
Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 16, 2013 12:14 PM



On Nov 16, 2013, at 11:49 AM, Wayne Bishop <wbishop@exchange.calstatela.edu> wrote:
> By 6th, however, some of them are so complicated that you sort of want to pull your hair out and scream, "Dammit, use algebra!".
If you review the tests I posted from schools in Singapore, and the solutions, that is what they are doing. Using algebra.
In Singapore, 6th graders sit for the PSLE which determines the type of secondary school and the secondary school they will attend. Harsh, even by my standards. However, I consider our system, where students aren't given a clue what what they will do, even during college, even harsher when you consider their economic outcomes (debt larger than any career they could manage). In any event, the pressure is enormous in Singapore and while the "problem sums" (the type of problem we are talking about) portion of the PSLE is the most challenging, many students do conquer it. But they do so through algebra or near algebra.
The level of difficulty of these 6th grade exams, the amount of tuition (tutoring) that must be involved and the amount of pressure these kids are under does explain the skewness in their TIMSS results. Back when I was analyzing the TIMSS results, I remarked how skewed the results were for Singapore and the other top countries. The distribution wasn't normal because the students were exceeding the upper limit of the (TIMSS) exam. Now we know why. Their curriculum is just that much further advanced and they are driven that much harder, especially in problem solving skills, but also in all of the technical details, like fractions, decimals and units.
The PSLE uses normalized grading, a curve, so it isn't that extraordinary that it be difficult. If they used something like the TIMSS, too many students would exceed its limits and you wouldn't get a good reading.
Bob Hansen

