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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2
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1answer
49 views

GRE Geometry Reference Request?

My brother is taking the normal GRE (not the math subject test), and I need to help him learn geometry. I know basic geometry myself, but I need a book that will present it well and will have good ...
4
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1answer
66 views

Research on the effects of simulation and interactive visualization

Are there any existing research on the effectiveness of computer simulation and/or interactive visualization for the learning of mathematical concepts? I ask because: There has been some efforts in ...
19
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2answers
421 views

Separating the roles of “teacher” and “assessor”

Teachers at the university level (at least what I've seen in the US) are responsible for both teaching students the material for a course, and assessing the students' understanding of the course ...
13
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3answers
763 views

Does the “how old is the shepherd” phenomenon occur for more relatable word problems?

A friend of mine just showed me this article about the "how old is the shepherd" problem: Link Of course, I'm shocked by the finding that 75 percent of kids give an answer other than "there isn't ...
6
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0answers
79 views

References for persistence of grades [closed]

I've recently been challenged on my proposal that a reasonable way to estimate a student's future GPA is to look at his/her current GPA. I am looking for any papers that study the correlation of ...
8
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2answers
141 views

Journals that feature challenge problems for high school students?

I'm interested in journals that present challenging problems for high school students and take answer submissions. I coach some talented high school students and would like to encourage them to ...
6
votes
0answers
45 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 ...
5
votes
0answers
160 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 ...
10
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4answers
748 views

Is there any advantage of plotting graphs using traditional paper and pencil method?

Why don't we discard the traditional pencil and paper method of graph plotting in high schools and for freshers at colleges since there are many electronic devices doing the graphing? And please where ...
21
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2answers
2k views

Gender and groupwork

What does current evidence suggest: doing group work in mixed/balanced gender groups or doing group work in single gender groups? Setting College level mathematics/science course Group size ...
11
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2answers
269 views

Importance of exercises for learning mathematics

For me it seem to be obvious that exercises and exercise courses are important for undergraduates to learn mathematics and skills like finding a proof or writing it down. Was there any research ...
7
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1answer
153 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
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1answer
104 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
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1answer
603 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
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3answers
170 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
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4answers
304 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 ...
7
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6answers
292 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
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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
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1answer
136 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
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2answers
171 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
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2answers
215 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
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1answer
183 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
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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 ...
16
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2answers
271 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
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1answer
200 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 ...
13
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3answers
217 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 ...
10
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20answers
6k 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 ...
16
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3answers
395 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
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2answers
197 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
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 ...
11
votes
2answers
640 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
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3answers
612 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 ...
7
votes
3answers
191 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
215 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 ...
15
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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 ...
13
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0answers
129 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
250 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
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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 ...
6
votes
2answers
268 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 ...
6
votes
1answer
126 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
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4answers
386 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
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2answers
165 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,...
22
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7answers
3k 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
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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 ...
5
votes
1answer
79 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 ...
20
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7answers
1k 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
197 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 ...
19
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2answers
807 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
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1answer
713 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
163 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 ...