## Tuesday, August 14, 2007

### Singapore Math - Primary Math 6B Placement Test...

[Note: As promised, I have now posted a lengthy comment to this post, which only scratches the surface. I welcome your comments.]

Although Singapore Math is no secret to many homeschooling parents and districts around the country, I thought that the sample placement test for Grade 6B, available for free downloading, might lead to some fruitful discussion. Pls try all 14 questions before commenting. I did and I will have much to say later. There are many other placement tests at the same site so have fun! Go to the Singapore Math home page for background if needed.

Dave Marain said...

As promised, I will make several comments about the 6B placement test.
1) I administered this test to a strong group of high school students (SAT prep course) and the results were fascinating. Many struggled with the ratio problems, #2 and #13. How do you think most high school students would fare on these? Not only does one need to have developed strong methods for dealing with ratios (both algebraic and part:whole thinking) but the wording of the questions was fairly sophisticated. I feel the questions were well-written and required above-average comprehension skills. The bottom line here is that our middle schoolers need more problem-solving experiences with ratios. These problems become much easier when one has been doing them over time.
2. A calculator was not permitted and you can imagine what the reaction was for those geometry problems that required using 3.14 or 22/7 for pi and actually computing! Feels like you were stepping back 2-3 decades? The students were not happy about the calculating but eventually adjusted. How would many educators and math specialists feel about requiring this kind of pencil-and-paper calculation for our students! How do most entering college freshmen do on the infamous precalculus placement test given by most colleges WITHOUT the calculator?
3. Do Singapore students have algebra as a tool for solving these 2 questions (particularly #13)? Well, consider this. From surveying my students (some of whom come from Korea, China, Japan, China, etc.), I learned that algebra is introduced as early as 3rd grade and by 6th grade it is used extensively. Are you surprised by this or everyone knows this to be true...
4. I love those geometry questions #9, #10. I see these as above-average SAT-type questions. they are wonderful for our geometry students. Agree?

I have many more comments about the implications here and surely this test does not tell the whole story about Singapore's math curriculum. But it does say something!

Totally_clueless said...

If this is a placement test for Grade 6 (which implies students who have completed Grade 5), that is impressive. I see this at the level of a student who has completed Algebra 1. The geometry problems are nice, but it is my impression that they require only material that is taught before middle/high school geometry here (I may be wrong!)

There were also a comment on the test that only the first two problems were applicable to the US ????

I looked at the test for 6A also, that goes through the steps for many algebra level 1 problems, thereby easing students into the process. Some students will benefit by doing problems that take such an approach.

Jackie said...

How did your students approach #11? My thought was to set up a system of equations...
Let x = the amount of starting \$ of each
y = the number of days in question.

x-36y=240
x-48y=0

I'm not sure how my freshmen would approach this problem... my feeling is that it will be guess and check.

As for the no calculator issue...I don't think many of my students would do well - at all. This concerns me with regard to the college placement tests (I'm teaching pre-calc to seniors this year and it will be interesting to see what (if anything) they can do without calculators when they hear about this college entrance exam w/o calculator).

mathmom said...

TC, I think the 6B placement test assesses mastery of the 6B curriculum. I believe in Singapore, students move from 6B to Algebra I, so this is sort of a pre-algebra final exam.

Dave Marain said...

mathmom, tc--
You're right, mm. Here's Jenny's explanation and some additional info re the differences between the US edition and the Singapore edition:

By the way, looking at the second comment on your blog, be aware that the 6B test covers 6B material, and is therefore more of an exit test. A student doing well on all the tests prior to 6A, for example, but doing poorly on 6A, would start in 6A.

Also, there are currently 2 editions, 3rd edition of and U.S. edition, of Primary Math. U.S. edition is almost identical to the 3rd edition, with the addition of a few things such as measurement in standard units used in the US, and changing some of the conventions, such as colon for time rather than period. However, it does have a new unit in the 6B that used to be in the 2nd edition, which is out of print, and was put back into the U.S. edition, and that is division of fractions. So the first two starred questions are pertinent only to U.S. edition, and the rest are pertinent to both U.S. and 3rd edition. We sell both edition, but since they are almost identical, produce only one test for both.

Here are some other interesting bits of info:

Bar models are a tool, and are used when needed. So they could be used for simple ratio problems. They are certainly used to introduce the concepts of ratios, and so initially are used with simpler problems. And there are likely to be better students who visualize the models in their heads, or use thinking more on the line of your algebraic approach. Students are encouraged to use a variety of problem solving approaches, though bars are used predominantly if appropriate.

Some organizations have concentrated on the bar models and have adapted bar models to a U.S. expectations and teach a step-by-step procedural approach, which works fine as an introduction to them and for problems that would be encountered in U.S. elementary texts, but tends to break down a bit for more challenging problems, but I suppose by then students will have more of a feel for them and be able to depart from following a specific set of steps in diagramming the problem. There are seminars in bar modeling (but in my opinion the Primary Math has much more to offer than just learning how to use bar models to solve word problems).

The best way to learn the material in order to teach or train someone else, I think, is to go through the textbook, workbook, and some of the challenging supplements and do the problems.

Jenny is being discreet yet honest.
The following quote struck me:

"...teach a step-by-step procedural approach, which works fine as an introduction to them and for problems that would be encountered in U.S. elementary texts, but tends to break down a bit for more challenging problems..."

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