Questions tagged [education-research]

Questions about education research are related to the various social scientific research work being done in areas related to mathematics education.

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67
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11answers
8k views

Whence the “everything is linear” phenomenon, and what can we do about it?

$$ \color{red}{(a+b)^2 = a^2+b^2}$$ $$ \color{red}{\sqrt{x^4+y^4} = x^2+y^2} $$ $$ \color{red}{e^{t^2+C} = e^{t^2}+e^C}$$ I've observed this phenomenon -- wherein, implicitly, students say, "...
38
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2answers
2k views

What does math education research know about difficulty vs. effectiveness?

I've asked basically the same question previously on on math.SE, then cogsci.SE without much response, surely here is the place to ask this. As anecdotal evidence is plentiful, but unfortunately ...
29
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3answers
510 views

What Math(s) Ed literature is accessible to the working math(s) educator?

This site is - as far as I'm aware - for what I would term working maths educators. That is, on the whole the users of this site are not researchers in mathematics education. Rather, we are the ...
22
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4answers
666 views

“Calculators are so twentieth century.”

Even though I studied maths, I became familiar with programming in my junior year at university. I'm indebted to the professor who encouraged me in that pursuit, as it provided me with an avenue not ...
19
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4answers
2k views

Is algebra really the gatekeeper to higher math, or is it multiplicative reasoning?

The National Mathematics Advisory Panel final report states that algebra is the gateway to higher math, to a college degree, and higher earnings from employment. It also states that success in algebra ...
18
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5answers
9k views

Learning Mathematics with the aid of spaced repetition systems

I am currently self-studying, so I learn using a textbook which I work through in a linear fashion. As I am introduced to new concepts I ask myself questions and I attempt to answer these questions ...
18
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4answers
546 views

“Function” vs “Function of …”: how much does it contribute to students difficulties?

Most textbooks I've seen (and teachers I've met, myself included) are rather careless about the distinction between variables and functions. For example, when we write $y=f(x)$ we all know that $f$ ...
17
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5answers
633 views

How can I retain the mathematics that I've supposedly learnt?

First off sorry if this question isn't suited to matheducators.stackexchange I just thought here would be a good place to ask seeing as you would probably have experience with students. Anyway here is ...
17
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1answer
985 views

Reason behind the dominance of particular countries in the IMO (International Mathematical Olympiad)

I was watching the result of IMO 2014 where I found that China was on Top and USA, Russia were following China. This is not the exceptional case, you can pick the results of each IMO in some of the ...
16
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5answers
801 views

Discovery-based and inquiry-based learning

In general, I think (and I am told by students) that I am good as a tutor. However, I would like to become more rigorously familiar with the discovery-based and inquiry-based learning applied to ...
16
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4answers
357 views

How can a research mathematician transition into a mathematics education researcher?

Mathematics education research is generally very different than mathematics research. I am interested in collaborating with mathematics education professors at my next institution, and possibly ...
16
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1answer
497 views

Research supporting “recipe-style” calculus in senior high school?

Anecdotally, I've heard it said that in (Australian) grades 11 and 12 calculus needs to be taught in a procedural way involving merely recipes for doing calculus, rather than teaching for ...
14
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5answers
544 views

When is it a good idea to avoid talking about why something works?

I am teaching, among other things, a college algebra course this semester. In this course we do a lot of conceptual things but we also do some techniques to prepare students for calculus. One of the ...
14
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2answers
495 views

Is there any research on the correlation between a professor's research ability and their ability to teach graduate level courses?

In most universities that I am aware of, graduate courses in Mathematics are taught almost exclusively by research mathematicians. My question has two parts: What is the justification for this ...
14
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2answers
326 views

Is there a framework to study the mathematical competence in problem-posing?

I've read some articles about it and those papers show us that there are some facts to understand the mathematical competence in problem-posing. Besides that, those investigations show that there are ...
13
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6answers
592 views

How to think mathematically?

Later this year, high school teachers from the region will visit our university for a day and be given special lectures on different topics. I've been asked to give a talk with the title "How to ...
13
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2answers
335 views

Research on how mathematics skills transfer to other areas

Briefly: I am looking for research on the extent to which learning mathematics (let's say "college algebra" if we want to be specific) impacts problem solving skills, abstract reasoning, etc. Less ...
13
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3answers
3k views

What research is there on the effectiveness of multiple choice questions for summative assessment?

This is perhaps the question that some thought Grading scale: how to handle multiple choice questions with different number of choices really was. I'm of the opinion that multiple choice questions ...
12
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3answers
186 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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2answers
273 views

Effectiveness of proofs in secondary education

I'll have a department meeting in about 10 days and I want to bring the subject of proofs up. While most teachers do proofs in the blackboard, I want to argue that we should put problems to prove in ...
12
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3answers
5k views

What math courses should be taught to undergrad electrical engineers: a 40 years update

I was browsing IEEE xplore the other day and found this gem called "What Mathematics Courses Should an Electrical Engineer Take? A Report on the National Study of Mathematics Requirements for ...
12
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2answers
354 views

Mathematics and the hermeneutic circle

Many students, teachers and parents view problems as confrontational. Many students develop a self concept in mathematics based on failed attempts to easily win such confrontations. This leads me to ...
11
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4answers
787 views

What does the research say about direct instruction vs. student centered approaches

I have heard contradicting views that both parties say are research based. Specifically, I am looking for research on which teaching methods (direct instruction or student centered approaches) are ...
11
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2answers
729 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 ...
11
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4answers
827 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 ...
11
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1answer
330 views

Typical rate of success in junior or senior level math courses at US universities

I am curious, if we define success or failure by grades earned, or pass-rate (pass meaning the student does not need to retake the course) then what is the typical pass rate for students in upper ...
11
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2answers
415 views

Does playing tournament chess result in high-level mathematical gains, and not merely a skill whose benefits can be gained through any other activity?

https://chess.stackexchange.com/questions/5199/does-playing-tournament-chess-help-one-in-the-field-of-chess-related-math I often wonder whether the visualization of the various types of chess-related ...
10
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4answers
1k views

Different Teaching Styles for Different Genders?

I was recently looking through job listings in my local area (US high school, ages 14-18) and I found two boarding schools with vacancies, one was male-only and the other was female-only. This got me ...
10
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4answers
603 views

Creativity in mathematics

I have recently been engaging more and more with my creative side by drawing, writing, and (trying to) playing piano. I have come to see mathematics as much more of a creative field of study than I ...
10
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1answer
267 views

Is there a literature database like MathSciNet for Mathematics Education?

Is there a literature database like MathSciNet for mathematics education?
10
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2answers
1k views

What is the difference between “numeracy” and “number sense”?

Is there a difference between numeracy and number sense, or are they synonymous? In my language they are often both translated to the same word (tallforståelse). I'm thinking that perhaps numeracy ...
10
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2answers
622 views

“Good” and “Bad” student intuitions when teaching and learning mathematics

I'm a college math/science tutor and I'm really interested in STEM education. I'm currently starting work on a project I hope to present in a couple of months at a tutoring conference and I was ...
10
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1answer
161 views

Rewards based educaton

How important are rewards - read marks/grades - for students in education? Can the thirst for grades/marks be replaced by a desire for learning? Context Problems are at the heart of mathematics ...
9
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1answer
435 views

Studies which compare students with and without math training

I am looking for studies which compare students who did not receive mathematical education beyond basic mathematics and those that learned maths upto introductory calculus, with the assumption that ...
9
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6answers
513 views

Book recommendations on mathematics education focusing on geometry

I will be teaching Euclidean geometry to future teachers, and I am feeling a bit lost (I know geometry, but I am not that familiar with mathematics education). Is there some recent (as concise as ...
9
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1answer
159 views

Adult Learners Returning to College Level Math

I am currently reflecting two educational experiences that have made me question if there's research around this particular topic. 1) A few years ago, I was an adjunct instructor for a Trigonometry ...
9
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1answer
166 views

Experimental results about the variability of grades on a math exam

"[Myth] that exams are objectively graded. Daniel Stark and Edward Elliot sent two English essays to 200 high school teachers for grading. They got back 142 grades. For one paper, the grades ranged ...
9
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0answers
84 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
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0answers
111 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 ...
8
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2answers
242 views

Math Education for Students who use Right-to-Left Written Languages

Does anyone know of any studies or have personal experience dealing with difficulties (if any) faced by students studying mathematics if they come from countries which use languages written from right-...
8
votes
1answer
154 views

What are some best practices for creating student groups?

I came across Small-group composition and peer effects (Wilkinson & Fung, 2002) which got me thinking about the pros and cons of grouping students based on ability levels. When is it a good idea ...
8
votes
1answer
107 views

Where can I publish on an undergraduate course that I helped develop and teach?

I co-developed and co-taught an interdisciplinary course with several colleagues from several departments for junior/senior college students. This was a very interesting experience, and I am wondering ...
8
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0answers
78 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 ...
7
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7answers
2k views

Teaching Calculus I to engineers

I am in a research project where one of our jobs is improving the first year university experience for our students. One of the topics we are looking into is changing the way we teach our introductory ...
7
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3answers
185 views

References on British, German and French educational system

I'm writing a comparative study between mathematical teaching in my country (which sucks by the way) with others. However, I don't want to make it about today, globalization gives us a good notion of ...
7
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2answers
178 views

Should basic exercises be solved before formulas are introduced?

I was watching (as a fellow teacher) a lecture on arithmetic progression. It so happened that a formula was rapidly introduced and used. The formula was $a_i = a_1 + (i-1)r$ (I trust the terms ...
7
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0answers
83 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 ...
6
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4answers
5k views

Should we finish algebra before starting geometry?

Comparing an old french mathematics book for grade 9 and a new one, one obvious difference is the ordering of the chapters. In the old book, all the algebra chapters are grouped together then all the ...
6
votes
4answers
347 views

Is the education system in Finland particularly good?

Inspired by this question: What makes education in Finland so good? Finland has marketed itself as a top country in education. Indeed, at some time, the Pisa results in Finland were quite good. ...
6
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3answers
250 views

How to overcome the frustration in teaching and doing research at the same time

I understand that this website is designated particularly for teaching-related topics. However as many of us do agree that being a lecturer, we are supposed to run both teaching and research duties at ...