For questions related to the teaching and learning of mathematics. Note that Mathematics Educators Stack Exchange may be a better home for narrowly scoped questions on specific issues in mathematics education.

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1answer
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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
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1answer
127 views

Literature for ODE undergrad class

I am teaching a undergrad ODE class. I am looking for some good (introductory) articles with applications of ODE's. In particular I would like some motivations for some special functions (Legendre, ...
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6answers
235 views

Not pi - What if I used 3? Teaching pi discovery to K-6th grade

So, in ancient Mesopotamia they knew that they didn't really have the correct number (pi) to determine attributes of a circle. They rounded to 3. If you acted as though pi = 3, what shape would you ...
10
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1answer
366 views

Is making the math learning process deliberately more challenging an effective teaching strategy?

I've often come across a view on teaching/learning math to the effect that forcing students to struggle rather then "spoon-feeding them" (as they put it) makes for much more able students in the long ...
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14answers
5k views

Do we need to formally teach the Greek Alphabet? [closed]

This is a question that I am purely interested in because I think we never thought about this before in Mathematics education... or even so was not discussed. When did we learn the Greek alphabets ...
3
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3answers
797 views

best books for learning algebra

My name is Aniket and I have started 11th class recently. I have studied only my school textbooks(NCERT Books) and I am not happy with them. I want to learn Algebra,i.e, all the topics covered in ...
3
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3answers
147 views

Do users of RTL languages adopt an LTR standard for mathematics (in the same way they often do when using LTR words or phrases in RTL text)?

Non-mathematician here. There is a discussion on this forum titled "Is “applying similar operations from left to right” a convention or a rule that forces us to mark one answer wrong?" I found it ...
0
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1answer
106 views

Nature of Points and Lines in Euclidean Geometry

It may be true that very few middle school student can grasp the meaning of lines and points in Euclidean geometry prior to a direct instruction. For example, it's possible that such a conversation ...
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3answers
415 views

Natural uses for the co-product of sets?

I had come across countless uses of the (Cartesian) product of sets long before I first ever met the concept of a "co-product"1 of sets. In fact, anyone who has learned basic analytic geometry in ...
0
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2answers
324 views

Find Vector and Parametric Equation

I'm having some trouble finding answers to these problems. When i try to find help online, all i find are (x,y,z) problems and I'm simply looking for a PreCalculus (x,y) problem solving technique: ...
11
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6answers
361 views

Can one show a beginning student how to use the $p$-adics to solve a problem?

I recently had a discussion about how to teach $p$-adic numbers to high school students. One person mentioned that they found it difficult to get used to $p$-adics because no one told them why the $p$-...
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0answers
88 views

Learning to write the style of mathematics texts

When learning how to write articles in mathematics (in style of articles published in journals) is there a good reference listing things like common outlines, style guides, phrases, common mistakes ...
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2answers
477 views

Fundamentals of Algebra - Cancelling Like Terms in Divison

When can, or can't, terms be cancelled. ie: $\frac{3x^2-1}{x^2}$ $x^2$ cannot be cancelled. Why not, and what are the rules?
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1answer
193 views

Looking for data science-oriented “Applied Maths for dummies” summer school

I'm a PhD candidate who critically lake of maths skills for his data science projects. I'm looking for a summer school that would enable me to take off in this aspects. This could be data-analysis/...
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2answers
323 views

Re-learning Math and becoming more comfortable

As someone finishing up their BSc in Electrical Engineering, it is becoming very clear that I need to improve my mathematically abilities significantly if I want to pursue any more education. I ...
6
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1answer
200 views

Transitioning to Higher Level Mathematics

I am just finishing grade 12 pre-calculus at my school and have strong interest in math. The problem is, it seems some important elements of higher level math are not in my schools curriculum that are ...
1
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1answer
94 views

function inversion and the horizontal shift

I am currently doing inverse functions and graphing radical equations of the form $y=a\sqrt{x-h}+k$ with my algebra class and one of my students asked me the following question. "Why is it that we ...
2
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2answers
117 views

Why doesn't this work? — The V.I. Arnold Primary School Problem (Two women started at sunrise…)

I've got a, perhaps silly, question. I understand the various solutions to this problem: Two women started at sunrise and each walked at a constant velocity. One went from A to B and the other ...
0
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1answer
180 views

Interpretation of First Isomorphism Theorem

I understand that the first isomorphism theorem basically says that any homomorphism f from group G to group G' induces an isomorphism from G/Ker(f) to the f(G). What I don't quite understand is the ...
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7answers
3k views

Why is there antagonism towards extended real numbers?

In my backstory, I was introduced to the geometric concept of infinity rather young, through reading about the inversive plane. In the course of learning calculus, I'm pretty sure I formed a concept ...
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3answers
1k views

How to explain to a small child that the area of a square of side a is a²?

I have a small child and I am always trying to find the best way to explain new things to her. The area of a square is a very basic concept that is related to the idea of area unity and can be used to ...
8
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4answers
221 views

Primary/Elementary Pedagogy: What is the rationale for the absent '+' in mixed fractions?

Why are elementary students taught to represent one and a half as 1 1/2 rather than 1 + 1/2? This mode of expression seems standard throughout at least North America. I think it is bad pedagogy for a ...
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2answers
39 views

Getting the Amps from Watts, Amps and the voltage of a line

What amperage capacity should the supplied wired be rated for a refrigerated fixture which has a 208V power supply and the following loads? 4 Evaporator fan motor rated at 9W each 4 Evaporator fan ...
6
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2answers
677 views

How to explain lagrange multipliers to a lay audience?

So I will be giving a seminar to a scientifically mature lay audience (think bio/social science undergrad level). I have been told that I should count on less than half the audience to have experience ...
10
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6answers
568 views

Evaluating the reception of (epsilon, delta) definitions

There is much discussion both in the education community and the mathematics community concerning the challenge of (epsilon, delta) type definitions in real analysis and the student reception of it. ...
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6answers
662 views

Thinking of mathematics in terms of analogs

I think the way that I've come to think about mathematics is becoming problematic and I'm wondering if I should abandon it. When I study mathematics, I find myself trying to compare the mathematical ...
3
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3answers
150 views

What Will Happen Without Decimal Expansion?

After a discussion on the complexity of decimal expansion (such as $0.\bar{9}=1$), some of my students (middle school) decided to throw away the decimal expansion of some numbers! Namely, the numbers ...
7
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1answer
409 views

Why do professors sometime hide the book from which they are really teaching? [closed]

Well, the title is almost self explanatory. I am in a graduate school and have two professors this semester both of who are telling me that they are not following any particular book, and yet when I ...
0
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2answers
285 views

What exactly do math education PhDs do?

I have been researching this for the past hour or so, but I have not really found a sufficient answer. What I have found is that vaguely, math education PhDs set policies for math education. However,...
2
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1answer
120 views

Bridge the gap to university mathematics [closed]

Can anyone suggest some good books to help an high school student to "bridge the gap" to university math? I've heard of http://www.amazon.com/How-Study-as-Mathematics-Major/dp/0199661316 and http://...
5
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4answers
1k views

Solve without a calculator: What is the possible value of 2*((1+1/100)^100)?

What is the possible value of $2·((1+\tfrac{1}{100})^{100})$? Google will give $2·((1+\tfrac{1}{100})^{100}) = 5.40962765884$. How can I find the possible value without Google or a calculator? How ...
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8answers
3k views

Active learning vs Passive learning in Math

I am trying to improve how I learn in general but specifically in math and a common suggestion I keep coming across is the difference between active learning and passive learning. The problem is, most ...
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1answer
54 views

Variational characterization of gradient?

Let $f: \mathbb{R}^n \to \mathbb{R}$ be a differentiable function. One way to define the gradient of $f$ is as the vector whose inner product with any other vector gives the directional derivative in ...
4
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2answers
194 views

Is there a systematic way to detect overcounting in simple combinatorics?

TL;DR: In simple combinatorics problems, is there a systematic way to detect overcounting before computing the counts and comparing them? Is it simple enough to be taught to undergrads: At my ...
1
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1answer
111 views

maths for a strong visual spatial thinker with sequential processing weakness?

Can someone with superior visual spatial thinking ability but weak sequential/word ability be successful in university maths and beyond? For example, for real analysis, would definitions with lots of ...
7
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4answers
1k views

Most useful books for a math undergrad

What are the most useful books an undergraduate in math should read? I found Alock's "How to study as a math major" and "how to study for a math degree" very useful. Are there any other good readings ...
0
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1answer
558 views

Max(x,y) and argmax(x,y)

I am writing my report and I got confused on this simple maths concept. What I need is: I have 2 values i.e x and y and I want to use the maximum of either x or y as my length. So which statement is ...
0
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1answer
46 views

How to define a set for a matrix

I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically. Is it ...
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1answer
1k views

Determine sin cos and tan from slope? NON CALCULator

I am used to finding this by drawing the triangle and knowing the angle measurement. With the angle measurement i can find sin cos and tan. But i dont have angle all I have is line. I have put a ...
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1answer
94 views

The right angled triangles ABD and BCD?

AB=5cm BD=4cm and angle ABD=x Find the exact value of cos(ABC) this is the trangle...: https://twitter.com/JxstyBiebs/status/432919494466752514
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4answers
57 views

The graph of the function is $g(x)=x^3-2x^2+x+1$ and the tangent to the curve is at $x=2$?

a) Find the equation of the tangent to the curve at $x=2$ HELP and then b) Determine the angle that this tangent makes with the positive direction of the $x$-axis Please help I really need to ...
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2answers
78 views

General solution to the integral of 4/x

A friend asked me what was the solution to the problem (which was on his test)$$\int\frac4xdx$$ I proceeded to tell him that you can take out the 4 in the numerator, and then just take the integral of ...
0
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1answer
61 views

Mean and Variance Statistics

$X_1, X_2, \dots , X_n$ ~ i.i.d $U[0,1]$ a) Find the mean and variance of $lnX_1$. b) Let $0\le a \lt b$. Find the $\lim_{n \to \infty} P(a \le (X_1,X_2, \dots ,X_n)^{(n^ -0.5)}*e^{ ( n^{0.5})}\le ...
9
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1answer
440 views

Are mathematics competitions important?

So I'm seventeen and currently a junior in high school. I love mathematics very much, it's developed into a strong passion over the past few years, after witnessing the president of the math club at ...
4
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3answers
2k views

How would you prove that the graph of a linear equation is a straight line, and vice versa, at a “high school” level? [duplicate]

This is something I've been wondering about. Namely, I've always accepted "on intuition" that the equation $$ax + by = c$$ is, when graphed, a line. You can plot the points $(x, y)$ satisfying the ...
5
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1answer
202 views

Software for basic math notes at 5th to 10th grade level (10 to 15 years old)

So I've looked around, here and otherwise, but sadly can't seem to find quite what I'm looking for. I don't know if it even exists, I figured it was worth trying to ask, though. I've found plenty of ...
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1answer
2k views

Applications of infinity in real life [duplicate]

I am writing a mathematical essay and would like to focus on the concept of infinity. I am not sure of any real life applications of infinity to write about or some way to narrow down the topics. Does ...
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3answers
662 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
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2answers
173 views

Resources for teaching introductory course in differential equations?

The first time I was assigned to teach an introductory linear algebra course, I was able to find a number of resources which were helpful. For example, Linear Algebra Gems and Resources for Teaching ...
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1answer
37 views

Teaching School Algebra via Programming

It seems that there are ideas to teach school algebra (i.e. using variables, working with algebraic expressions and solving equations) via computer programming. I need a book or a collection of ...