About 15 years ago, I heard a math education professor give a talk about how computer algebra systems would change the kinds of questions teachers would ask high school and first year college students. Exercises in factoring and polynomial long division would become de-emphasized just as those asking students to extract square roots by hand to the third decimal place were deemphasized after calculators became widespread. New types of questions exploring patterns would be possible.

The need for remote teaching and assessment rising this past year has renewed my interest in this topic. Many instructors have had to make all their assessments open-book, open-internet.

So my question has two parts. One is about a curriculum, particularly at the precalculus level: Is there a curriculum that emphasizes topics and skills that CAS would not render "irrelevant" (for lack of a better term) and that utilizes CAS to enrich understanding? The other part is about assessments/problem sets: is a there a body of wolfram alpha-proof questions out there for assessing students?

Edit: I regret implying that factoring will be irrelevant with CAS. In that particular case, I am looking for questions that would build or assess this skill even if the student answering the questions has access to CAS -perhaps something like this Open Middle problem.

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    $\begingroup$ I think "utilizing CAS to enrich understanding" is a great direction to go, but I'm skeptical about trying to focus on "skills that CAS would not render irrelevant". There are plenty of valuable mathematical intuitions to be gained from skills that CAS do render irrelevant. Also, specific "how to use a calculator to solve this kind of problem" skills may be rendered obsolete with new technology. $\endgroup$
    – TomKern
    May 18 at 1:17
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    $\begingroup$ Actually, I see on computerbasedmath.org that..."Our mission is to reconceptualise the mainstream mathematics curriculum by assuming computers exist" $\endgroup$
    – Nick C
    May 18 at 1:48
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    $\begingroup$ Possibly relevant is this 12 June 2006 sci.math post (and follow-up post), which discusses a talk I gave in November 1998 (11th ICTCM Conference). A useful search term for what @TomKern brings up in the second sentence of his comment is "scaffolding", an education-specific term I don't think I was aware of when I was thinking about these things back then. $\endgroup$ May 18 at 17:48
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    $\begingroup$ The example I go to is how my students are so used to performing calculations involving fractions with their calculators that they don't have those skills memorized when working with fractions in College Algebra. Admittedly, this is something that can also be done with calculators, but the real lesson -- that algebraic formulas can be manipulated the same way numbers can be -- is something calculators don't currently communicate as well as I would like. $\endgroup$
    – TomKern
    May 18 at 19:09
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    $\begingroup$ If the goal of mathematics instruction is for students to understand the calculations rather than just do them then the concept that a calculator removes the need for teaching is likewise removed. $\endgroup$ May 20 at 20:40

You could look at https://neilstrickland.github.io/maths_with_maple/. This is a full set of material for a CAS-based course which is mostly calculus but has some precalculus. It was originally taught using Maple, but I have recently added files that do most of the same work using Maxima instead. (Maxima is open source, but Maple is not.) Everything is released under a Creative Commons license. The idea of the course was to deemphasise routine calculation and use CAS to enhance understanding; you can judge for yourself how well I succeeded.


Some brief resources-




In particular, https://www.wolfram.com/books/profile.cgi?id=9764

Is there a calculator centered secondary school curriculum somewhere?

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    $\begingroup$ Feel free to expand to paragraphs, add explanations and other resources. $\endgroup$
    – nickalh
    Jun 2 at 9:35

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