Wednesday, April 2, 2008

Math problems of the week: grade 2 Trailblazers vs. Singapore Math

Today we'll see how another Reform Math program, Trailblazers, stacks up with Singapore Math.

A.  An exercise from half-way through Trailblazers Grade 2 (Student Guide, Book 2, p. 293).

Which Answer Makes Sense
Look at each problem.  Decide which number is the best estimate of the correct answer. Explain why you think so in the space below the problem.

1.
60 45 30 50
-27
-----
[space]
2.
50 30 40 15
-18
----
[space]
3.
50 30 70 20
+22
----
[space]
4.
94 50 40 75
-38
----
[space]
5.
71 40 50 60
-34
----
[space]

B. An exercise from halfway through Singapore Math Grade 2 (Workbook 2B, p. 9)

Write the missing numbers.
(a) 99 + __ = 100 (b) 95 + __ = 100
(c) 96 + __ = 100 (d) 91 + __ = 100
(e) 80 + __ = 100 (f) 35 + __ = 100
(g) 84 + __ = 100 (h) 63 + __ = 100
(i) 42 + __ = 100 (j) 58 + __ = 100
(k) 6 + __  = 100 (l)  9 + __ = 100

In short, estimation and verbal explanation vs. systematic practice calculating precise answers to more difficult problems.

bky said...

I like those Singapore problems, the "completing a hundred" or, earlier on , completing ten. The point of those exercises, if I recall correctly, is to learn this as mental math -- think of 100 as 90 + 10 and get the tens place to sum to 90 and the ones place to sum to 10. Kids pick up practical strategies for calculation. Singapore also gives them estimation problems, but not by the Trailblazers multiple choice method. They have kids round the terms and then add or subtract. It seems truly odd to give kids 3 choices and and then ask them to say why they picked what they did. Can they just say it's closest to the actual answer? Or that it is the answer they got when they rounded and estimated? What sort of answer is expected?

lefty said...

Good points!

I wonder how a teacher would handle "it's closest to the actual answer"? Presumably the kid would then need to explain, in words, how s/he got the actual answer. Or perhaps would be taken to task for calculating a precise answer rather than estimating it.

As for estimation, if it's being taught as a practical skill, how often does real life present us with situations with multiple estimation choices?

bky said...

You have to be careful with appeals to "real life." People commonly use appeals to real life to suggest that any given thing is pointless. In real life you don't add fractions or maybe not even do any arithmetic. For some people that's true. I think you have to commit yourself to a subject and agree to learn what that subject requires. So, how to estimate; multiple choice questions do a poor job helping you learn estimation compared to, say, actually estimating.

In real life, no one reads a sonnet. Isn't that true, for most people? Then should we rip poetry from the curriculum?

lefty said...

Indeed! I agree that perceived real life usefulness is a poor basis for deciding what to teach (and has wreaked havoc on grade school curricula).

But even assuming real life usefulness is a reasonable criterion (the premise of my rhetorical question), Reform Math, which so highly prides itself on this, comes up short--as this estimation problem shows.

Indeed, it seems to me that many of Reform's "real life" problems turn out, on close inspection, to be highly contrived and thus unrealistic (I'm recalling the IMP Haybaler problem recently cited on ktm).