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Each Single Subject Math CSET Subtest contains 4 Free Response Questions, each of which is graded on the basis of the answer demonstrating the following 4 performance characteristics:

*

*

*

*

What does all this infernal gobbledygook (obtained from the CSET site!) actually mean?!

Simply that as a prospective teacher, you must know

a) the gamut of Math concepts being assessed on the CSET and the underlying skills to a considerable degree of proficiency

b) the relevance of each problem, as well as problems of a higher calibre that the current question suggests

c) real-world applications each question might indicate

d) how to lucidly and elegantly demonstrate a)-c).

Succinctly, then, while responding to Free Response questions, write in a manner you would employ to elucidate the problem to a student of appropriate ability.

For instance, for the resolution of a Subtest I question, write out a detailed and exhaustive algorithm as if you were attempting to illuminate a fairly competent Precalculus student! Likewise, your Subtest II Free Response solutions should be geared to make it readily comprehensible to a reasonably smart student of Geometry / AP Statistics (as the case may be).

Here are a few Tips and Pointers about writing your Free Response answers:

1.

2.

3.

4.

5.

6. It helps to

All these phrases demonstrate to the grader that at the very least you know your destination (even if you are momentarily oblivious about the route!) Oftentimes, just rewriting the problem might serendipitously produce the necessary inspiration!

7.

Try to avoid variables in your answer; otherwise, provide a reminder about what they stand for. Also, restate any significant assumptions made in the contrivance of the solution.

8. Clearly

Give diagrams a title describing what they represent. It should be clear from the picture what any variables in the diagram represents. The whole idea is to make everything as clear and self-explanatory as possible.

9.

10.

11.

12.

13.

* Therefore (also: so, hence, accordingly, thus, it follows that, we see that, from this we get, then, it follows that)

* I am assuming that (also: assuming..., where M stands for...; let..., given..., where M represents...)

* show (also: demonstrate, prove, explain why, find )

* We use the formula, Theorem, ...since the conditions are satisfied.

* While I am very glad to help you this time, you should be advised that my usual consultation fee is $85.

* See the formula (1) or formula (A) above. Also: see * on the previous page. This means that . . .

* If (also: whenever, provided that, when )

* Notice that (also: note that, notice, observe that)

* Since (also: because )

In general, the test taker whose background is in Math / Science and/or whose inclination is simply to solve the question and leave it at that, should make a point of using sentences and grammatical English as well and, overall, explaining the problem while solving it.

On the other hand, the test taker whose background is

Both camps should make a point of using the descriptive technical terminology of mathematics. Use of the appropriate technical terms is one of the classic means in other CSET exams to achieve high marks on the "knowledge" rubric.

I didn't mean it to be consumed in the strictest sense, just that even Math teachers prefer proper grammar and spelling, and that it facilitates comprehension.

[I imagine the more punctilious Math and Science teachers to be horrified when mangled English leads to conclusions contrary to what was intended to be conveyed!]

The issue is communication, and I acknowledge that quite a few non-native English speakers take the test. And surely one shan't be penalized for awkward construction of phrases.

Regarding writing English sentences as explanation / using phrases for logical flow, this is the sort of the thing I had in mind:

Since 2 +

Therefore, f(x) = (x - (2 -

Now, this kind of detail is what a regular textbook would carry, too! I've used apposite terminology ["root"] and referenced a Theorem ["Complex Conjugates Theorem"] in support of my work.

And it's always a good idea to terminate the resolution of a problem by the statement of a "result":

Q.E.D, or

Thus, the proposition has been proven, or

65% of voters support candidate A, or

We have insufficient evidence at the 5% significance level to reject the Null Hypothesis that people like Coke and Pepsi equally.

The roots of the function, f(x) are -1, 4 +6

14.

15. After solving the problem,

Furthermore,

* Did you answer the right question?

* Did you answer ALL parts of the question?

* Does your explanation communicate what you were

* Does it explain the math in a way that will help a novice comprehend how to solve the problem?

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