All Questions

7
votes
1answer
141 views

Best practices in teaching math to future elementary teachers

This question is about references in current best practices in teaching math to future elementary teachers at a university level. I am asking it because I do not see any question so far on this site ...
6
votes
2answers
128 views

Studies about group tutoring sessions

I’m not sure if this question belongs here, so I apologize if it doesn’t. I work in a tutoring center at my university where we tutor every subject. Mathematics is in high demand, and occasionally my ...
5
votes
2answers
123 views

Published papers for Intro Stat students to read

I am looking for studies and experiments in the literature that I can share with undergraduate students in an intro statistics course. I do not expect students to understand everything, and I plan to ...
7
votes
3answers
177 views

Resources on solving systems of polynomial equations in multivariable calculus setting

Whenever I teach multivariable calculus I find students really struggle with both finding critical points and the method of Lagrange multipliers. I think that the reason is the same: solving systems ...
13
votes
4answers
275 views

Pedagogical advice/articles for graduate student teaching assistants

Are there any good pedagogical resources or articles that you would recommend to math graduate student teaching assistants (TAs)? Is there any sweeping advice that you would give a TA to improve their ...
4
votes
0answers
108 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, ...
12
votes
3answers
151 views

Tasks that encourage argumentation

I am looking for resources that have tasks such as the one below that encourage argumentation. I want tasks that 8th graders could do but would also be appropriate for high school students. I want to ...
2
votes
0answers
194 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 ...
8
votes
0answers
91 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
votes
5answers
435 views

Math for Social justice curriculum

Recently, a friend of mine who plans to work as a "social-impact consultant" (she is currently a College senior with a background in intro statistics) requested that I offer some kind of curriculum ...
9
votes
0answers
100 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 ...
10
votes
2answers
454 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 ...
19
votes
2answers
717 views

Should we “program” calculus students, like the physicists seem to want us to?

If it is true that we first learn formalism...how to do things that we don't understand, should we regard teaching students mathematics as programming dumb machines with formal rules (to the greatest ...
4
votes
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
votes
2answers
416 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 ...
5
votes
0answers
159 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
votes
4answers
685 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 ...
11
votes
2answers
260 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 ...
10
votes
2answers
205 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 ...
12
votes
1answer
199 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
votes
3answers
215 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 ...
8
votes
1answer
214 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 ...
9
votes
0answers
183 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 ...
8
votes
4answers
381 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 ...
19
votes
2answers
749 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 ...
7
votes
3answers
119 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'...
6
votes
2answers
167 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-...
15
votes
2answers
397 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
3answers
172 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 ...
5
votes
3answers
924 views

Honors project idea for linear algebra

At my institution there is an Honors program which encourages (or requires) students to petition classes for Honors. Basically, what this amounts to is the student has to write a 10 page (not set in ...
13
votes
5answers
384 views

Hands on activities for a college history of mathematics course

I will be teaching a course in history of mathematics to juniors/seniors who are math and math education majors, many future school teachers. It should include highlights from antiquity to early 19-th ...
20
votes
3answers
947 views

Which universities teach true infinitesimal calculus?

My colleague and I are currently teaching "true infinitesimal calculus" (TIC), in the sense of calculus with infinitesimals, to a class of about 120 freshmen at our university, based on the book by ...
12
votes
2answers
235 views

Resources on how to mark a maths exam

I am looking for some resources which tells someone how to mark a (1st year undergraduate level) maths exam paper. Ideally it would cover the basic stuff, like making an error at the top doesn't ...
10
votes
1answer
177 views

Can we motivate undergraduates by saying they will be able to read famous papers?

I have a differential equations student who said the following (I'm paraphrasing of course): A long time ago, my math teacher told me that when I finished differential equations, I would be able to ...
5
votes
5answers
3k views

Extremely “hard” books (or handouts) for undergrad studies

Can you suggest me some REALLY hard books on calculus and analysis. By hard I don't mean difficult in explanations, but with extremely challenging exercises (all worked out if possible) and useful ...
4
votes
2answers
93 views

Looking for an online mathematics practice resource

Forgive me if this is off topic, but I've been looking for an online resource that I can use to polish up and improve my math skills. I've looked at math.com and purplemath.com but they don't have ...
16
votes
4answers
484 views

Becoming a better instructor: where to start?

I just finished a PhD in math at a top department, but not one that placed much emphasis on graduate student teaching. Grad students here teach only as TAs, and the training is minimal. I got great ...
5
votes
1answer
129 views

Empirical papers on “interactive engagement” in calculus education?

I was discussing this with a colleague, who showed some papers on "interactive engagement" in physics education. Another keyword there was "force concept inventory", and the realted (newer) "calculus ...
10
votes
1answer
341 views

Alternative remedial courses before calculus

I have seen remedial courses before a first undergraduate calculus course that consist of a mix of algebra, trigonometry and coordinate geometry. However, have there been any experiments with remedial ...
8
votes
0answers
186 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
4answers
410 views

Examples of Research Level Math Discoveries Done by Undergraduate Students

A good way for motivating young students in undergraduate level is telling them that you can do great works! Question. What are good examples of research level mathematical discoveries done by ...
10
votes
6answers
180 views

Books/(auto)biographies/references on how mathematicians study/studied (as students)?

As Geoff Pointer commented: [...] As a composer I've learnt a lot from studying famous composers why wouldn't that also apply to studying maths and mathematicians of note as well? [...] Are there ...