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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14
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5answers
602 views

How to get through the boring stuff?

It frequently happens that there's some material I have to cover which is, frankly, boring. The subject itself may be boring, or it may be the particular exercises, but in any case I have to get ...
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2answers
401 views

Common Core Question: What is included and excluded in high school mathematics?

I took pre-calculus in high school, and I did not get to learn about matrices, and conic sections, vectors law of sines and cosines, and etc. I took geometry as well and found that matrices were also ...
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3answers
258 views

Monty Hall challenge

Thinking about the counterintuitive Monty Hall Problem (stick or switch?), revisited in this ME question, I thought I would issue a challenge: Give in one (perhaps long) sentence a convincing ...
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1answer
643 views

Is the current education system as bad as most critics and famous pure mathematicians try to convey? [closed]

Throughout elementary, middle and high school mathematics is quite merely about memorizing concepts and formulas, understanding the theorems (without their proofs) and applying acquired knowledge in ...
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7answers
4k views

A Lexicon of Math Mistakes

Neil Postman wrote an interesting (and freely available) article called "The Educationist as Painkiller." I highly recommend you read the article for your own enjoyment and as a background to this ...
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3answers
420 views

Calculation versus writing in mathematics

Writing mathematics is an important activity of the mathematician. In trying to write one's mathematics, one finds ways to balance intuition and rigor and to efficiently communicate concepts and ideas ...
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3answers
1k views

Group theory for high schoolers, want the opinion of other educators

So I am going to be teaching the basics of group theory to high schoolers in a few weeks, and I want to hear what the Stack Exchange network has to say on the matter. What are the applications and ...
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2answers
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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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0answers
197 views

How is cooperative learning being used in vector calculus, and what are the origins of this work?

I'm doing some research about cooperative learning in vector calculus. It seems like what cooperative learning in calculus is referred to varies over time. In 1987, there was an MAA book, Calculus ...
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3answers
491 views

Immersive attention when learning mathematics

In Jennifer Roberts' article The Power of Patience: Teaching students the value of deceleration and immersive attention she talks about intentionally slowing down to contemplate deeply a work of art. ...
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3answers
467 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 ...
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4answers
652 views

Complex analysis (Applied versus pure)

I am studying Electrical Engineering and I want to specialize in signal processing. However, I have to study complex analysis first (I am an undergraduate, so I lack some terminology). In your opinion:...
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3answers
515 views

A good antonym for reducing/simplifying equivalent fractions

I am looking for a good antonym for reducing/simplifying equivalent fractions: 'reduce' and 'simplify' both make sense to me when dividing, but I'm struggling to name what it is we do when we multiply ...
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2answers
221 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 ...
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1answer
198 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" ...
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3answers
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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 ...
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0answers
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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 ...
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1answer
387 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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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 ...
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6answers
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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 ...
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4answers
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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 ...
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3answers
229 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 ...
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5answers
736 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 ...
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14answers
8k views

Justifications for: Why learn mathematics?

I wonder how you teachers walk the line between justifying mathematics because of its many—and sometimes surprising—applications, and justifying it as the study of one of the great ...
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3answers
281 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. ...
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3answers
222 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 ...
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1answer
544 views

Is there a Piagetian age at which proofs can be comprehended?

I am wondering if there is literature on the developmental age (pre-adolescent?, adolescent?) at which the notion of a "proof" can be understood? I am less interested in mathematical proofs and more ...
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2answers
168 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 ...
5
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1answer
141 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 ...
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0answers
144 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 ...
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0answers
302 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 ...
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2answers
412 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 ...
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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 ...
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8answers
3k views

Helping a reluctant 12 year old

How can I help my 12 year old daughter strengthen her math skills? My strategy up until a year or so ago had been relaxed. I subscribe to the idea that the best motivation for learning is the ...
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4answers
177 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 ...
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5answers
1k views

Cost and benefits of compartmentalization in k-12 curriculum

This is a soft question perhaps not well suited for the format of the site but I'm interested to hear opinions from this community on this topic. K-12 mathematics textbooks (understandably) divide ...
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3answers
616 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 ...
9
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1answer
220 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 ...
14
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2answers
479 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 ...
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2answers
382 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 ...
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2answers
311 views

Placement tests for middle school math

Our district has changed its approach to placing students in grades 6 and 7 math classes. Students considered for placement above grade level must now take a test composed of problems drawn from the ...
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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 ...
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6answers
954 views

How to present $\Bbb Z/n\Bbb Z$ to highschool level audience

I have the oportunity to talk to a highschool class about mathematics, the topic I got to present are the integers modulo $n$, ie, $\Bbb Z/n\Bbb Z$ , however I don't want to be very heavy and formal, ...
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1answer
212 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 ...
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8answers
2k views

What things should one know in order to enjoy their undergraduate degree?

From looking at undergraduate mathematics programmes it's quite apparent that mathematics degrees are demanding, one could even say the work load is gruelling. However I'm certain that there are ...
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0answers
90 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-...
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4answers
3k views

Traditional “long” method of multiplication versus grid and partial products — evidence of better outcomes?

I'm not a math teacher but am actively involved in teaching my children mathematics (elementary age). I learned the traditional "long" approach to multiplication, but the school systems now emphasize ...
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4answers
293 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 ...
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4answers
238 views

Using original texts while introducing new concepts in class

I'm still a undergrad math student, and my experience in education in math is very limited, however I've been lucky enough to meet teachers that encourage students who are interested in teaching, like ...
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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 ...

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