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```					                    Vacationing in Hawaii with Linear Functions

Russell Takashima
Title III 2003

Pilot course: MAT1033C Interme diate Algebra

Identification of Proble m and Goals

One of the course competencies of MAT1033C, Intermediate Algebra, is the study of
linear functions and modeling through applications. Many students have difficulty
understanding the concept of linear functions and their graphs when given an equation to
graph. Students learn the formulas and methods to draw the graph representing an
equation. The understanding and knowledge stops there with no understanding of what it
may represent. I would like to further the understanding and knowledge of this topic by
applying it to a real life situation, “Planning and taking a Vacation to Hawaii”.
My question is “Will students learn and understand linear functions through
applications?” My goal is for students to understand linear functions through the use of
real- life applications.
When addressing the topic of linear functions, many students memorize the proper
formulas to develop a function representing a specific problem. I would like students
learn the formulas involving slope and slope-intercept and relate these to some
application that will have some personal meaning to them. I would like students to
THINK about and VALUE their process of developing a linear function using topics of
distance, rate, time, and real- life business applications relating to a vacation. Some of
these business applications involve, plane fare, hotel accommodations, rental car fees,
food costs, and shopping expenses. Applications involving distance, rate and time
include air travel time, time and distance relating to land travel. In previous classes
students have stated that there was no connection for them when given the for mulas
concerning slope. They could not see it as a rate of change. I feel that giving students
the opportunity to see daily occurrences of rate of change will help students understand
the concept. Students always state that since the material is presented at such a rapid
pace that they take much longer to understand the concept. I will use classroom
assessment techniques such as the muddiest point and minute papers to review student
progress. I will also use classroom questionnaires addressing instruction to help me in
my presentation of material.
Many instructors have stated that students have difficulty applying linear equations and
functions without reference to some real life situation. Although the formulas and
methods are an integral part of learning this course objective, some application must be
presented so students can contextually visualize what is being represented with the
function and its graph.
In the past I have presented material on linear equations and functions but failed to make
some reference to an application. The student’s reaction was negative as they saw it as
just another “skill and drill” problem they were required to learn. The comment of
“When will we use this?” always arises. When I presented problems involving cell
phones, mountain climbing, and truck rentals students made a connection to the topic of
linear functions.
The goal of this project is for students to have a better understanding of linear functions.
I predict that the outcome of this project will be successful. I will incorporate cooperative
learning strategies and classroom assessments used in this project in another course
objective, quadratic functions. I am confident that providing some theme-based context
pertaining to any mathematical topic will help students understand it.

Lite rature

Angelo, T. A. & Cross, K. P., (1993), Classroom Assessment Techniques: A Handbook
for College Teachers, 2nd ed., Jossey-Bass

Brookfield, S. D., (1995), Becoming a Critically Reflective Teacher, 1st ed., Jossey-Bass

Cross, K. P. & Steadman, M. H., (1996), Classroom Research: Implementing the
Scholarship of Teaching, 1st ed., Jossey-Bass

Huba, M.E. & Freed, J. E., (2000), Learner-Centered Assessment on College Campuses:
Shifting the Focus from Teaching to Learning, Allyn & Bacon

Walvoord, B. E. & Anderson, V. J., (1998), Effective Grading, A Tool for Learning and
Assessment, Jossey-Bass

Wlodkowski, R. J. & Ginsburg, M. B., (1995), Diversity and Motivation: Culturally
Responsive Teaching, 1st ed., Jossey-Bass

Seminars

Title III Kickoff with Stephen Brookfield, Classroom Research

Technology Showcase

Assessment Seminar with Wendi Troxel

Core Competency Seminar

Inclusion Seminar with Susan Ledlow

LifeMap/Critical Thinking Seminar with Skip Downing
The classroom action research workshop with Stephen Broofield helped me develop my
action research plan and to understand what is actually included in such a project. I have
included his CIQ’s and muddiest point papers in my project. The core competency
seminar helped me learn how to connect my learning outcomes to Valencia’s Core
Competencies (TVCA). I have used Walvoord’s , Effective Grading, A Tool for Learning
and Assessment, chapter 6, “Calculating Course Grades”, to re-evaluate my assessment
process for student grades. In chapter 7 I have taken ideas involving communicating with
students about their grades, especially speaking to the learner and not the mistakes.

Appropriate Methods

1. Learning Outcomes-What learning outcomes are you seeking?

I am addressing the topic of linear functions in this project. I would like students to fully
understand this concept by relating it to some personal situation. I would like students to
learn and interpret the concept of slope as a rate of change. The MAT1033C course
competencies I am addressing in this project are: 1) Solving linear equations,
2) Calculating the slope of a line and describing its meaning, 3) Describing the
relationship between the graph, its points and its equation. Students will interpret data
points, plot these points and derive a linear function. Students will represent this linear
function graphically and be able to explain its meaning. One activity to be used is the
renting of a car. Students will research the cost of renting a car for the trip. There are
many options here and I want students to select a car that they can afford within an
assigned budget and be happy with. Students will need to create a graph, create a linear
function representing this graph and be able to explain what the significant points are.
These points may include the initial cost including insurance, cost for x number of miles
driven. A second linear function will be created for another rental car company and a
cost comparison will be made. Students will be able to select the better deal by
examining their graphs and functions. The linear function will enable students to
determine their total cost for renting a car. Other activities include cost of hotels, plane
fare and food.

2. Performance Criteria

Students will be given the formulas and methods for deriving linear functions. Students
will show their knowledge by calculations of the slope of a line and deriving the equation
or function. These activities will help students address the mathematical skills necessary
for this topic. Students will show their understanding of the topic through their
interpretation of various data and developing a function representing this data. Students
will be able to explain the meaning of all given data, interpret the data pertaining to the
situation, and make a conclusion from the linear function. An example activity would
address rental car fees while on vacation. Given all the data necessary, will students be
able to derive a function for the cost of a rental car? Given more data, will students be
able to compare the cost of renting from different rental car companies?
Will the students be able to interpret their research and make a valid conclusion towards
renting a car?
Students will be using cooperative learning activities and share their findings through
functions presented.

3. Assessment Techniques

Students will be assessed using quizzes and tests on the topic of slopes and equations of a
line. This would address the learning of the mechanics and algebraic skills necessary to
find the slopes and the linear equations. I want students to further their knowledge of this
topic and be able to understand and explain what a linear function represents. My
project revolves around students planning a trip to Hawaii. With each segment of their
planning, I will assess their knowledge of linear functions by requiring students to
research various necessities of a vacation. Plane fare, hotel accommodations, car rental,
etc., are a few necessities students will research, develop a linear function for each, be
able to interpret each function and make a valid conclusion. Students will be required to
THINK about their choices and VALUE their decisions. Students will enter all
completed activities in a “Vacation Portfolio” that will be assessed for understanding of
the topic. The “Vacation Portfolio” will include all necessary research data, linear
functions, their graphs, and their representations for each segment of the trip. This
portfolio will be assessed by the instructor and the student. Students will use a scoring
rubric to assess their portfolio. Students will self score their completion and
understanding of the assignments. The learning outcome will be a success if students
will be able to create a function given any situation that may be represented linearly.
I plan to use assessment techniques from Angelo and Cross’, Classroom Assessment
Techniques. These include the minute paper and the muddiest point. I will use these to
ensure understanding of the topic at hand and if everyone is “getting it”. I would also
like to use a revised version of Stephen Brookfield’s, Classroom Critical Incident
Questionnaire.
4. Instructional Strategies

Teaching students how to find the slope or rate of change and how to find the linear
functions are essential. Formulas for finding the slope and equations of lines are a
requirement for students to learn. Having students use applications in learning this
course objective will enhance student understanding and learning. I plan to use
collaborative learning activities in the research stage of the planning of their vacation.
The collaborative learning activities will be structured using the format presented by
Susan Ledlow. In the car rental phase, for example, student 1-will be the researcher,
student 2-the recorder, student 3-time keeper/on task master, student 4- formula deriver
(person doing the math). For each phase these roles will change. Students will work
together in the research of all data points necessary to develop a linear function for each
different phase of their vacation.
As part of each assignment, while researching data for each vacation phase, students will
be required to write about an occupation associated with each phase.

Effective Presentation

I plan to present this project at a Title III Showcase on June 4, 2003. The audience will
be members of my Title III team and other Title III and Title IV project participants and
other colleagues. I also plan to present this project to the West Campus Mathematics
faculty in August, 2003 during our initial department meeting for the Fall Term.

Significant Results and Reflective Critique

These will be addressed during the Spring 2004 term at the conclusion of the pilot

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