## CSETMathGuru: THE Site for Single Subject Math

**Are the CSET Subtests**

**valid****?**

Personally, I don't regard Subtest I to be a "valid" assessment tool: one calculated to measure what it proposes to. The relevance of Number Theory and Abstract Algebra is moot [in a High School curriculum], and being relatively abstruse and inaccessible, invites guess-work. And likewise, Subtest III is inadequate since it is not challenging enough for the level of courses it "qualifies" one to teach.

The test creators ought to have gone about their tasks making an "imperative" of it [qv.

__Kant's Categorical Imperative__: "Act only according to that maxim whereby you can at the same time will that it should become a universal law."]

Simply: I'd want an Algebra II teacher - and beyond - for any son / daughter of mine to be a virtuoso re the curriculum. I should wish the same for any son / daughter.

On the other hand, I don't give a rat's arse as to whether the teacher really grasps Groups, Rings, Fields, or Euclid's Algorithm. Especially, if it detracts from the mastery of Algebra II / Precalculus: test preparation is somewhat Zero-Sum. Time taken out to "study" - however superficially - Abstract Algebra and Number Theory is a period that might be more lucratively employed becoming a Jedi of Precalculus (!).

As an aside, I warm to the notion of devising a Teaching Methods oriented Math test for the Middle School Math teachers that, content-wise, may assess them till Algebra II only. Requiring those poor blighters to know as much as High School chaps is ridiculous. I do want middle school teachers to be creative in fostering ideas of fractions, percentages and so on. [In this matter, Praxis has an interesting Pedagogy subtest that primarily addresses approach and procedure.] And, if one chose to migrate to the H.S. level, then one would, perforce, take the High School test to demonstrate competency.

In the current dispensation, we're likely losing some brilliant individuals who find Precalculus-level Math daunting. That's a blasted shame.

It all comes down to relevance. For those that protest: Why

*not*Number Theory, Abstract Algebra, Euclid's Algorithm, and Algebraic Structures? That a able math teacher should not only be well-versed in the topics she will teach, but should also have a broad base of foundational-level knowledge in tangent topics.

Um, this sort of "interesting" argumentation could conceivably apply to numerous other topic areas! Where does one limit the ken of assessment knowledge? Why aren't, say, Eccentricity and Rotational Conics; Polar Functions; Matrix concepts as Rank, Orthogonality; Vector Fields and 3-dimensional Geometry; Areas and Volumes of Curves Rotated about an axis; Beta and Gamma Functions; etc.

*not*included as part of the domain?

Each of these could be deemed "tangential" topics that a chap could self-teach quickly.

The touchstone

*ought*to be relevance in a HS classroom. Very persuasively could one argue for the inclusion of the afore-mentioned topics in

*lieu*of Abstract Algebra.

I concede - actually there's nothing to "concede": I've consistently maintained such an opinion...- that the sophistication of the teacher ought to be considerably higher than than of the students, but each of the topics I've mentioned could rate as "special" topics a H.S. Math teacher could explore with bright and motivated students. I'm not sure if the same could be said about Number Theory and Abstract Algebra.

Is the Calculus assessed in Subtest III adequate for teaching AP Calculus? Certainly not!

For that matter, one might persuasively argue that the Trigonometry wouldn't suffice for Precalculus!

In short, here's a queer conundrum: while Subtests I and II mandate that a candidate for the Foundation Level Credential know considerably more than what is required - after all, it enables one to teach till Algebra II but demands far far more sophisticated knowledge than one would conceivably encounter in a conventional High School classroom Geometry / Algebra II - still, Subtest III "under-assesses" [if I might fashion a term!] for skills in the upper-level Math classes such as Trig-Precalculus [albeit, granted that algebraic Precalculus is covered by Subtest I] and Calculus AB / BC.

I cannot account for it.

Having said that, a novice Math teacher shan't - realistically - cross the portals of a Precalculus / Calculus class till quite a few of hair strands have turned grey - oh, that circumstance shall transpire after a couple of years teaching Algebra I in a High School setting, what! - notwithstanding however acute one might believe one's Math skills to be be. Veteran teachers customarily seek - and are vouchsafed - such classes: experience is often equated with virtuosity [in general!] - however fallacious that argument might be... - and the perception also resides that an older teacher "deserves" - in a manner of speaking since such an individual has "put in the time" - the more motivated students that advanced Math sections are bestowed with.

The long a.s. of it is that No, Subtest III is not sufficiently rigourous; but it isn't likely that one shall be thrust upon upper-level classes anytime soon.

Otherwise, the scoring is in the form of ambiguous Quartiles: 25th, 50th and 75th percentiles [or higher] denoted by +, ++, +++ and ++++. I can't imagine why those blokes can't revert to a straight-forward - and more precise - Percentile scoring so that comparisons may be facilitated. Perhaps, the aim is to forestall precisely that: in an education environment where competitiveness is frowned upon [unlike the Asian dispensation] and collaborativeness sought to be fostered so that fragile self-esteems may not be marred, declaring a chap to have only Passed appears reasonable.

Less cynically (and more charitably...since there is that facet of mine, too!) though, to what purpose? If 220 is the benchmark and surpassing said score is the object, does it matter what one's exact grade is? This is not an Entrance Exam (like the SATs / GREs). So, while it is profitable to know how poorly one did [in the case of failure], it is not beastly illuminating if success were achieved.