Brad Frey
EPSY 590 ASA
Final Project
Spring, 2007

Stage 1

Background Information

This is my 7^th year of teaching mathematics at Johnsburg High School in Johnsburg, Illinois, School District 12. For my first 4 years I taught only honors courses, but the last 3 years have been split between upper-class honors courses and under-class pre algebra courses. I am constantly changing my method of instruction for the freshmen Intro to Algebra class based on a topic, student population and student needs. I would like to determine if changing my types of assessment or altering assessment based on individual students and their needs would be beneficial and at the same time practical.

Project Objectives

To determine if my current use of assessments meets the needs of my students and is preparing them for their next level of mathematics learning or class.

To create assessments that gauge and/or promote understanding of the material for all students.
To create a wider variety of assessments for different learners and learning styles.
To ensure that all my lessons and assessments align with state standards.

What I Know

What I Want to Know

What I Learned

Many of my students have a predetermined belief that they are poor at math. The self defeating attitude creates a feeling among these students that hinders their ability to perform well in math class
Students in my class don’t like quizzes or tests.
I base grades on a combination of homework, in class work, tests, projects and work habits.
Students in my lower level math classes missed more school than the rest of the student population.
Most assessment in the classroom is informal.

What can I do to motivate these students to do their best in class and on assessments?
Are my grade category breakdowns fair? Should the percentages be changed to better assess students?
Should in class assignments be looked at more closely to better determine understanding? Is the time required to complete this justified?
Will changing the type of assessment or frequency of formal assessment change the attendance rate of this class?
Is there a fair way or any way at all to include informal assessment into the grading process? Do the students have the necessary skills and knowledge base to move into the next topic?

Stage 2

This curriculum map is for my Introduction to Algebra class for the months of February, March and April of 2007. My Intro to Algebra class' population consists of primarily freshmen, but older students who struggle with math are also in the class. This map will serve as one of my guides to align the class with Illinois State Standards. In the past few years, the assessments for the this class have been primarily paper and pencils quizzes and an occasional project. I play to implement more technology into the class and assessment along with different styles of projects and a math journal / portfolio.

Curriculum Map
	February, 2007	March, 2007	April, 2007
Content	Solving Equations Using Addition and Subtraction	Mathematical Formulas	Graphing Horizontal and Vertical Lines
	Solving Equations Using Multiplication and Division	Ratios and Rates	Graphing Lines Using Intercepts
	Solving Multi- Step Equations	Percents	The Slope of a Line
	Solving Equations with Variables on Both Sides	The Coordinate Plane	Direct Variation
	Solving Linear Equations	Graphing Linear Equations	Graphing Lines Using Slope-Intercept Form
	Solving Decimal Equations		Functions and Relations

Skills	Balancing Equations	Understanding what mathematical formulas are	Review and/or learn vocabulary – horizontal line, vertical line, x coordinate, y coordinate, domain, range, constant function
	Addition and Subtraction	Deriving formulas	Find x-intercept and y-intercept
	Find reciprocals	Finding area of simple polygons	Sketch quick graphs using intercepts
	Multiplication and Division	Understanding ratios	Choosing proper scale when graphing
	Properties of Equality	Understanding rates, including unit rate	Use various methods to find slope of a line
	Combining Like Terms	Unit conversions	Use rise/run to find slope
	Use of Algebra Tiles	Unit analysis	Find negative, positive, zero and undefined slopes
	Understanding coefficients	Convert fractions to decimals and percents	Direct variation and applications
	Converting fractions into decimals	Cooridinate plane	Graph lines using y = mx + b
		Understanding origin, x-axis, y-axis, ordered pairs, quadrants and scatter plot	Determine the relationship between parallel lines and perpendicular lines
		Graphing lines using function form	Become introduced to the graphing calculator
			Determine the difference between functions and relations

Assessments	Worksheets	Worksheets	Worksheets
	Homework	Homework	Homework
	In CIn Class Assignments and Group Work	In Class Assignments and Group Work	In Class Assignments and Group Work
	Weekly quizzes	Weekly quizzes	Weekly quizzes including graphing with Geometer’s Sketchpad
	Online math review	Online math review	Chapter Test
	Chapter Test	Chapter Test	Alternative Assessment – Math Journal
		Planning a Car Wash Project

NCTM Standards	6.A.4 Identify and apply the associative, commutative, distributive and identity properties of real numbers, including special numbers such as pi and square roots.	6.B.4 Select and use appropriate arithmetic operations in practical situations including calculating wages after taxes, developing a budget and balancing a checkbook.	7.B.4 Estimate and measure the magnitude and physical quantities (e.g., velocity, force, slope) using rulers, protractors and other scientific instruments including timers, calculators and computers.
	6.B.3a Solve practical computation problems involving whole numbers, integers and rational numbers.	6.C.4 Determine whether exact values or approximations are appropriate.	8.B.3 Using graphing technology and algebraic methods to analyze and predict linear relationships and make generalizations from linear patterns.
	6.B.3b Apply primes, factors, divisors, multiples, common factors, and common multiples in solving problems.	6.D.3 Apply ratios and proportions to solve practical problems.	8.C.4a Analyze and report the effects of changing coefficients, exponents and other parameters on functions and their graphs.
	6.C.3a Select computational procedures and solve problems with whole numbers, fractions and decimals.	6.D.4 Solve problems involving recipes or mixtures, financial calculations and geometric similarity using ratios, proportions and percents.	8.D.4 Formulate and solve linear and quadratic equations and linear inequalities algebraically and investigate nonlinear inequalities using graphs, tables, calculators and computers.
	8.A.3b Solve problems using linear expressions, equations and inequalities.	7.A.4b Apply formulas in a variety of theoretical and practical real-world measurement applications involving perimeter, area, volume, angle, time, temperature, mass, speed, distance, density, and monetary values.
		7.C.4a Make indirect measurements, including heights and distances, using proportions.
		8.D.3b Propose and solve problems using proportions, formulas and linear functions.

Stage 3

Stage Three – Revising the Assessment

I have included four revised assessments for my Introduction to Algebra classes and my reasons for amending the previously used assessments.

Previously Used Assessment	New Assessments	Rationale for Changing Assessment
Chapter Test 40 points total 20 Questions – 2 points each (1 point for correct answer, 1 point for work)	Chapter Test - Taken One on One with Instructor 40 points total 4 questions – 10 points each (2 points for correct answer, up to 4 points for correct steps shown to instructor, up to 4 points for properly explaining steps to instructor)	This class is over 50% IEP and most of their accommodations require that tests be read aloud and the students take their tests in another setting. By taking each test with an instructor in the classroom next door, we are satisfying both of these requirements. Additionally, having students explain each of their steps and thought processes enables the teachers to better assess their understanding of the material presented.
Weekly Quiz 20 points total 10 Questions – 2 points each (1 point for correct answer, 1 point for work)	Solving Equations Online Quiz 24 points total 8 Questions – 3 points each (1 point for correct answer, 2 points for work)	This assessment is not much different from the original. However, a technology component has been added. Students will answer their questions online and will receive their percentage correct instantly. Also, the students will be allowed to retry questions. I am hopeful this will encourage students to continue with problems that they might have normally given up on.
Planning a Family Vacation – Car Travel 100 points No set scoring rubric – grade based on neatness, work in class, and mathematical computations	Planning a Family Vacation – Air Travel 60 points Rubric clearly defined – see: Scoring Rubric	This is my favorite of my revisions. I have previously given the planning a vacation project as my first semester final exam, but never created a useful rubric and it became very difficult to grade. I had prepared a different project for a previous CTER class in the hopes of replacing the old exam. However, I wasn’t able to. So, after tweaking the Vacation planning project, I gave it out right before spring break as students were in the vacation mood. This assessment is far superior to my previous attempt in many ways. It is far more organized and the directions and expectations are very clear to the students. The added technology component kept the students far more engaged throughout the project, but the most valuable component was the rubric created to help guide the students and help the instructors when it became grading time.

Car Wash 50 points No scoring rubric – grade based on appearance of final presentation	Car Wash 50 points Clearly defined rubric – see: Car Wash Rubric	This has long been a favorite project of mine for Intro to Algebra. The basis tenets of the project haven’t changed; there is still a great underlying algebraic theme. The biggest change is the removal of the written paper conclusion. I have changed the presentation vehicle to Power Point or movie. This project was very hands on to begin with, students needed to find information about some real life situations and incorporate them into their project but adding the Power Point or movie option has enticed students to work harder and faster getting the research and math parts done. Previously, students were not enthused about writing the paper and therefore spent most of their time doing the math and / or procrastinating about the paper. With the introduction of the video component, students tried to “out do” their classmates and produce the best possible product. Another huge change from the previous version of the project is the addition of a scoring rubric. This project had previously been scored holistically, checking a few random facts and primarily based on effort, good use of class time and neatness of the final paper. The rubric has definitely made it easier on the teacher to grade it, but also lets the students know what is important when they are preparing it.

Stage 4

Completed KWL Chart

What I Know

What I Want to Know

What I Learned

1a. Many of my students have a predetermined belief that they are poor at math. The self defeating attitude creates a feeling among these students that hinders their ability to perform well in math class.

1b. Students in my class don’t like quizzes or tests.

1. What can I do to motivate these students to do their best in class and on assessments?

1. The students that don’t like math have acquired this feeling over a number of years and in many of them runs very deep. By giving them different types of assessments and projects, some of them started to change their mind about math. Changing students’ philosophies will take more than one quarter.

2. I base grades on a combination of homework, in class work, tests, projects and work habits.

2a. Are my grade category breakdowns fair? Should the percentages be changed to better assess students?

2b. Should in class assignments be looked at more closely to better determine understanding? Is the time required to complete this justified?

2. I gave students too much credit for just being busy. Students worked hard during class, but the hard work wasn’t equating to good grades on quizzes, tests and projects. Students were receiving A’s and B’s when their skills should have given them C’s and D’s.

3. Students in my lower level math classes missed more school than the rest of the student population.

3. Will changing the type of assessment or frequency of formal assessment change the attendance rate of this class?

3. This was the most disappointing piece of the project. Even though most traditional paper pencil quizzes and tests were removed, student still continued to show up for school sporadically. In one class, 25% of the students failed to show up for their final presentations.

What I don’t know however is if their missing school was entirely due to math class or if other factors or classes were involved.

4. Most assessment in the classroom is informal.

4. Is there a fair way or any way at all to include informal assessment into the grading process? Do the students have the necessary skills and knowledge base to move into the next topic?

4. I learned to check for accuracy during in class work more often. While this slowed down our class because of the work entailed, it did improve our students’ grasp of the information. Because they were now all getting the concept, it was easier to judge when to move on to the next topic.

Abstract

The project I developed is geared toward our school’s lowest level of math students. About 40% of these students have an IEP, about 30% are behavioral issues, but all of them are self proclaimed “math haters.” I was hoping to create one or two units in our Intro to Algebra class that would enable students of all backgrounds to have success in math class and gain a better appreciation of the importance of math in their school career and life beyond school.

The project took place over the 3^rd quarter of our school year and covered two chapters in our Algebra book. The project was relatively simple and straight forward; take current assessments and teaching strategies and implement a more varied approach. Introduce technology when available and craft different types of assessments to match the different learning styles and different backgrounds of the students.

After completing the project, it was clear that students who struggle or don't like math have deep seeded feelings about the subject and will need more time and more effort to change their ideas and values. However, for about 40% of my students, changing the style, type and variety of assessments seemed to encourage them as students and helped them to improve as students in the Intro to Algebra class.

What I’ve Learned

I learned many little things about this process and project. One opinion that I was able to solidify in my own mind was how different students react differently to different types of assessments. This part of my learning process played out just as I thought it might. Some students did very well on simple paper and pencil quizzes, while others did very poorly. The very same students who performed well on traditional quizzes, were sometimes my greatest opponent to different non standard types of assessments, often times arguing “why don’t you just let me take a regular test?”

I learned that not one unit can change deep seeded feeling toward math. While I did use far more different assessments during this quarter, it was just an extension of what my goal is from day one in this class “Get the students to open up and give math a chance.” My biggest aspiration is to have one student say that they don’t hate math class anymore.

I learned that grading homework and in class assignments for my honors classes are completely different than in Intro. I give credit in my honors classes for getting the work done; I leave the correctness of each assignment up to the student. These are great students who want to know if they are getting the work done correctly. This is just the opposite in the Intro class; they are just interested in getting the points for getting it done. I changed how I graded in class work as this project went on. Problems were graded, suggestions were made and students were required to “try again” until they got the problem correct. This slowed down the pace of our class, but it was a cheap price to pay for doing it the right way. When all students were up to speed, we were comfortable moving on.

I learned that no matter how much fun we had, how many games we played, how different and exciting assessment were, students who don’t like school and have the opportunity will continue missing classes and getting behind in their work.

The most important lesson that I learned during this process is to raise the bar, expect more from this class. They have convinced themselves that they are poor math students and that they cannot accomplish things. This is so far from the truth. While many will continue to struggle and will need to work very hard to just get by, there were many students (around 15 out of 42) that I found did a remarkable job and flourished with the different styles and types of assessments and lessons given during the last three months.

What I would do differently

This is always the most important question when completing a project. If you haven’t learned anything or can think of ways to improve the project, I don’t think the project can be considered successful.

I would like to apply even more technology than I presently do. Although budget, time and space are big issues. I will continue to develop the easier and cheaper alternatives such as online tests, blogs and available software.

I will enhance the math journal concept for my Intro to Algebra students and include it as a part of a bigger math portfolio. I am also contemplating making this portfolio an e-portfolio.

From what I learned about this project with my Intro to Algebra classes, I am going to re-implement the use of a portfolio in my Pre Calc classes (something I did years ago but stopped.)

The biggest thing I learned was that creating alternate assessments or applying different versions of assessments is something that can and should be done from the first day of class, not just for a quarter as a requirement for a class.

Questions

I felt the one of one assessment given during the project was one of the most valuable ideas I have ever implemented. Would this be practical to use more often? Could I spare all the time it takes?
Do you think that giving students different options for producing projects a fair assessment? During the Car Wash Project I let students create their final presentations by writing an essay or creating a Power Point. One student even wrote and illustrated a graphic novel (I still call them comic books.)

What I Want to Know

Previously Used Assessment

New

Assessments

Rationale for Changing Assessment