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.

Filter by
Sorted by
Tagged with
7
votes
1answer
273 views

Native language, writing, and mathematical problem solving

This question is meant to explore the intuition that mathematical thought does not most naturally proceed from writing in one's native language. The hackneyed and not entirely satisfying slogan that ...
4
votes
1answer
110 views

References on the effectiveness of manipulatives (virtual vs. physical) [duplicate]

I am in need to find references for my thesis proposal. My topic is "Virtual manipulative versus physical manipulative: which way do students learn faster?". Do you know any authors that worked on ...
10
votes
1answer
794 views

Effectiveness of multiple-choice versus short answer questions

I want to know if there is any research on whether students' learn better by answering selected response (multiple choice) questions than constructed response (written) questions. My gut feeling is ...
12
votes
3answers
188 views

What is the correlation between students' contentment and educational quality?

In order to evaluate new educational material the contentment of students with this material is often measured. However, just because a student is contented doesn't mean that he/she has actually ...
12
votes
4answers
338 views

request for evidence about class perspectives in math word problems

A recent publication: Anita Bright. Education for Whom? Word Problems as Carriers of Cultural Values. Taboo: The Journal of Culture and Education. (Spring 2016). pp. 6-22. Link No paywall. observes ...
9
votes
8answers
668 views

Definition of the term, equation

What is the definition of an equation (as a mathematical terminology)? I have been using this term, equation, for a long time. I don't even remember when and where I have learned this term (Possibly, ...
14
votes
5answers
1k views

Soft questions for 8 - 12 year olds

I am concluding my second year in mathematics at the university of Milan. I also happen to be an educator for 8 - 12 year old children (as a Scout). Recently I have tried to fill some dead time by ...
7
votes
1answer
163 views

Subtraction Methods in School Mathematics

I have studied long ago different method for subtracting numbers, for instance the borrow method or the Austrian method (I hope I am using the right names; I am not an English native speaker and these ...
7
votes
2answers
175 views

Paper on Replicating Test Questions

I recall reading a paper a few years ago (though I think it was in physics) on a class where they decided to repeat a midterm test question on the final exam and students performed noticeably worse on ...
10
votes
2answers
232 views

Is there any research on the value of extra credit in the college mathematics classroom?

After teaching mathematics for a year, where in each class I had opportunities for my students to earn extra credit, I am reflecting on whether this has any value. The reason why I am questioning ...
15
votes
1answer
218 views

Reference request for studies on gender in math examples, homework problems, or math exams

I am looking for a study or reference on gender in math problems given in mathematics. In math texts or even on math exams, if there is a word problem involving people, these people or "characters" ...
2
votes
0answers
67 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 ...
19
votes
2answers
426 views

Literature on learning from errors in mathematics

In teaching undergraduate mathematics, I implemented some strategies to encourage the students to look at errors they made or at "typical errors" in the current topic. One attempt was to compile a ...
12
votes
1answer
223 views

How important is the act of writing his own script for the learning outcome?

There are several styles of delivering a lecture: The lecturer uses the blackboard and the students write their own lecture notes. The lecturer uses the blackboard and also provide a script so that ...
14
votes
3answers
234 views

Resource request: incorrect "proofs" for undergrads to correct/critique

I am teaching an intro to proof course for undergraduate math majors at a medium-sized american research university. I would like to provide my students with some incorrect proofs for the purpose of ...
13
votes
23answers
16k views

Examples of vocabulary that have different meanings in Mathematics compared to "everyday" English

I am asking this question here to obtain a nice reference list. I am asking for examples of words which have different connotations or meanings in Mathematics compared to English as taught in ...
18
votes
3answers
571 views

Evidence for or against the claim that some students are "algebra people" and others are "geometry people"

Where I live and work, there is a widely-accepted and often-repeated claim that there are two kinds of students: "algebra people" and "geometry people". This claim sometimes gets expressed in ...
12
votes
2answers
213 views

Do "overview" sections increase learning outcome?

I write a math textbook for which I want to make an overview chapter for each part of the textbook. In those overview chapters I want to motivate and introduce the new mathematical concepts. I also ...
3
votes
0answers
121 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 ...
12
votes
2answers
761 views

Physical vs. Virtual manipulatives in the high school classroom

I notice that geometry students frequently have difficulty with representations of 3-dimensional objects in 2 dimensions. Today, we worked with physical manipulatives in order to help visualize where ...
11
votes
4answers
900 views

Teaching algebra to visually impaired or blind students

I am currently writing an independent project investigating the teaching and learning of algebra for students with a visual impairment. I am struggling to find literature specifically about teaching ...
6
votes
3answers
210 views

References for graduate education

A search in Google returns lots of studies and thinkings about teaching in undergraduate schools. Could anybody come up with any research/references about teaching in graduate schools (graduate ...
8
votes
1answer
243 views

Educational styles for writing proofs

Can someone please point to research papers that analyze different ways of expressing informal proofs from an educational point of view? I am particularly interested in proofs by induction but I would ...
16
votes
1answer
1k views

The general and particular in the psychology of mathematics education

Many students I have spoken with who are drawn to becoming mathematics teachers chose their mathematics major because they enjoyed doing routine exercises in high school. The comfort of a definite and ...
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 ...
10
votes
2answers
278 views

How important is it to show students an application of the topics seen in an undergraduate course?

I am currently designing a proof-based Math course for my University. I already designed and ordered all of the theoretical content in the course and included some ad hoc exercises for practicing each ...
5
votes
0answers
54 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 ...
6
votes
2answers
293 views

Difference in difficulty between removing and adding structures?

In Fantasy math, Peter Saveliev remarks: Removing structures from consideration is hard; adding is much easier. Compare how you start with point-set topology -- by removing the geometry from the ...
7
votes
1answer
183 views

John Dewey and Educative Mathematical Experience

In John Dewey's Experience and Education, he proposes a qualitative measure for an experience (please simply understand this in common usage for the purposes of this question) to be educative. Namely, ...
8
votes
4answers
591 views

Elementary physics course for pure math student

Are there any mathematical departments which present the course "elementary physics" for pure math undergraduate students, separately? Is there a way to present this course with the most pure ...
10
votes
2answers
173 views

Could you suggest books, papers or problems that could be used as good "general" motivating examples of calculus application?

I would like to stress the kind of reference I am looking for: In statistics there are lots of motivating (and sometimes unexpected) examples that are interesting for everyone such as Birthday Problem,...
24
votes
7answers
5k views

When should we first teach variables in school math? And how?

From a pedagogical point of view, when is the "right" moment to introduce letters and variables to school children? Let's say we taught arithmetic, the four operations, did computation exercises, or ...
4
votes
0answers
76 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 ...
5
votes
1answer
102 views

Looking for a classic paper "Vinner and Hershkowitz"

I can't find this ZDM article: Vinner, S., & Hershkowitz, R. (1983). On concept formation in geometry. Zentralblatt für Didaktik der mathematik, 83(1), 20-25. Could you help me? I was ...
21
votes
7answers
2k views

Good examples of functions defined as definite integrals of elementary functions?

I am writing some Calculus content, and I would like a "big list" of useful functions which are defined by definite integrals, but are not elementary functions. Two examples of such functions are $$ ...
8
votes
2answers
224 views

Coverage of Fundamentals of Lines and Planes

I was helping a high school student with some fundamental concepts of planes and lines, when I realized I am rusty on some definitions myself. I found some minimal coverage in his high school math and ...
26
votes
2answers
1k views

Can students tell the difference between the "definition if" and the "theorem if"?

The word "if" is used in two meanings in mathematics: Definition. A topological space is compact if every open cover has a finite subcover. Theorem. A topological space is compact if it is ...
11
votes
1answer
1k views

Method for teaching factorization

A while back I stumbled on teacher's website that advocated a different way to teach factorization. Rather than jumping straight to factorization practice, the teacher first had their student's ...
11
votes
1answer
193 views

Has any research been done on the topic of "fact-based" versus "rule-based" understanding?

Consider the following piece of reasoning: $$x+3 = 5$$ $$x=5-3$$ Based on my own experience back in school, and helping people with their math homework, as well as in talking to other people about ...
9
votes
1answer
111 views

Is there an introductory book on linear algebra that makes use of simple concrete examples to teach the underlying theory?

I'm a third year philosophy student and considering pursuing an academic career. I'm comfortable with formal logic, set theory, and the calculations taught in high-school math. I've noticed that my ...
14
votes
1answer
330 views

Spiral learning in real analysis

Has there been any attempts at developing a curriculum for teaching analysis (here let us be narrow and say real analysis in the sense of rigorous integral and differential calculus) in a multipass, ...
7
votes
3answers
123 views

Looking for a reference for highschool level readers

I was wondering if there exists a book that talks to highschool level audience who wish to study pure mathematics for their undergraduate years. I'm not talking about problem solving kind of books (I'...
5
votes
1answer
221 views

Research on reciprocal teaching of mathematics?

Reciprocal teaching seems to have started as method of teaching how to read difficult texts (with respect to the level of the reader). Has reciprocal teaching been applied to teaching mathematics? Is ...
8
votes
2answers
201 views

Second Order Differential Equation Example Request

I am looking for some non-complicated second order differential equations to illustrate certain techniques for control engineering. It doesn’t matter if the differential equations are linear or non-...
7
votes
2answers
224 views

Are there more modern or computation oriented applications of complex analysis in science and engineering?

No doubt that complex analysis is a tremendously useful with plenty of applications in engineering and physics. Common raw applications of complex analysis includes: evaluation of ordinary and ...
10
votes
5answers
237 views

Lesson-planning: Teaching probability concepts via geometry

I am intending to teach a lesson covering some topic related to "Probability via Geometry" and, if possible, I would appreciate references or materials (or good ideas) that can help me. The target ...
15
votes
2answers
428 views

Logic in symbols or words

Making precise logical statements is an important part of teaching and learning mathematics. There are many ways to write such statements, and let me divide them into two main types1: writing in ...
6
votes
4answers
189 views

Recommendations for free, basic resource on discrete probability for a discrete structures class?

I'm teaching a course this fall on Discrete Structures for Computer Science. It's taught out of the math department but is a service course for the CS department with 90-95% of students being CS ...
14
votes
3answers
332 views

How to measure the understandability of a proof?

Is there a way to measure the understandability of a proof? From a search in the internet I have only found methods for measuring the understandability of software or tests for measuring the ...
6
votes
1answer
200 views

Resources for Pell's equation

What is the best way to introduce Pell’s equation on a first elementary number theory course? Are there any practical applications of Pell’s equation? What are the really interesting questions about ...