Saturday, March 10, 2007

A tale of three math books

This is a hoot!

Here is an example from the fabulously encyclopedic old Kitchen Table Math of the quality of different textbooks. The first two problems are from Singapore Math and Saxon, respectively. The last "problem" is from the egregious and execrable fuzzy math text Trailblazers. Compare and contrast indeed!

Posted on May 26, 2005 @ 20:05 by CatherineJohnson

problems in three grade 5 textbooks

from the last page of Primary Mathematics 5B (U.S. Edition):

18. A fish tank is 2/5 full after Sara poured 14 gal of water into it. What is the full capacity of the tank in gallons?

final problem in Saxon Homeschool Math 6/5 3rd Edition:

Change each of these base 10 numbers to base 5:
a. 31
b. 51
c. 10
d. 100
e. 38
f. 86

from the last page of Math Trailblazers Grade 5:

4. Write a paragraph comparing two pieces of work in your portfolio that are alike in some way. For example, you can compare two labs or your solutions to two problems you solved. One piece should be new and one should be from the beginning of the year. Use these questions to help you write your paragraph:

Which two pieces did you choose to compare?

How are they alike? How are they different?

Do you see any improvement in the newest piece of work as compared to the older work? Explain.

If you could redo the older piece of work, how would you improve it?

How could you improve the newer piece of work?
With "math" instruction like that, the U.S. is sure going to remain competitive with the rest of the world.

Parents, don't let educationists ruin your child's opportunities in life. Fight the fuzzy math plague!


Anonymous said...

You say "compare and contrast indeed," but the person who assembled this comparison has done so in bad faith. Does anyone really think that like is being compared to like here? We have two problems pulled from a section of math instruction or from an assessment (it's impossible to know which) set against a portfolio review activity, which is not intended to be math instruction per se, but rather an exercise in reflection and, if one is lucky, some measure of metacognition. Let's engage in the debate, to be sure, but let's do it honestly. Pull an actual math problem from the Trailblazer series, and set it against the two other problems we see listed.

NYC Math Teacher said...

That such tripe exists at all is reason enough to denigrate the Trailblazer series.

Anonymous said...


If you say that it's not an "actual problem" then isn't it the case that some teachers will be using these pseudo-math problems in class? What are they in the book for if not to be used?

In general American math programs talk the reader to death.

Do you see any improvement in the newest piece of work as compared to the older work? What would you like to eat for lunch? Why? Can you make a list of that? How does your choice differ from your friends? Is your hair prettier and longer than other girls? Do these pants make me look fat? Ooo, did you see the pretty pattern? Describe it..

But rather listing the real math problems in Trailblazers, how about giving a sample of the pseudo math problems in Saxon and Singapore?

Diana said...


Even if the Trailblazer problem were an exercise in metacognition, it's too vague to be useful. Ask a vague question, and you're likely to get a vague answer.

It would be much more useful to ask students to find work that demonstrates mastery of a particular concept or process. If one is to engage in metacognition, there should be some cognition to sustain it.

On the other hand, I agree in this case that the comparison of texts is somewhat lopsided. It would indeed be interesting to compare problems of a similar nature.

Robert said...

I left this comment over at Joanne Jacobs before coming here, and rather than repeat myself, I'll just copy and paste:

"As much as we all want to jump on the last “problem” as an example of What’s Wrong with Math Teaching Today, let’s be objective and remember that context is everything. What were the math problems that appeared earlier in the text? Were they problems like the first two mentioned above? Where they more rigorous, less rigorous, or what? Just because a student might be making a portfolio doesn’t necessarily mean the curriculum is any better or worse than anything else, and it’s not necessarily informative to compare just what happen to be the last problems in their respective books."

See also "confirmation bias".

Instructivist said...

Some of the responses (Anon, Robert) are far too serious. The comparison isn't a meticulous scholarly study. On those grounds, the objections are valid. It's more on the light-hearted side but nevertheless gives a hint of the nature of fuzzy math.

Barry Garelick said...


Any math class in K-5 that asks a kid to pull together a portfolio gets me pulling on my hip boots.

Robert said...

Instructivist, what I am objecting to is cherry-picking three problems that are in no way similar, and then they are treated as similar for the basis of comparison (something you ask us to do in your article) and the comparison used to illustrate the "execrable" nature of the odd duck of the three problems. That doesn't give a hint about nature of anything other than the propensity of some folks to believe that anything that isn't Saxon or Singapore is automatically a tool of the Devil.

I'm not saying that Math Trailblazers *isn't* actually a tool of the Devil, mind you -- I don't have any idea what it is. Nor can anybody form an objective idea from that one example you cited. You may call that being "too serious" but I call it intellectual honesty.

Instructivist said...

"Nor can anybody form an objective idea from that one example you cited."

I'll grant you that if you have nothing else to go by. But the readers of KTM from which this was taken are an attuned bunch. So you have to see it in this context.

On the other hand, if you knew nothing about any of the books (Trailblazers doesn't even have a textbook, only activities), and you had to guess which have the most content, which ones would you choose on that limited basis provided by the selection of the last item in in case?

Barry Garelick said...

The problem Robert raises is valid and the objections he raises point to how other excerpts from programs such as Trailblazers, or Everyday Math, or Investigations could lead one to believe that they are comparable to Saxon and Singapore which they very definitely are not.

For example, looking at the workbook for Everyday Mathematics (you can't look at the textbook because there isn't one), you would see problems in the sixth grade text asking: "If a dress is discounted 20% and Linda paid $120 for it, what was the original price of the dress?" Similar problems are in Saxon and Singapore. The difference is that those texts build up mastery of the concepts and skills that enable students to be able to solve such problems. EM's presents a rather hasty explanation of presenting percentages as proportions and solving the problem that way. Which is valid, but the time spent on proportions, ratios, percents and decimals up to that point has been spotty, with not a lot of time spent doing problems, not a lot of time spent with explanations, with the results that students have little to no mastery of the concept/skill needed to understand EM's explanation du jour.

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NYC Math Teacher said...

I agree with anonymous above. (For the record, the first two characters are "Zhong guo", and together they mean China -- literally "Middle Country", as they, like other ancient civilizations, thought themselves to be the center of all being. Sorry. Off topic. I know.)