Questions tagged [mathematical-pedagogy]

for questions on general considerations and problems of teaching mathematics, i.e., issues specific to teaching mathematics yet relevant to various contexts and courses.

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19
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3answers
1k views

Should I teach Laplace Transforms? How much?

My question is in the title. Let me elaborate and give some context: I'm teaching a first differential equations course, essentially for engineers, at the university. I'm developing the syllabus ...
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3answers
506 views

In what ways can educators introduce polynomials in grades 7 to 9?

Q: Is there a way we can teach polynomials, avoiding the "watch me do it & now you do it" training method, that will allow students to anticipate and predict the existence or formulation of ...
10
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2answers
223 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 ...
11
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3answers
3k views

Tips to improve blackboard writing

During the internship I recently finished I came to realise how important it is to have a good and structured use of the blackboard when teaching mathematics to 12-14 year pupils. Circumstances forced ...
14
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4answers
507 views

Is there research for or against such an approach in teaching calculus?

Copying from Calculus Made Easy by Silvanus Thompson (2nd ed., 1914): CHAPTER I:TO DELIVER YOU FROM THE PRELIMINARY TERRORS The preliminary terror, which chokes off most fifth-form boys from ...
15
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1answer
204 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" ...
18
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0answers
1k views

Is metacognition ever bad?

Metacognition seems pretty universally positive. I'm wary of viewing it as such. Aside from the obvious criticisms like "you can't learn to ride a bicycle by thinking about and writing a 200 page ...
11
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3answers
643 views

Summary of the mechanism of reification

The concept of "reification" in mathematics education is interesting. Roughly, if I understand this correctly, one "reifies" processes into mathematical objects. Very recently, it occurred to me that ...
10
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4answers
2k views

Mathematical concepts and techniques that **pay off the most**? [closed]

There is a smart way of learning, and it consists in first finding out what are the most valuable pieces of knowledge to acquire. The ones that will give you the highest value for your investment in ...
7
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1answer
394 views

Polya's “Nearby Problem” Heuristic and Inquiry Based Learning

I've often wondered about the "devise a plan" part of Polya's "How to solve it" outline. What we call "problem solving" can be thought of as what to do when you have no idea what to do. From this ...
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3answers
230 views

Do iPhones help students in their math class?

While the question is stated with reference to the iPhone, my actual question is about phones in general. Just as there was much talk about the use of Computers in the classroom over the past fifty ...
5
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4answers
1k views

How are the basic trigonometric functions introduced to students?

The fundamental trigonometric functions $\sin(x)$ and $\cos(x)$ are used throughout the sciences, but I believe students are often introduced to a very limited initial understanding where it is ...
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13answers
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What books are like Knuth's Surreal Numbers?

I'm looking to find more examples of books which bridge the gap between "story" and "mathematics" using narrative and all those other wonderful features we might find in Harry Potter or some other ...
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2answers
1k views

What methods successfully identify and eliminate severe math anxiety?

What methods are effective in identifying and eliminating severe math anxiety, this most terrible and unfortunate part of modern mathematics education? This question is not about ordinary math anxiety ...
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2answers
139 views

How are geometric proofs related to geometric pictures?

When teaching geometry it is common to use pictures/figures to "show" the problem and its solution. It's also common to say things like "more than one figure can be shown which demonstrates the same ...
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5answers
811 views

What is a variable?

There are two kinds of answers I'm looking for: What do students think a variable is? What do YOU, the teacher, think a variable is? I'm also interested in why you think a variable is what you think ...
12
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3answers
225 views

Pedagogical Purpose in Making Students Do Problems in A Less Efficient Way First

Let's assume that a group of students need to learn to solve a certain type of mathematical problem for which there is two general methods of solving it, $X$ and $Y$. We also assume that $Y$ is more ...
9
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2answers
173 views

Rigor in secondary mathematics

If rigor doesn't mean more challenging problems, then what does it mean? There is a big push for rigor in common core mathematics, but I'm not sure exactly what rigor means (I'm pretty sure it has to ...
10
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2answers
532 views

Developing mathematical stories

In a comment on a recent post, Steven Gubkin pointed out that in doing mathematics he likes to develop stories. This motivation for mathematics is perhaps familiar to many practicing mathematicians. ...
7
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3answers
289 views

Should one justify formulae in middle school?

Consider two possible lesson outlines: Check homework. Show a visual demonstration for the area of a circle, e.g. https://tube.geogebra.org/student/m279 Calculate the area of a circle as an example. ...
15
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6answers
2k views

Are precise drawings important in geometry?

In Finnish middle school (yläkoulu) the students learn to measure distances and angles, draw geometric figures and do certain calculations (area, volume, surface measure, trigonometry). There are also ...
15
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0answers
150 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 ...
5
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1answer
149 views

In Text Exercises

For an undergraduate mathematics textbook, what are the pitfalls of inserting all of the exercises in the text? (As opposed to grouping every exercise at the end of the section). IMO I feel it is ...
13
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0answers
307 views

Was math education following a western trend?

After some research on the recent history of math education in the U.S., from the new math movement to the beginning of the 21st century, I understood that the historic flow of the math education ...
6
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2answers
289 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 ...
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3answers
1k views

Mathematical education slang

Amir Asghari recently asked a question about mathematical slang. He was "looking for "non-mathematical" terms or phrases that are used to refer to mathematical objects (of any kind) mainly for ...
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4answers
516 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 ...
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4answers
2k views

Why do students only see the last term of a sum abbreviated with an ellipsis?

It's very common in learning mathematical induction to prove statements like $$ 0^2+1^2+2^2+\cdots+n^2 = \frac{n(n+1)(2n+1)}{6}.$$ I've found that very frequently, on this sort of problem, when ...
24
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7answers
4k 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 ...
35
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23answers
6k views

Imbuing a six year old with a sense of mathematical wonder

My six year old started school a few months back and he's loving it. This first year is more about social skills than anything academic and I like that approach. But we're spending some time at home ...
10
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4answers
181 views

Specific examples (like elementary proofs,or simple problems) which appear rich in abstractions when observed through the lens of abstraction

I am looking for pedagogically motivated examples (like elementary proofs,or simple problems) of "abstraction in action" ? I am looking for good specific examples (pre-university level or first year ...
14
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3answers
632 views

How to use false theorems or proofs?

I would like students to be critical and not believe that every proof they see is correct. Lecturers make mistakes and students should not think: "That must be a valid argument/proof/syntax because it ...
12
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2answers
1k views

How early to start “abstract” math education, or, How to prevent smart kids from never getting exposed to math?

Everybody who is in graduate mathematics had a moment where they realized that mathematics was "their thing", and they decided to dedicate their academic career to it. I don't know of many people who ...
10
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1answer
236 views

When did the term and taught technique 'cross multiplication' enter into common use?

The title says it all, I suppose. I'm interested to know when/where the term/technique cross multiply came into use. Sources would be nice. In case it's unfamiliar to anyone, or in case the usage of ...
20
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12answers
2k views

What could be good non-mathematical analogies to explain the difference between the words theorem, proposition, lemma and corollaries?

What could be good non-mathematical analogy/analogies to explain the difference among the words - theorem, proposition, lemma and corollaries to high school students? I am looking for analogies that ...
15
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2answers
483 views

Students problems with reasoning, not exactly math

Consider the following problem: Maria always buys ice-cream when she goes to the beach. She bought ice-cream today. So, she must have gone to the beach. Obviously this statement is wrong. Maria ...
11
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2answers
390 views

What are your opinions of a flipped classroom at the secondary level?

Warning: a lot of this post borrows heavily from education theory. I'm in my student teaching semester right now, so a lot of what I explain is taken from research papers and things like that. So how ...
12
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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 ...
10
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1answer
216 views

How can I improve my concept map?

I've decided to create a concept map of a chapter I covered in a textbook, it's about basic set notation. What I want is suggestions on how to improve the presentation of the map. It seems quite ...
5
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0answers
103 views

Making co-ordinate geometry interesting for XI grade students

I am presently teaching eleventh grade (XI standard) students an introductory course in co-ordinate geometry with a focus on preparations for competitive exams. I have seen books like S.L.Loney's co-...
3
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1answer
107 views

Textbooks for mathematical/computing/physics teaching that are based on empirical research [closed]

I am looking for any (and all) books (on math, physics and Computer Science) that discuss how to teach and selects methods based on empirical research and solid evidence. My biggest interest right now ...
14
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1answer
251 views

Impact of philosophy of mathematics upon effectiveness of instructor

Is there any research out there on how an instructor's philosophical beliefs about mathematics might affect some aspect of his or her impact as a teacher? My intended meaning of 'impact' is broad, ...
24
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6answers
724 views

Too much motivation?

This is something that I felt like was difficult for me in some classes, especially lower division differential equations and linear algebra classes. I know professors want to motivate certain topics ...
8
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2answers
189 views

Can a constructivist learning model be applied to online lower division math courses?

I'm using the word constructivist as it is used in this paper, not in the sense used in logic. The abstract should be sufficient to understand at least roughly what the model is. The important part, ...
9
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4answers
294 views

Teaching mathematics and its charms to non-mathematicians

I am teaching English in Japan and I have a student who speaks English well, and to keep up his level, in our weekly lessons would like to learn some subjects related to my degree in mathematics. I ...
3
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1answer
364 views

What are sources for non-routine problems involving quadratic functions (in one variable)?

I'm planning to get some sources which explain beautiful problems about quadratic function. I know that there are another kind of functions, but the quadratic function has different applications in ...
8
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1answer
452 views

Tips for teaching A-level Maths/Further Maths students

I recently withdrew from a maths PhD to focus on other career options, and one of them that I'm very keen on is mathematics teaching. I applied for a college A-level maths lecturer role (teaching ...
15
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2answers
415 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 ...
10
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3answers
474 views

How many problems do we have to do as undergraduate mathematicians in order to learn a subject?

I'm wondering how many problems are needed in order to learn a subject, let's say Calculus of Several Variables. We know that the professors often assign us a list of problems to solve as homework, ...
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0answers
66 views

How many problems do we have to do as undergraduate mathematicians in order to learn a subject? [duplicate]

I'm wondering how many problems are needed in order to learn a subject, let's say Calculus of Several Variables. We know that the professors often assign us a list of problems to solve as homework, ...

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