Unanswered Questions
66 questions with no upvoted or accepted answers
13
votes
0
answers
203
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 ...
- 231
11
votes
0
answers
139
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 ...
- 7,374
10
votes
0
answers
706
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 ...
- 30k
10
votes
0
answers
135
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 ...
- 33
9
votes
0
answers
105
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 ...
- 25.7k
8
votes
0
answers
419
views
The importance of note taking in mathematics
I'm asking this question right now due to the fact that a lower back problem has made it very difficult for me to do much but lie down for large sections of the day when it flares up, and the fact ...
- 4,845
8
votes
0
answers
585
views
Can Compare and Contrast be used in Mathematics Teaching and Research?
I happen to be a fan of the "theme and variations" approach to problem solving. In certain cases, a certain question had drawn enough to attention to generate dozens of solutions.
Ways to Prove the ...
CommunityBot
- 1
8
votes
0
answers
121
views
3-D printing of formulas encoded in LaTex for the visually impaired?
There is software available on the Net for 3-D printing of math expressions encoded in LaTex. What such technology is available off-the-shelf for the visually impaired to learn mathematics? And, ...
- 627
8
votes
0
answers
91
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Literature on skill transfer
Motivated by this other question I'm interested in getting to know the literature on mathematics skills transfer within itself.
All I know is what I've read in David Perkins's book "Knowledge as ...
CommunityBot
- 1
8
votes
0
answers
213
views
Effective use of Maple T.A
I am considering using Maple T.A. as a tool for formative assessment (and possibly at some stage, summative assessment) for courses such as calculus and linear algebra. What are your experiences and ...
CommunityBot
- 1
7
votes
0
answers
96
views
Literature on teaching and learning probability
In an earlier question, the book Exploring Probability in School (2005) (Link) was mentioned. It gives an overview of the research on the teaching and learning of probability up to that point.
Does ...
CommunityBot
- 1
7
votes
1
answer
237
views
Research into how students read algebraic expressions
In answering another question What is the justification to teach the (redundant) use of parentheses in multiplications? I was left wondering what we actually know about students' progression in terms ...
- 107
6
votes
0
answers
75
views
Potential topics for a university level mathematical thinking module
Social science training typically involves statistics as equivalent to "quantitative methods", particularly statistical modelling but also some material about data quality and exploratory ...
- 161
6
votes
0
answers
220
views
Tablet whiteboard app w e-pencil
(I've generalized the original question as @BrendanW.Sullivan suggests.)
I would appreciate recommendations for a whiteboard app for a tablet using an e-pencil. For me: an iPad, using an Apple pencil....
- 30k
6
votes
0
answers
181
views
Mathematical undergraduate education in Syria
I'd like to learn some things about undergraduate mathematical education in Syria EDIT: In particular I'm interested in students 15-16 years old.
What are the main differences from the European ...
- 111
6
votes
0
answers
89
views
Long-form, multi-step, skills-integrating applied mathematics problems in calculus I, II, III
When recently teaching Calculus II to college students, I instructed my students to read and be ready to work through the first 8 or so questions of James Walsh's climate modeling differential ...
- 161
6
votes
0
answers
191
views
Learning math historically
What is meant by learning math historically (NOT learning math history only, but learning math with a historical development perspective)? I've seen some sources that to learn a math topic X, you need ...
- 349
6
votes
0
answers
71
views
How to control for numerical factor in mathematics education research?
I am going to carry out a small scale action research on ratio problems. I would ask the same questions in different ways and see whether wordings would affect students' performance. However, past ...
- 161
6
votes
0
answers
183
views
Catalog of undergraduate's misconceptions / problems while proving
Selden & Selden (2011) listed 41 difficulties their students had in an experimental proving course into 9 categories. Unfortunately I haven't found similar work. Thus, my question is:
Is there ...
- 2,031
6
votes
0
answers
86
views
Appropriate journals for case study article about teaching math to learning-disabled student
Many scholarly articles have been written about the relationship between low working memory and math learning difficulties. There's not much written about what to do about it.
I would like to write ...
CommunityBot
- 1
6
votes
0
answers
330
views
Importance of "Calculus->Analysis Transition Books"?
E.S.E. advisers,
I am a college sophomore with a major in mathematics and an aspiring mathematician in the fields of computation theory and cryptography. I am always curious about the importance of "...
- 557
6
votes
0
answers
315
views
Links between mathematical folklore and educational success
I would like to ask if, in the research field of mathematical education, some work has been done to investigate the relationship between 1) and 2):
mathematical education and student motivation
the ...
- 5,883
6
votes
0
answers
177
views
Undergraduate maths research
I am looking for:
an undergraduate research program
in mathematics/theoretical physics
offered online (e.g. via skype or something)
given by a good institution
which can be followed while attending ...
CommunityBot
- 1
5
votes
0
answers
176
views
Comparison of texbook for "how to write proofs"
I posted this question in the math stackexchange https://math.stackexchange.com/questions/4681694/comparison-of-textbooks-on-how-to-write-proofs and one person suggested that I cross-post it here. I'...
CommunityBot
- 1
5
votes
0
answers
130
views
Is it possible to learn some basic mathematics using an app?
I am interested in developing an app for students that are starting a grade career involving mathematics. It is a real problem that they start with almost no knowgladge of basic mathematics and there ...
5
votes
0
answers
206
views
Montessori mathematics for HS/college students
My children attend a Montessori school (as did I when I was a child), and I have visited several other Montessori schools and spoken with their teachers. Numerous times I've had Montessori teachers ...
5
votes
0
answers
162
views
What do you think, is teaching on an actual board more efficient than using an online board?
I am a sophomore math undergraduate and so far all of my university courses have been online due to the pandemic. I am really curious what you guys think about the efficiency of teaching mathematics ...
- 179
5
votes
0
answers
100
views
Objectives for group work in undergraduate pure maths
Whether we are preparing undergraduates for research in industry or academia effective collaboration is an important higher skill. I think there are two aspects to this in mathematics - thinking ...
- 151
5
votes
0
answers
172
views
Intuition: 5 regular polyhedra, 6 regular 4-polytopes, and then 3 regular d-polytopes
I have struggled to offer an intuitive explanation
(to U.S. college students)
why the number of regular polytopes in dimension $d$ is:
$d=2$, number: $\infty$.
$d=3$, number: $5$, the five Platonic ...
- 30k
5
votes
0
answers
114
views
the role of context in mathematical discussions of units and measurement in web design
Knowing that pedagogy for each age group is different, I will say right off the bat I am talking about working adults.
I am noticing more and more, that despite people's phobias about math, they are ...
- 878
5
votes
1
answer
106
views
Conferences dealing w/challenges of teaching higher level math to STEM audiences
I'm interested in knowing whether there are conferences that have, among other topics, the difficulty of teaching higher level mathematical concepts to folks with prior established skills in STEM, e.g....
4
votes
0
answers
176
views
Is it better to teach category theory in the background of type theory than set theory?
I have been going over some applied instances of category theory in Programming, and also by a book by conceptual Mathematics by Lawvrere, and I think an issue of applying category theory to real life,...
4
votes
0
answers
105
views
Studies on the effects of using online platforms in teaching mathematics on students' beliefs about mathematics
Are you aware of any research examining the impact of utilizing online platforms in teaching mathematics, on students' beliefs about mathematics? To give you an example of the kind of beliefs that I ...
- 1,102
4
votes
0
answers
62
views
Looking for papers with teaching-oriented style
I am looking for papers that have the similar style to Hervé Lehning's 1989 The American Mathematical Monthly article "From Experimentation to Proof" (PDF link via lehning.eu). It's like ...
- 141
4
votes
0
answers
279
views
How must the "ungrading" idea be adapted to work in a math class?
After seeing no direct responses to this question, I'll instead be more direct myself. Ungrading is a buzzword being tossed about for assessing students' progress without focusing on quantitative ...
- 4,845
4
votes
0
answers
158
views
What effect does giving numerical or written grades have on learning?
When I was in school, pupils were given numerical grades, or the equivalent of numerical grades but disguised as words, on their performance in various school subjects and also behaviour. A key ...
- 7,374
4
votes
0
answers
466
views
Seeking Your Recommendation on Problem-Solving Books (preparing for Putnam)
E.S.E advisers,
I am a college sophomore in US with a major in mathematics and an aspiring mathematician in the computation theory and cryptography. I apologize for this sudden interruption but I ...
- 111
4
votes
0
answers
188
views
What is the point of using half range Fourier series for standard functions?
If we have a standard function, like $f(x) = x$ or $g(x) = x^2$, defined between $0$ and $\pi$, then why should we be interested in extending this function to give a Fourier series that resembles this ...
- 7,722
3
votes
0
answers
93
views
How to make student work in think-pair-share?
I have been trying the think-pair-share technique in my undergraduate linear algebra class of about 30 students. Some students quite enjoy the experience. But I noticed that some other students simply ...
- 21.7k
3
votes
0
answers
149
views
The propagation of the wave equation in even versus odd dimension
I am about to teach a second year undergraduate class on applied differential equation (first time) and, while I won't have time to go into the details, I wanted to show my students the difference ...
- 31
3
votes
0
answers
76
views
Formal linear combinations: motivating examples
I want to introduce formal linear combinations in an upper-level undergraduate combinatorics class. By this I mean expressions like $7 \operatorname{cat} + 5 \operatorname{dog} - \sqrt{2} \...
- 139
3
votes
0
answers
78
views
Is the annual system still in vogue anywhere in Europe, North America, Australia, or East Asia? And what about the 2-year B.A. / B.Sc. degree?
In Pakistan, we have until now had 2-year B.A./B.Sc. and 2-year M.A./M.Sc. university degrees after our 12th grade F.A./F.Sc. qualifications. Thus the former was a 14-year academic qualification, ...
- 319
3
votes
0
answers
243
views
How many secondary-school students are working on achieving independent understanding?
If mathematicians and math teachers and textbooks in all cultures in all eras say that a certain theorem has been proved, then the reasonable layperson trusts them.
At the same time, a student who ...
- 1,915
3
votes
0
answers
185
views
How to promote more elegant and beautiful proofs by students?
Following the premise that mathematics is an art as well as a science, I want to encourage students to produce not only correct proofs but also to try to find a particular beautiful/elegant proof.
...
- 544
2
votes
0
answers
192
views
When Did They Start Using Ohm's Triangle for Arithmetic Topics?
I am here with a historical question about maths education. I hope I have chosen the right SE as there are confusingly three that pertain to historical research into mathematics.
Any quantitative ...
- 7,374
2
votes
0
answers
106
views
Is there national grade distribution data for introductory service courses?
I am looking for US average national or state grade distribution data for courses that are typically considered as math service courses: precalculus, calculus 1,2,3, linear algebra, differential ...
- 7,374
2
votes
0
answers
131
views
"Tools" (literarily) for solving linear or quadratic equations
Since a few weeks, I teach as a tutor (not from that school) a support course in a German 9/10 class. I quickly noticed a horrible lack of basics. (Partly based on just different names - I had to ...
- 7,374
2
votes
0
answers
121
views
Is there any way of explaining the Cayley/Beltrami–Klein metric to undergrads?
How to explain the Cayley-Klein or sometimes called Beltrami–Klein metric concept to find the distance between two points in a hyperbolic space to an audience with no higher education than maybe a ...
- 21
2
votes
0
answers
160
views
Worldwide standard textbooks vs textbooks from one's home country vs lecture notes by various people - pros and cons
So far I've had three types of professors in my undergrad studies when it comes to choosing the main text for the course:
Type A: these are the professors who pick some standard textbook(s) in English ...
- 179
2
votes
0
answers
208
views
What are differences and the examples of syntactic knowlede and substantive knowledge in mathematics?
There is a distinction between substantive and syntactic knowledge particularly in mathematics. There are several definitions for both knowledge. However, what are the indicators and the examples of ...
- 21