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13 votes
6 answers
3k views

A visualization for the quotient rule

Context: first year didactics of mathematics course for middle school teacher students (in Norway). I have a reasonable visualization for the product rule of derivatives: Consider a rectangle with ...
0 votes
0 answers
51 views

Wanting explore mathematics [closed]

Hi everyone I am student. Since few months I am using discord to improve my mathematics understanding. It helps a lot so I am here to ask I know there are many good discord servers but I don't why I ...
0 votes
0 answers
28 views

Assigning a semi-independent project for current math I students to learn a topic in Math II overlap with math I, and teach a math II class, how to?

How can I foster a growth mindset and sense of belonging to the intellectual realm among Algebra II students by having them undertake a semi-independent project where they learn to teach an ...
4 votes
2 answers
212 views

The easy and the hard problems involving independent events

In probability, two events are independent if the incidence of one event does not affect the probability of the other event. Math textbooks often have a problem checking if two events are independent ...
1 vote
5 answers
288 views

Truth tables. What does a truth valuation of a formula even mean?

What does a truth table even mean? Does anyone actually spell it out anywhere? (reference please). People feel like the are not taught rigorously like limits are. Edit: What does it mean for a (non-...
-2 votes
1 answer
72 views

Seeking journal for theoretical papers publishing

I want to publish a short review article on some aspects of mathematics education. Can you please introduce some Scopus indexed journals which consider such these paper for publishing? I do not look ...
6 votes
7 answers
452 views

Can we define length and perpendicularity not via an inner product?

A traditional way to model Euclidean geometry is to consider an inner product vector space $V$ and to define that the length of $v$ is $\sqrt{(v, v)}$ and that $v$ is perpendicular to $u$ iff $(v, u) =...
11 votes
5 answers
2k views

How to justify formula for area of triangle (or parallelogram)

I'm going to be teaching my kids the concept of area soon. The concept of area of a rectangle (or square), $\text{base} \times \text{height}$ is fairly easy to both explain and intuit: you can break ...
5 votes
1 answer
222 views

Please identify this American elementary textbook series from the 1950s

I'm reading a book chapter (written in 1992) about the teaching of mental arithmetic and estimation techniques in elementary school. The author refers to a particular series of books as "Out-of-...
18 votes
5 answers
1k 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 ...
1 vote
3 answers
323 views

Why can't I teach that picking (un)popular integers doesn't lower Probability of winning lotteries?

Every year at my secondary school, some student always insists that "picking unpopular numbers" lowers your probability of winning lotteries, as follows. Presuppose that lotteries let ...
3 votes
1 answer
155 views

Examples of different languages with mathematically different names for concepts

Multilingual classroom Having pupils of many different native languages, and many languages in general, has been getting quite common in Norwegian classrooms, too. In many other countries this has ...
49 votes
14 answers
6k views

Should we avoid indefinite integrals?

I am very uncomfortable with indefinite integrals, as I have difficulty giving them a precise sense that matches how they are written and the usual meaning of other symbols. For example, when one ...
9 votes
6 answers
27k views

Teaching the difference between standard deviation and interquartile range

Are there any good examples for high school studends where: Interquartile range is "better" to describe "spread" in an (empirical) statistical distribution of data standard deviation is a "better" ...
21 votes
6 answers
5k views

Do I really need to cover solids of revolution in my Calculus I class?

I will be teaching Calculus 1 soon, using Stewart's Calculus: Early Transcendentals as a reference. I can't help but recall my time in high school AP Calculus and my first semester undergraduate ...
6 votes
2 answers
409 views

Is there an equivalent for "tiervenner" in English or other languages?

In Norway a widely used concept is that of "tiervenner", "ten friends" (my translation to Finnish is "kymppikaverit"). This simply means numbers (implicitly positive ...
0 votes
1 answer
38 views

Recommended math site or app for 7th/8th grade

I am looking for an app or website that teaches math at 7th or 8th grade level (for my son). The emphasis should be on fun, game-like experience, that would maintain his natural excitement and ...
0 votes
0 answers
87 views

A Question for Math Instructors [closed]

The following question is for math instructors: How would you approach a student that questions what you’re teaching since that student knows that in mathematics, there are all these different ...
2 votes
2 answers
1k views

Is Morris Kline's 'Calculus: An Intuitive and Physical Approach' a Good Book to Learn Calculus From?

Would I have to read a standard textbook in addition — i.e. Stewart, etc. — or would Kline's Calculus: an Intuitive and Physical Approach be sufficient? My interest is in applications: dynamical ...
-4 votes
2 answers
179 views

Preparing students to face challenges caused by artificial intelligence

Before the invention of computers, the main objective of teaching was to impart subject-related knowledge and train students in memorization. However, with the advent of computers and their vast and ...
2 votes
4 answers
538 views

Logarithms properties, continuity and circular reasoning

I have a doubt relating to logarithms. Anticipating some answers, I know that a "mathy" way of doing things is defining the function by its properties ($f(xy)=f(x)+f(y)$) and then just build ...
39 votes
18 answers
10k views

How do I show students the Beauty of Mathematics?

I teach many high school students, and all of them complain about being unable to fully understand mathematical concepts. I try to show them the joy of learning and deepen their understanding through ...
6 votes
1 answer
281 views

Resources for Pell's equation

What is the best way to introduce Pell’s equation on a first elementary number theory course? Are there any practical applications of Pell’s equation? What are the really interesting questions about ...
10 votes
3 answers
3k views

What to do when uncertain about a question while tutoring

I tutor various math subjects online for a large tutoring company. I know that as a math tutor, it's my responsibility to be able to explain any concept in a way that makes sense to the student, or to ...
32 votes
2 answers
5k views

Which product of single digits do children usually get wrong?

(I was inspired by the comments in this answer to ask this question.) I have some multiplication table cards from Kumon that have a list of commonly mistaken multiplications: $7\times 8, 4\times 8, 11\...
42 votes
3 answers
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 ...
41 votes
6 answers
3k views

Effects of early study of advanced books

Context: There was recently a question on Math.SE: Inferior to Other Younger and Brighter Kids which starts as follows: I'm a high school student (Junior/Grade 11) and I'm currently studying ...
4 votes
4 answers
495 views

Why don't these 'solve in 2 sec' tricks work?

I am a med student and left maths in 10th class. Log and antilog and calculus etc are taught in 11th and 12th. Every time I have any exam that includes usage of these topics I go to Youtube and search ...
2 votes
1 answer
213 views

How to grade a flipped class to improve participation and attendance

A flipped service course for me is an arrangement where videos are online and on-campus class time is used for problem solving by students. I usually have a homework due date the day after the ...
4 votes
2 answers
305 views

Correct notation of a Sample space

From the very beginning I have used the notation $ S = \{ H , T \} $ as the Sample space for tossing a coin once and $ S = \{ HH , HT , TH , TT \} $ in the case of tossing a coin twice.I have several ...
37 votes
5 answers
14k views

Which cognitive psychology findings are solid, that I can use to help my students?

I read recently on this site that the growth mindset seems not to be real. I did not know that (I admit that I don't follow research into learning as closely as I would like). Can I turn that ...
21 votes
10 answers
5k views

Inner voice when reading mathematics

I am writing some notes for my students, and am curious about how others read mathematics: do you have an inner voice when reading mathematics? What about when you come across a symbol which you don't ...
8 votes
6 answers
4k views

Would you correct grading mistakes downwards if there is a mistake in grading?

In a recent exam, I give student a true or false question asking them to decide if a statement is true. After the grades have been published, a student pointed out that I misread the statement and ...
11 votes
7 answers
4k views

Is it a good idea to give partial points in grading

When grading problems on quizzes and exams, I often break them down into sub-problems, each worth a portion of the total points. I use rubrics to award partial credit for each sub-problem. However, ...
0 votes
0 answers
74 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 ...
31 votes
4 answers
7k views

When is it appropriate to warn about the difficulty of a subject?

I've been a TA across every class in the calculus sequence, under the assignment of professors with different teaching styles and curricula. It's often clear to me ahead of time when a certain subject ...
7 votes
11 answers
6k views

Earliest real-world uses of Calculus and Linear Algebra

I want to illustrate in class that real-world applications of mathematics might take time to come to fruit. In this context, I want to find what the earliest real-world applications of Calculus and ...
0 votes
2 answers
120 views

Math Progress for Year 2 Student?

Have a year 2 student that is years above his peers. Each topic I introduce he has already learnt and understood. I've extended the topics we work on for him but the topics I introduce are rudimentary ...
0 votes
7 answers
442 views

How Can I Encourage Students to Use AI Like ChatGPT Across Math Courses?

I've been using ChatGPT (GPT-4) to help with creating quiz questions, solving math problems, and answering students' queries in my classes. Although it sometimes gets things wrong, with the right ...
0 votes
3 answers
459 views

What is this symbol called?

I know how to pronounce the first symbol as "theta", but the other symbol that looks like a circle with a vertical slash, I don't know what to call it. I would appreciate any help. Thank you
14 votes
7 answers
8k views

What Basic Math Skills Should Be Expected of Students in a University-Level Linear Algebra Course?

I am currently teaching a university-level linear algebra course and recently encountered an issue that made me question the assumed foundational math skills for students in this course. The issue ...
1 vote
1 answer
161 views

Theory of semiotic mediation in teaching math at high school [closed]

I am working on the theory of semiotic mediation in teaching math at high school. According to the theory I need an artefact that is appropriate for high school (secondary school). In many papers ...
-1 votes
2 answers
178 views

What are your most recommended resources to teach fractions?

Please share your resources for learning and teaching fractions...sites, videos, worksheets etc. I am looking for online resource similar to this: https://worksheetgenius.com/math/fractions-add/ with ...
6 votes
3 answers
1k views

What are the essential topics in undergraduate financial mathematics?

When I was an undergraduate 15 years ago I did not take any financial mathematics courses. Recently I was approached by an undergraduate, whose ultimate goal is to go into the financial sector, and he ...
4 votes
1 answer
201 views

Producing defective matrix examples

It's easy to come up with examples of interesting diagonalizable matrices $A\in M_n(\mathbb{C})$ with a prescribed set of eigenvalues $\lambda_1,\dots,\lambda_n$ because you can start with your ...
23 votes
6 answers
8k views

What skills do algebra teachers wish their students had mastered before taking algebra?

I am designing 10 hour weekly summer math learning opportunities for students taking algebra next school year. I would like to know from algebra teachers what skills they wish their students had ...
9 votes
1 answer
2k views

What is the term for the marks used to show congruence in geometric figures?

When looking at a given picture to be used in a geometric proof, often times single, double, or triple "slashes" mark off equal line segments or arcs. What is the correct term for these? I've seen ...
25 votes
14 answers
17k views

What can I do when advanced undergraduate and/or early graduate STEM students cannot perform correct math manipulations?

I have helped to TA and taught several courses with mixtures of advanced undergraduate and early graduate students in engineering/STEM. These courses are the classics: signal processing, control, ...
-6 votes
3 answers
249 views

The value of homogeneous divisibility rules and of a numeration

Everyone knows about several divisibility rules. But any teacher knows how difficult students are even with the criterion of three in base ten. For example, many teachers have encountered the classic ...
5 votes
3 answers
636 views

What is a corequisite course?

My department has eliminated its remedial mathematics courses and implemented a corequisite system. I did not participate in the original design, so I found myself unable to understand the new system. ...

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