Reply to Options for child who aced Geometry but is struggling in Algebra 2

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[quote=Anonymous][quote=pettifogger][quote=Anonymous]As a tutor I can say that Algebra Ii is a very common place to fall apart, and it’s usually because kids haven’t learned to keep strictly to a linear organization of algebraic manipulation and haven’t learned to write equations.  It also can be [b]because they are not memorizing formulas and key concepts[/b] (sometimes not even able to recognize what is “key”).  And, in Algebra 2 it can be that[b] their underlying memorization[/b] and application of fractions and exponents/roots and graphing is weak, so [b]because they don’t know or remember[/b] they can’t apply the simple rules to more complex ideas.

Some kids really need a good tutor to do homework with them and explicitly enforce the linear organization/manipulation, re-teach earlier concepts and [b]identify what current concepts and formulas have to be memorized.[/b]

Some schools have some kind of after school help program but often there’s no higher level math teacher there.  Sometimes peer tutors are good but sometimes they can only explain an answer not identify the underlying student problems. Asking the teacher for help at lunch isn’t a great long term solution. (Sometimes the teacher is actually the problem.)

Dropping down from honors is OK, but can be frustrating for bright students because the non-honors pace is much slower and the kids have even more, different kinds of problems with the math.  Those students just need better or different explanations than they get from class. [/quote]
I'm quite surprised that as a tutor, you put so much emphasis on memorization. I've found that the exact opposite is true; the kids who try to memorize things have not understood the ideas, and as a result can only remember very little the following year. They continue to try to do this, but memorizing becomes harder and harder to do, due to the faster pace of new concepts introduced in higher level math classes. In their world, math is just a huge number of facts to be memorized. But in reality, everything is quite tightly connected by a [i]small [/i]number of key ideas. If they would instead focus on understanding these key ideas well, they would not need to memorize almost anything because whenever they forget, they will be able to reconstruct most of the things they memorize, similar to first principles thinking. In addition, practicing problem solving by wrestling with problems that they don't initially know how to approach (as opposed to mechanical/procedural exercises that are solved by straightforward application of rules) also gives them the techniques and ability to quickly reconstruct things whenever they don't remember the details.

Math is very much like a sport or a hobby; in order to do well and improve, one has to actively practice and challenge themselves in order to be able to extend the range of their abilities and become more skilled at it.[/quote]

A thread with a pettifogger comment is always a good thread. Pay attention.

Memorizing equations is like  trying to study for an English test by memorizing sentences from the books you've read. It doesn't work, and even it did, it completely defeats the purpose of learning the material. [/quote]

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