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Questions tagged [mathematical-pedagogy]

For questions on general considerations and problems of teaching mathematics, such as issues specific to teaching mathematics that are relevant in various contexts or courses.

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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 ...
Willie Wong's user avatar
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13 votes
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What studies exist, comparing the efficacy of exercise sheets with or without worked solutions?

I've been tutoring mathematics at university level for over 10 years, and one of the more common requests from students is worked solutions for sheets of exercises. Most educators I've worked with ...
Theo Bendit's user avatar
13 votes
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512 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 ...
Henrique Augusto Souza's user avatar
12 votes
0 answers
349 views

Books on meta-cognition that would be relevant for those involved in mathematics?

In 1992 Schoenfeld wrote an excellent "review" of (among other things) metacognition as it applies to mathematics: whether from the perspective of a student, or a teacher. Metacognition, as quoted ...
bzm3r's user avatar
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8 votes
0 answers
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3-D printing of formulas encoded in LaTex for the visually impaired?

There is software available on the Net for 3-D printing of math expressions encoded in LaTex. What such technology is available off-the-shelf for the visually impaired to learn mathematics? And, ...
Tom Copeland's user avatar
6 votes
0 answers
114 views

Maximize retention

I tutor high school math students. Students often struggle with a problem they had completed few months prior. Like any skill, it's natural to forget what you learned after a while. As high school ...
okzoomer's user avatar
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6 votes
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89 views

Long-form, multi-step, skills-integrating applied mathematics problems in calculus I, II, III

When recently teaching Calculus II to college students, I instructed my students to read and be ready to work through the first 8 or so questions of James Walsh's climate modeling differential ...
Sinister Cutlass's user avatar
6 votes
0 answers
147 views

Flow diagrams and summarizing strategies in proof-computation courses: good or bad for learning? Unsuitable for Inquiry-based learning?

For concreteness lets keep our discussion to calculus courses where there is a balance of proof and computations (computing limits but also doing epsilon-delta proofs) I can understand that in more ...
Thomas Kojar's user avatar
6 votes
0 answers
314 views

Links between mathematical folklore and educational success

I would like to ask if, in the research field of mathematical education, some work has been done to investigate the relationship between 1) and 2): mathematical education and student motivation the ...
Dal's user avatar
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6 votes
0 answers
207 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 ...
James S.'s user avatar
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5 votes
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128 views

Is it possible to learn some basic mathematics using an app?

I am interested in developing an app for students that are starting a grade career involving mathematics. It is a real problem that they start with almost no knowgladge of basic mathematics and there ...
Paula Cardoso's user avatar
5 votes
0 answers
348 views

Word problems written in past tense, present tense, or future tense

Does anyone have extensive classroom experience regarding the best verb tense to use when writing word problems at an elementary or middle school level? I have been writing some lessons recently and I ...
Ari's user avatar
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5 votes
0 answers
99 views

Objectives for group work in undergraduate pure maths

Whether we are preparing undergraduates for research in industry or academia effective collaboration is an important higher skill. I think there are two aspects to this in mathematics - thinking ...
Cong Chen's user avatar
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5 votes
0 answers
186 views

Is there a name for 'simple' two-input-one-output word problems?

Andy has 4 apples, and then eats 2. How many does he have left? Beth drives for 3 hours at 80 km/h. How far did she go? Carl, Debbie and Earl earned $30 together shoveling driveways. How much does ...
NiloCK's user avatar
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4 votes
0 answers
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Activities that encourage students to create or evaluate mathematical notations

I'm looking for references about activities that encourage elementary school students to create or evaluate mathematical notations. do you know any?
Humberto José Bortolossi's user avatar
4 votes
0 answers
168 views

Studies on the change in effectiveness of pedagogical practices over time

Are there any studies that have investigated this question? Why certain pedagogical practices that used to be effective up to a few years ago, may suddenly become less or even no longer effective? I ...
Mahdi Majidi-Zolbanin's user avatar
4 votes
0 answers
210 views

When dealing with sequences, should we teach students to start at 0 or 1?

The reason I prefer starting at 0 is due to a computer science background and also, I think it helps to start at 0 because there are certain reasons that demand it (in particular, combinatorics) and I ...
Lenny's user avatar
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4 votes
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What are your experiences with Buck’s Advanced Calculus?

I stumbled across the book when searching for rigorous alternatives to Rudin with some solutions. It’s an “old school” (1965) calculus text but, I think, covers similar material to Rudin in a more ...
akm's user avatar
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4 votes
0 answers
188 views

Mathematics Self-Efficacy Questionnaire

Good Day! I need help in finding a free validated and reliable tool in assessing (elementary or high school) students' Mathematics Self-Efficacy.
AYA's user avatar
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4 votes
0 answers
114 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-...
Spai's user avatar
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2 votes
0 answers
128 views

"Tools" (literarily) for solving linear or quadratic equations

Since a few weeks, I teach as a tutor (not from that school) a support course in a German 9/10 class. I quickly noticed a horrible lack of basics. (Partly based on just different names - I had to ...
Hauke Reddmann's user avatar
2 votes
0 answers
321 views

Which areas of maths should underperforming western countries focus on?

I am not sure which StackExchange to ask this question but I am interested in the relative underperformance of Western countries such as Australia, US, UK compared to other higher performing countries ...
Poidah's user avatar
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2 votes
0 answers
92 views

Math websites/apps for high school students

I am undergraduate math student who is interested in being a high school math teacher. I have been given an assignment to present to my class (for a total of about 20 minutes) a teaching tool or a ...
AfronPie's user avatar
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2 votes
0 answers
91 views

Teaching aid for online mathematics course

Crossposting from the math.stackexchange (Question) Online classes will start again as the semester will start, I bought an XP-Pen deco 03 to help me with online teaching. I will be teaching ...
mukhujje's user avatar
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2 votes
0 answers
218 views

why don't we do labs in/for math?

(this is in the US and at a high school level) why don't we dedicate a day of the week each week to do a lab for math for exploration? I mean we already do that for Earth Science, Physics, Chemistry ...
Lenny's user avatar
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2 votes
0 answers
209 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 ...
David Roberts's user avatar
2 votes
0 answers
99 views

what is the standard subdivision or classification of calculus related rates problems?

I am working on a project where I have to group/classify calculus problems. Now with most the calculus topics, it's usually obvious how it's divided in various textbooks, but when it comes to related ...
K. Ali's user avatar
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1 vote
0 answers
113 views

Book or curriculum for teaching base-16 numeral system to elementary, middle, or high school children?

In 1862, John W. Nystrom promoted the base-16 (hexadecimal) number system, which he called the "tonal system": Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed to ...
Geremia's user avatar
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1 vote
0 answers
141 views

When Interpreting "If A, then B" as "A coupled with B" is rational?

It is known that the meaning of a conditional statement in fuzzy logic can vary depending on the interpretation and context. As we know, some ones interpret "if A, then B" as "A coupled ...
hasanghaforian's user avatar
1 vote
0 answers
176 views

What to cover on a first ordinary differential equations module?

I will have to teach a first course in differential equations. What should I cover in this module? For example, in most books, have Laplace Transforms which is fine but I would not use LT to solve ...
matqkks's user avatar
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1 vote
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419 views

Is it more efficacious, productive to jump to perusing full solutions — before and without attempting to solve problems?

Too many students lack the luxuries of time and effort to mull exercises and problems. They must juggle MULTIPLE jobs to pay exorbitant tuition fees. Single parents or adult learners must prioritize ...
user avatar
1 vote
0 answers
214 views

Do you avoid examples or test questions that showcase an algorithmic plug'n'chug approach?

If we accept that there's not much learning from doing the "same" questions, like find the derivative of $x^2$, and $x^3$, and $x^4$ due to the algorithmic way of how it's done, then what ...
user avatar
0 votes
0 answers
65 views

Resources to introduce Modular arithmetic

We have Clock arithmetic in grades 5 , 6 and thereafter nothing related to the Modular arithmetic is taught until students enter to the universities. Since this is very important topic in Number ...
Janaka Rodrigo's user avatar
0 votes
0 answers
76 views

Engaging in a puzzle without a guidance of a leader while simultaneously being a component of that puzzle

I have done couple of activities and experienced how interestingly students are engaging. At the end I explained the Mathematical concepts related to the activities. Here I'm suggesting two of those, ...
Janaka Rodrigo's user avatar
0 votes
0 answers
822 views

Prerequisites to study Laplace Transform completely?

Hello to all the professors who read this. I'm an electrical engineering undergrad student. I wanted to ask for advice on what I should learn beforehand to fully grasp the Laplace transform. I also ...
CalebWilliamsUIC's user avatar
-2 votes
1 answer
63 views

Relational understanding for a specific topic

I want to aproach the undertanding of the trigonometric function based on the concept of relacional undertanding, but I have problems to came up with and problemic situation for it. I mean I don´t ...
George's user avatar
  • 101
-3 votes
2 answers
152 views

Best natural language(s) for conveying, conceptualizing, teaching, understanding, and learning Probabilistic & Statistical concepts & theory?

English can be precise but it is rather 'flowery' and easily gets in its' own way. East-Asian natural languages like Mandarin, Cantonese, Korean, and Japanese are notorious for permitting the ...
NoYouNaiveBaye's user avatar