Thursday, April 16, 2009

Math problems of the week: 6th grade Connected Math vs. Singapore Math

1. The final 6th grade Connected Math problems involving area and perimeter of circles ("Covering and Surrounding," p.76):




2. The final 6th grade Singapore Math problems involving area and perimeter of circles (Primary Mathematics 6B, "Circles," p. 36-37):




3. Extra Credit:
Given that Connected Math students can use their calculators "whenever you need it," compare the skill sets involved in each problem set. Does the ability to do the first problem set entail the ability to do the second one? Conversely, does the ability to do the second problem set entail the ability to do the first one?

12 comments:

jd2718 said...

Please tell the Connected Math publisher to have kids measure area in square, not linear, units. (problems 6 and 7).

Jonathan

bky said...

Hold on there, jd2718! The kids will measure length (cm) and then compute area (cm^2)! Such is the magic of mathematics!

jd2718 said...

And that is better than covering the figures with unit squares?

How do we know the publisher's intent?

"Use your ruler to measure distances in cm, then calculate the perimeter and area" - if they'd said that, then we'd know.

But they didn't.

Jonathan

Anonymous said...

Should I point out that the problems in Singapore, while fewer in number, are more 'complex' in three ways.

1. the use of negative space.
2. combinations of circles and rectangles leading to a new definition of number (rational + transcendental)
3. use of half circles and a quarter circle and a half triangle. Not to mention the shape with three half circles.

All of this is certainly reasonable and age appropriate for a sixth grader.

Problem 3 from CMP is the only problem that might be solved using fractions (radius = 2.25 in)

This number is written as a decimal so the intent one must assume is the students will be using calculators.

An alternative 'best' answer is

18*pi/4 (one could do it in their head) so it is trivial.

reform math is bogus.

bky said...

Anon -- I think you are going too far in comparing these two problem sets. No transcendental numbers are coming up in the Singapore problems: they are working with the idea that pi is 3.14, so everything is rational. What kids need to be able to do are (1) convert from linear measurements of distance to area, one way for rectangles, and using the magic number 3.14 for circles, and (2) add and subtract area, which seems more like a question of logic (in the informal sense of the word) than anything else. This latter aspect is what makes these problems so valuable in building up mathematical intuition.

Anonymous said...

That is not true. In Singapore, students learn to use Pi. Students are not computing a number, until they have simplified the number. Computing a number is not the primary goal of the problem.

Also this is an email from Oak Norton who is helping spearhead a petition to oust reform math in Utah:

It's been a while since we've had some news to report on Singapore math, but at a recent conference in Washington D.C., I understand there was standing room only for the Singapore math presentation. Among the things presented was a study conducted in Massachusetts that clearly shows Singapore math working very well to accelerate student learning. This is using the Primary math series (which we feel is the very best series of all available). To view the powerpoint presentation (pretty fast reading and only 20 or so slides), please visit: www.utahsmathfuture.com. Also, kudos to David Wiley at BYU for his forward thinking on higher education. Check out this article in which he discusses the need for open learning. “At its core, the open education movement and the larger open content, copyleft movement has “a fundamental belief that knowledge is a public good and should be fully shared,” explains Catherine Casserly, senior partner with the Carnegie Foundation for the Advancement of Teaching. Wiley, she says, is viewed in the open education realm as an imaginative innovator who is always thinking of new applications for disseminating knowledge to the many instead of keeping it “locked up” for the benefit of the few.”

http://www.deseretnews.com/article/1,5143,705298649,00.html

Anonymous said...

Along with standardized testing, reform math has created a goldfish paradigm. The only truth is the propaganda being produced by the colleges supported by NSF grants. Singapore Math was not part of the first adoption committee - that's why it was conveniently discarded during the second round of funding. YOU should know that.

Anonymous said...

My use of the term transcendental was meant more as a variable. I could have used the word CAT instead - but the crux of the issue is that doesn't matter what I use for PI.

The area of a shape is -

4 + 4*CATS

CATS could mean 3.14 or 22/7 or x.

One of the keys to learning algebra is that students learn to write an 'area' as a product of two factors - so we regroup (factor out the 4) and then

4 (1 + CATS ) is a product that means the same thing as the sum of two areas.

This is not present anywhere (grades 1 - 12) in the math reform 'curriculum'. Except! in College Preparatory Math.

Traditional (structural) math teaches this concept but without the'area model' - you learn a formula. The textbooks are gradually making revisions to be par with Singapore.

Hence, a^2 - b^2 = the difference of two squares = (a+b)(a-b)

Anonymous said...

What I cannot accept is that reform curriculum is being sold on the pretense that it is good for low performing students. That is an opinion which is pretentious, discriminatory, wrong-headed, and in some cases, an intentional lie. The data shows exactly the opposite will result. More students will drop out of high school.

bky said...

Anon, when you say

"That is not true."

I can only guess at what you might mean. That it isn't true that these Singapore problems do not require a notion of transcendental numbers? Well, that is true. They use a rational approximation to pi and so not even irrationality let alone transcendence comes up.

When you say

"Students are not computing a number, until they have simplified the number."

and

"My use of the term transcendental was meant more as a variable."

I can only wonder what in the heck you mean. But not for very long.

Anonymous said...

No, meaning what Singapore students do learn from doing problems such as what is presented before you on this blog.

There is no magic here. Far more 'advanced' math is being taught in the Singapore sample, than the sample from Connected Math.

Problem 4 shows an example of adding a negative space and how perimeter increases when pieces of the circle are removed from the square (not decreases) as most US students will answer incorrectly.

Area and perimeter are both subjects that US students do poorly in school and this is well-documented.

When the models used for teaching are poor, teachers resign themselves to teaching rules, not concepts and rules once learned break down quickly over time.

Everyday math has even more pitfalls - beginning with teaching students non-standard algoritms. The absurdity of the math wars is American children are taught algorithms using reform math, just not standard algorithms. So the best tools they're given can only multiply whole numbers. Most cannot/will not multiply 3.14 unless given a calculator.

Everyday math is no math, no education, no future. haha.

Anonymous said...

3. Area = 3/2 pi*r^2 + (2r)^2
r^2 (3/2 pi + 4)
100 (3*3.14/2 + 4)
100 (3.14 + 1.57 + 4)
100 (8.71)
871 cm^2

Perimeter = 3/2 pi*d + d
d(3/2 pi + 1)
20 (3.14 + 1.57 + 1)
20 (5.71)
114.2 cm

This is how the problem would be done by 6th grade students in Singapore. No calculators.