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Computer Based Maths, list of educational outcomes.

Computer Based Maths ( https://www.computerbasedmath.org/about ) wish to consult you on our list of educational outcomes. These are the long-term goals that we want students learning mathematics to achieve through their schooling.

As valuable members of our community, we would like your feedback, to critique, compliment or suggest improvements upon the fundamentals that drive the initiative.

So please take the time to step through the list of outcomes, including the details and provide some feedback on what you think (comment / post below).

https://www.computerbasedmath.org/outcomes

This link is for the online list of the outcomes, found on that same page is a link to download the outcomes in PDF format should that prove useful!
POSTED BY: Mark Braithwaite
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POSTED BY: David J M Park Jr

When I clicked through the linked, I was under the assumption it would list the outcomes of CBM that are beneficial over traditional math programs. Indeed, this is the sort of information I'm constantly on the look out for. What I found instead was quite a lot of information (well laid out mind you) that was more focused what a general math curriculum would be if CBM was implemented? Is my understanding of your intentions correct? I have bookmarked previously from that site a description of CBM's explicate benefits over traditional math but a running total of all the research to date might be more helpful to people like myself interested in influencing policy. People seem to resist the idea letting the computer or calculator do the computation lets students focus to a much greater extent on the math concepts. One can't even get them into the computer if they don't understand the math.
POSTED BY: Blair Birdsell

I'm having trouble figuring out whether "Mainstream Maths" is meant to be the same as mainstream mathematics, OR whether it is meant to replace mainstream mathematics, OR whether it is proposed as something valuable to learn along side mainstream mathematics, while being distinct from but related to it. The lead sentence of the linked page seems to claim they are the same thing. Thus the claim seems like the first alternative, but to quote IF, "something just 'smells' wrong." Basically, I don't think the outcomes, taken as "axioms" defining an undefined object, "Mainstream Maths," to cast my point in a mathematical framework -- the outcomes do not define mainstream mathematics as I understand it/them. So maybe it's the second alternative (a replacement)?
POSTED BY: Michael Rogers

One need not be headed towards being an academic mathematician in order to benefit from constructing proofs. Constructing a proof is one way, of often a very good way, to be sure you really understand the precise meanings of the mathematical concepts involved. For example, for the meaning of "eigenvalue", to prove that if λ is an eigenvalue of a square matrix A, then λ2 is an eigenvalue of A2, and to give a proof without using determinants. Or to use a little epsilontics to prove that a convergent sequence is bounded. These are at the college 1st year to 2nd year level. And to prepare the way for that, at the school level, to deduce simple properties of integers or rational numbers. And to do such things carefully and precisely, and not just by computational examples or making analogies or drawing diagrams, however "convincing" such means may seem.
POSTED BY: Murray Eisenberg

Let me re-word that last line to "I beleive that the outcomes that I listed cover the key elements of proof construction do you disagree?"

One of the things that we debated at length as we worked on these was the role of proof in maths. If you are, or are headed towards, being an academic mathematician, then being able to construct proofs is the central goal of the educational path. However, I beleived, that if you look at the wider application of maths in other research, and practical problem solving, there are different levels of "making a case" that are still informed by mathematical thinking. These range from 'showing plausability', through proviiding a strong argument' with 'proof at the top. Our outcomes were trying to cover the range, rather than focus only on proof.
POSTED BY: Jon McLoone

"I wonder if those outcomes miss a vital component of being able to construct a proof?" --

Exactly the crux of my question!
POSTED BY: Murray Eisenberg

Your statement packs together a lot of ideas that we have tried to break down into sub-concepts.

All of AM (abstraction) outcomes are a first step, IN5, much of the CV (critiquing and verifying) and the CCV, CCD, (communicating and collaborating). A logical argument in this breakdown is, creat an abstraction infer something beyond the immediate observation, make sure that you understand assumptions that you have made and their impact, and then explain all of that to someone else.

I wonder if those outcomes miss a vital component of being able to construct a proof?
POSTED BY: Jon McLoone

Whether computer-based or not, surely one of the goals should be something like: "Be able to construct a logically correct argument to establish a mathematical fact." (i.e.: constructing a proof).
POSTED BY: Murray Eisenberg
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