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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
139 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
315 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
526 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
408 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
206 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 ...
8
votes
0answers
130 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 ...
8
votes
0answers
184 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 ...
8
votes
0answers
69 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 ...
8
votes
0answers
345 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 ...
8
votes
0answers
559 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 ...
8
votes
0answers
341 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 ...
8
votes
0answers
194 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.
8
votes
0answers
107 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, ...
8
votes
0answers
82 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 ...
8
votes
0answers
280 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
votes
0answers
307 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....
8
votes
0answers
202 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 ...
7
votes
0answers
153 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 ...
7
votes
0answers
158 views

Which calculus textbook is aligned the most with the CollegeBoard course description?

The CollegeBoard website lists many AP calculus BC references. But it also mentions that "The materials on this List range in alignment from 59% to 100%." So, which of them is aligned the most with ...
7
votes
0answers
88 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 ...
7
votes
0answers
48 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 ...
7
votes
0answers
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 ...
7
votes
0answers
264 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 $m$, ...
7
votes
0answers
229 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 ...
7
votes
0answers
270 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 "...
7
votes
0answers
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
1answer
638 views

Does there exist an international certification of mathematical skill?

I think that an international certification of math level would be really important also for non-math educators. Here in Italy primary school teachers actually teach math without being proficient at ...
6
votes
0answers
175 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?
6
votes
0answers
85 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 ...
6
votes
0answers
72 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 ...
6
votes
0answers
192 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....
6
votes
0answers
289 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 ...
6
votes
0answers
173 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 ...
6
votes
0answers
368 views

What books properly address the properties of $a^b$?

Many students think $\sqrt{a} \sqrt{b}=\sqrt{a\ b}$ $\sqrt{a^2}=a$ $\frac{1}{\sqrt{a}}=\sqrt{\frac{1}{a}}$ but none of the above are true when (a) and (b) are negative. To avoid such problems, ...
6
votes
0answers
83 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 ...
6
votes
0answers
129 views

Flow diagrams and summarizing strategies in proof-computation courses: good or bad for learning? Unsuitable for Inquiry-based learning?

For concreteness lets keep our discussion to calculus courses where there is a balance of proof and computations (computing limits but also doing epsilon-delta proofs) I can understand that in more ...
6
votes
0answers
167 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 ...
6
votes
0answers
155 views

How was this maths educational video made?

I would like to make math videos in the manner of this YouTube video. The specific features which I like in this video are: the interactive freestyle drawing (see the beginning of the video) the way ...
6
votes
0answers
133 views

Questions similar to Wason Selection Task

The Wason Selection Task (described by Pete Clark here) is a great problem for getting students to grapple with all of the intricacies of logical implication. I will be teaching a discrete ...
6
votes
0answers
168 views

Adding one to numbers bigger than ten

If someone asks you Tell me the next number (add one) after the number one million two hundred thirty-one thousand ninety-nine, do you known if it is a common error that the first number that ...
6
votes
0answers
149 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 ...

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