Monday, October 13, 2008

Dr. Wilson says: Math Expressions is the best

Last year The State Board of Education hired the consulting firm, Strategic Teaching Inc, to complete the WA Math Standards revision process after the state legislature grew dissatisfied with the work being done by OSPI. Dr. Stephen Wilson is a math professor at Johns Hopkins University and a consultant for Strategic Teaching. Brief bios can be found at:
and at

Strategic Teaching is also involved in the state’s math Curriculum Review process and Dr. Wilson has recently written an interesting analysis of several math curriculums for elementary and middle school grades. He has taken several key math concept threads and compared their development across several curricula. I find his approach very appealing in that it provides both a meaningful content comparison of the curriculums for these key threads and it makes some significant deficiencies visible. Dr. Wilson’s report can be found at:

While the overall report is 42 pages I would encourage you to read the few pages devoted to describing the math concept threads he has selected for review. For the elementary grades the key math threads he has selected are:

1. Whole Number Multiplication

2. Area of a triangle

3. Fractions and the arithmetic of fractions

After the introduction of each thread he then follows it with a description of how it is handled in each curriculum (TERC Investigations, Math Expressions, Bridges in Mathematics, and Math Connects). Even if you don’t have time to read the details, Dr. Wilson’s conclusions for each curriculum are quite interesting to read.

His overall conclusions (copied directly from his report) are:

Summary Conclusions for Elementary School

TERC Investigations

The necessary components of whole number multiplication are there, but the connecting thread is not. Finally, fluency with the standard algorithm is not developed.

In the area thread, there is no formula for the area of a rectangle although it is computed. Parallelograms and triangles are not considered.

Addition and subtraction of fractions using common denominators is not done.

Math Expressions

The whole number multiplication thread is done extremely well.

The area thread is done extremely well.

The adding and subtracting fractions thread is also done extremely well.

It should be pointed out that almost all of the mathematics in these threads is in the student materials with the exception of the work on common denominators.

Bridges in Mathematics

With the help of the Washington state supplement, this thread is well covered. It suffers somewhat from a lack of coherent goal to reach the standard algorithm. The thread is there, but it branches continuously.

The area thread suffers significantly. The regular program never defines area properly or arrives at formulas. The supplement includes the content, but there are problems. The derivation of the formula for the area of a parallelogram is mathematically incorrect and the derivation of the formula for the area of a triangle is inadequate.

There is a serious mathematical error in a major example used to illustrate a central point about the addition of fractions and common denominators are not developed. The thread is inadequately covered.

Math Connects

The whole number multiplication thread is nicely done. The standard algorithm is more thoroughly dealt with than in the other programs even though the nice numerical model is missing.

The area thread is incomplete, lacking a formula for the area of a parallelogram and lacking any consideration of the area of a triangle.

The adding and subtracting fractions thread is nicely done except that the common denominator, although present, is downplayed.

All of the mathematics is very nicely presented and everything that is done is in the student materials.

Final Conclusions

Judging by the three very important threads evaluated here, Math Expressions is the best program. Math Connects is very well done mathematically but is somewhat incomplete. These two programs are mathematically acceptable. Bridges in Mathematics has mathematical errors and is incomplete. TERC Investigations lacks far too much content. Neither of these programs is mathematically acceptable.

Final Conclusions for Middle School

Overall, Math Connects ranks first, Prentice Hall and Holt tie for the middle place, and Math Thematics is clearly at the bottom.

Fractions are very important. None of these programs does fractions well enough to justify their use in a classroom where students are expected to understand what they are doing instead of just learn by rote. Grade 5 Math Expressions does a better job at multiplication and division of fractions than any of these programs does. It is not that difficult to explain why multiplication and division of fractions is done with the formulas presented in all of these programs, but none of them bothers. Ratios, rates and proportions are completely dependent on a student’s understanding of fractions, so, even if they are done well, if the foundation of fractions isn’t there, it isn’t likely to matter.

---- this article was written by David Orbits
Great Thanks to David


Anonymous said...

You are running into the same issues with research bias that you have with mostly all the other curriculum. Math expressions is Houghton-Mifflin.

Robert Slavin, also at Johns Hopkins, judged research for both Math Expressions and Everyday Math and found "limited evidence of effectiveness" for both programs.

Is he correct? I don't trust his research either. He is "Mr. Success for All"

Robert Slavin is currently Co-Director of the Center for Research on the Education of Students Placed at Risk at Johns Hopkins University and Chairman of the Success for All Foundation.

He received his B.A. in Psychology from Reed College in 1972, and his Ph.D. in Social Relations in 1975 from Johns Hopkins University.

Math Expressions isn't that great of a textbook, but it is traditional or whatever that means anymore. Somewhere between EDM and Saxon? You can't really judge books until you do the problems and try to understand what the authors were thinking. Most of the time they weren't thinking at all - with Singapore and CPM the problems do go somewhere and that's where experience counts.

e.g. Ways to solve equivalent fractions. 1) giant 1; 2)inverse property; and 3) cross multiply. All standard methods of solving for x, yet students need to know when to work smarter; not harder.

I write my own problems now, because I know where I want to direct my kids. I give them my reasons and we just go. Heck, I don't use either worksheets or books because my students won't open books and they write nasty epiphets. They hate the other school. Their learning is all done on lined paper and my kids do much better and they're happier, because they're not afraid of failing.

Mike Bravo

dan dempsey said...


Where are you located?
I agree with your comments about the problems and the need for there to be a plan to go somewhere with the problems.

Several years ago Mr. Baker High School had there algebra classes not use a book. The kids were learning ( I believe) 8 very fundamental principles of algebra from Math faculty generated materials. It worked well and sounds a lot like what you are doing.


dan dempsey said...

As I understnad it at John's Hopkins the Math department does not have much contact with Robert Slavin.

Anonymous said...

MBHS has its share of problems too. There are kids with IEPs or ELLs leaving that school and attempting to make it in local towns like Burlington and Bellingham, often with even more disasterous consequences. There's a charter formed in Alger and another on Samish Island where some of these kids end up. There's also a teacher I ran into from the Lummi reservation who does home visits.

These communities need far more support than they are getting. Some of these kids are ones that I've described sleeping in cars or living with gangs in apartments. Insufferable conditions.

Where I am at now is a large city with about 185,000 people and 70% Hispanic and better educated. Parents are often from universities in Mexico.

We have tag crews, but not SD or MS13 or ICP...there's a huge difference.

Some of the poorest kids are from a community north of us and we run into kids who's parents were heroin addicts for instance and there are medical complications with the children - kidneys, livers, and hearts....

Autism is fairly common. Hearing impairments often because of our coastal location. But we also take kids with hearing, vision impairments, and children confined to wheelchairs.

Its interesting, we have a kid, who's mostly blind, and has memorized her schedule so she can walk to classes without any assistance. You cannot tell that she is blind.

My own students would end up in a learning center or home-schooled if they weren't in my class. I have a few that are unidentified -one is being tested for Williams syndrome, sort of the opposite of autism.

Since we started three kids have been hit or hit cars while on bikes and skateboards. Nothing serious thank goodness, but its only a matter of time. We should be telling kids to wear helmets and stay in school. But they need a reason to come and grades are an important reason.

Having a diverse group does make for a better learning environment although martial arts is popular and the other day a boy that was mouthing off, got a concussion from a roundhouse kick.

I've got three that race dirtbikes semi-professionally. A 17 yo girl told me she took first in her division racing 100 miles on a dirtbike last weekend (Math 12) These kids just want to graduate from high school. They know they're not ready for college, and so I see my job differently than other teachers.

I was helping a kid the other day with factoring trinomials in another class and finally I wanted to see his notes from his teacher and I couldn't follow what the teacher was doing. My method was far easier, write down pairs of factors and make good guesses....I don't know where this is leading, but teachers have got to start understanding their community better and answer their needs first. Eventually, schools will need those kids, more than kids need school.

Anonymous said...

At my HS serving 2400 students, we have 4 Assistant Principals, 7 Counselors, 2 Academys, and a Learning Center - we are serving kids with two extra periods before and after school. Sports is a big part of student's lives, but so is academics. And students who earn above a 3.0 qualify for 4years free tuition at a state university.

Anonymous said...

Same school has ROP classes so kids can take classes and learn job skills. Very interesting attempt at making school useful for the community and for students. Also, I looked up the population and we've grown in the last two years to 250,000 from 183,000.

Gigi said...

Math Expressions has been proven effective now in a large Federal Study - Math Investigations proved to be ineffective. Saxon Math was also proven to be effective.

Anonymous said...

Have you read who actually developed this article. It was written by HM.