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.

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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
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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
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306 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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10 votes
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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
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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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9 votes
0 answers
154 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
130 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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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
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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
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8 votes
0 answers
326 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
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8 votes
0 answers
211 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
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7 votes
0 answers
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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
1 answer
224 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
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6 votes
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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
378 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, ...
Ted Ersek's user avatar
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6 votes
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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 ...
Thomas Kojar's user avatar
6 votes
0 answers
181 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 ...
pasaba por aqui's user avatar
5 votes
0 answers
266 views

A video game for teaching the concept of a mathematical proof

Two students in my game development course would like, as a final project, to develop a video game for teaching mathematics. In contrast to the many other games for teaching maths, which focus mainly ...
Erel Segal-Halevi's user avatar
5 votes
0 answers
155 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 ...
arivero's user avatar
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5 votes
0 answers
180 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 ...
Stephan Kulla's user avatar
5 votes
0 answers
56 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 ...
gregory_byler's user avatar
4 votes
0 answers
167 views

Studies on the change in effectiveness of pedagogical practices over time

Are there any studies that have investigated this question? Why certain pedagogical practices that used to be effective up to a few years ago, may suddenly become less or even no longer effective? I ...
Mahdi Majidi-Zolbanin's user avatar
4 votes
0 answers
156 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 ...
Tommi's user avatar
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4 votes
0 answers
269 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 ...
BostonBrooks's user avatar
4 votes
0 answers
80 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 ...
Mika Ike's user avatar
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3 votes
0 answers
115 views

References for visualizing numbers in base 10 flats

Base 10 blocks (units, rods, flats and cubes) are a widespread manipulative material for teaching place value. However, piling rods on top of each other is not very stable, so it is not easy to build ...
Jaume Oliver Lafont's user avatar
3 votes
0 answers
82 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. ...
celeriko's user avatar
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2 votes
0 answers
124 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 ...
Hauke Reddmann's user avatar
2 votes
0 answers
73 views

Where can I find the solutions manual to Beginning Statistics with Data Analysis by Mosteller, Fienberg and Rourke?

I am planning to teach a course on Statistics using Beginning Statistics with Data Analysis by Mosteller, Fienberg and Rourke. On page xii of the book, the authors said "A solutions manual is ...
Zuriel's user avatar
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2 votes
0 answers
101 views

Reference request for 1960s-1970s Australia/NZ primary-level textbooks

Where could I find a list, and ideally discussion, of primary school mathematics schemes (textbook series) in common use in Australia and New Zealand in the period immediately following decimalization ...
Dave's user avatar
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2 votes
0 answers
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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 ...
user11235's user avatar
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2 votes
0 answers
207 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 ...
David Roberts's user avatar
2 votes
0 answers
73 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 ...
Jon Bannon's user avatar
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2 votes
0 answers
126 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 ...
Heisenberg's user avatar
1 vote
0 answers
119 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 ...
Saaqib Mahmood's user avatar