# All Questions

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5answers
324 views

### Is it a good idea for elementary school students to observe and discover the "circle perimeter formula" themselves without being dictated to?

Let them discover $\;\ell=2\pi R\;$ by their own, at least the invariance of $\ell/R$ Do you think that the following method works well in a mathematics class of elementary school? What do you think ...
2answers
125 views

### Arithmetical Progression

I recently came across a very old Algebra textbook from the 1860s, and on the chapter discussing "arithmetical progression", it says there are "20 cases for arithmetical progression&...
9answers
4k views

### Why do we introduce the notion that triangles are "congruent" instead of just saying that they are "the same" or "equal"?

The assumed age of the students is 10-15 years old. What is the danger in saying that two triangles are "the same" or "equal" instead of saying that they are congruent? It seems to ...
4answers
1k views

### Different Teaching Styles for Different Genders?

I was recently looking through job listings in my local area (US high school, ages 14-18) and I found two boarding schools with vacancies, one was male-only and the other was female-only. This got me ...
11answers
6k views

### What can (and should) an educator do about ambiguous terms like "triangle", "square", etc?

The imagined students are in elementary school, say around 9-13 years old. I want to use rather precise terminology when talking to my students. However, it seems like we typically use the same ...
1answer
167 views

### When and where were textbooks that use set notation for basic algebra solutions?

A past question described a school where many teachers insisted that answers to algebra problems had to be phrased in set-theoretic language or notation. For example, when asked to solve $2x+3=6−x$, ...
3answers
195 views

### What are strategies that a 10-13 year old could use to convert 6/27 into decimal notation?

Background: I am working with 10-13 year olds. I saw a problem which requires the students to convert $6/27$ into decimal notation. I can think of some methods, but I have not tested using any of the ...
2answers
2k views

### What does research indicate about how one should treat units in elementary school?

Background: My friend told me that when she was in elementary school, the teacher would ask questions like "If you have $6$ apples and eat $2$ of them, how many apples do you have left?" A ...
1answer
106 views

### Why is Pure Mathematics so much easier than Applied Mathematics? [closed]

I love pure mathematics, so much. However, I recently did probability and statistics and applied mathematics courses, and I'm confused with statistics. There's no proofs and logic in applied math ...
1answer
172 views

### Are there any mathematics based game apps which require students (between 10 - 16 years) to apply their maths knowledge to play the game

So, what we essentially mean is students will apply their knowledge on divisibility, factorization, prime numbers, lcm, gcf, decimals, fractions, etc to play the game. A somewhat different approach to ...
3answers
632 views

### Is there a study that compares 8-week vs 16-week math classes?

I see a push toward having undergraduate curriculums built around 8-week classes. This is mostly in the online education in the USA. Recently I have seen a number of these in sophomore or junior-level ...
2answers
202 views

### Are there any list of mathematical constructions which can challenge 12-16 year old students?

Mathematical (geometric) constructions are an interesting way to engage students. It also helps in better understanding of different geometrical properties. For example, Sierpinski triangle or square, ...
3answers
195 views

### If one wants to conduct a 1/2 day workshop in Mathematics for 12-16 year old students - how one should go about preparing the workshop

The questions that I want ask are the following: What are the most important and effective topics to conduct a workshop? What fraction of workshop should include lectures, activity, problem solving, ...
1answer
205 views

### How to teach if calculations and algebraic manipulations are off limits

This question may be just too broad in scope, but some form of it has been on my mind during this year of remote learning as I imagine a future cycle of educational upheaval. Much of what we teach in ...
0answers
60 views

### What are different Mathematical concepts which can be introduced to 12-16 year students in an activity based way

Activities are a great way to engage students with Mathematics. And that also helps them to visualise mathematical facts. For example, Pi in its decimal form appears to have no pattern (we used to say)...
1answer
93 views

### Hourly math contests online

You can play chess online anytime you want to, even against a human opponent of your level, even in hourly competitions. It would be nice to have the same thing in math, at least for kids. Everyone ...
2answers
190 views

### Importance of asking questions in a mathematics class

It is observed many times that students do not ask the right questions in the classroom. They just attend the lectures passively. Rather than asking the questions o get their doubt cleared, they ...
2answers
403 views

### Is there a math curriculum that is aware of CAS and the internet?

About 15 years ago, I heard a math education professor give a talk about how computer algebra systems would change the kinds of questions teachers would ask high school and first year college students....
2answers
177 views

### Looking for an educational game from long ago, possibly called Mother Goose [closed]

OK so this is really old school. Back in the 1980s, as a latchkey kid, I played on the computers in the library in elementary and middle school. There was this one bizarre educational game that I'd ...
3answers
1k views

### How to test student's skills in programming or using software?

I am going to teach an undergraduate statistics course next year. My plan is to spend less time on theory and a more time on teaching students to doing some statistics on computer. However, this ...
5answers
624 views

### Example of why proof by exhaustion is inelegant

There's a nice example of why people dislike proof by exhaustion on the Wikipedia page. The problem statement is "prove that all years in which the Modern Olympics are held are divisible by 4&...
3answers
337 views

### What's a good notation to show elements of relation composition?

Teaching discrete mathematics, we pose (from the textbook) questions on finding compositions of relations, notably, relations on very small finite sets with only 3 or 4 elements (as an introductory ...
2answers
155 views

### Study multiple subjects at the same time or deep dive into one?

I want to learn probability theory and discrete math. However, I also need to brush up on computational calculus and linear algebra. Would you recommend only studying one subject at a more intense ...
3answers
170 views

### Looking for a collaborative drawing solution

Preparing for a class I teach this summer and stumbled upon a technology problem. I want to show my students a graph, ask students to annotate it privately (eg mark mean on a histogram) and then ...
2answers
180 views

### manual solutions to graduate textbooks [closed]

Where can I find manual solution for textbooks like Advanced Linear Algebra by Rotman or Introduction to Smooth manifolds by Lee? any help would be appreciated
2answers
556 views

### Calculus limits taught in the US vs Spain?

So, I realize this can be a broad question, so I'll narrow it down. I have lived in Spain and own several Math textbooks from that country (the equivalent of 8th grade and high school Math). Has ...
0answers
85 views

6answers
639 views

### Why do we write $x$ instead of $1x$?

I am currently student teaching for an Integrated Math 1 class (which is similar to Algebra 1) that consists of 9th graders. I have been teaching my students how to solve linear systems using ...
0answers
85 views

### Converting an Online Course Back to In-Person

As I wrap up my Spring semester online courses, I'm starting to think about next Fall when (hopefully) our university will return to full in-person classes. Because of COVID, over the last year I have ...
1answer
339 views

### Are there real life examples of normed vector spaces?

I'm trying to explain some basic concept to my kid (he just started learning basic algebra following Discovering Algebra: An Investigative Approach by Jerald Murdock ). For example homeomorphism means ...
4answers
238 views

### Showing applications of calculus to intro students

So I'm wrapping up my second year teaching high school calculus, and my first as an AP course. In addition to review, I'd like to end the year by giving the students a taste of the kinds of real-...
9answers
5k views

### Children's counting problems: Is this question phrased correctly?

Look at the following example: Which picture has four apples? A B C D B is the expected answer but should not the correct answer be BCD? Technically if a set has exactly $m$ elements, then it ...
0answers
87 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 ...
4answers
388 views

### Is it necessary to teach the definition of a limit for engineering majors? [closed]

I have always wondered whether it is necessary or not. For me, it seems that it is enough to teach them the intuitive idea, that is, limit is just an approximation of a certain process. what do you ...
2answers
226 views

### Geometric and Graphical perspective on completing the square

I just read an interesting article that helps to understand completing the square, and prove the quadratic equation from a geomterical perspective. My question is how do I understand the graphical ...
2answers
258 views

### Looking for rigorous books to review geometry, trig, and precalculus

I've taken Calculus 1 and it's time to relearn because I've forgotten some of it. But it's been a couple months since I've done any solid mathematics. I was hoping for a book that would include ...
0answers
170 views

### Resource request: 3-4 page review of exponentials and logs

I'm teaching a physics class that has a year of calculus as a prerequisite, but as so often happens, many of my students have forgotten a lot of the much more basic math from earlier classes. In ...
2answers
209 views

### How to make an introductory course on Statistics interesting

I am going to teach this probability and statistics course in a couple of weeks. The probability part can be made very interesting, in my opinion, easily. But I am a little worried that I might make ...
2answers
313 views

1answer
74 views

### simple statistics (binomial) terminology

Say I have the problem: I roll a die three times and I am interested in the probability of ending up with two 1's. My impression is that a single roll is called a trial. What is the full 3-roll action ...

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