2
votes
1answer
57 views

Elementary “bugs” in computer algebra systems?

There's a discussion of bugs in CAS's here, but these are technical errors of interest mainly to the professional mathematician. I am more interested in simple errors which might arise in the use of ...
2
votes
0answers
68 views

What are some cool projects that can be done in a high school math class?

I'm studying to be a secondary math teacher and will be starting student teaching next month (an algebra 2 class). It's difficult to find activities and projects that are actually informative and time ...
1
vote
3answers
132 views

How would you explain confidence intervals to a beginner with very weak algebra skills

Let us say that you are taking AP Statistics. The prerequisite is a passing grade of D or above in Algebra II. The kids that you are working with struggle with algebra and do not retain information ...
0
votes
0answers
43 views

How to get a top-notch Math education (high school level) online?

For the past years, it is becoming more and more accessible to get college level content from many different sources, and, if one is willing can get very far with his math education (not only by ...
1
vote
0answers
35 views

What is the less confusing way to explain confidence intervals to a beginner

Let us say that you are back in high school and you have a friend who has missed class for a week. He needs information to be spoonfed to him, because its not his style to overthink. If you push for ...
6
votes
4answers
322 views

Teaching irrational numbers?

I'm interested in teaching the irrational numbers to high-school students, and I need your ideas on how to do in an 'optimal' and innovative way. And my question is: What should the teacher know ...
2
votes
0answers
63 views

Exercises or courses to improve logical rigor and reasoning skills

There is plenty of math that is beautiful without needing much explanation of theory, such as fractals, geometric patterns and the Game of Life, that may interest beginners in mathematics. However, if ...
2
votes
0answers
40 views

What is a sound curriculum for exponent rules in freshman algebra in high school?

We all know the the rules of exponents covered in freshman algebra. The question is, what is the best way to approach these topics as most 9th graders struggle in this area? I work as an after school ...
2
votes
2answers
76 views

Explaining how to simplify a quotient with negative exponents?

I work as an after school tutor at my high school. I've had kids come up to me asking how to do these types of problems: $\left(\displaystyle \frac{5xy^{-2}}{3z^{-1}} \right)^{-2}$ My approach is ...
44
votes
8answers
1k views

How to maintain enthusiasm and joy in teaching when the material grows stale

I recently finished my third semester of teaching calculus to freshman college students. This means I was drawing the same pictures, solving the same example problems, and discussing the same ...
6
votes
2answers
120 views

Teaching algebra in a culturally relevant way while fitting Common Core standards

I've been assigning algebra textbook and worksheet problems (from the publishers and my own) that look like this: Simplify the following expressions. $x^{- 3} y^2$ $c^2 d^{-5}$ ...
4
votes
2answers
351 views

Examples of open ended calculus “class project” ideas

I have instructed calculus I an II, each once, at the college level and would like to emphasize that math is not just about memorizing formulas and concepts for a test and that applied math is not a ...
114
votes
31answers
11k views

Stopping the “Will I need this for the test” question [closed]

I am a college professor in the American education system and find that the major concern of my students is trying to determine the specific techniques or problems which I will ask on the exam. This ...
6
votes
1answer
135 views

How to combat memorization

As a student in high school, I never bothered to memorize equations or methods of solving, rather I would try to identify the logic behind the operations and apply them. However, now that I've begun ...
1
vote
2answers
96 views

Explaining the concept of $z$-scores in high school statistics

The students have so far studied the uniform probability distribution and have a working familiarity with relative frequency histograms and the 68-95-99.7 empirical rule. They still have trouble with ...
208
votes
32answers
30k views

Pedagogy: How to cure students of the “law of universal linearity”?

One of the commonest mistakes made by students, appearing at every level of maths education up to about early undergraduate, is the so-called “Law of Universal Linearity”: $$ \frac{1}{a+b} ...
55
votes
23answers
10k views

How would you explain to a 9th grader the negative exponent rule?

Let us assume that the students haven't been exposed to these two rules: $a^{x+y} = a^{x}a^{y}$ and $\frac{a^x}{a^y} = a^{x-y}$. They have just been introduced to the generalization: $a^{-x} = ...
4
votes
2answers
202 views

How can I explain my 9 years old brother that $8a\cdot4a \neq 64a$

My youngest brother had a pre-algebra test yesterday and he was asked to tell if two expressions are equal or not. We agreed on most of the things but on this one I find it hard to make him accept my ...
2
votes
4answers
280 views

How would you create a math class that centers on the cultural experiences of African American and Latino students [closed]

I need to write a paper on "Ethnocentric Mathematics" and I have no idea what kind of effective teaching strategies are available. We read an article from this scholar named Tate who explained that in ...
2
votes
0answers
57 views

(Actual) applications of basic differential and integral methods

If this isn't the place, I apologize: At the end of my calculus class, we asked the students (among other things) what some applications of calculus methods are. Disappointingly, many focused on the ...
4
votes
0answers
347 views

Soft question : First year student and confused

I hope I won't tire the fellow mathematicians with this question but I am very, very confused... I am a first year undergraduate student of Mathematics. I can't say I am a prodigy, maybe having an ...
9
votes
4answers
227 views

Is studying mathematics chronologically a good idea or not and why?

In high school nowadays most mathematics you learn is fairly 'old'. You have your geometry, all of which (taught in high school) was known to the Greeks more than 2 thousand years ago. You have ...
1
vote
0answers
59 views

How would you explain the pdf of the normal distribution to high school students (11th/12th graders)

I will be teaching the normal distribution in January and I need to know how to effectively explain the concepts that does not in any way confuse students or make them feel that the material is ...
4
votes
2answers
178 views

What is a good example to show high school students why a proof for induction is a reasonable kind of proof?

I teach average-level high school students who have not had much beyond Algebra 1. I want to show them why induction makes sense. I want the sort of problem where it is intuitive that a statement is ...
2
votes
0answers
44 views

Resources for Teaching High School Statistics

I am a student teacher looking for resources to teach high school Probability & Statistics (untracked). The second semester will be inferential statistics and will include these following topics: ...
4
votes
1answer
69 views

Planning a mockup maths class for high school related to river reactivation

I have to plan a mockup maths lesson where the "main topic" should be river reactivation. The given suggestion is to focus on computing cross-sectional areas of rivers using basic geometry and for ...
1
vote
0answers
201 views

What are some good ideas in teaching combinations and permutations

I am a student teacher trying to brainstorm some effective lesson plans for combinations and permutations for a high school statistics course. My master teacher has decided that he will introduce ...
2
votes
0answers
53 views

understanding maths by translating it to real world? Any learn to formulate Initiatives? [closed]

I am CSE graduate, I was very much interested in physics. I had several theories during my higher secondary school like i thought of vacuum as a special medium than nothingness and like gravity is ...
1
vote
0answers
50 views

Evaluating elementary school math textbook

My daughter's elementary school is currently using Saxon curriculum, and I'd like to figure out what other sources, if any, should be age appropriate for elementary school children to enhance their ...
0
votes
1answer
84 views

interactive training in mathematics olympiad competition for 8th Grade: Ages 13–14.

I'll enjoy your kindness to ask this question, despite that it seems it'snt the right destination. Please show me an url, for training in mathematics olympiad competition for 6th Grade: Ages 11–12. ...
3
votes
2answers
121 views

Trying to teach supremum and infimum.

I'm helping out my former calculus teacher as a volunteer calculus advisor, and I have under my supervision 5 students. They've already had an exam and... well, they failed. I read their exams and I ...
4
votes
1answer
174 views

Workshop on Pascal's Triangle for Middle School Students

We're going to hold a three-hour math workshop for some middle school students. It'll about the Pascal's triangle. Well, we can ask the students to find patterns in the triangle, or try to prove some ...
5
votes
6answers
338 views

“$n$ is even iff $n^2$ is even” and other simple statements to teach proof-writing

I am supposed to teach undergraduate students who do not major in mathematics and I would like to give them a short introduction to mathematical reasoning and to the concept of proof. I am looking for ...
3
votes
5answers
98 views

Motivation for Studying Combinatorics (Middle School Version!)

I'm going to teach very elementary combinatorics (limited to basic enumeration) during two weeks to middle school students. At the beginning, I want to demonstrate the importance of counting in real ...
4
votes
2answers
123 views

What is the most motivating way to introduce modular arithmetic?

What the best way to introduce congruences in a number theory course? I am looking for something which will have an impact. What are the really interesting applications of congruent mathematics?
3
votes
1answer
254 views

About game theory for high school students

I am a mathematician with a background in analysis who is teaching at a local high school in his spare time. There is some room for extra curricular math subjects and I want to use it for game ...
6
votes
4answers
567 views

How to convince a high school student that differentials don't work like fractions in general?

It all started when I tried to convince a 10th grader that if $f$ is a function defined on $\mathbb{R}^n$ the differential is defined by: $\large \displaystyle df = ...
4
votes
4answers
123 views

Resources to help an 8yo struggling with math

Friends of mine asked me for suggestion for one of their children (age 8) who had bad scores at the local Star test (the family is based in California). Both parents work, so they have also limited ...
12
votes
7answers
710 views

Should a high school introductory calculus class teach $\varepsilon$-$\delta$ proofs?

It seems to me that most high school students are comfortable with the intuitive notion of a limit ("as $x$ gets arbitrarily close to $c$, $f(x)$ gets arbitrarily close to $L$") and gain little ...
1
vote
0answers
69 views

What's the acceptance of rational trigonometry in current mathematics courses?

I've been reading about Wildberger's rational trigonometry and I'm willing to learn it. I'm wondering if it's usage is accepted in undergraduate mathematics courses. It seems there's a redefinition on ...
80
votes
11answers
10k views

How to convince a math teacher of this simple and obvious fact?

I have in my presence a mathematics teacher, who asserts that $$ \frac{a}{b} = \frac{c}{d} $$ Implies: $$ a = c, \space b=d $$ She has been shown in multiple ways why this is not true: $$ ...
0
votes
1answer
183 views

Examples of Metaphors in Statistics and Probability?

I have a couple of questions about teaching of Probability and Statistics for high school students: 1. Can I find metaphors for the teaching of basic concepts of Probability and Statistics? (Please, ...
0
votes
1answer
95 views

Graphical Demonstration of Linear Transformations on $\mathbb{R}^2$

I'm looking for some applet, program, software, demonstration etc. to use it in a class while teaching linear transformation in $\mathbb{R}^2$, so that the students can graphically understand the ...
0
votes
2answers
142 views

Request for reference and technical support

I am going to write my master thesis in order to become a teacher of mathematics (with second subject business management). Supported by the ERASMUS program I have the opportunity to do this in ...
7
votes
2answers
384 views

How to teach a High school student that complex numbers cannot be totally ordered?

I once again need your precious knowledge! I am not sure which is the best pedagogic way to teach a High school student about why complex numbers cannot be totally ordered. When I was in High school ...
10
votes
2answers
346 views

Is “problem solving” a subject to be taught?

Note: This question has been cross-posted to MathOverflow: see here. I am witnessing a new curriculum change in my country (Iran). It includes the change of all the mathematics textbooks at all ...
1
vote
1answer
66 views

I'm gonna give probability regularization classes

There's this group of high-school level kids that failed probability and they want me to teach them so they can pass that subject, i agreed to be their teacher for this 2 weeks, however i'm not ...
6
votes
3answers
613 views

Importance of Neatness / Organization / Speed in Math?

Pretty simple question here but it does relate to math. I ask this as my writing is quite messy, possibly a cause of silly mistakes. How important is neatness in math? Does having messy writing put ...
5
votes
3answers
208 views

Statistics Workshop for High School Students

We are going to hold an introductory workshop about the statistics. The participants will be students who have just finished their 8th or 9th grade. The workshop consists of 10 two-hour sessions. The ...
6
votes
3answers
941 views

Should I try to change the way Abstract Algebra is taught at my university? If so, how?

[This (soft) question should be Community Wiki.] Background: A year ago, I did a one-semester long course on Abstract Algebra at my university. When we started, I was excited, because I knew the ...