5
votes
0answers
40 views

Has Benezet's teaching experiment ever been reproduced?

In the 1930's, Louis Bénézet, a superintendent of several schools in New Hampshire made the interesting experiment of teaching no formal arithmetic until grade 6: In the fall of 1929 I made up my ...
1
vote
2answers
90 views

Is AP Calculus AB really necessary?

High school student here... This coming school year I'm scheduled to start AP Calculus AB and then my school is looking into taking Multivariable Calculus at a local university. The school's calculus ...
3
votes
0answers
46 views

CoTeaching Elementary Linear Algebra

I and my colleague will teach an elementary linear algebra next few weeks, but the way our course is planned mostly is by turn teaching. By that I mean, my partner will teach the first 8 weeks of the ...
-7
votes
0answers
24 views

Please give correct answer of these [on hold]

Q1. Which statement is about the sets N and Q (a) N=Q (b)Q subset N (c) N subset Q (d) non of them Q2.An upper bound for the set {P€O:p^2<9} (a) 3 (b) -3 (c) -1 Q3. Which of the ...
0
votes
0answers
97 views

Project ideas for prime numbers [on hold]

I and my friend had decided to do a project based on prime numbers in science Fair. We are highschool students. We have already collected details about some prime finding ways, prime number encryption,...
1
vote
0answers
71 views

Downloadable MCQs on Mathematics

I am looking for multiple choice question (MCQ) based tests on some Mathematics' topics (details below), which could be downloaded in most preferably tex (LaTex) format or doc/docx format. Kindly ...
1
vote
1answer
61 views

Books similar to “Teaching Developmentally”, but for high school math

I've been extremely excited by my reading of the book Elementary and Middle School Mathematics: Teaching Developmentally by Johan A. Van de Walle et al. Does anyone know of similar books (or other ...
0
votes
0answers
64 views

Evaluation and feedback using Optical Mark Recognition systems in secondary school

OMR in exit tickets I plan to use an OMR, Optical Mark Recognition systems at the end of (some of) my classes. I want to use the same OMR system for exit tickets scattered over the academic year (...
5
votes
1answer
156 views

Curriculum for self taught Maths degree

Someone has made this template for a self taught CS degree. I am a CS grad and found it quite good. As I don't have much idea about a proper pathway to learn degree level mathematics in my own. Please ...
5
votes
1answer
91 views

Why emphasize moment generating function over characteristic function in a probability course?

I've noticed that some undergraduate introductory probability textbooks and courses emphasize or seem to prefer the moment generating function $m(t) = \mathbf E(e^{tX})$ of a random variable $X$ ...
2
votes
1answer
62 views

Existing Tools for Math Expression Equivalence Logic

Note - this question was posted here and garnered some decent replies before it was closed as off-topic in Stack Overflow. Online systems, such as ALEKS, Cengage's WebAssign, and even Khan Academy ...
-3
votes
0answers
83 views

exponential equations

I'm looking for exponential equations that require the application of the properties of logarithms and can be solved without a calculator (by evaluating the logarithm). example: 27 = 3^(5x) . 9^(x^2^...
3
votes
4answers
134 views

What are standard (or good) textbooks for undergraduate graph theory?

I'll be teaching graph theory this fall for the first time. The only undergraduate graph theory book I am familiar with is Doug West's book, which I like. But I'd like to consult some other ...
6
votes
2answers
217 views

Should students be given partial scores when they gave an incomplete proof by contradiction?

In a quiz, there was a question asking students to show something doesn’t exist. A lot of them gave proofs by contradiction. Initially, I designed the marking scheme so that an incomplete proof by ...
3
votes
2answers
252 views

Why are proofs written in flowery language incomprehensible?

Let's take an example in Wu-Ki Tung, Group theory in physics: Theorem 3.4: Irreducible representations of any abelian group must be of dimension one. Proof: Let $U(G)$ be an irreducible ...
8
votes
2answers
244 views

Is There Such Thing as Learning Disability in Math?

I am currently tutoring a student who is really lacking in math. At first I thought she was just resistant; perhaps she thought that her teacher had no choice but to pass her. What truly stunned me ...
9
votes
3answers
283 views

Integral calculus from the modern viewpoint

This is a soft question. What is the purpose of teaching techniques of integration at the college level? More specifically, in the sense of putting integration into practice, what value does ...
7
votes
8answers
1k views

What is an intercept?

I have always taught my students that the $y$-intercept of a line is the $y$-coordinate of the point of intersection of a line with the $y$-axis, that is, for the line given by the equation $y=mx+y_0$,...
6
votes
2answers
78 views

Online quiz with slightly different questions for each student

I am looking for an online quiz that can generate multiple versions of a multiple choice question. What I want is: The same question can have a different text for each student Alternatives are ...
5
votes
4answers
166 views

What is the value in creating distinguishing terminology between the $x$, $y$, and $(x, y)$ values of a possible point of extremum?

I've been out of a math program for about four years now. My wife is starting a CS degree, and finished her first calculus course last semester. I tutored calculus throughout my entire undergrad, ...
4
votes
1answer
121 views

Encouraging students to learn probability

Background: I’m not exactly a Math educator, but I’m currently a TA of an elementary algebra course aiming at students of age 14-15. I found that a lot of people have misconception about probability ...
7
votes
4answers
227 views

Should homework be graded in an undergraduate math course?

It seems like the internet has made it very difficult to prevent cheating -- simply looking up the solutions to textbook problems -- on undergraduate math homework. So there is a danger that grading ...
1
vote
0answers
75 views

What is the best term for “probability measure” in an undergrad introduction to probability course?

The function $P$ that takes an event $A$ as input and returns the probability $P(A)$ as output is called a "probability measure" when we are developing probability using measure theory. I have also ...
0
votes
1answer
89 views

How to present the order of factors and summands for the usual multiplication procedure

In the following multiplication example, $$\begin{align} 34\;& \\\underline{\times\;\; 7\;}& \end{align}$$ first one would multiply the units digits, producing the partial product $28$ as ...
2
votes
1answer
129 views

Better strategy on math graduate school

I'm just starting graduate school (master in mathematics) and there we have absolute freedom in choosing the number of courses that we can attend each term. In consequence, I'm wondering what is the ...
4
votes
1answer
106 views

Polar form before Cartesian form when introducing complex numbers

When I teach complex numbers to undergraduate engineering students, I invariably start, as appears to be customary, with $a + bi$ (or $a + bj$ for electrical engineers) and then follow up with the ...
4
votes
0answers
119 views

Learning math historically

What is meant by learning math historically (NOT learning math history only, but learning math with a historical development perspective)? I've seen some sources that to learn a math topic X, you need ...
5
votes
2answers
214 views

Trends in math education: Majors? Applied math? Statistics?

I would be quite interested in learning of trends (in the U.S. or internationally) of student interest at the undergraduate level in pure math vs. applied math, say, measured by majors at graduation. ...
9
votes
2answers
188 views

Good real-life examples of transformations of function graphs

I am a gradudate student teaching college algebra at a larger state school and transformations of graphs of function, i.e.: given the graph of a function $y =f(x)$, what do the graphs $y = f(x) \pm C$,...
2
votes
0answers
103 views

Are there any books on how mathematicians reason about infinite sets? [closed]

From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 457. For an account ...
3
votes
1answer
104 views

How can students self-learn creativity in math that “demand more than just deduction”? [closed]

From: Philip Johnson-Laird BA PhD Psychology (UCL), Stuart Professor of Psychology Emeritus at Princeton. (Author isn't a logician.) How We Reason (1st edn 2008). p. 112.   You might ...
5
votes
3answers
223 views

Should I describe the function $x \mapsto f(x_0) + f'(x_0)(x - x_0)$ as “linear” in a freshman calculus class?

One of the most important ideas of calculus is $$ f(x) \approx f(x_0) + f'(x_0)(x - x_0). $$ The approximation is good when $x$ is close to $x_0$. This approximation is very useful because the ...
6
votes
2answers
206 views

On fractions and least common multiple

At least in my country, the explanation of the basic operations over rational numbers is done very near to the concept of primer number, prime factorization and calculus of least common multiple. In ...
10
votes
7answers
478 views

Why don’t all professors let students use notes, books, etc. on exams?

Last semester I had a teacher who let us use any type of information in the exam, for example the course notes, books, solved exercises, etc. The only thing he did not let us use was something ...
7
votes
4answers
233 views

Small 'new things' to confront talented high-schoolers with

Something my students* often struggle with is how to react on being confronted by 'new things', including functions, notation or definitions for which they are given sufficient definition but with ...
6
votes
2answers
184 views

Teaching logic through “high school algebra”?

I am going to be teaching a discrete math class in the fall. One of the major goals of the course is a solid understanding of the basics of logic: the precise meanings of "and", "or", "not", "implies"...
2
votes
1answer
64 views

How to become really interested in math [closed]

I'm a high school senior. What can I do to be really interested in mathematics ? I know some of my batch-mates (from meeting them at several math Olympiads) are like insanely good at math (know lots ...
2
votes
2answers
79 views

Urn (containing colored balls) generator?

I am looking for a nice app that would enable me to create "automatically" nice urns filled with balls of two different colors, following the illustration below (actual colors do not matter, being ...
-2
votes
2answers
72 views

What are the uses of calculus in every day life? [closed]

Can anybody say me what is differentiation and integration and what is the use of these ?
1
vote
2answers
86 views

Subject advice in Number Theory [closed]

At my University, we have the optional feature to write a project like a Bachelor Thesis. This semester have finished and I would like to work in the summer in project like this. So, I'm searching for ...
6
votes
6answers
269 views

Simple, elegant ways to teach the idea of what functions are for the first time

The context In my country, when the concept of function needs to be introduced in math classes, most teachers will simply talk about $f(x)=c$, $f(x)=ax+b$ and $f(x)=1/x$ (constant, linear and inverse ...
2
votes
0answers
57 views

Reference for study about good teachers in a US state

Several years ago I have read about a study in a US state where standard test scores were used to identify teachers whose students consistently improved far above the average and then film and analyse ...
3
votes
2answers
92 views

Supplemental text for undergraduate real analysis

Context: I am an assistant professor at a small college in the US. Next semester I am teaching real analysis for the first time, and we are using Steven R. Lay's book. (It also happens to be the ...
7
votes
6answers
146 views

Simple Number Theory Task

I am doing exercises with middle grade students and looking at their capacities to create arguments for simple number theory conjectures. I want three tasks, and I have two so far: 1. The sum of three ...
4
votes
1answer
74 views

One course/subject, one class, two lecturers

This is my first question here, so please correct me if I'm wrong in my way of asking. My question is suggested directly by the title. In my college institution, for each subject, half of the ...
4
votes
2answers
130 views

Why bother completing the square to find the minimum/maximum of a quadratic function?

Given a question like Find the coordinates of the minimum point on the curve $y=3x^2+2x+9$. students are often taught to solve this by completing the square. The class I am currently teaching ...
9
votes
3answers
185 views

Quizzes (with questions known in advance) instead of homework in a graduate mathematics class. Good Idea or Bad Idea? Pros and Cons?

I'm teaching a graduate course in mathematics next semester. I'm planning to have a midterm and a final exam. But I'm thinking about having weekly (or once-every-two-weeks) in-class quizzes instead of ...
4
votes
0answers
83 views

Why is problem solving important for all of us?

I am looking for academic references related to this questions. In fact, I need to write a paper which shows the importance of problem-solving approach for everyone. Certainly, this should include ...
2
votes
3answers
122 views

Easy tool to draw stencils

I'm looking for a simple tool (preferably online or at least that works on Linux) to draw stencils. When teaching and creating notes for students, I often feel that it would make understanding in some ...
5
votes
0answers
110 views

How was this maths educational video made?

I would like to make math videos in the manner of this YouTube video. The specific features which I like in this video are: the interactive freestyle drawing (see the beginning of the video) the way ...

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