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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 ...
Willie Wong's user avatar
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13 votes
0 answers
200 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 ...
Theo Bendit's user avatar
13 votes
0 answers
513 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 ...
Henrique Augusto Souza's user avatar
13 votes
0 answers
313 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 ...
LSpice's user avatar
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12 votes
0 answers
350 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 ...
bzm3r's user avatar
  • 465
11 votes
0 answers
473 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 ...
user avatar
11 votes
0 answers
138 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 ...
Tommi's user avatar
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10 votes
0 answers
197 views

Examples for advanced math courses based on measurable learning objectives

Background. I teach math at a German university (both undergraduate courses and courses for Master programmes), mostly for students who major in mathematics or very similar programmes. Students ...
Jochen Glueck's user avatar
10 votes
0 answers
164 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. ...
LarsH's user avatar
  • 201
10 votes
0 answers
703 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 ...
Joseph O'Rourke's user avatar
10 votes
0 answers
450 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 ...
Nate Bade's user avatar
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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 ...
Mike Pierce's user avatar
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10 votes
0 answers
124 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 ...
jonsca's user avatar
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9 votes
0 answers
163 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 ...
Jochen Glueck's user avatar
9 votes
0 answers
346 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 ...
Anonymous's user avatar
9 votes
0 answers
104 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 ...
Steven Gubkin's user avatar
8 votes
0 answers
187 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 ...
Alan's user avatar
  • 301
8 votes
0 answers
333 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 "...
EJ Mak's user avatar
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8 votes
0 answers
144 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 ...
J Fabian Meier's user avatar
8 votes
0 answers
193 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 ...
Matt Brenneman's user avatar
8 votes
0 answers
305 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 ...
lyk's user avatar
  • 83
8 votes
0 answers
73 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 ...
Red Banana's user avatar
8 votes
0 answers
417 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 ...
Nethesis's user avatar
  • 181
8 votes
0 answers
583 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 ...
john mangual's user avatar
8 votes
0 answers
377 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 ...
Keith's user avatar
  • 587
8 votes
0 answers
205 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.
Mike Shulman's user avatar
  • 6,580
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, ...
Tom Copeland's user avatar
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 ...
Mark Fantini's user avatar
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8 votes
0 answers
294 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 ...
dtldarek's user avatar
  • 8,957
8 votes
0 answers
330 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....
Jon Bannon's user avatar
  • 6,173
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 ...
J W's user avatar
  • 4,753
7 votes
0 answers
213 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 ...
bingus's user avatar
  • 71
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 ...
Dag Oskar Madsen's user avatar
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 ...
Stephan Kulla's user avatar
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 ...
Mitchell's user avatar
  • 299
7 votes
0 answers
387 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 $m$, ...
vonbrand's user avatar
  • 12.3k
7 votes
0 answers
242 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 ...
Thomas's user avatar
  • 1,794
7 votes
0 answers
200 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 ...
Eric Auld's user avatar
  • 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?
Russasmita Sri Padmi's user avatar
7 votes
1 answer
235 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 ...
TomKern's user avatar
  • 4,425
6 votes
0 answers
154 views

What are the differences between the $n$ permutations of the Edwards & Penney Differential Equations books?

Edwards and Penney are the authors of a popular differential equations textbook. Bizarrely, there seem to be $2^4$ permutations of the title: Some versions have "Elementary" and some don't ...
SRobertJames's user avatar
6 votes
0 answers
117 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? ...
Maesumi's user avatar
  • 1,410
6 votes
0 answers
171 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 ...
Dan's user avatar
  • 989
6 votes
0 answers
74 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 ...
JenB's user avatar
  • 161
6 votes
0 answers
115 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 ...
okzoomer's user avatar
  • 341
6 votes
0 answers
217 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?
Red Banana's user avatar
6 votes
0 answers
106 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 ...
Aeryk's user avatar
  • 8,019
6 votes
0 answers
78 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 ...
Rico1990's user avatar
  • 325
6 votes
0 answers
219 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....
Joseph O'Rourke's user avatar
6 votes
0 answers
310 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 ...
Džuris's user avatar
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