47

I couldn't agree more with @Steve's comment. The following response is written with elementary-to-high-school mathematics in mind. A lack of a decent number sense really does encumber making sense of and parsing word problems, as well as the process of exploring solution strategies. It is akin to interpreting a passage written in a not-so-familiar dialect: ...


23

I find the ability to estimate calculations quite useful and I think you need to be able do do calculations to estimate them. If you are keeping a grocery budget, I would suggest you should know what your groceries will cost within $10\%$ before they are rung up. To know that, you need to be able to add and multiply in your head. You don't need many ...


19

Yes! But the virtue doesn't lie in being able to do the calculation but in gaining a feel for numbers as well as algorithmic thinking. I teach Computer Science freshmen and one of the first things we need to do is introducing base 2 as well as number systems working with modulo (two's complement). We also introduce basic circuitry to do addition/...


15

I taught at the elementary and high school levels. At times we used calculators and at times we didn't. Students benefit from experience both ways. Students need to learn that calculators are only a tool and they still have to think. Students also need to learn that having a calculator doesn't guarantee that their computation will be correct. Finally ...


9

Brian D. Rude, "The Case For Long Division." 2004. HTML link. This is a somewhat long (unpublished) article (which I haven't studied carefully), but maybe the excerpt below suffices to give the gist of it. Before this excerpt, among his closing sentences are: "But a calculator should be more than a paperweight. Let’s teach for understanding.&...


9

I attended the Computer based math educational summit back in 2016 and found their ideas interesting. I agree with some of their points and disagree with others, but it is certainly interesting to look at the following diagram from their website. They argue, that if we let computers (proper ones, not handheld calculators) do the repetitive calculations, ...


7

I have thought a lot about this question since posting it, and having read the other answers and the many comments, I want to add a perspective that no one else seems to have given. Most of the real work in doing math is understanding and conceptualizing the problem rather than in computing an answer. This will be apparent to anyone who has read a ...


7

Beyond having worked as a programming teacher I have no experience with math education, but this is a topic I have been fascinated with for years. Arguments in favor of mental/manual arithmetic can be typically categorized as: It's important in daily life The argument typically goes that you need to be able to do arithmetic a lot in daily life with the ...


4

If you can ignore the specific UBC context, this might be the type of paper the OP seeks: Eric Eich. "The Cognitive Science of Learning Enhancement: Optimizing Long-Term Retention." (2011). Univ. British Columbia. HTML link. Here's an excerpt comparing "massed" vs. "spaced" learning: "The advantage of spacing over ...


4

Calculus student had a final result of $\frac{1}{2\pi}$ Which she told me was 1.57. I immediately realized that she had calculated $\frac12\pi$ from keying in 1/2$\pi$. There’s no going back on calculator use, I realize. What I strive for is to have the student who performed a series of calculations (for, in this case a related rates problem in calculus) to ...


3

You really need to be able to do sums in your head when debating or negotiating. To prove this, show your students these famous car-crash interviews: (1) Diane Abbott (Labour) floundering horrifically over numbers she could neither remember nor even estimate in her head. The coolness and speed with which the interviewer questioned her numbers must itself ...


3

By hand =/= in your head. Having some faculty for mental arithmetic is good. Having a fluency for deconstructing a 'problem' into basic mathematical operations is pretty essential. However many people learn, and continue to benefit, by writing out the 'sums'. If Fred drives at 45 miles per hour, how far will he go in 45 minutes? I expect most people ...


3

To add to the excellent suggestions already made, I intersperse findings from this article (https://www.aft.org/sites/default/files/periodicals/dunlosky.pdf) throughout the semester in all my classes. The article reviews the results of a 2013 deep dive by educational psychologists into the effectiveness of 10 of the most popular study strategies students use ...


3

The Canvas class for Dartmouth's Spring 2020 course in Graph Theory, Math 38, seems to be mostly open. According to the syllabus, the course uses the 2nd edition of West's Introduction to Graph Theory. Course Description This course will cover the fundamental concepts of graph theory: simple graphs, digraphs, Eulerian and Hamiltonian graphs, trees, ...


2

I think if we can introduce a variety of algorithm's for teaching addition and multiplication, it'd be beneficial for the student. No matter what mathematics level you are, algorithmic thinking is always important. When I say algorithmic thinking, I mean to say that we have a set of rules to tackle a problem such that applying the rules in the correct order ...


2

In an attempt to answer your question: Are the PISA data detailed enough to measure effects by such AI based approaches in mathematics? I found three things that point to the answer being no. I dug through the 2018 PISA School Questionnaire, which is administered to school principals, and found no question on AI that would allow the data to be parsed in ...


1

You can't be overly reliant on technology. I once bought an item from a shop during a power outage. Cash register was non-functional. Not enough light to power a solar calculator. The cashier had to compute a 10% discount by hand. She did it.... the long way.


1

You're entirely correct and there is huge value to being able to compute by hand. For a most basic instance from the real world, here in the UK I once interviewed a candidate for office manager who had spent about 10 years working in a tax office, and been promoted three times. To me, that should have meant he ate, breathed and slept numbers. I asked him ...


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