Review by Mathematically Correct

Seventh Grade CMP booklets

Please note, most of the units detour around before coming to central ideas which are in the last couple chapters.

1. Variables and Patterns: Introducing Algebra
The main goal of the Introducing Algebra unit is to teach the student the linear equation y = ax. This is mainly taught near the end of the unit. To get there, the students are led through detours of three chapters of learning about non-linear graphs such as those of hunger and happiness. (Please note that Okemos schools teaches students to read graphs starting in Kindergarten). In the case of my daughter, she was weak in understanding and writing linear equations at the beginning of this unit. At the end, she was still not proficient in it.

In the first year, the teacher also introduced graphing calculators for simple straight line graphs. This practice was abandoned after parents complained. It really bother me that problems used in the book such as temperatures distributions in the day and/or bike tour obscure the simplicity of math about straight line The only positive things I can say about this unit is that at the end (after 4 weeks), my daughters could plot nice graphs. However, she was weak in understanding and writing linear equations at the beginning of this unit. At the end, she was still not proficient in it.

Being a trained experimentalist, I may be one parent who wrote things down. There are many parents and students who hated these type of open questions of bike tour or suggesting a scenario for the graphs which show the sale of popcorn as a function of time. Some kids are so bored by these type of writings that they refuse to take these problems home because they do not want to do them. Others like my daughters would get frustrated and cry.

2. Moving Straight Ahead : Linear Relationships
Similar complaints as above. Additionally, the homework assignments consists of many irrelevant word problems containing nonlinear graphs of happiness and hunger. While most parents share the concern that students should learn to solve word problems instead of just crunching numbers, CMP provides some of the worst word problems under the pretense of offering "real life problems." In a recent seventh grade homework assignment, students were asked to do several problems similar to the following one (Moving Straight Ahead, p. 29):

The 1996 Olympic gold medal winner for the 20 kilometer walk was Jefferson Perez from Ecuador. His time was 1 hour, 20 minutes, 7 seconds. Perez's time was not good enough to beat the olympic record set in 1988 by Josef Pribilinec from Czechoslovakia. Pribilinec's record for the 20 kilometer was 1 hour, 19 minutes, 57 seconds. What was the walking rate of each person?
My daughter dutifully punched the numbers into her calculator and wrote down the answers as:

Jefferson Perez : 0.00416 km/s
Josef Pribilinec : 0.00417 km/s

When I asked my daughter what she was supposed to learn from this exercise, she looked at me with a blank expression. When I asked her why she chose the unit of kilometers/second instead of meters/second or meters/hour, she gave me the standard CMP reply that her teacher said there is no absolute correct answer in math homework. The book asked for rate, so she calculated a rate. She then continued to do similar problems that evening by punching more numbers into her calculator. No new light was shed the next morning when her teacher graded her homework.

If the problem meant that the student should calculate speed in certain terms, it should have said so clearly instead of using the fuzzy term "rate." Most 7th graders have a pretty good concept of speed (Just ask any parent who has been caught speeding by their child who reads speed limit signs). However, 0.00416 km/s means nothing to most 7th graders, and even to some parents. They cannot relate that to their daily experience. If the problem meant to compare the rate of winners, the original description of how long it took a winner to walk 20 kilometers is the most sensible description. Can you imagine a sportscaster announcing that the winner Jefferson Perez's walking rate was 0.00416 km/s, compared to the Olympic record of 0.00417 km/s achieved by Josef Pribilinec?

Word problems that do not relate to the context of real life will train only low-skilled employees who cannot function without cash registers. Unfortunately, this type of problem is prolific throughout the CMP booklets.

3. Accentuate the Negative: Integers
My daughter cried her ways through drawing chips (red and black). That is the unit that convinced her to get out of Kinawa math to go to CHAMP -- about the most positive thing I can say regarding CMP.

4. Stretching and Shrinking : Similarity
Stretching and Shrinking teaches scaling factors and similarity in geometry. The main goal of this unit is to teach students to understand geometric similarity. More importantly, for a curriculum that stresses real life problems, the unit advertises teaching students applications, e.g.. using the properties of similar triangles to determine the height of objects. Unfortunately, after all the detours of drawing wumps and Rep-tiles, the students never mastered the shadow method of determining object height.

Let me use some real life examples to illustrate the points I want to make. One night, my daughter spent nearly three hours drawing four "wumps." I have enclosed a wimp for your reference. Instead of drawing all those wumps, most of the points in the lesson could have been taught by drawing a rectangle, using much less time. Another example is the Rep-tile exercise. In the October parent math meeting, the parents were asked to find "a way to divide each shape (copy attached for your entertainment) into four congruent, smaller shapes that are similar to the original shape." When I asked what the students were supposed to learn from this, the question derailed the lesson. One teacher said that the objective was to teach the concept of reduction, which obviously was wrong. The exercise was to create "Rep-tiles," a term I could not find in any college or high school geometry books. I asked several Math and Physics professors, and none had heard the term nor could they see the reason for teaching this. Can you explain to me why precious class time is spent teaching this or drawing wumps instead of teaching students the essence of this unit, i.e. how to use the properties of similar triangles or scale factors to find distance or height?

5. Comparing and Scaling : Ratio, Proportion and Percent
It reads like Bits and Pieces II. Thus I don't think much about it in teaching ratios, proportions and percent. Moreover, I will be surprised if most kids at this age will find the population census data interesting. However I do find Chapter 5 about estimating populations of deer in Michigan by sampling to be interesting. On the other hand, I remembered my older child learned similar method to estimate the number of bats in a cave in 6th grade in a non-CMP math class. Still I found the method interesting that I would not mind my 7th grade child repeat it.

This is the CMP unit currently used to teach proportional reasoning. The teachers said that the last two chapters will barely be touched upon. For example, the sampling methods used in polling to estimate population which we hear everyday in the media will not be taught. Instead, my daughter and I went through a torturous explanation about the number of visitor hours spent in the Federal Recreational Park Service.

6. Data around us: Number Sense
I don't know how to make out of the book. The only thing I can say is that both of my kids hate working with large numbers. I would say a couple problems to illustrate the points will be all they can take. They are definitely not interested in census data. However, for other kids, this may be good and is good PR to parents to hear that the kids are working with real data.

7. Filling and Wrapping: Three Dimensional Measurement
I believe this units can be taught with formula in a week to calculate surface area and volume. I think it is good that they illustrate the surface area and volume by folding cardboard. However, I have strong reservations about calculating the surface area of a cylinder by counting squares on a grid paper though. It is much easier to explain to the kid about area of the circles and multiply that by the length to get volume.

I believe the following unit was left out by mistake. I notified Lee Gerard already.

8. What Do you Expect : Probability and Expected values (not mentioned)
There is one unit about Probability which I believe the teachers left out inadvertently, (I hope).  I do not know how much experiments they do with coins and dice. Tossing coins 10 times is all my kids can take. I think analyzing one stage and two stage games especially if this is accompanied by software that illustrate the points may be fine. However putting out a page of nonsense pictograms on Pg. 71 is ridiculous. If they just want the kids to guess, it is not necessary to go to such extreme waste of paper.

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