Thursday, February 18, 2010

Math problems of the week: 2nd grade Investigations vs. Singapore Math

1. Two of the last addition problems in the 2nd grade Investigations (TERC) workbook, p. 61 of Unit 8 (Partners, Teams and Paper Clips):


Solve each problem. Show your work.

Kira has trouble with 7 + 9.  Write a clue that will help Kira remember 7 + 9.

9 + 7 =
7 + 9 =

Clue: _______________________


Franco has trouble with 8 + 6. Write a clue that will help Franco remember 8 + 6.

6 + 8 = 
8 + 6 =

Clue: _______________________

2. The last addition problems in the 2nd grade Singapore Math Primary Mathematics Workbook 2B, p. 17:

Add.
(a) 183 + 99 =
(b) 246 + 98 =
(c) 199 + 99 =
(d) 206 + 98 =
(e) 99 + 556 =
(f) 98 + 235 =
(g) 99 + 408 =
(h) 98 + 399 =

3. Extra Credit:

What do you think is the best way to help Kira and Franco?

15 comments:

Anonymous said...

Did you know the last word in the English dictionary is zyzzyva, a South American weevil that tends to infect plants? Your superficial analysis above (comparing one page of TERC with Singapore Math) is what parents should expect from a blog like this. No real analysis just scare tactics and tabloid like discussion. It is be insulting to parents, scientists, and engineers and who want real discussion. If you really wish to have a meaningful impact, then you will not resort to such shallow comparisons and tactics. A real analysis of the two texts might show that Singapore Math is more rigorous in numerical concepts in the early elementary grades. Of course, such analysis should examine what part of the curriculum is sacrificed for this early focus on number? The soon to be made public common core math standards will argue for a more numerical focus in the early grades (similar to Singapore). I am sure your blog will be the first to attack the common core for other superficial reasons. Maybe you should look up the last word in the Singaporean dictionary and compare it to zyzzyva.

bky said...

Anon - I am very familiar with Singapore math. Right, it is more rigorous early on. But nothing is sacrificed, as far as I can tell. Kids learning Singapore math are going to have a firmer concept of number, place value, and what operations mean. Thus in 2nd grade they don't have to worry over what 9+7 might be. They are past that and on to something else. What must be sacrificed in other, fuzzier, curricula, is the opportunity to learn what, for most kids, they are really capable of learning.

JC said...

"Of course, such analysis should examine what part of the curriculum is sacrificed for this early focus on number?"

Huh? This is math. The focus should be on numbers. They are what math is about. It is no wonder education is a disaster in this country when we have people who think 2nd grade math should not be focused on numbers. And how do weevils connect to anything you said?

Anonymous said...

So according to bky and JC, 2nd grade should be only about teaching simple computation with number. Math is about numbers - no, not at all. With that kind of thinking, we surely we create a generation of great math thinkers - not. If you truly know Singapore math, then I implore you to look at the content more closely as it is not just about number. The soon to be released common core will focus more on number (similar to Singapore) but will not be solely about number. Oh and by the way, Singaporean math pedagogy is much more about inquiry than direct instruction. But you shouldn't let the facts get in the way of your rhetoric.

Anonymous said...

Mathematics - The study of the measurement, properties, and relationships of quantities and sets, using numbers and symbols.
http://dictionary.reference.com/browse/mathematics

"Singaporean math pedagogy is much more about inquiry than direct instruction."

I do Singapore math with my kids. It is largely direct instruction, at least in the early grades. Inquiry is fine for kids who have a good grasp of the basics. But the kind of inquiry based learning that is common in America today is producing a generation of math ignoramouses. Do you seriously think that the fuzzy math that is so popular in American schools today will really create a generation of great math thinkers? I know middle and high school kids, who if given a simple arithmetic problem resort to counting on their fingers to solve it.

Inquiry based math is a disaster that needs to be rooted out of education. The Indians and Chinese learn using direct instructions. They are seriously outperforming our kids on international math tests. Our kids will be competing with them for jobs. We need to stop fooling around with nonsense like inquiry based math before it's too late.

JC said...

Advocates for inquiry-based learning have strong views about how children should and should not learn. Ideology trumps evidence for them. Inquiry-based learning has been proven to be a failure for decades but it's still around.

The fact is our students cannot do math. Students from countries where direct instruction is used significantly outperform us. This is especially true on the PISA test, which tests the ability to apply knowledge.

"Mayer (2004) has recently reviewed evidence from studies conducted from 1950 to the late 1980’s comparing ‘pure discovery learning’, defined as unguided, problem based instruction, with guided forms of instruction. He suggests that in each decade since the mid 1950’s, when empirical studies provided solid evidence that the then currently popular unguided approach did not work, a similar approach popped up under a different name with the cycle then repeating itself. Each new set of advocates for unguided approaches seemed either unaware or uninterested in previous evidence that unguided approaches had not been validated. This pattern produced discovery learning which gave way to experiential learning which gave way to problem-based and inquiry learning which now gives way to constructivist instructional techniques. Mayer concluded that the "…debate about discovery has been replayed many times in education but each time, the evidence has favored a guided approach to learning.""
-- Why Minimally Guided Instruction Does Not Work (This is a PDF document, so it may take some time to load)

If you want your children to be good at math you will either have to homeschool or afterschool them. Inquiry-based learning is deeply entrenched in our schools and it won't be "rooted out" any time soon.

For anyone who is concerned about the state of education, I highly recommend that you read Why Minimally Guided Instruction Does Not Work. I also recommend The Schools We Need by E.D. Hirsch.

Anonymous said...

Again the facts get in way our your rhetoric. Asian pedagogy, by far, is more inquiry based especially in Japan & Singapore. The TIMSS video study proved exactly that.
http://hub.mspnet.org/index.cfm/9517

The amazing paradox is that you support Singapore Math (which is fine with me) but you only want traditional drill with this text. This is in contradiction with how Singapore math is taught in Singapore (maybe not in your home). Not to mention the many alternative algorithms that are prevalent in the Singaporean texts.

The majority of Asian students do their computational drills at home or afterschool but NOT in school. School hours are for inquiry, problem solving, and critical thinking. If you are truly interested in learning about what really occurs in Asian mathematics classrooms (and not just your false rhetoric) then buy Mathematics Curriculum In Pacific Rim Countries- China, Japan, Korea, And Singapore.
Available at:
http://tinyurl.com/y8qx837

Katharine Beals said...

Besides comparing Reform Math with other curricula, it would be interesting to compare the different tones used by those on each side of the debate. As an example, one might look at the different tones used in this very comment thread.

"Your superficial analysis above (comparing one page of TERC with Singapore Math) is what parents should expect from a blog like this."

"Superficial" is the wrong word. "Narrow" is better here. This blog has presented one narrowly-focused math problem comparison per week for over two years. Comparison of specific problems must absolutely be part of the debate over math curricula.

"Maybe you should look up the last word in the Singaporean dictionary and compare it to zyzzyva."

Dictionary entries are another source that come in handy, depending on what you are analyzing. If one's goal were to compare the English and Malay lexicons (there's no language called "Singaporean"), it's useful to compare specific entries in the English and Malay dictionaries. On the other hand, if one wants to make a more shallow comparison, one could compare the last two entries, as you suggest.

"So according to bky and JC, 2nd grade should be only about teaching simple computation with number. "

Here another comparison is in order: what bky and JC actually said about what aspects of number should be taught, with what Anonymous says they said.

"Oh and by the way, Singaporean math pedagogy is much more about inquiry than direct instruction."

I've often pointed this out on this very blog. There's a lot of Inquiry, in the best sense of term, built into the Singapore Math curriculum.

"But you shouldn't let the facts get in the way of your rhetoric."

Indeed.

"The amazing paradox is that you support Singapore Math (which is fine with me) but you only want traditional drill with this text."

Again, it's interesting to compare this characterization of bky, JC, and anonymous 2's comments with what they actually wrote.

"The majority of Asian students do their computational drills at home or afterschool but NOT in school."

The book "The Learning Gap" argues otherwise.

"School hours are for inquiry, problem solving, and critical thinking."

As seen in this blog's weekly comparisons, inquiry, problem solving, and critical thinking are very present in the Singapore Math curriculum, and very different from the "inquiry," "problem solving," "critical thinking" seen in Reform Math.

Barry Garelick said...

Discovery or inquiry based learning can be done well or poorly. I have written an article that explores discovery learning in math. Singapore uses discovery well, via well-scaffolded problems. Also its sequence of topics is such that students build upon an ever increasing foundation of skills and concepts.

Anonymous said...

Thanks for Garelick for admitting that discovery/inquiry learning can be done well. That it is not the cause of all America's woes as you read in the attack traditionalist blogs.

To read more about Asian pedagogy, read from analysis of many Asian countries: Mathematics Curriculum In Pacific Rim Countries- China, Japan, Korea, And Singapore.
Available at: http://tinyurl.com/y8qx837

You will find that Asian pedagogy is majority inquiry based and that combined with a streamlined curriculum (as proposed by the common core which the blogs by traditionalists have already opposed) are the reasons for their success.

The vast majority of students - some reports are over 95% - in Singapore and Korea and a significantly high proportion of students in Japan attend after-school tutoring schools that often match or exceed the amount of time spent in school on mathematics.

Katharine Beals said...

Does anyone out there know which "attack traditionalist blogs" Anonymous is referring to?

I.e., blogs that say that math should consist only of rote drills and that inquiry can't be done well?

Andrei Radulescu-Banu said...

Gotta love these 'math' problems: "Write a clue that will help Kira remember 7 + 9"

Any answer goes. My clue is 'it's 6+10'. Yours might be 'it's not 17'. The best, of course, is 'it's 16'.

I have a feeling, Kira would prefer the last clue.

bky said...

I was thinking about these TERC problems again. Look at the instructions: "Solve each problem. Show your work." The point to take away is that in 2nd grade the TERC authors think of adding two one-digit numbers as a "problem" for which work needs to be shown. I would consider that a "fact" that one should know by automatic recall by now, and let's get on to more and more and more (for example, adding numbers close to 100 to other two- and three-digit numbers).

But the two problem sets are still related, because the TERC problem set is based (if I infer correctly) on the "making 10" strategy for learning the basic math facts that have to do with adding "large" one-digit numbers (9, 8, 7, 6). The Singapore problem set is for practicing the strategy of adding 98, for example, by adding 100 and subtracting 2.

What Singapore does very well is they explicitly teach these kinds of strategies. Eventually kids don't need a strategy any more for adding 9+7, they will recall that; but they will always need a strategy for adding 98 (even if they get to where they can do it quickly).

So this comparison of problems shows two things about TERC vs Singapore: (1) Singapore will get kids to automatic recall of simple things early on, and then move on to harder stuff; and (2) Singapore explicitly teaches kids strategies for computation (mental math, let's call 'em) and problem solving (think of the bar models and so on).

It seems a waste of time and energy to be still worry about how to "solve" 9+7 when you're in second grade. In first grade, however, that counts as a problem that needs to be solved ... until you just know it. What counts as a problem is like the horizon. The further you go, the more it recedes.

Andrei Radulescu-Banu said...

Very nicely explained, bky.

Anonymous said...

My clue for 9+7 was 8+8, and for 6+8 was 7+7... I guess I missed the point.

What they might be sacrificing in Singapore? I don't know, but in Q3 my son got a failing score in one of the math categories on his report card because he didn't know what a trapezoid was. In Kindergarten, in the US. On the bright side, his school uses Math Expressions, which does seem to teach kids actual math as well (plenty (too many?) of worksheets with adding and subtracting single digit numbers, and adding single digit numbers and 10, although I usually throw the homework away, or write some digits in front of the single digits to turn them into two-digit addition and subtraction problems). By Q4 I'd found some shape songs on YouTube and gotten my son to memorize what a trapezoid is so he could pass math.