Inverses of Functions

[jkerr]

Hello,

I’m having a bit of trouble justifying the approach to inverses in high school. I’m not sure what lasting knowledge students will gain from F.BF.4a if that is the full extent of the coverage in Alg 1 & 2. It is a good place to start with inverses, but without extending the coverage in the same school year it seems like this standard is on it’s own little island. It appears as though we will be losing the opportunity to use inverses to make the connection between various types of functions.

Maybe F.BF.4a is saying more than I think it is. Could you explain the rationale behind the approach to inverses of functions in Algebra 1 and 2?

Thanks

[Cathy Kessel]

Have you looked at p. 13 of the Functions Progression? It can be downloaded here: http://ime.math.arizona.edu/progressions/.

[jkerr]

Yes, that’s where I first went for clarification. Overall, F.BF.4abcd is fine coverage of inverses. My question is about the thinking behind separating F.BF.4a apart from the rest. Maybe my problem stems more with the progression doc stating that formal notation and language are not important at this stage. My thinking is that if we don’t at least call this thing an inverse, then what are the students actually going to get out of this? Students wouldn’t be doing much more than was done in standard A.CED.4.

[Bill McCallum]

The dividing line been regular standards and (+) standards shouldn’t be viewed as a demarcation in the curriculum, but rather in assessment. There are a number of instances where for reasons of coherence one would want to include some (+) standards in the curriculum. Notice the statement on p. 57:

All standards without a (+) symbol should be in the common mathematics curriculum for all college and career ready students. Standards with a (+) symbol may also appear in courses intended for all students. [Emphasis added.]

That said, I do think there’s a difference between F-BF.4a and A-CED.4. The procedure is the same, but conceptualizing the procedure as “finding an input to a function which yields a given output” is a step up. Seeing functions as objects in their own right, and algebraic procedures as ways of analyzing those objects, is a sophisticated viewpoint.

[jkerr]

That makes sense.

I hope other teachers and administrators aren’t lost on this idea. I can envision a “why are you wasting time covering this standard, it won’t be assessed” scenario. I see a similar situation with rational functions, where graphing won’t be assessed. However, it would be logical to teach some graphing so that students would have that tool to check the rational expression operations and equation solving that will be assessed.

Thanks for your reply.

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