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Unanswered Questions

25
votes
0answers
426 views

Do “gateway tests” work?

Here is an overview of the practice of "gateway testing", which explains it much better than I could: https://sites.lsa.umich.edu/michigan-math-in-action/2015/09/24/25-years-gateway-testing-at-...
14
votes
0answers
384 views

Is metacognition ever bad?

Metacognition seems pretty universally positive. I'm wary of viewing it as such. Aside from the obvious criticisms like "you can't learn to ride a bicycle by thinking about and writing a 200 page ...
13
votes
1answer
440 views

The Fundamental Theorem of Calculus and Vegetables

When I was an undergraduate, someone presented to me a proof of the Fundamental Theorem of Calculus using entirely vegetables. I found this incredibly fun at the time, but I can't remember who ...
12
votes
0answers
258 views

Was math education following a western trend?

After some research on the recent history of math education in the U.S., from the new math movement to the beginning of the 21st century, I understood that the historic flow of the math education ...
12
votes
0answers
188 views

Exercises to go with Simon's “Representations of finite and compact groups”

I am teaching an independent-reading course from Simon's "Representations of finite and compact groups". I chose this book based on fond memories from a previous reading course in which I had ...
11
votes
0answers
112 views

Research on the use of outlined / structured proofs in instruction

Has there been any research into comparing the effectiveness of using "structured proofs" or "outlined proofs" in higher level mathematics education, compared to traditional "prose" proofs? For the ...
10
votes
0answers
167 views

implication vs equivalence when solving equations

I remember we were taught in high school (Eastern Europe) the difference between implication ($\Rightarrow$) and equivalence ($\Leftrightarrow$) and were instructed, when solving equations to be ...
10
votes
0answers
182 views

What is known about discrimination and difficulty in test questions?

I am interested in looking at any design resources or "guiding principles" on the distribution of different types of question difficulties on evaluative examinations. We can use Item Response Theory ...
10
votes
0answers
84 views

Literature on student understanding of assumptions

In a discussion with a physics lecturer he mentioned that one major area where students fail is understanding assumptions - for example, if we are interested in two objects hitting each other and then ...
9
votes
0answers
95 views

Recommend a vector calculus textbook/resource with an algebraic geometry flavor

Is there a resource or textbook that presents the basics of vector calculus, specifically the gradient, directional derivatives, curves and surfaces, and extrema, from a more algebraic geometry ...
9
votes
0answers
156 views

Shanghai math — what is it, and how good is it?

Some schools in the UK are adopting English translations of a grade school math textbook from Shanghai. The book appears to be designed to work with a specific teaching approach, the only specifics ...
9
votes
0answers
153 views

How important is it to show students an application of the topics seen in an undergraduate course?

I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each ...
9
votes
0answers
73 views

How can instructors bridge the gap between an engineering course in stochastic systems and a more rigorous Stochastic Processes course?

Systems and electrical engineering graduate students often take a course on stochastic systems (a.k.a. "Probabilistic Systems Analysis"). A typical course will present such topics as multivariable ...
8
votes
0answers
80 views

Studies into the effects of having fewer classes per term

Have there been any studies done into the effect of having fewer classes per term on a student's comprehension of their mathematics course material? Also are there any examples of schools that have ...
8
votes
0answers
603 views

What is the failure rate of students in Algebra 1?

Hello fellow educators, I've been hearing a lot recently that many students struggle with Algebra 1 in the US. The dropout rate is supposedly very high and some educators argue that Algebra 1 and ...

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