NCTM 2001 Annual Conference
Orlando, FL     Session 703.1

CLEAR Math and How It Improves Algebra Performance  

See Demo online            

  NEW CLEAR Math information sheet

April 6, 2001, Friday, 12:00 noon -- 1 P.M. at Room 224F, Orange County Convention Center, Orlando, FL

Kristen Herbert  
Wayland Middle School, Wayland, MA


Kenneth J. Najjar  
Maynard High School, Maynard, MA




Scott Kellett  
Dover-Sherborn Middle School, Dover, MA


Andrew S.C. Chen  
MIT/ EduTron, Winchester, MA




Dr. George L. Johnston  
EduTron, Acton, MA


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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1


Computer-based Learning Environment with Advanced Remediation



Wayland (1 Computer in Classroom)

Maynard (20 Computers in Lab)

Dover-Sherborn (24 Computers in Lab)

From Wayland Students

See Demo online


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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1


What is CLEAR Math?   

Computer-based Learning Environment with Advanced Remediation

CLEAR Math is designed by MIT scientists and engineers for middle and high school use. It is being developed by expert groups of teachers and math faculty and a continuing collaboration between the EduTron team ( and college and school teachers, students, and administrators.


CLEAR Math is a learning resource for Pre-algebra, Algebra I, and Algebra II. It combines active concept explorations, dynamic tutorials, interactive step-by-step practices, applications, and testing in an integrated, intelligent environment. Its imbedded intelligence assesses student competence on a detailed level, reports its findings to the state-of-the-art classroom management system, and remediates students on the fly. Its competence and tirelessness in the areas of concept explorations, tutorials, and practices shift the effective teacher/student ratio closer to 1:1. Furthermore, it thereby frees teachers to engage in important class and individual instruction.


CLEAR Math has been proven to be very effective in improving students’ Algebra performance.  See Demo at EduTron Web Site.


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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1

Wayland Middle School’s Experience with CLEAR Math

One PC in Classroom   

Kristen Herbert

(508) 655-6670

Wayland Middle School, Wayland, MA

Hi Andrew!

We just finished up Chapter 10 of CLEAR Math in my modified algebra course.  The students performed well on the final test.

As you know, we used one computer hooked up to the overhead to use the program.  Although this method of presentation does not take advantage of all of the capabilities of the program, it worked pretty well. The lessons and examples were at an appropriate level for these students. Also, I appreciate the fact that there aren't a lot of glitzy graphics to take students' attention away from the content.

One student each day worked the computer.  First we would listen to the "lesson" and students would take notes.  Students asked the student who was working the computer to "pause" when it was needed.  Then we would do the practice exercises and the activities.  Each student would work the problem at their seat individually or with a partner.  Then I would call on one student to answer the question.  If the rest of the class generally agreed with the response, we would enter it as the response and check it with the computer.  This worked well.

The one issue with using the program as the base of our math program for these students is homework. I wanted to use homework to reinforce the concepts we covered in class.  However, I could not use our regular algebra text (UCSMP "Algebra") for this purpose because the concepts are not grouped in the same manner.  I decided to photocopy pages from Barbara Poole's "Introductory Algebra" text as homework.  Although the concepts are not introduced in the same order, the examples and problems have a similar approach and depth so that there was a seamless transition from working with CLEAR Math in class and doing the homework.

For our next topic in this class, we have returned to our algebra text. However, I am planning on using the program again after our February break.  I will call you to invite you in at that time.  I think the students would really like to meet you in person because they have heard so much about you!  Actually, now that I am thinking about it, if you had some time to come and talk with them before February break, I think they would love to give you feedback in person!

Thanks!   -Kristen Herbert

Since January 2000, Kristen has used her Massachusetts DOE Lighthouse Grant to build up a Math Lab with more than 20 computers running CLEAR Math.

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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1

Maynard High School’s Experience with CLEAR Math

 ….20-Compuer Lab….

Ken Najjar

(978) 897-8891

Maynard High School, Maynard, MA

 Dear fellow teachers:

I have been using CLEAR Math at Maynard High School for more than two years.  I have used it as a teaching tool and for the purpose of review for classes.  The students find the immediate response given by the software helpful.  Also, the visual lessons that the software provides add to the clarity of mathematical concepts that I, as a teacher, provide with the lessons in the classroom.  On the mathematical concepts that the software has available, I have found that the more students master the concepts and achieve a deeper understanding, as well as, retain the information better.

The student reaction to CLEAR Math is very positive.  They like the idea of moving at their own pace and being able to go back over lessons as they wish.  Students have found the software easy to run and need little time to learn how to move through it.  Even students that do not like computers find that CLEAR Math is interesting and a very helpful addition to classroom lessons and texts.

I like to use CLEAR Math to introduce concepts and then I can add to the depth, as I deem necessary depending on the capability of the class.  Also, I find that using as a review of concepts taught in a prior course has refreshed the students’ knowledge quicker, clearer, and in less time than I could do in the classroom.  It allows me to get around to those students that may have more difficulty, to give them more individual attention. 

Feel free to contact me if you have questions on CLEAR Math.

Ken Najjar

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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1

Dover-Sherborn Middle School’s Experience with CLEAR Math

 ….24-Compuer Lab….


Scott Kellett

(508) 785-0635 x 52

Dover-Sherborn Middle School, Dover, MA


Math Connections

Course Description

(Semester course meeting alternate days)


The Math Connection course is designed to improve and/or enhance the mathematical skills of all students in the seventh grade in preparation for both algebra one and the MCAS test in grade eight.  The curriculum utilizes a computer program called CLEAR Math.  The nature of the program is such that it provides instruction, exploration opportunities and practice while continually giving direct feedback to both the individual student and the teacher.  Additional enrichment units include topics dealing with spatial relationships, game strategies and inductive and deductive reasoning.


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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1
Wayland Middle School Students’ Comments on CLEAR Math

 One PC in Classroom   

Kristen Herbert

(508) 655-6670

Wayland Middle School, Wayland, MA

Hi Dr. Chen!

Thanks for your inquiry.  We are using the program in my period 4 modified algebra class. I am projecting it on to a large screen.  I did change the desks around in my room so that all the students could see the screen and the board at the same time. 

The students love the program!  Everyday, I have the students fill out evaluation sheets.  Here are some of the comments (direct quotes from students):

I have written copies of all the evaluations.  I can show them to you when I see you next.  Obviously, some of the suggestions are problems caused by the speed of our machines not your program.

Thanks so much! 


Since January 2000, Kristen has used her Massachusetts DOE Lighthouse Grant to build up a Math Lab with more than 20 computers running CLEAR Math.


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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1

What are students and teachers saying about CLEAR Math? 


Interactive Concept Exploration and Step-by-Step Practices




Dynamic Tutorials





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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1

Other Teacher Comments 

"I believe CLEAR Math will be extremely useful for classroom and for self-paced settings. I am intrigued by how much detailed thinking, planning and programming were put into this thing. If you ever need me to speak up in your future marketing campaign, I will be more than willing to do it. This is because I REALLY believe it will do great things for the teaching communities!"

"This is wonderful! I witnessed students being engaged in math activities in CLEAR Math for long periods of time. CLEAR Math is almost the perfect learning tool - something one only dreamed of."

"I believe most students will find it easy to use, they would learn better because their attention has been sparked and they can go over and over at own pace."

"Diagnosing students as they progress is the best feature…I also liked the content and the user interaction."

"It is flexible, has a variety of formats. ... The voice instruction is very clear."

"It is clearly written and the transferring between screens is great!"

"CLEAR Math represents a novel and revolutionary way in harnessing technology to ease the teaching and learning process. I am totally impressed by what is being offered."

"I am a visual learner, and I just learned from the dynamic example you showed... I wish we had this program when I was learning Algebra…"

"This is by far the best Algebra Software I have seen. I would require all of my students to use it, not just the students requiring additional attention."

"I can see CLEAR Math increase learning efficiency for first time learners as well as remedial students… our assistant superintendent definitely should see it soon."

"This may be the optimum mix of (NCTM and traditional) material… Personally I am biased, I prefer to see mostly open-ended and not pre-canned content. Your stuff is good - it does allow student manipulation … it also has multiple presentations… It contains many facets and components of useful stuff. I like it. Although I have no economic interests in it, it has the potential for becoming a successful product."

"All of my students will be able to use and learn from an environment like CLEAR Math. The exploration parts that offer students a chance to construct their own knowledge is very good. The lessons are well done, in fact, I think our teachers will also learn from them…"

"It looks like an exciting product. I have not seen any system quite like it. Does it run on Macs?"

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NCTM 2001 Annual Conference
Orlando, FL     Session 703.1

CLEAR Math Table of Contents


0. Arithmetic Review

1.01 Whole Numbers

1.02 Fractions

1.03 Decimals

1.04 Percents


1. Whole Numbers

2. Fractions

3. Decimals

4. Practical Geometry

5. Ratio and Proportion

6. Percent

7. U.S. Units of Measure

8. Basic Statistics

9. Signed Numbers

10. Variable Expressions

10.01 Properties of Real Numbers

10.02 Evaluating variable expressions

10.03 Simplifying variable expressions

10.04 Translating Expressions


11. Linear Equations in One Variable

11.01 Solutions to Equations

11.02 Equations: x + a = b

11.03 Equations: ax = b

11.04 Equations: ax + b = c

11.05 Equations: Multi-Step

11.06 Equations with Fractions

11.07 Percent Equations

11.08 Translating Words to Algebra

11.09 Absolute Value Equations


12. Basic Inequalities

13. Exponents

14. Polynomial Operations 

15. Polynomial Factoring

15.01 Common Factors

15.02 Factoring Trinomials, a = 1

15.03 Factoring by Grouping

15.04 More on Trinomials

15.05 Special Factoring

15.06 Factoring Strategy

15.07 Solving Quadratic Equations 

16. Rational Expressions

17. Linear Equations in Two Variables

17.01 Cartesian Coordinate System

17.02 Tables and Graphs

17.03 Slope

17.04 Linear Equations 

18. Linear Inequalities

19. Systems of Linear Equations

19.01 Graphical Method

19.02 Elimination Method

19.03 Substitution Method

19.04 Graphing Calculator Methods

19.05 Graphing Linear Inequalities

19.06 Solution Space


20. 3x3 Systems of Linear Equations

21. Roots and Radicals

22. Rational Exponents

23. Complex Numbers

24. Quadratic Equations

25. Parabolas

26. Conic Sections

27. Functions

28. Matrices

29. Exponential and Logarithmic Functions

30. Probability

31. Statistics

32. Sequences and Series


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