Newest Questions
4,026 questions
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Why would replacing “standard high school” algebra, with “considerably more abstract topics”, enable dyscalculia students “to see things faster”?
I am baffled by the counterintuitiveness in this May 21 2012 essay by Prof. Andrew Lo.
Before we can make truly significant improvements in our school systems, we need to develop more refined metrics ...
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3
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146
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Are calculus curricula typically differentiated for mathematics majors versus engineering or physics majors? U.S. or Europe institutions
I am interested in how undergraduate calculus curricula are commonly structured across different majors, particularly:
mathematics
engineering
physics or other applied sciences
In many programs, ...
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3
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0
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154
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On the order of multiplication. On elementary school arithmetic education in Japan
Put $5$ flowers into each of $4$ vases. How many flowers are needed in total?
Expression: $5\times 4=20.$
Answer: $20$ flowers.
Since it is four groups of five, it is not “$4\times 5$,” right?
I have ...
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2
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0
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Is omission of the context-dependent nature of the meaning of "log" from elementary textbooks due to lack of communication?
Textbooks used in the prerequisite courses to calculus almost always assert without the least qualification that $“\log”$ with no subscript indicating the base of the logarithmic function means $“\...
- 2,558
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1
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How can a NotebookLM video explanation help a traditional teacher-created explanation (in terms of clarity, accuracy, and educational value)?
A colleague who was demonstrating to me the power of Google’s NotebookLM tool to generate a video explanation of a topic 'Fourier Transforms' uploaded it here: https://www.youtube.com/watch?v=...
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8
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2
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What are some commonly taught inaccuracies in mathematics? Should we correct them?
There are a few commonly taught inaccuracies in mathematics such as:
$\log ( x^2 ) = 2\log ( x ) $ (it should be $2\log|x|$ unless $x$ is known to be positive);
$\int \frac{1}{x} \mathrm{d}x = \ln|x|+...
- 4,407
8
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Attempts at the early teaching of abstract thinking? (E.g., Davydov, but more recent)
(To give some background for this question: I am informally teaching some children topics in "abstract" fields like algebra and first-order logic; certain things turn out to be much easier ...
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3
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6
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952
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Using LLMs for rephrasing and as reasoning partners for autodidacts (personalization of explanation from original source)
What I want to ask is opinion of community of Math Educators on using "reasoning" or "thinking" LLMs like the latest ChatGPT, Gemini, and others as a kind of reasoning partner or ...
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2
votes
1
answer
102
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How to explain geometric meaning of dot product of two vectors without using essential concepts
My dilemma is projections and angle between two vectors are not in the syllabus. I am not supposed to teach those concepts. Only up to Cauchy Schwarz inequality. I have already been warned to stick to ...
3
votes
1
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188
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Which persistent calculator usage errors hinder student understanding?
In your experience, what specific calculator errors do students repeat that reveal conceptual gaps (e.g., misuse of parentheses, order of operations, or misunderstanding inverse functions)? I’m ...
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2
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1
answer
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Teaching first-order logic with explicit Abstract Syntax Trees (ASTs) and De Morgan Normalization: existing tools or classroom practices?
I am exploring ways to help students better understand the structural aspects of first-order logic formulas beyond purely linear symbolic notation.
One possible approach is to represent formulas as ...
8
votes
3
answers
274
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Do any calculus textbooks in current use treat the expression $\sqrt{(dx)^2+(dy)^2}$ as central to finding arc lengths?
Many calculus textbooks state the "arc length formula" as follows:
$$
\left[ \begin{array}{c} \text{length of the graph} \\ \text{of } f \text{ between points} \\ a \text{ and } b \text{ in ...
- 2,558
6
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What design principles can make a calculator reveal the process behind solving linear equations?
I'm exploring calculator designs that combat black-box syndrome—where students get answers without understanding steps. For linear equations (e.g., 2x + 5 = 13), I ...
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Do math curriculum designers intentionally behave like gold miners? [closed]
Those who mine gold dig up several tons of soil in order to extract an ounce or two of gold.
Much of the math curriculum seems intentionally designed to work like that: Students majoring in poetry or ...
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1
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What resource to use before "Linear Algebra Done Right"?
Is Sheldon Axler's popular "Linear Algebra Done Right" intended as first experience with linear algebra ? If so then why doesn't it seem to contain a section or teach you how to do Gaussian ...
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