Unanswered Questions

198 questions with no upvoted or accepted answers
16
votes
0answers
174 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 ...
13
votes
0answers
328 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 ...
13
votes
0answers
265 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 ...
12
votes
0answers
138 views

What studies exist, comparing the efficacy of exercise sheets with or without worked solutions?

I've been tutoring mathematics at university level for over 10 years, and one of the more common requests from students is worked solutions for sheets of exercises. Most educators I've worked with ...
11
votes
0answers
360 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 ...
11
votes
0answers
314 views

Books on meta-cognition that would be relevant for those involved in mathematics?

In 1992 Schoenfeld wrote an excellent "review" of (among other things) metacognition as it applies to mathematics: whether from the perspective of a student, or a teacher. Metacognition, as quoted ...
10
votes
0answers
104 views

toys/manipulatives for exploring graph theory

I was talking recently with my daughters about non-planar graphs, like $K_{3,3}$, $K_5$, and the 7 bridges of Königsberg. They got pretty interested in it, and seemed to catch on to the core ideas. ...
10
votes
0answers
525 views

Use of Lockhart's *Measurement* in a course?

I greatly admire Paul Lockhart's Measurement (Harvard Press). Many of you know him through A Mathematician's Lament. One review of Measurement said, “Here Lockhart offers the positive side of the ...
10
votes
0answers
406 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 ...
9
votes
0answers
117 views

Should I upload slides before or after a class

I used to post my slides before a class. But I noticed that many students simply read it while in class instead of listening . So I am thinking not doing it in the future. But they can still get it ...
9
votes
0answers
204 views

Is there such thing as a 1 kg "decimeter cube?"

Base 10 sets are readily available from educational suppliers and retail sites, as are the largest element in these sets, sometimes known as "decimeter cubes" (10 x 10 x 10 cm). The "...
9
votes
0answers
86 views

Research into the mathematical education of adults with no prior formal mathematical experience

I am curious about the experiences of people who had no formal mathematical training in their youth, but learned mathematics as adults. I imagine that there are a fair number of people in the US who ...
9
votes
0answers
114 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 ...
9
votes
0answers
110 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
102 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 ...

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