University of South Carolina Upstate
SELD 446 – Math Disabilities and Math Methods
Course Syllabus –Fall 2009
Instructor: Dr. Valerie Duarte Telephone: 503-5507 (O)
Office: HEC 3014 Time: Wed: 1:40 – 4:10 HEC 2007
Email: firstname.lastname@example.org Office Hours: Tues/Thurs 11:00 – 1:00
III. Course Materials Required:
Reys, R., Lindquist, M., Lambdin, D., Smith, N. (2007)
Helping Children Learn Mathematics (9th Ed.), NY: Wiley & Sons
A USC Upstate email account – You are responsible for maintaining a USC
Upstate email account for this course
Use of websites:
//www.ed.sc.gov/agency/offices/cso/standards/math (scroll down)
IV. USC Upstate Catalog Description – SELD 446. Math Disabilities and Math
Methods(3). Learning disability specific methods designed to facilitate the
development of mathematics concepts and skills. A practicum experience is required.
Prerequisites: SMTH 231, SMTH 232, SMTH 233 and admission to the professional
program. Corequisites: SELD 410; SELD 412.
V. USC Upstate Conceptual Framework
The USC Upstate School of Education aims to be recognized nationally for its
outstanding teacher preparation programs whose graduates are excellent,
learner centered practitioners and professionals.
a. Core Dispositions: The faculty and candidates of the USCS School of
Value reflective teaching practice.
Value learner-centered pedagogy.
Value performance-based assessment.
Are committed to and affirm diversity.
Are committed to professional responsibility.
b. Undergraduate Program Organizing Theme: Teachers prepared at USC
Upstate possess a broad knowledge of the liberal arts and applicable content
areas, the latest developments in curriculum and instruction, and the
foundations of education. They understand and respect cultural diversity and
place the welfare and educational needs of their students first. As reflective
practitioners they are committed to a service ideal which is built upon
professional standards and ethics.
c. Philosophy: The faculty members and administrators of the SOE have
developed a set of consistent principles and values that serves as the
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 1
foundation of the school’s approach to curriculum, pedagogy and program
A general exposure to and an appreciation of the traditional liberal arts
and sciences of both western and non-western traditions.
A specific exposure to the most up-to-date pedagogical theories and
A set of ethical principles, values, and dispositions.
A commitment to the principle of equality of educational opportunity for
all students regardless of group or individual differences.
A commitment to knowledge of both theory and practice and an
understanding of how one informs and strengthens the other.
d. Theoretical Underpinnings: The theoretical underpinnings of the SOE are
consistent with the tenants of progressivism and constructivism. Practices and
behaviors consistent with these approaches include:
Application of problem-solving and scientific inquiry
Use of cooperative learning experiences and self-discipline
Emphasis on how to think not what to think with the teacher serving as
Appreciation of the interdisciplinary nature of learning
Preparation of all students for full participation in a democracy
VI. Rationale – Mathematics can be described as a study of patterns of relationships,
a way of thinking, an art, a language, and a tool. It plays a prominent role in the
school curriculum, second only to reading in the amount of time devoted to it. This
course will provide an opportunity for you to examine your own dispositions towards
mathematics and how children learn mathematics. It will challenge you to keep an
open mind and continue your own learning about teaching children mathematics.
VII. Course Goals and Objectives
A. General Goals
This course will introduce students to current research and methods in the field of
mathematics instruction. It is based on the recommendations of the National Council
of Teachers of Mathematics as well as the State of South Carolina Mathematics
Standards. Students will be expected to participate in hands-on experiences with the
use of manipulatives for the purposes of expanding their knowledge base in
mathematics as well as gaining knowledge regarding current pedagogical processes
on the subject of teaching mathematics to children.
B. Instructional objectives:
The purposes of the course are related to mathematics/mathematics education and
your professional development that can be expressed as the following outcomes:
1. to increase your knowledge and understanding in the teaching and learning of
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 2
2. to increase your knowledge and abilities in the appropriate use of manipulatives for
mathematics instruction and the appropriate use of additional tools (i.e., technological
tools) in the teaching of mathematics
3. to analyze current methods and theories of mathematical instruction regarding the
National Council of Teachers of Mathematics Standards and state standards, and how
these standards are implemented in the classroom
4. to reflect on the practice of teaching for the purposes of improvement
5. to increase your knowledge and understanding about the diverse ways in which
children learn mathematics
6. to maintain a positive attitude towards the teaching of mathematics
VIII. Course Requirements
A. Administrative Requirements:
Attendance: Each absence after the first will result in a 3% loss of points from your
final point total. Please do not plan Doctor/Dentist appointments for you or your
children during class time. They are not excusable. Funeral attendance must be
accompanied by documentation from the funeral director. Missing more than three (3)
scheduled classes (this includes the 1 permitted above), results in a grade of F for the
course. Arriving late, leaving early or leaving the class for an extended period of time
(over 15 mins) will result in a tardy. Three tardies are equivalent to one absence.
It is the student’s responsibility to have projects and papers handed in on time. If you
are going to be absent, plan ahead (if possible) and have a peer bring your work to
class, or ask a colleague to hand it in for you. DO NOT email any projects or papers
to the instructor unless informed by the instructor that this is acceptable. All available
points will be reduced at the rate of one point per day (including weekends) for every
day late. After 5 days, assignments will no longer be accepted except in extenuating
In the event of an absence, it is your responsibility to work with a peer to assist you in
obtaining information regarding what was covered in class. It is not the instructor’s
responsibility to re-teach a concept due to an absence.
Inclement Weather: In case of adverse weather conditions, students are to utilize
their own judgment as to the safety of traveling to class. The university does NOT
close or dismiss class due to adverse weather except in unusual circumstances.
Students should listen to one of the local radio stations, contact the university or check
the website for information pertinent to altered class schedules.
Honor Code: Students are expected to adhere to the strictest standards of academic
honesty. Each student should review the Academic Honor Code printed in its entirety
in the USC Upstate Student Handbook. This code strictly prohibits plagiarism.
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 3
B. Professional Behavior: This category includes the way in which you conduct your
professional duties as a student and as a teacher in the classroom. Not meeting any
of the following expectations in behavior will result in loss of points (up to 15 points):
(1) As a student: You are expected to be on time for class, participate, and pay
attention; you will show respect for instructor and other students by not interrupting the
class with idle conversations or distractions.
(2) As a teacher, you are expected to attend all required practicum sessions
and/or conferences, and to present yourself in such a way that positively reflects the
University in dress, manner, and attitude.
C. Academic Requirements and Assessments
The following list of assignments and their point values will determine the student’s
grade for the course. Students are encouraged to keep records of each assignment
so that they are aware of where they stand academically in the course. If the student
has questions regarding a grade, it is suggested that s/he communicate and
conference with the instructor regarding those concerns. Changes to the Course
Syllabus: The instructor reserves the right to make changes in the course of study by
adjusting requirements or the schedule. Any changes necessary result from an effort
to meet the needs of the curriculum and to better meet the needs of the students.
1. Short Assignments: (i. e.) Homework, in-class activities, pop-quizzes on assigned
readings, use of email will be required. Points (if any) vary with assignment.
2. Field Experiences - Field Experiences: You must be enrolled in this course
concurrently with a clinical experience. If, for any reason, this is not the case, please
see your advisor. Observations, creating and implementation of lesson plans for the
purposes of mathematics instruction in a clinical setting is required for the course.
Students enrolled in a clinical experience will be evaluated using the ADEPT form by
your clinical or classroom instructor. This evaluation will be collected for your file.
3. Exams (2): 45-65 points each. Note: No make-up exams will be given without
instructor approval. Cell phones are not permitted during examinations. If you have a
cell phone, it should be turned off and not visible to anyone in the room (concealed in
a book bag, pocket, etc). Late entrance to an exam is not permitted.
4. Projects: The following class projects will be assigned throughout the course. For
more detailed information regarding these projects, see attached explanations. (total of
100 points for projects)
Project 1: A Position Paper 14 points
Project 2: An On/Off Task – Observation Tool 12 points
Project 3: An Interview: Using Problem Solving as
Informal Assessment with a Child 10 points
Project 4: A Model Lesson 15 points
Project 5: A Mathematical Game 17 points
Project 6: Lesson Plan 20 points
Project 7: A Reflective Analysis of Your Teaching 12 points
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 4
IX. ADA Compliance Statement: In keeping with University policy, any student
with a disability who requests academic accommodations should contact
Disability Services at 503-5195 to arrange a confidential appointment with the
Disability Services Coordinator. Students are encouraged to seek an
appointment as early in the semester as possible, as accommodations are not
provided retroactively. Letters of accommodation must be signed and printed on
letterhead from the Disability Services office. It is the student’s responsibility to
provide these letters to professors in a timely manner so that accommodations
may be put in place.
X. Education and Economic Development Act (EEDA) –The following SC
Education and Economic Development Act (EEDA) standards require that teacher
education candidates be proficient in the following: (1) the career guidance process,
(2) career clusters and Individual Graduation Plans, (3) SC career guidance standards
and competencies, (4) character education, (5) contextual teaching, (6) cooperative
learning, and (7) diverse learning styles. Depending on your program, some of these
standards may be addressed in this course. You can obtain additional information
about the EEDA at the SOE website.
E. Grading System
A = 93% or more of available points C = 74% - 78% of available points
B+ = 89% - 92% of available points D+ = 69% - 73% of available points
B = 84% - 88% of available points D = 64% - 68% of available points
C+ = 79% -83% of available points F = below 64% of available points
XI. Course Schedule – See attached calendar
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 5
Position Paper - Project #1
Appropriate for including in your portfolio under
APS #6: Teaching Content for Learners
You are required to submit a position paper. For our purposes, the position paper will
be relatively short (minimum of 1000 words). In this position paper, you should:
Select a question of controversy that sparks your interest, and that you would
like to research.
Email your topic to the instructor for an OK to go ahead. Each person must
have a different topic. Instructor will keep track of the topics.
Select two articles on the topic from the following NCTM journals: Teaching
Children Mathematics, or Mathematics Teaching in the Middle School. Your
research is restricted to these periodicals.
Make a copy of the articles to attach to your paper.
Underline or highlight sections of the articles that you consider important.
Do not select articles published before the year 2000.
At the end of the document, include the word count.
The title of your paper should reflect the question that you are developing.
In the first paragraph of the paper, briefly present both sides of the question. Continue
by selecting one side of the argument, either pro or con, and discuss your opinion.
The authors of the two articles that you have chosen should support your opinion. Cite
the authors in the text where they support your argument, and list them as references
in a reference list at the end of the paper. Sources that give additional information
may also be used; however, your two primary sources will be from the articles you
have selected. All references must be included in the text and in the reference list.
Use only primary sources, (i.e. do not quote NCTM from another source – quote only
from the original source).
Your written communication skills will show a good command of English, and standard
rules of grammar, spelling, punctuation, and composition will be expected. Your paper
will be word-processed, and double-spaced. Your references will need to be cited
using APA (American Psychological Association) style. Go to the writing center for
help if you are unsure about APA. You will be graded on the creativity of the
argument you present, the clarity of your writing and quality of the work.
Appropriate and accurate citations will be considered in the grading (see rubric).
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 6
Note: Attach the following checklist and rubric to your paper. Answer the
questions on the checklist before you hand in your paper.
Yes Answer these questions and attach this page to your paper.
1. Is the title of my paper a question?
2. Did I describe both sides of the argument at the beginning?
3. Did I focus on only one side – pro or con?
4. Did I use APA format?
5. Do my citations in the text and my reference list match?
6. Did I attach the two articles (full articles) as required and are they
from the required journals?
7. Did I give my opinion and not include long passages stating or
restating what the author said?
8. Did I check to be sure that my topic is original?
Scoring Rubric for Assignment One
A Position Paper
14 Question is interesting and writing demonstrates a thorough understanding of the
argument. References are appropriate and articles are attached. This work shows
clarity of thought; it is well written with correct grammar, syntax, and spelling. Citations
and reference list are entirely or mostly correct. Selection of journal articles is
appropriate. Word count is attached.
11 Question is interesting, but topic is overused. Writing demonstrates a good
understanding of the argument. References are appropriate and articles are attached.
This work shows some clarity of thought. Response is well written, but needs some
editing. Citations and/or reference list are somewhat correct. Selection of journal
articles is appropriate. Word Count is not appropriate.
8 Question is interesting; references are appropriate; articles are attached. However,
the writing needs editing and clarity of thought and/or either citations or reference list
mostly written incorrectly. It meets minimum requirements for this project.
0 Paper needs to be resubmitted for reduced points as determined by instructor.
Note: Student may be required to visit the writing center and show proof of visitation
before paper will be accepted.
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 7
Project #2: Classroom Observation Report: Students On/Off Task
Appropriate for including in your portfolio under
ADEPT Performance Standard # 3 – Use of Assessments
ADEPT Performance Standard #7: Monitoring Student Learning
ADEPT Performance Standard # 9: Classroom Management
The intent of this observation is to determine the degree to which individual
children are engaged in the task or tasks that the teacher indicated are appropriate,
and to make inferences regarding the impact of behaviors on learning. To conduct
the observation, follow these steps:
After you enter the classroom, become acquainted with what the teacher expects the
children to be doing during a given classroom period. Look around the room and
select a child to observe for the time period you are there. Position yourself in a
section of the room where you are able to observe inconspicuously.
Create a legend to represent each type of inappropriate behavior observed. Fill in the
chart on the next page, listing the names of types of behaviors you will observe in
addition to “on-task.” Some examples of additional behaviors might be: (1) stalling,
(2) walking around the room, (3) talking to neighbors, (4) doing school work other than
that requested by the teacher. Do not use more than five categories of behaviors;
focus on just five behaviors.
Systematically examine (not less than every 3 minutes) the behavior of the child in
order to determine whether the behavior is on-task, that is, doing what the teacher
considers appropriate. Repeat this process every three minutes for the duration of
the observation, each time indicating what kind of behavior the child is exhibiting and
placing a checkmark in the box that indicates that behavior. The checkmark should
match the interval of observation. For example, if you are observing the first interval
(the first three minutes) place the checkmark under “1,1” for on-task; in the second
interval (the second three minutes) place the checkmark under “2,2” for stalling and so
on. Mark the time of each interval. Only one behavior should be marked in each
column. Fill out the data sheet accurately and completely.
Write a commentary that examines your analysis. This commentary should be no
more than 4 pages including the data sheet. Follow the framework available on the
rubric (see next page) and be sure to label each section.
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 8
Scoring Rubric for Project #2
Use of Observation Tool: ON/OFF Task
Prepare a commentary where you discuss the following points. Be sure to label each
section of the paper that addresses the points below. Do not leave it to the reader to
have to find the passages that address each section.
Section 1: What is happening in the classroom? (Score 0-1 points)
Identify who you are, tell the date, time and place of the observation.
Describes what is happening in the classroom in detail and sets the stage for the
reader giving a little background about the lesson, school, age group, (whatever the
writer feels is important).
Section 2: The Data Sheet (Score 0-3 points)
Completes the data sheet, accurately. Discusses each type of behavior selected for
the chart and tells why it was selected.
Section 3: Inferences about learning (Score 0-6 points)
Discusses (infers) the strengths (at least 2) and weaknesses (at least 1) of the child
based on observation. Makes inferences about the outcomes of these behaviors and
how behaviors will impact on achievement in the future.
Section 4: Improvements (Score 0-2 points)
Infers what the writer might do (if s/he were the teacher) to improve the learning
situation and how these changes might impact on learning. Tells why these changes
are important for learning.
1. Did I label each section?
2. Did I discuss what is happening in the classroom?
3. Did I discuss each type of behavior that I selected and tell why I selected it?
4. Did I include the data sheet ; is it filled out completely and accurately ?
5. Did I make inferences regarding strengths (2) and weaknesses (1) of child?
6. Did I make inferences regarding the impact of behaviors on achievement in
7. Did I make inferences about how the situation could be improved?
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 9
Data Sheet for Observation Tool: ON/OFF Task
Name ____________________________________ Date _______________
Category of 1 2 3 4 5 6 7 8 9 10 11 12 TOTAL PER
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 10
Project #3 – Mathematical Interview
Appropriate for including in your portfolio under - APS #3: Assessment
APS # 7: Monitoring, Assessing, and Enhancing Learning
Select a child from the classroom in which you are assigned for the purposes of
Find a problem solving task for the interview. Be sure it is age appropriate. (If
you are unsure as to the quality of the problem, send it to me by email and I will
advise you.) Also – see chapter 6 in your text.
Type the problem on a piece of paper that you will give to the child.
Turn in that same piece of paper with the child’s work along with a commentary
Observe and document/record how the child solved the problem.
As the problem is being solved, ask the child to use the “think-aloud” method,
so that you can capture an understanding of how the child is thinking. (A tape
recorder would be useful for this purpose.)
Listen to or transcribe the interview (not necessary to hand this in, but it will give
you accurate information). Analyze your documentation and report on what you found
out about the child’s mathematical abilities during the interview. Make some
recommendations regarding the child’s work in mathematics. Lastly, include
some of your own dispositions regarding the use of problem solving for informal
Think about designing the interview questions so that the child is giving you
information about the topics below as s/he solves the problem.
Did the child understand the problem? What questions did you ask to gather this
information and what were the responses given by the child? (Use specific
conversation from the child.)
Did the child have a plan for solving the problem? What was reported by the child
regarding the plan?
Was the child cued into a process for problem solving right from the beginning, or were
there expressions of confusion?
Did the child move easily through the process?
What particular strategies did you notice? List them. (draw a picture, act it out, etc.)
As the problem solving process progressed, how confident was the child regarding the
implementation of his/her plan?
Did the child use trial and error or did the child stick to the plan?
How sure was the child that s/he arrived at a correct answer?
Was the child able to tell why (or why not) the solution was correct?
How accurate was the child in computation?
Has the child ever solved a problem like this before? Often or rarely?
What questions did you ask to move the child’s thinking along? Give at least three
examples. Did you give any hints? Give an example.
What additional observations or recommendation can be made regarding the abilities
of mathematical learning of this child?
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 11
After the interview:
Create a commentary that discusses the data you accumulated regarding the
mathematical task. This assessment should be about 2.5-3 pages, typed.
Attach the typed sheet with the problem on it that you gave to the child along
with the child’s work.
Do not include any personal information about the child except for the first
name. See the calendar for the due date.
Be sure to read the rubric below before beginning the task.
Scoring Rubric for Interview
10 This reflection demonstrates that the developer has explored the problem
solving process with a child. The problem chosen provided ample opportunities
for mathematical thinking and problem solving. The analysis shows insight into
assessment of the child’s attitudes about mathematics as well as demonstrating
the child’s ability to think and make connections about mathematical ideas. It is
supported by actual statements of the child. It reflects meticulous attention to
detail: style, grammar, spelling, and punctuation. It analyzes the interviewer’s
own disposition and skills in mathematics.
8 This reflection demonstrates that the developer has explored the problem
solving process with a child. The problem chosen was appropriate for the age
of the child and provided some opportunities for mathematical thinking and
problem solving. The analysis shows some insight into assessment of the
child’s attitudes about mathematics. It needed to document the child’s ability to
think about mathematical ideas better. It needed to use actual statements that
the child said. It reflects some attention to detail: style, grammar, spelling, and
punctuation. It reports some details regarding the interviewer’s own
dispositions and skills in mathematics.
6 This reflection demonstrates that the developer has explored the problem
solving process with a child. The problem chosen could have provided more
problem solving opportunities and more mathematical thinking. The analysis
shows little insight into assessment of the child’s attitudes and thinking
regarding mathematical ideas. It requires editing to reach clarity. It does not
report enough detail regarding the interviewer’s own dispositions and skills in
4 This reflection is mainly descriptive and shows little or no insight into
children’s thinking regarding mathematically relevant ideas expressed by the
children interviewed. It does not meet expectations for this level.
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 12
Project #4 – A Model Lesson
Appropriate for including in your portfolio under APS # 5: Instructional Strategies;
APS #6: Teaching Content to Students
Select a topic from the list provided and sign up to present a lesson to your peers.
The purpose of the peer lesson is for each of you to have an opportunity to develop,
and practice presenting a mathematics lesson appropriate for your grade level focus.
Each student will design and present a mathematics lesson based either on an
inventive algorithm for teaching a skill, or a conceptually developed mathematical idea
for specific content. Each lesson should be accompanied by a one-page handout that
gives the information needed so that the audience is able to recreate the lesson in the
future. Plan for no less than 20 minutes, and no more than 30 minutes. Each activity
should be based on conceptual learning and should include a hands-on activity using
manipulatives. See calendar for scheduled dates for teaching the class.
Your handout is not a lesson plan, but should include:
Your name, grade level for which the lesson is appropriate, content area, and
any references that you used to create the lesson.
Rationale: Tell why this is meaningful mathematics
Materials: List all necessary materials so anyone could duplicate the lesson.
Don’t forget manipulatives.
Standard: Identify the grade level standard indicator – one indicator only
Prerequisites: Briefly note the necessary cognitive skills students must possess
in order to participate successfully in this lesson.
Launch: How would you begin the lesson – question, book, problem?
Investigation: Describe the actual steps involved in teaching the lesson
Assessment: Discusses/demonstrates an example of the kind of assessment
that would support individualized assessment for a work sample.
Each presentation will be assessed using the scoring rubric for the model lesson
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 13
Scoring Rubric for Model Lesson
3 points 2 points 1 point
Accuracy Presentation was Presentation was Presentation lacked
accurate and provided somewhat accurate accuracy
the basis for and provided
Preparation Well planned and well Well planned and Too procedurally
connected to somewhat connected oriented; strong
conceptual learning or to conceptual elements of direct
conceptual learning, but instruction; some
development of skills contained elements steps needed for
of direct instruction instruction were
Handout Useful; more than Useful; Meets the Useful but lacked
meets the criteria for criteria for this specifics needed for
this project. project recreating lesson
and/or was not on
Launch Highly creative Creative; did a fine Lacked motivation
Did a great job at job of capturing needed to capture
capturing audience interest of audience interest of the
Teaching Well organized and Organized, and well Few opportunities for
orchestrated orchestrated; some conceptual
flawlessly; provided opportunities for development; used
ample opportunities problem solving and commercially made
for problem solving or conceptual worksheets ; gave
conceptual development; information as
development of skills: demonstrates a type opposed to having
demonstrates of assessment but audience think; does
individualized could be more not include a viable
assessment individualized form of individualized
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 14
Project #5 – A Mathematical Game
Appropriate for including in your portfolio under ADEPT Performance Standard # 5: Instructional
Strategies; ADEPT Performance Standard #6: Teaching Content to Student
Games have long been found to be a source and inspiration for mathematics.
Mathematical games can serve many purposes in the classroom, besides just being
fun. Games can become an integral part of activity time in your classroom by
providing the basis for practicing strategies, problem solving, learning to work together,
as well as reviewing skills. This project presents an opportunity to look at diversity of
cultures by using games.
Directions: Make a game that is appropriate for use in your practicum setting. Recall
that you game must have a win factor. It may either stress reasoning, or reinforce skill
development in mathematics. Play the game in your clinical setting.* This hand-
made game will stress reasoning, or will reinforce skill development.
We will devote one class period to the sharing of games. To facilitate that sharing and
add to your “Bag of Tricks”, you will be asked to prepare a handout (one-page) for
each person in the class. Your handout should list:
Your name, name of the game, where you got the idea from (if it is totally
original, give yourself credit);
Materials needed, directions, suggested age/grade level;
A short discussion of the mathematics concepts used;
A sketch of the game. A small sketch is essential and must be included on
your handout, even if you are using items that are familiar, i.e. flash cards
or a checkerboard. If using a board game you will need a sample of
On sharing day, bring the game and handouts to class for demonstration purposes.
We will not have time to play all of the games, but will be able to share and
*Note: Your school clinical setting is the only acceptable environment for
playing the game. Social settings are not acceptable for this project.
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 15
Scoring Rubric for Project #5: A Mathematical Game
Connectedness 0- 2 point):
Game stresses reasoning and uses strategies or provides practice in
mathematical skills. (2)
Submission is a nice activity, but not a game (0)
Originality (0-2 points):
Game shows a good amount of original thinking. (2)
Game is not original, but a modification of an existing game (i.e. Bingo) (1)
Game is a commercial product (0)
Quality of the Product (1-3):
Game is elaborate. (3)
Game is not elaborate, but is durable and well made. (2)
Game is simply made – uses worksheet, pencil and paper, chalkboard (i.e.
chalkboard races) (1)
Usefulness of Information sheet (1-2)
Information sheet includes a sketch/diagram of game board or
Sample question cards (2)
Information sheet is useful but contains no sketch (1)
Information sheets were available when the class began (3)
Played the game with children (5)
To obtain the 5 points for this category, you must have your clinical instructor or
classroom teacher send an email to email@example.com or sign a note
stating that you have been observed playing the game with children.
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 16
Project #6: A Lesson Plan for Teaching
Appropriate for including in your portfolio under APS # 2: Lesson Planning
APS#6: Teaching Content to Students
Theorists like Dewey, Piaget and Vygotsky claim that learning is constructed by
interacting with the environment, other persons (peers and teachers) and through
hands-on experiences. This project has been created to support these ideas, as well
as to support and show evidence of teaching in conjunction with NCTM Standards.
This project will also support aspects of the Teacher Work Sample.
Part I: Create the lesson plan. Your task will be to create a formal lesson plan for
teaching in the classroom to which you have been assigned. Follow the lesson plan
format available to you in this syllabus and submit your plan for grading as scheduled.
All handouts (or scratch ideas) being used in the lesson must accompany the plan.
You may be allowed to resubmit the plan (one time) making specific corrections to
show that you have the knowledge and ability to construct an appropriate lesson plan
to meet performance dimension #2. This lesson plan may (or may not) be the plan
that you will teach in a formal setting, however, it will serve as a guide if your
classroom instructor wants you to teach a different lesson. If you need to create a
different plan for your formal lesson, be sure to have your classroom instructor looks at
and initials the plan. The plan that you teach must be included in your final
Before you teach the lesson, the instructor of this course will read and grade the plan
for teaching. Notes may be included on the plan and this plan will be included in your
final project due at the end of the course. The plan may or may not be appropriate for
use in your assigned classroom. Your classroom teacher may require you to write a
second plan. Be sure to save all drafts for your final project
NOTE: Plan only lessons that result in children’s work samples. This is
required for your reflection and analysis.
Following the lesson plan format on the next page, create a lesson for the topic you
will teach. Hand in the lesson plan on the required date for grading. In the first round
of grading, the plan is work a total of 20 points if you meet all of the criteria listed on
the lesson plan format. Each succeeding submission diminishes the total points
available by 5 points. Four submissions are possible.
Points for each section are in parenthesis.
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 17
Lesson Plan Format
Name ________________________________________ Grade Level ______
Upstate email address ____________________________________________
Content (select one) Num and Op; Algebra; Geometry; Measurement; Data Analysis
Rationale: Indicate reasons why you would teach this lesson. (1 point)
Standard: Identify the Standard from the South Carolina Mathematics
Curriculum that this lesson supports (it has 2 parts – the standard and the
indicator) (1 point)
Objective: What do you expect the children to learn as a result of your
teaching this lesson? Be sure it is measurable. (1 point)
Materials: Include all student materials, teacher materials, manipulatives, and
equipment needed. Attach a copy of all handouts (commercial handouts or
workbook pages are not acceptable) (1 point)
I. Launch: Tell what you will be doing to create interest, get attention,
and motivate students to focus. Include and label three higher order thinking
questions that you will ask the children, and include the expected responses. (3
II. Investigate: List the steps necessary to develop the lesson. Give a
description of what you will be doing and what the children will be doing. Use a
conversation format (question/answer). Be sure to include the use of
manipulatives and opportunities for critical thinking. (5 points)
Include and label five higher order thinking questions you will ask as the
lesson proceeds, and include the expected responses from the children. (5
III. Summarize: Describe how you will bring the lesson to a close, and
how you will discuss your findings. (Summary does not include
assessment.) (1 point)
IV. Assessment: Create and attach an independent (teacher made)
work sample that will assess how well the students met your objective. It will
be given at the end of the lesson and is needed for you to complete the last
project in this course (2 points).
NOTE: If you do a worksheet with the entire group, be aware that this is
NOT an independent work sample. It can be considered guided practice,
but then you must follow with an independent work sample.
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 18
Project # 7: A Reflective Analysis of Teaching
APS #3: Assessment; APS # 5: Instructional Strategies;
APS #6: Teaching Content to Students
The Commentary. At the end of your practicum experience, you will be expected to
reflect and analyze your mathematics teaching through a written commentary that may
be added to your professional portfolio. Your commentary must be supported with
evidence, therefore as you participate in your practicum, collect samples of
children’s work to be used as evidence of meeting objectives and other statements
you make in your commentary.
************************************ NOTE ***********************************************
Label each of the three sections of your commentary (Introduction, Analysis, and Reflection).
This instruction if very important – do not leave it to the reader to determine where you have
addressed the points needed.
Write a commentary that uses the following bulleted points as guidelines:
1. Introduction :
Briefly describe the contextual factors of the setting. Tell something about the
nature of the teaching in the classroom, the age level of the children, and
characterize the expectations of the school regarding mathematical
achievement. Briefly describe the lesson you conducted with the children.
Tell about the socio-economic status the community.
Tell how you think these contextual factors of the environment impact on
Objective #1: Write the objective from your lesson plan.
Did the children meet your objectives?
Examine each of your work samples and tell how you determined if each
student met your objective or not. (Cite each paper by name (Student #1,
Student #2, and Student #3).
Discuss what you would do next to improve achievement for each child. Be
On a scale of 1-10, what grade would you give this lesson for promoting problem
solving? (i.e. Was there ample opportunity for mathematical thinking and learning?)
Based on your assessment of student performance in class, what was more
effective in your teaching? Less effective?
What insights do you have about the teaching of mathematics?
Have your attitudes about the teaching of mathematics changed as a result of this
course? Why or why not?
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 19
Scoring Rubric for Project #7:
A Reflective Analysis of Teaching
4 Inferences regarding individual children’s abilities to meet objectives are clearly
discussed and supported by work samples. Infers ways in which the teacher’s
performance could improve and tells how those changes might improve student
3 Some connections made between work samples of children and children’s abilities to
meet objectives. Shows some insight into the ways in which the teacher could improve
his/her performance and how those changes might improve student learning.
2 Weak connections between work samples and children’s abilities to meet objectives.
Is mainly descriptive and shows little inference for improvement of performance or the
resulting changes in student learning.
1 Poor or no connection between work samples and children’s abilities to meet
objectives. Shows little/no insight into how teacher performance and student learning
4 Tasks are primarily based on problem solving and critical thinking. Is able to
connect strengths/weaknesses to improving performance.
3 Tasks show some problem solving and/or critical thinking. Is able to identify some
strengths/weaknesses and how that might improve performance.
2 Tasks mainly support skill development. Is able to identify strengths and
weaknesses of his/her performance but unable to connect to improving performance.
1Tasks are not meaningful for enhancing thinking skills for children. Is unable to
identify strengths/weaknesses of his/her performance.
C. Packaging of the Product. In this section consider your grammar, syntax, and
construction of the document.
4 This response is outstanding, visually appealing, well written, above
expectations for this level.
3 This response clearly meets expectations for this level.
2 This response is basic and barely meets expectations for this level.
1 This response is below basic and does not meet expectations for this level
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 20
****************** Check-off List for Final Packet *******************
The check-off list that follows should be the top page of your project.
Please do not use three ring binders – paper folders or clips are most
Name ____________________________ Date _______________________
Email ______________________ Classroom Instructor __________________
School _______________________ School Telephone # _________________
Grade Level _________ Concept Taught ______________________________
The following items need to be placed in this document:
1. This check-off list will be your first page.
2. A draft Lesson Plan - The plan reviewed by the instructor –which
includes instructor notes and grade.
3. The Actual Lesson Plan that you taught (this may be the same as
#2). Be sure the teacher initials it if it is different from the draft.
4. Commentary - This commentary should be at least 4 pages.
Examples of student work are not counted as pages.
5. Children’s work samples (at least 3-5 samples completed by
children that assess objectives) – DO NOT USE LAST NAMES
OF CHILDREN. It is not necessary to include all work samples
from a class, just the work samples that show something about
how the children achieved the objectives of the lesson.
6. Rubric for the Reflection
V. Duarte Fall 2009 SELD 446 Teaching Math in the Elem School pg. 21