in solving a problem. The purpose of my hint was to jump

start a student who drew a blank when starting a question, as is common with test anxiety. If a

student asked for a hint, it was noted on the test and one point was subtracted from the score of

the test for each hint given. Students were allowed to ask for help on any number of questions,

but were limited to one hint per question. This process required me to have point totals for each

question displayed on the test and also necessitated my complete attention to the class for the

duration of the test.

Design

         This action research project used a mixed methods approach. Statistical analysis using

mean, median, mode and standard deviation was done on all assessments where cheat sheets or

hints were used. When I analyzed tests allowing hints, I noted the number of hints given.

         Surveys were given to all participating students in both classes to analyze the perceived

effectiveness of cheat sheets and hints in reducing test anxiety. A preliminary survey (see

Appendix B) was given to get a baseline for student sentiment toward tests and mathematics.

Surveys were also given after the tests are handed back to the students. Post-test cheat sheet
                                                                                                   16

surveys (see Appendix C) included questions about using the cheat sheets along with general

questions about tests and math. Post-test surveys after tests that allowed hints (see Appendix D)

included questions about hints together with general questions about tests and math.

       Qualitative analysis was done in two ways. A free response comment section was

included on all surveys to try to uncover advantages or disadvantages I had overlooked during

my teaching. I also kept a journal to document general observations of anxiety in my students.

For tests involving cheat sheets, journal entries were made describing the differences in the

amounts of information on the cheat sheets between the two days. On days I allowed hints on

tests I noted in my journal the effects on student anxiety as well as any advantages or

disadvantages to the teacher.

Description of Methods

       The Minot State University Institutional Review Board (IRB) needed to provide written

approval before my study (see Appendix E). Written approval was also requested from the

school principal to allow the study to take place in my classroom (Appendix F). All participants

in the study were informed of the study by a letter preapproved by the Minot State University

Institutional Review Board (Appendix G) and signed an attached consent form stating they

agreed to participate. Every student’s parent/guardian in this study signed a consent form stating

they agreed to their child’s participation in the study a week in advance of the first test

(Appendix H). All information presented in this project was presented only in aggregate form so

the confidentiality of all participants was maintained.

       My study took place in the second semester of the 2011-2012 school year. The first and

second tests of the semester required the students to create a cheat sheet for use on the test.

Students were given instructions for the cheat sheets at least one week before the first test. In this
                                                                                                   17

way they were given the opportunity to start making their cheat sheets several days before the

test.

        The day before the test, students were required to turn in their cheat sheets for a

completion grade. I arranged to have another teacher make copies of the cheat sheets during the

class period so that students would have them back before the end of the period. The students

also turned in their original cheat sheets with the test. In my journal I noted observations on the

apparent effectiveness of the cheat sheets in reducing test anxiety during the test. Reductions in

test anxiety were also indicated by the students’ responses on the survey given after the test was

returned.

        The third and fourth tests of the semester involved using hints. Students were informed

how to ask for hints verbally before they were used. When correcting the tests using hints, I kept

track of the number of times each student asked for a hint. I tallied the number of correct answers

in instances where a hint was given, which helped demonstrate how effective this type of

dynamic assessment was. Students who answered the question correctly after a hint tended to

indicate they drew a blank due to anxiety, where students who could not complete the problem

despite getting a hint indicated they were not prepared for the test question. It seemed unlikely a

student could answer a free response question correctly if he or she had little understanding of

the test question, even after receiving a hint.

        After a test was given back to the student, a survey was given to determine students’

experience using hints. This gave students time to reflect on the assessment and comment. It was

not given directly after the test, as test takers who used most of the period might have been

rushed to finish the survey. I returned the assessments within one or two school days so the

assessment experience was fresh in their minds.
                                                                                                   18

Expected Results

       As a result of my study, I expected my Geometry students to have more completed

problems, more correct answers, and less anxiety during both types of tests. It was anticipated

that their grades would improve slightly, but I did not predict a dramatic change. I hoped that

some or all students realized they were not referring to their cheat sheets during the test as often

as they expected. This would demonstrate the use of cheat sheets was a good study technique

even when they were not allowed on tests.

       After using cheat sheets to reduce anxiety and illustrate a study technique, I expected

using hints would reduce anxiety for those students who prepared themselves for the test.

Students who studied less thinking hints would get them through the test, may have found they

were wrong. Thorough knowledge of the content was still required to answer a question

correctly.

       I anticipated some awkwardness when first using hints for the students and me. It was

expected that students would want more of a hint than what I gave them, especially if they were

underprepared. I predicted that I would need to adjust how much or what kind of hint I gave

students on the questions for the second test using hints.

Timeline for the Study

       My study began and ended during the second semester of the 2011-2012 school year.

Therefore, all tests and quizzes in this study were given between the dates of January 16, 2012

and April 14, 2012 to allow for sufficient time to study the use of hints and cheat sheets. Data

was analyzed and interpreted before the end of the school year.

Summary

       In this chapter I have established where, when, and how I used cheat sheets and hints to
                                                                                                  19

study if either alleviated math test anxiety. Both qualitative and quantitative methods of data

collection were used to collect data during the study. Student anxiety was expected to decrease

from both methods of alternative assessment. Chapter Four describes the data collected from the

aforementioned methods and the interpretation of that data.
                                            Chapter Four

                          Data Analysis and Interpretation of Results

       The purpose of this project was to determine if hints and cheat sheets reduced test anxiety

in my Geometry students. In this chapter I described how data were collected in the classroom.

The collected data from surveys and tests were analyzed, along with my own observations, to

determine if they were effective. The combination of analysis, observations, and participant’s

grades were used to determine if cheat sheets and/or the use of hints were effective in reducing

anxiety.

Data Analysis

       Preliminary surveys were given to my Geometry students to get a baseline of their

sentiment toward math and test anxiety, as well as several other questions concerning math tests.

The same four questions were asked on surveys given after the tests were returned to the students

to see if their sentiment toward math and test anxiety had changed after the use of cheat sheets

and hints. Additional questions on cheat sheets and hints were asked on those corresponding

surveys. These surveys can be seen in Appendices B, C and D.

       To evaluate the reactions to each Likert-like survey question with an odd number of

responses, a number value ranging from 1 (Strongly Disagree) to 5 (Strongly Agree) was

assigned, with a value of 3 given to those who chose to give no opinion on the question. These

numbers were then averaged for each statement to see if the collective sentiment of the class was

in agreement or disagreement. A score higher than 3 corresponds with agreement, while the

opposite is true for numbers less than 3.

       Table 1 showed the cumulative results of the preliminary survey. There were several

indicators that seemed to show cheat sheets and the use of hints would be successful. Student
                                                                                                          21

sentiment was the greatest toward the statement “I feel I could do better on math tests if I had

something to jog my memory” as shown in Figure 1. This result predicted cheat sheets and hints

would indeed be beneficial to students on tests, which could in turn lessen student anxiety.

Another indication the project would be beneficial was that over half of the students agreed they

struggled memorizing information. Secondarily, I was not surprised by how many students

admitted to not knowing how to study for math tests, but it was my hope that they would see how

memory was improved by making a cheat sheet and develop student confidence in their ability to

do well on tests.

Table 1

Preliminary Survey Results (n = 28)
 Item                                                 SD   D   N   A SA                       M     SD
 I draw a blank on questions during math              4% 29% 14% 29% 25%                    3.43   1.26
 tests.
 I feel I could do better on math tests if I had      4% 11%          7% 32% 46%            4.07   1.15
 something to jog my memory.
 I struggle trying to memorize information           11% 14% 21% 36% 18%                    3.36   1.25
 needed on math tests (formulas, definitions,
 etc.)
 I know how to study for math tests.                 11% 50% 18% 14%                 7%     2.57   1.10
 I study enough to achieve the grade I want           4% 32% 25% 29% 11%                    3.11   1.10
 on math tests.
Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation

        Students were informed before the chapter started that they would be allowed cheat

sheets on the chapter seven test (see Appendix I). I collected all of the cheat sheets the day

before the test and had a fellow teacher make copies of them. The cheat sheets were returned to

the students before the end of class. Students were awarded ten points for turning in a cheat sheet

the day of the test and two bonus points if they had not changed their cheat sheet from the day
                                                                                                     22

before. The bonus points were used to encourage students not to cram by making the cheat sheet

the night before the test, and having copies from the day before allowed me to see their progress.


               I feel I could do better on math tests if I had
                        something to jog my memory.



                                                                                 Strongly Disagree
                                                                                 Disagree
                                                                                 No Opinion
                                                                                 Agree
                                                                                 Strongly Agree




Figure 1. Student response to a question on the preliminary survey indicating cheat sheets and

hints would be helpful in reducing math test anxiety.


       While most took full advantage of using cheat sheets, two of the students in the survey

chose not to use cheat sheets. There were also others I had observed quickly write down

formulas at the last second to get the ten points for handing in the cheat sheets. Seventeen of the

twenty-nine students surveyed received the two points for having their cheat sheets completed

the day before the test.

       Looking at Table 2, it was evident that more students felt stress relief when using cheat

sheets than not. About two-thirds of the students responded they could concentrate more on

concepts without having to memorize formulas (see Figure 2). Only five students of the twenty-

nine surveyed felt that making a cheat sheet was more work than it was worth. These findings
                                                                                                          23

voted positively for the use of cheat sheets. This was reinforced by several comments on surveys,

such as “Cheat sheets for all tests” and “The cheat sheet was excellent help.”

Table 2

Chapter 7 Survey Results After Using Cheat Sheets (n = 29)
 Item                                             SD    D  N   A SA                           M     SD
 I felt less stressed before this test because I 10% 10% 31% 31% 17%                        3.34   1.20
 knew I could use the cheat sheet.
 I felt less stressed during the test because of     17% 14% 10% 48% 10%                    3.21   1.32
 the cheat sheet.
 I did better on the test than if I had not used     10% 14% 41% 24% 10%                    3.10   1.11
 a cheat sheet.
 I could concentrate more on understanding            3% 21% 10% 41% 24%                    3.62   1.18
 concepts because I didn’t worry about
 memorizing.
 I studied enough to achieve the grade I             10% 45% 31%             3% 10%         2.59   1.09
 wanted on this test.
 Making a cheat sheet was more work than it          24% 34% 24% 10%                 7%     2.41   1.18
 was worth.
 I did not need to use the cheat sheet as much 17% 28% 17% 21% 17%                          2.93   1.39
 as I thought I would.
Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation

        The average score on the chapter seven test was 76.7% with a standard deviation of

17.9%. Unfortunately, eight students failed the test even with the use of cheat sheets which

accounted for the large standard deviation. The median score on the test was 81.1% with modes

of 75.7%, 86.5%, and 92.6%. Analysis of these students’ cheat sheets showed most had a

complete sheet of formulas. This led me to believe the students genuinely struggled with the

concepts, although it was questionable if those students did all they could to prepare for the test.

I state this because of the difficulties I had in getting several students to complete their

homework assignments.
                                                                                                     24


               I could concentrate more on understanding
                  concepts because I didn't worry about
                              memorizing.


                                                                                Strongly Disagree
                                                                                Disagree
                                                                                No Opinion
                                                                                Agree
                                                                                Strongly Agree




Figure 2. Student response to a question on the chapter seven post-test survey indicating cheat

sheets proved useful in allowing students to focus more on understanding than memorizing.


       For the chapter eight test (see Appendix J), I decided to help the students with the

creation of their cheat sheets. This was in contrast to chapter seven where the students were

responsible for what they produced, although I had hinted to important formulas and concepts

along the way. Several factors resulted in 100% of the students using cheat sheets on this test.

These factors include my input about what to put on the cheat sheets, class time to complete

them, and familiarity with cheat sheets from the previous test. Most students had a complete

page covered with notes which were also organized as to be easy to use. Some even added notes

from the previous chapter.

       Table 3 contains the results of the surveys given after the chapter eight test using cheat

sheets. This survey indicated many students experienced less stress and felt they achieved higher

scores than if they had not been able to use cheat sheets. Although all stress before the test was
                                                                                                          25

not eliminated, over half of my student felt less stressed before and during the test. A full third of

students strongly agreed they could concentrate more on understanding concepts without

worrying about memorizing. In fact, there was only one student who disagreed with this

statement. This reduced anxiety seems to relate to the 82.2% mean on the chapter eight tests,

which was by far the best average grade of all the tests. The median of the test was 83.5% and

the standard deviation was 11.4%, with modes of 87.5% and 89.7%.

Table 3

Chapter 8 Survey Results After Using Cheat Sheets (n = 27)
 Item                                            SD     D  N A                       SA       M     SD
 I felt less stressed before this test because I 7% 7% 22% 56%                       7%     3.48   1.01
 knew I could use the cheat sheet.
 I felt less stressed during the test because of     11% 15% 15% 41% 19%                    3.41   1.28
 the cheat sheet.
 I did better on the test than if I had not used      7% 15% 15% 30% 33%                    3.67   1.30
 a cheat sheet.
 I could concentrate more on understanding            0%      4% 30% 33% 33%                3.96   0.90
 concepts because I didn’t worry about
 memorizing.
 I studied enough to achieve the grade I              4% 26% 37% 26%                 7%     3.07   1.00
 wanted on this test.
 Making a cheat sheet was more work than it          26% 48% 15%             7%      4%     2.15   1.03
 was worth.
 I did not need to use the cheat sheet as much        4% 26% 33% 30%                 7%     3.11   1.01
 as I thought I would.
Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation
                                                                                                     26


               I felt less stressed during the test because of
                                the cheat sheet.


                                                                                 Strongly Disagree
                                                                                 Disagree
                                                                                 No Opinion
                                                                                 Agree
                                                                                 Strongly Agree




Figure 3. Student response to a question on the chapter eight post-test survey after using cheat

sheets for a second time. This chart indicates over half of the students experienced less stress as a

result of using cheat sheets.


       Chapter nine was the first chapter in which I gave hints on the test in order to assist

students that became stuck on a problem. The cost for receiving a hint was one point. Each

question on the test had a designated point value on the test so the students could weigh the cost

of the hint in comparison to the value of the question.

       The results of the surveys given after the chapter nine tests (see Appendix K) are in Table

4. While the results of this data were spread out more than previous surveys, the responses to two

of the statements indicated that hints were not as affective in relieving stress as cheat sheets. As

seen in Figure 4, almost two-thirds of the students disagreed with the statement “I felt less

stressed because I could ask for a hint on the test.” This seems to be related to how many

students responded they were reluctant to ask for hints for fear of losing points.
                                                                                                          27

Table 4

Chapter 9 Survey Results After Using Hints (n = 27)
 Item                                             SD   D   N   A                     SA       M     SD
 If felt less stressed because I could ask for a 26% 37% 22% 11%                     4%     2.30   1.10
 hint on the test.

 I studied less because I knew I could ask for       15% 30% 33% 15%                 7%     2.70   1.14
 hints on the test.

 I felt comfortable asking for a hint on the         11% 15% 41% 22% 11%                    3.07   1.14
 test.

 I used less hints than I should have.                7% 19% 48% 11% 15%                    3.07   1.11

 I was reluctant to ask for a hint because I         11% 15% 19% 41% 15%                    3.33   1.24
 did not want to lose any points on the test.

 I studied enough to do well on this test.            0% 26% 52% 11% 11%                    3.07   0.92

Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation



                If felt less stressed because I could ask for a
                                 hint on the test.



                                                                                      Strongly Disagree
                                                                                      Disagree
                                                                                      No Opinion
                                                                                      Agree
                                                                                      Strongly Agree




Figure 4. Student response to a question on the chapter nine tests survey using hints. Hints seem

to be unsuccessful in alleviating stress for most of the students.
                                                                                                          28

        Only thirteen hints were asked for out of twenty-eight tests, each with eighteen questions.

A large percentage of the hints requested during the test were used to ask for formulas needed to

complete the question, which probably would have been at their disposal on their cheat sheet for

the previous test. The mean score on the chapter nine tests was 78.6% with a standard deviation

of 15.1%. The median for the test was 82.1% and the mode was 83.9%.

        The chapter ten test (see Appendix L) was the second chapter test on which I allowed

hints. It was my hope that students would be more comfortable with asking questions this time

around. Again, I observed the biggest reason for requesting a hint was to ask for a formula. The

amount of hints asked increased to twenty-one, but this still seemed low in comparison to how

many students struggled on the test.

Table 5

Chapter 10 Survey Results After Using Hints (n = 27)
 Item                                             SD   D   N   A                     SA       M     SD
 If felt less stressed because I could ask for a 11% 26% 37% 26%                     0%     2.78   0.97
 hint on the test.

 I studied less because I knew I could ask for       15% 33% 30% 15%                 7%     2.67   1.14
 hints on the test.

 I felt comfortable asking for a hint on the          7% 22% 30% 33%                 4%     3.04   1.04
 test.

 I used less hints than I should have.                7% 22% 33% 26% 11%                    3.11   1.12

 I was reluctant to ask for a hint because I          4% 22% 15% 37% 19%                    3.46   1.17
 did not want to lose any points on the test.

 I studied enough to do well on this test.           15% 33% 41% 11%                 7%     2.66   1.08

Note. SD = Strongly Disagree, D = Disagree, N = No Opinion, A = Agree, SA = Strongly Agree, M = Mean, SD =
Standard Deviation

        While this survey indicated the chapter ten test caused less stress than the previous test

(see Table 5), it still did not have the desired effect of reducing stress for many students. As
                                                                                                     29

Figure 5 demonstrates, it was also evident that several students were still reluctant to give up

points in exchange for hints on this test. The mean score for the chapter ten tests was 71.7%,

which was by far the lowest average of all the test scores. The median was even lower at 71.5%.

The standard deviation was 13.2% and modes for the test were 56.1% and 78.9%. I observed as

an instructor that the students had less background in the content of chapter ten than other

chapters. This hurdle along with the ineffectiveness of the hints explains in part the lower test

scores for this chapter.


                 I was reluctant to ask for a hint because I
                did not want to lose any points on the test.


                                                                              Strongly Disagree
                                                                              Disagree
                                                                              No Opinion
                                                                              Agree
                                                                              Strongly Agree




Figure 5. Student response to a question on the chapter ten post-test survey using hints. Even

after on the second test using hints, over half of my students did not want to trade the cost of a

single point for a hint on the test. This was a major problem in using this type of alternative

assessment technique.


       Table 6 shows the results of the first four questions that were kept consistent on each

survey. I asked these questions to determine if using cheat sheets and hints would change student
                                                                                                     30

sentiment toward math and testing as the project went along. Students were given only four

possible answers to these questions so they had to make a decision one way or the other.

Table 6

Comparison of Student Sentiment for each Survey
                                                             Chapter       Chapter   Chapter   Chapter
                                                                   7             8         9       10
                                                  Pre-        (Cheat        (Cheat
 Item                                           Survey       Sheets)       Sheets)   (Hints)   (Hints)
 I like math.                                     2.61          2.24          2.48     2.19      2.37
 I like math class.                                2.68          2.31         2.78      2.63      2.48
 I worry before taking all tests.                  2.39          2.34         2.44      2.52      2.41
 I worry before taking math tests.                 2.68          2.62         2.81      2.74      2.70
 Number of students questioned:                  28.00         29.00         27.00     27.00     27.00
 Average test grade:                                          76.7%         82.2%     78.6%     71.7%
Note. 1 = Strongly Disagree, 2 = Disagree, 3 = Agree, 4 = Strongly Agree

        As can be expected, the students liked math more when their grades were better. What

did not correlate was how much worry students experienced in comparison to their average

scores. Student worry decreased from chapter eight to chapter ten, even though their grades were

getting worse. An explanation for this may be that as students worried less about their tests their

performance decreased as a result.

Interpretation of Results

        The results of my project indicate there was a connection between using cheat sheets and

a reduction in anxiety on math tests. Not only were they an excellent study tool, but they

provided a safety net to those students who had difficulty remember formulas.

        It could be argued that cheat sheets decrease the rigor of tests in the classroom, but I also

found that students could concentrate more on understanding the concepts in the chapter. This

means more rigorous, high level problems can be asked of students on tests, instead of asking

questions that are sheer feats of memory.
                                                                                                      31

        Hints were shown to be ineffective in reducing anxiety. It was my hope that the use of

cheat sheets in previous chapters would lead students to this technique of studying, and I could

fill in the gaps with the use of hints. My idea was the combination of the two would lead to even

less anxiety. To the contrary, hints did little to reduce test anxiety according to the results of the

surveys.

        Unfortunately, by aiding the students in making cheat sheets during class, I think the

students learned they did not need to study on their own as much. The studying done by making

the cheat sheets in class was gone on the next test, but the students did not take up the slack by

studying on their own time. The students who needed to study, but lacked the motivation to do so

on their own, struggled on the tests using hints. When it came time to take the test the students

were anxious, and now it was going to cost them a point to get a hint, whereas previously they

could refer back to their cheat sheet without penalty. Some or all of these factors could have

contributed to the lack of success with hints. Without a control group, it is difficult to say if the

tests using hints caused more or less anxiety than tests using no hints at all.

Summary

        Cheat sheets were successful in reducing anxiety for many of my Geometry students as

indicated by the results of the surveys and student comments. Hints were much less successful. It

is uncertain if the success of the first affected the lack of success in the second directly, but it is a

possibility. In the next chapter, I conclude my project and proceed to make suggestions and

recommendations from my observations.
                                          Chapter Five

                Conclusions, Action Plan, Reflections, and Recommendations

Conclusions

       The two methods of alleviating math test anxiety used in my study had very different

outcomes. Using cheat sheets did seem to lessen anxieties in my students during those tests.

They were especially effective when the students were given some direction on the creation of

their cheat sheets. Giving hints in exchange for a one point deduction did not seem to lessen

anxiety in most of my students. This finding was reflected in both the survey results and

collective sentiment of the comments given by the students on the surveys.

       It seems clear that cheat sheets lessened the worry of forgetting test materials for my

students. This was shown by the results of the surveys as well as the less anxious demeanor of

the students I observed before and during the test. While the cheat sheets reduced worry, I do not

think cheat sheets made it easier for the students. Cheat sheets do not take the place of homework

and studying, which was evident when eight of the twenty-nine students in the study failed the

chapter seven test, an abnormally large percentage for my Geometry students.

       Secondarily, I think it was evident that many Geometry students lack the know-how to

study for math tests properly, and cheat sheets are one way of teaching this skill. This idea was

reinforced by responses to the surveys. One student comment from the chapter eight surveys hit

it on the head: “What really helped was making the cheat sheet, because writing it down so many

times was like studying.”

       Hints proved unsuccessful in alleviating test anxiety in my Geometry students. I do think

with some practice and refinement this method could be an effective way of giving a “jump

start” to those students that draw a blank due to anxiety. This conclusion comes from the fact that
                                                                                                     33

more than half of those who asked for a hint got the question correct after getting the hint. Many

of the hints involved giving a formula needed to answer the question. The students still needed to

know how to use the formula to get the correct answer. On the other hand, hints were not helpful

to those students who had no conceptual understanding of the problem, and so they still got the

question wrong. In conclusion, the rigor of a question is maintained as long as the hint given aids

the student only in one specific part of the problem.

Action Plan

         In the future, I do plan on using cheat sheets again, especially when the emphasis of the

test is more on problem solving skills and less on the memorization of formulas. When I do, I

will definitely assist my students in the design of the cheat sheet on the first assessment or two to

help students get an idea of the types and amount of information to put on the cheat sheet.

Eventually I will hand the creation of the cheat sheets over entirely to the students when I use

them, as this will allow them to be creative and give them the responsibility of making their own

sheet.

         I will continue to use hints selectively as well. They will be useful as an aid for those

students who have trouble starting a problem. Hints may be especially effective in upper level

high school math classes, where a question worth ten points can make or break a test grade. A

simple hint that allows the student to find the correct solution for most of the ten points is a more

accurate assessment of the student’s ability than if they lose all of those points because they

forgot one formula. As stated before, if they did not understand the concept, hints did not help.

Reflections and Recommendations for Teachers

         Overall I think the study was a positive experience; I took several good things from it. I

will continue to refine and use these practices in the future. I would modify a few parts of the
                                                                                                      34

study if given the chance to do so. First and foremost, I would give my students instructions on

creating cheat sheets the first time I used them in class. This guidance gives the students a feel

for what they need to put on a cheat sheet. It also gives the students some formal instruction in

taking notes, which is a skill in which many of my students were lacking. I found that even

students that previously would not bother to take out a pencil for notes made a cheat sheet when

given some class time, instructions, and a few points for their work. While some will argue these

tasks should be left to the student, I feel this approach was more productive for a difficult student

than staring blindly into space.

       An issue I would warn against is using cheat sheets and hints together. This problem was

evident immediately; after earning points for creating a cheat sheet on the first two tests, I then

allowed them no sheet on the second two tests and told them it would cost them a point for a

hint. My intention was for hints to ease the transition out of using cheat sheets, but instead it was

like yanking the rug out from under their feet. This was definitely a case where principle and

practice did not align.

       Ultimately, I found cheat sheets and hints are two different ways to lessen the impact of

anxiety on test scores. Cheat sheets help students study for a test and give them something to fall

back on should they get anxious. Hints do little to lessen the anxiety before and during a test, but

they allow a lifeline should their memory fail them due to worry or other distraction. A hint is

like helping place one key piece of a puzzle that leads to the eventual completion of the entire

picture. Both methods have their merits and pitfalls that must be addressed.

        While the methods described and implemented in this project may be used in other

disciplines as well as mathematics, there are some obvious places cheat sheets and hints would

not work. Any assessment on terms, definitions, formulas, etc. that the student could simply copy
                                                                                                   35

from a cheat sheet to the test would defeat the purpose of that examination. I think the same

could be said for giving hints during this type of assessment. There are instances when reciting

from memory is very important and no aid should be given. For example, if the purpose of an

exam in an Anatomy class is to assess the identification and naming of all 206 bones in the adult

human body, cheat sheets and hints will not work. This would be equivalent to my orthopedic

surgeon constantly looking at a chart to tell me the names of the muscles, bones, and tendons on

which he is going to operate, and I would prefer he did not have this preoccupation.

       I believe tests allowing a cheat sheet more realistically reflect problem solving in real

world situations. If one is posed with a problem in a profession, it is often a person’s

resourcefulness in conjunction with their knowledge of content that leads to a solution. For

example, a licensed automotive mechanic can use references for parts and specifications of every

type of vehicle they encounter to supplement their understanding of how automobiles work.

Reference material is used because there is so much to memorize otherwise, and this

memorization is unnecessary. Even engineers taking the professional engineering exam are

allowed to bring in books and notes to use on the test. Tests that require students to perform

strictly from memory in many cases do not model tasks outside of school.

Summary

       In closing, I have learned much about the use of alternative assessment techniques and

test anxiety. Cheat sheets and hints can be valuable tools for the classroom teacher, but they take

work to perfect and modification to specific teaching and testing styles. When used properly,

they both allow more accurate assessment of higher order thinking skills for those students who

experience anxiety on math tests. Cheat sheets can also be used to teach note taking skills and

stimulate the under motivated student who may be otherwise indifferent to properly preparing for
                                                                                                36

a test. While there are some instances where they are not appropriate, both cheat sheets and hints

can be useful tools to improve student success.
                                                                                                37

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Beilock, S. L., & Carr, T. H. (2005). When high-powered people fail. Psychological Science

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Bloom, B. S., & Krathwohl, D. R. (1956). Taxonomy of educational objectives: The

       classification of educational goals: Handbook I, cognitive domain. New York, NY:

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Appendices
                                                                                                    41

                                            Appendix A

                                    Cheat Sheet Requirements

Geometry
Mr. Dennis
Cheat Sheet Requirements

Students:
For the next two tests, you will be required to make a cheat sheet to use during the test.

The requirements for the cheat sheet will be:

   1) The cheat sheet will be of paper with maximum dimensions of 8.5 by 11 inches. One or
      both of the dimensions may be smaller.

   2) You many only use one side of the sheet. The other side of the sheet must only have your
      name on it.

   3) The cheat sheet must be hand written. Use of a straightedge, protractor, compass, etc.
      may be used for hand drawn illustrations, but no pictures or computer graphics are
      allowed.

   4) A completion grade of ten homework points will be awarded for making the cheat sheet,
      which must be produced at the beginning of class the day before the test. The sheets will
      then be copied and returned to you before the end of class.

   5) Should a cheat sheet be deemed unacceptable by violating any of rules 1-3 when
      collected the day before the test, you will be allow to fix it. If the cheat sheet still in
      violation the day of the test, it cannot be used for the test.

   6) The original cheat sheet will be handed in along with the test. Your grade will be out of
      ten completion points based on the copied version.

   7) You are allowed to add to your cheat sheet after it has been copied. If nothing new has
      been added to your crib sheet, you will be awarded two bonus points which will be added
      to your completion grade.
                                                                                                 42

                                          Appendix B

                                  Geometry Preliminary Survey

Geometry Preliminary Survey                           Name________________________

Please circle the number that best represents your response to each question.

                                         Strongly                          Strongly
   Question:                             Disagree Disagree       Agree      Agree

1. I like math.                             1           2          3            4

2. I like math class.                       1           2          3            4

3. I worry before taking all tests.         1           2          3            4

4. I worry before taking math tests.        1           2          3            4


                                         Strongly                No                   Strongly
   Question:                             Disagree               Opinion               Agree

5. I draw a blank on questions during       1           2          3            4       5
   math tests.

6. I feel I could do better on math         1           2          3            4       5
   tests if I had something to jog
   my memory.

7. I struggle trying to memorize            1           2          3            4       5
   information needed for math
   tests (formulas, definitions, etc.)

8. I know how to study for math             1           2          3            4       5
   tests.

9. I study enough to do achieve             1           2          3            4       5
   the grade I want on math tests.
                                                                                                           43

                                               Appendix C

                               Geometry Post Test Survey: Cheat Sheets

Geometry Post Test Survey (after using cheat sheets)          Name_________________________

After reflecting on the test, please circle the number that best represents your response to each question.

                                             Strongly                               Strongly
    Question:                                Disagree     Disagree      Agree        Agree

10. I like math.                                 1            2            3           4

11. I like math class.                           1            2            3           4

12. I worry before taking all tests.             1            2            3           4

13. I worry before taking math tests.            1            2            3           4

                                              Strongly                  No                      Strongly
    Question:                                 Disagree                 Opinion                  Agree

14. I felt less stressed before this test        1            2            3           4             5
    because I knew I could use the
    cheat sheet.

15. I felt less stressed during the test         1            2            3           4             5
    because of the cheat sheet.

16. I did better on the test than if I           1            2            3           4             5
    had not used a cheat sheet.

17. I could concentrate more on                  1            2            3           4             5
    understanding concepts because
    I didn’t worry about memorizing.

18. I studied enough to do achieve               1            2            3           4             5
    the grade I wanted on this test.

19. Making a cheat sheet was more                1            2            3           4             5
    work than it was worth.

20. I did not need to use the cheat              1            2            3           4             5
    sheet as much as I thought I
    would.

Additional comments/ideas:
                                                                                                    44

                                           Appendix D

                               Geometry Post Test Survey: Hints

Geometry Post Test Survey (after using hints)          Name________________________

After reflecting on the test, please circle the number that best represents your response to each
question.


                                         Strongly                           Strongly
   Question:                             Disagree Disagree        Agree      Agree

1. I like math.                              1           2          3           4

2. I like math class.                        1           2          3           4

3. I worry before taking all tests.          1           2          3           4

4. I worry before taking math tests.         1           2          3           4


                                          Strongly                No                    Strongly
   Question:                              Disagree               Opinion                Agree

5. I felt less stressed because I            1           2          3           4           5
   could ask for a hint on the test.

6. I studied less because I knew             1           2          3           4           5
   I could ask for hints on the test.

7. I felt comfortable asking for a           1           2          3           4           5
   hint on the test.

8. I used less hints than I should           1           2          3           4           5
   have.

9. I was reluctant to ask for a hint         1           2          3           4           5
   because I did not want to lose
   any points on the test.

10. I studied enough to do well              1           2          3           4           5
    on this test.

Additional comments:
                    45

   Appendix E

IRB Approval Form
                                                                                                  46

                                             Appendix F

                                     Principal Consent Form


I. Research Background (to be completed by researcher)

        Title of the Study: Using Alternative Assessment Methods to Alleviate Math Test Anxiety

        Name of Researcher: Bradley Dennis     Phone: (701) 290-1288

        Street address: 644 Meadow Lane      City: Bismarck, North Dakota Zip: 58504

        E-mail: brad_dennis@bismarckschools.org

II. Description of Research Proposal

The purpose of this action research project is to determine if using cheat sheets and hints will
decrease test anxiety on math tests. Cheat sheets will be used for the first two Geometry tests of
the semester, while hints will be used on the third and fourth Geometry tests of the semester.
Surveys will be given after each test is returned to the students to obtain student sentiment for
each type of alternative assessment.

III. Agreement (to be completed by principal)

I, ___________________________, principal of ____________________school, understand

      the study and what it requires of the staff, students, and/or parents in my school,
      that the privacy and confidentiality of any staff or student will be protected,
      that I have the right to allow or reject this research study to take place at my school,
      that I have the right to terminate the research study at any time,
      that I have the right to review all consent forms and research documents at any time during
       the study until project is completed and defended.

   I grant permission to the researcher to conduct the above named research in my school as
    described in the proposal.
   I DO NOT grant permission to the researcher to conduct the above named research in my
    school as described in the proposal.
   I understand that data should be released only by the departments that own them. My staff
    and I shall not release data to the researcher without approval from the IRB.

Signature of Principal: _______________________________________
                        Ken Erickson, Principal, Bismarck High School

Date: _________________
                                                                                                                         47

                                                     Appendix G

                                      Research Participant Assent Form

Invitation to Participate
You are invited to participate in a classroom study! The purpose of this study is to determine if changing how I
administer tests will decrease test anxiety. I, Bradley Dennis, will be conducting this study in all of my Geometry
classes at Bismarck High School. Mr. Ken Erickson, principal of Bismarck High School, has approved this research
study.

Basis for Selection
You have been selected because you are a Geometry student in one of my classes. In using students from both
classes, I hope to collect enough data to come to a conclusion on the effects of using cheat sheets and hints to reduce
math test anxiety. Cheat sheets and hints are described later in this document.

Purpose of the Research
The purpose of this research is to help determine if changing how I administer tests will decrease test anxiety for my
students. My main goal is to more accurately assess students’ knowledge without the distractions of heightened
anxiety. My findings may be beneficial for myself and other mathematics teachers. This study is one of the final
steps toward the completion of my Masters of Arts in Teaching: Mathematics degree through Minot State
University.

Explanation of Procedures
If you decide to participate, you will be asked to do the following:

    1.   Participate in a preliminary survey asking you general questions about taking tests and math.
    2.   You will be required to create a cheat sheet to use on the first two Geometry tests of the second semester of
         the 2011-2012 school year.
    3.   You will take tests using hints for the third and fourth tests of the semester.
    4.   After each of these tests is returned to you, you will be asked to take another survey reflecting on your
         feelings about the test.

Additionally, the researcher will be keeping a journal to document observed anxieties in the classroom.

The identity of all participants will remain confidential. Students will not be identified in the research report. All
research and observations will be done in the classroom.

Duration of Participation
You will participate in approximately a twelve week collection of test and survey data. I will record scores and other
data from student tests. I will collect data from each survey to find out if either cheat sheets or using hints have an
effect on test anxiety.

Benefits to the Individual
Cheat sheets allow students to write down material that normally must be committed to memory. Not only does this
help students study for a test, it allows more efficient use of time and brain power to concentrate more on learning
higher order skills, such as understanding concepts and problem solving. Such abilities reflect a higher level of
learning than memorization.
                                                                                                                        48

Hints are a type of dynamic assessment designed to help students who forget on tests due to test anxiety. If
prompted, I plan on giving you a predetermined hint to the troubling question during the test. This hint will give you
a better chance of finding the correct answer, in exchange for losing one point. This allows you, the student, a better
chance of answering questions correctly and therefore a chance for a better grade. It also reduces the anxiety
associated by students with the tendency to freeze up during test. It is your right to ask for as many hints as you
would like during the test, or ask for no hints at all.

Another potential benefit for both of these assessment techniques is increased test scores. Studies have shown there
is more working memory available to use during a test if test anxiety is diminished. More working memory will
hopefully allow you, the test taker, to think clearer and be better able to answer questions on the test.

Alternatives to Participation/Withdrawal from Study
If you decide not to participate, you will still take all of the tests. Your participation in this study is voluntary, and
choosing not to participate in this study will not affect your grade in any way. You will not complete any surveys,
and you will take all tests as they are normally administered. Cheat sheets using the same criteria as the participants
will be allowed for nonparticipants to maintain fairness in grading. The grades of students who choose not to
participate will not be used in the research. If you decide to participate in this study, you may withdraw at any time
during the study by contacting me.

Assurance of Confidentiality
All data will be treated confidentially by the researcher. Names of participants and their data sets will be kept in a
locked file cabinet in the researcher’s office and on a password-protected computer and will be destroyed once the
paper has been defended and approved. The researcher agrees to maintain strict confidentiality which means your
name will not be discussed or divulged with anyone outside of this research project. The researcher will also make
sure confidential information will not be discussed in an area that can be overheard that would allow an
unauthorized person to associate or identify the student with such information.

Offer to Answer Questions
If you have any questions or concerns during the study, feel free to contact me at 701-323-4800 ext. 6112 or email
me at brad_dennis@bismarckschools.org. If you have questions about the right of research subjects, contact the
Chairperson of the MSU Institutional Review Board (IRB), Dr. Vicki Michels at 701-858-3594 or
Vicki.Michels@minotstatu.edu.

Thank you for your consideration.

Participant Assent:
You are voluntarily making a decision whether or not to participate. You signature indicates that, having
read and understood the information provided above, you have decided to participate. You will be given a
copy of this assent form to keep.

     Yes, I approve.                                                  No, I do not approve.

__________________________________________
Participant (Please Print Your Name above)
___________________________________________Date________________
Signature of Participant
___________________________________________Date________________
Signature of Researcher
                                                                                                                         49

                                                     Appendix H

                                 Parent/Guardian Research Consent Form

Invitation to Participate
Your child is invited to participate in a study to determine if changing how I administer tests will decrease test
anxiety. I, Bradley Dennis, will be conducting this study in all of my Geometry classes at Bismarck High School.
Mr. Ken Erickson, principal of Bismarck High School, has approved of this research study.

Basis for Selection
Your child has been selected because he/she is a Geometry student in my class. In using students from both classes,
I hope to collect enough data to come to a conclusion on the effects of using cheat sheets and hints to reduce math
test anxiety. Cheat sheets and hints are described later in this document.

Purpose of the Research
The purpose of this research is to help determine if changing how I administer tests will decrease test anxiety for my
students. My main goal is to more accurately assess students’ knowledge without the distractions of heightened
anxiety. My findings may be beneficial for myself and other teachers. This study is one of the final steps toward the
completion of my Masters of Arts in Teaching: Mathematics degree through Minot State University.

Explanation of Procedures
If you decide to allow your child to participate, your child will be asked to do the following:

    1.   Participate in a preliminary survey asking you general questions about taking tests and math.
    2.   Your child will be required to create a cheat sheet to use on the first two Geometry tests of the second
         semester of the 2011-2012 school year.
    3.   Your child will take tests using hints for the third and fourth tests of the semester.
    4.   After each of these tests is returned to your child, they will take another survey reflecting on their feelings
         about the test.

Additionally, the researcher will be keeping a journal to document observed anxieties in the classroom.

The identity of all participants will remain confidential. Students will not be identified in the research report. All
research and observations will be done in the classroom.

Duration of Participation
Your child will participate in approximately a twelve week collection of test and survey data. I will record scores
and other data from student tests. I will collect data from each survey to find out if either cheat sheets or hints have
an effect on test anxiety.

Benefits to the Individual
Cheat sheets allow students to write down material that normally must be committed to memory. Not only does this
help students study for a test, it allows more efficient use of time and brain power to concentrate more on learning
and understanding concepts. This reflects a higher level of learning than memorization.

Hints are a type of dynamic assessment designed to help students who forget on tests due to test anxiety. When
prompted, I plan on giving predetermined hints during the test. In exchange for losing one point, students will
receive a hint that gives them a better chance of finding the correct answer. This allows the student a better chance
                                                                                                                         50

of answering questions correctly. It also reduces the anxiety associated by students with the tendency to freeze up
during test.

Another potential benefit for both of these assessment techniques is increased test scores. Studies have shown there
is more working memory available to use during a test if test anxiety is diminished. More working memory will
hopefully allow your child, the test taker, to think clearer and be better able to answer questions on the test.

Alternatives to Participation/Withdrawal from Study
If you decide to not allow your child to participate, he/she will still take all of the tests. Your child’s participation in
this study is voluntary, and choosing not to participate in this study will not affect his/her grade in any way. They
will not complete any surveys, and they will take all tests as they are normally administered. Cheat sheets using the
same criteria as the participants will be allowed for nonparticipants to maintain fairness in grading. The grades of
students who choose not to participate will not be used in the research. If you decide to allow the participation of
your child in this study, you may withdraw at any time during the study by contacting me at 701-322-4800 ext. 6112
or at brad_dennis@bismarckschools.org.

Assurance of Confidentiality
All data will be treated confidentially by the researcher. Names of participants and their data sets will be kept in a
locked file cabinet in the researcher’s office and on a password-protected computer and will be destroyed once the
paper has been defended and approved. The researcher agrees to maintain strict confidentiality which means your
student’s name will not be discussed or divulged with anyone outside of this research project. The researcher will
also make sure confidential information will not be discussed in an area that can be overheard that would allow an
unauthorized person to associate or identify the student with such information.

Offer to Answer Questions
If you have any questions or concerns during the study, feel free to contact me at 701-323-4800 ext. 6112 or email
me at brad_dennis@bismarckschools.org. If you have questions about the right of research subjects, contact the
Chairperson of the MSU Institutional Review Board (IRB), Dr. Vicki Michels at 701-858-3594 or
Vicki.Michels@minotstatu.edu.

Thank you for your consideration.

Guardian Consent
 You are voluntarily making a decision whether or not to allow your child or legal ward to participate. You
signature indicates that, having read and understood the information provided above, you have decided to
permit your child or legal ward to participate. You will be given a copy of this consent form to keep.

     Yes, I approve.                                                  No, I do not approve.

__________________________________________
Participant (please print student name)

___________________________________________Date________________
Signature of Parent or Guardian

___________________________________________Date________________
Signature of Researcher
                     51

   Appendix I

Chapter Seven Test
52
53
54
                     55

   Appendix J

Chapter Eight Test
56
57
58
                    59

  Appendix K

Chapter Nine Test
60
61
62
63
                   64

  Appendix L

Chapter Ten Test
65
66
67

				
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