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Questions tagged [reference-request]

A reference request is a request to be provided with (links to) documentation, official papers, and specs related to one or more specific algorithms or mathematical procedures, to provide a trusted base for what's being said or written.

29 questions with no upvoted or accepted answers
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14
votes
0answers
135 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 ...
12
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0answers
213 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 ...
10
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0answers
339 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
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0answers
119 views

Recommend a vector calculus textbook/resource with an algebraic geometry flavor

Is there a resource or textbook that presents the basics of vector calculus, specifically the gradient, directional derivatives, curves and surfaces, and extrema, from a more algebraic geometry ...
9
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0answers
101 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
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0answers
103 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 ...
8
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0answers
76 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
271 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
240 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
187 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
89 views

Resources for high school teachers about APOS theory

As far as I can find, the major resources available to the layteacher about APOS (Action, Process, Object, Schema) theory refer to "undergraduate" concepts such as group theory and vector spaces (such ...
7
votes
0answers
47 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 ...
6
votes
0answers
124 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
150 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 ...
5
votes
0answers
274 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, ...
5
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0answers
139 views

Textbooks explicitly showing the injections for the sum of sets

Asking for methods to produce the sum of natural numbers from the disjoint union of sets, it seems that the obvious way is to use the general definition, as coproduct, of the sum of sets. The accepted ...
5
votes
0answers
164 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 ...
5
votes
0answers
51 views

Resource request: superposition of triangular lattice and its hexagonal dual lattice

I was wondering if anyone knew of a source for pdfs of graph paper with both the triangular lattice and its dual hexgonal lattice superimposed over each other? I would like this to hand out to my ...
4
votes
0answers
126 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 ...
4
votes
0answers
228 views

“Indicated Arithmetic” or “Delayed Evaluation”

In the recent past, I've come across a pedagogical strategy for teaching/learning algebra that is sometimes called "Indicated Arithmetic" or "Delayed Evaluation". However, I've been unable to find any ...
4
votes
0answers
110 views

Are there any high school level summer program that teaches Analysis?

All summer programs I know for highschool students focuses on number theory, combinatory, graph theory, logic, and all kinds of stuffs in discrete mathematics. (I am mainly interested in UK, US, ...
4
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0answers
72 views

What are the best expository pieces related to the Van Hiele models?

The Van Hiele model (wikipage) "is a theory that describes how students learn geometry." I would appreciate further insights into the original model, later models that expanded or re-worked it, and ...
3
votes
0answers
259 views

Quantifying arthmetical skill

Question for a research project: What is the standard way of quantifying a student's skill in arithmetic ranging from having to look up numbers on a times-table to computing large sums in their head ...
3
votes
0answers
113 views

Sketching paraboloids on paper

I have to teach sketching paraboloids on paper by looking at it's equation. Last year when I taught this topic no one was interested in learning this particular thing. They felt the topic difficult ...
3
votes
0answers
78 views

Student input in secondary teacher evaluations

this is something I have been wondering about for a while now. In my school district (urban setting in Pennsylvania) student input amounts to exactly 0% of the final assessment for observed teachers. ...
2
votes
0answers
67 views

Reference for study about good teachers in a US state

Several years ago I have read about a study in a US state where standard test scores were used to identify teachers whose students consistently improved far above the average and then film and analyse ...
2
votes
0answers
100 views

Which book to use concurrently with each of these mathematics texts?

I'm in search of a good book that I can read --- and recommend to my proteges to read --- along with each one of the following books. Topology by James R. Munkres, 2nd edition Introductory ...
2
votes
0answers
195 views

Introduction of the power set as a collection of *labels* or *names* for subsets

The way that naïve set theory is usually presented in undergraduate education is via very concrete examples of sets, often involving non-mathematical elements. When power sets are treated, having a ...
2
votes
0answers
62 views

Request for IBL Script for Putnam-type Problem Solving Course

One of the major benefits of a good IBL script is that it effectively organizes the experience of students so that their effort does not need to be used on such organization. A good script leads from ...