All Questions
242
questions with no upvoted or accepted answers
19
votes
0
answers
243
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 ...
- 2,731
13
votes
0
answers
183
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
13
votes
0
answers
498
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
0
answers
297
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 ...
- 916
11
votes
0
answers
423
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 ...
user507
11
votes
0
answers
337
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 ...
- 455
10
votes
0
answers
149
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. ...
- 201
10
votes
0
answers
669
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 ...
- 29.5k
10
votes
0
answers
442
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 ...
- 1,941
10
votes
0
answers
134
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 ...
- 6,731
9
votes
0
answers
143
views
Course materials for developing a mathematical theory from "natural questions to ask"
Educational setting.
I'm teaching math courses - typically consisting of lectures, weekly homework sheets, and an exercise class where the homework questions are discussed - for undergraduate and ...
- 1,695
9
votes
0
answers
309
views
Long division layout in French-speaking Switzerland
This question is addressed to those familiar with mathematics teaching in French-speaking Switzerland.
The main textbook in use in grades 3 to 5 in the canton of Vaud from 1957 to about 1972 appears ...
- 91
9
votes
0
answers
101
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 ...
- 24.3k
9
votes
0
answers
126
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 ...
- 4,606
9
votes
0
answers
119
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 ...
- 733
8
votes
0
answers
179
views
References for mathematical notation for foreign students in the U.S
I teach quite a few foreign students at a U.S. university. Frequently students are placed in our most remedial math class due to not having placement scores and failing to test out of the course.
I ...
- 311
8
votes
0
answers
331
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 "...
- 329
8
votes
0
answers
140
views
Good Source for German Tank Problem
I would like to teach the German Tank Problem to bright students with little prerequisites. They are 16 year old high school students with a lot of maths competition experience, but no prior knowledge ...
- 250
8
votes
0
answers
191
views
Are there standard questions for testing how an instructor grades calculus?
My institution is now in the process of "standardizing" our calculus classes. One issue we have is the variation among instructors in grading problems. I am interested if there are ways to objectively ...
- 691
8
votes
0
answers
72
views
Where can I find a comparison of mathematical subjects taught for primary and secondary school around the world?
I have been searching this for a long time, but most of what I find spends more time on cultural aspects and what is expected from the teacher, etc. Perhaps this is really trivial to find, but I am ...
- 241
8
votes
0
answers
406
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 ...
- 181
8
votes
0
answers
575
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 ...
- 878
8
votes
0
answers
368
views
"Extension Mathematics" by Tony Gardiner
I would like to know if anybody has experience with the British textbook series Extension Mathematics in three volumes, by Tony Gardiner.
It claims to be "the first structured KS3/S1-S2 programme for ...
- 587
8
votes
0
answers
201
views
Moore method projective geometry
Has anyone written a set of Moore method notes for synthetic projective geometry? It seems like it would be well-suited, but I haven't been able to find any such thing on the Internet.
- 6,520
8
votes
0
answers
117
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
90
views
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 ...
- 3,030
8
votes
0
answers
292
views
What else we miss?
Context:
Some time ago there was a post on a brief study conducted by Alexis Wiggins (she was shadowing two students for two days), you can find it here, which got quite an attention. One interesting ...
- 8,907
8
votes
0
answers
324
views
Guided Lecture Notes for Calculus
Last semester I taught Linear Algebra using the standard textbook of Lay. Online one can find nice "class handouts" that serve very well as lecture notes for students to follow along with during class....
- 6,045
8
votes
0
answers
210
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 ...
- 4,625
7
votes
0
answers
176
views
How to recognize possible dyscalculia in a student?
I am looking for input/advice regarding whether a student I just began tutoring may have dyscalculia - and, if so, how to go about broaching the subject / assisting them as best as possible.
I'd ...
- 71
7
votes
0
answers
265
views
Compare depth and scope of math syllabus between Malaysia's STPM, Gao Kao and A level
Are the math syllabi of these three exams comparable? Which syllabus' scope is wider and deeper? Which helps students to be better prepared for math in undergraduate level?
I believe that A level is ...
- 73
7
votes
0
answers
94
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 ...
- 2,520
7
votes
0
answers
53
views
Effectiveness of audio / video feedback
Hattie & Timperley (2007) mention a meta-analysis about video or audio feedback with a mean effective size of .64 (Table 2 on page 84). They state that this analysis was part of the meta-analysis ...
- 2,021
7
votes
0
answers
1k
views
Teaching a Pre-Calculus Course using Basic Mathematics by Serge Lang
I am considering using Basic Mathematics by Serge Lang as the primary text for my High School Pre-Calculus course. My students have all spent a year working through the first six books of Euclid and ...
- 299
7
votes
0
answers
357
views
Examples of multiple induction
It is easy to find/construct cases that can be proven by nested induction, i.e., some variation of the theme to prove the statement $P(m, n)$ you prove $P(1, n)$ by induction as a base case for $m$, ...
- 12.3k
7
votes
0
answers
240
views
Is WebAssign ADA compliant?
I hope this is a good place to ask about this. My institution uses WebAssign for homework in many classes. A concern has come up about being compliant with ADA. From a page on the WebAssign site, it ...
- 1,794
7
votes
0
answers
306
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 "...
- 559
7
votes
0
answers
195
views
Teaching an alternate definition for a compactness via the induction principle
In this post on Reddit, a user proposes an alternate definition of compactness, as an "induction principle":
A topological space $X$ is compact iff given a statement $P$ whose
truth or falsity ...
- 179
7
votes
0
answers
64
views
Statistics for Primary School: Informal Inferential Reasoning
Is there anyone that is experienced in teaching Informal Inferential Reasoning in primary school? Mind to share your experience?
7
votes
1
answer
214
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 ...
- 3,927
6
votes
0
answers
104
views
Is there ADA-compliance certification for mathematics text books?
What factors are there to consider when adopting a text as far as ADA (Americans with Disabilities Act) is concerned? Is there a certification? What do you look for in the digital version of the text? ...
- 1,084
6
votes
0
answers
160
views
Online math quiz: students make short video explaining solution
I am teaching high school math. My students are generally hardworking and competent. Class sizes are about 35.
We were recently forced online due to the pandemic, and I have been searching for a way ...
- 771
6
votes
0
answers
72
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
113
views
Maximize retention
I tutor high school math students. Students often struggle with a problem they had completed few months prior. Like any skill, it's natural to forget what you learned after a while.
As high school ...
- 341
6
votes
0
answers
208
views
Are there measurements of how much mathematics people remember after high-school?
These days I got curious about something: Are there measurements of how much mathematics people remember after high-school?
- 241
6
votes
0
answers
97
views
Converting an Online Course Back to In-Person
As I wrap up my Spring semester online courses, I'm starting to think about next Fall when (hopefully) our university will return to full in-person classes. Because of COVID, over the last year I have ...
- 7,500
6
votes
0
answers
77
views
Support modelling cycle through differentiated means
I plan to work with my students on solving real-world problems through modelling them. Now it is my idea to follow the modelling cycle below.
The idea is to find with the help of two values that have ...
- 325
6
votes
0
answers
213
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....
- 29.5k
6
votes
0
answers
301
views
What is the controversial 8th grade algebra mentioned on this answer?
An answer on this site mentions that it would be more appropriate to criticize
Efforts to force kids to take algebra at lower and lower ages, such as attempts in California to make all kids take ...
- 737
6
votes
0
answers
178
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