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121 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 ...
3
votes
1answer
107 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 ...
5
votes
2answers
175 views

When working with 12-16 year olds, how should I graph functions when the domain technically isn't $\mathbb{R}$?

Let us assume that I want to graph any of the functions below. A) A can of soda costs $\$1$. Draw a graph depicting the total cost as a function of the number of cans you buy. Comment: One cannot ...
8
votes
6answers
7k views

Why should or shouldn't we teach functions to 15 year olds?

Background The students in my country are supposed to be able to work with and answer questions about functions at the age of around 15. This is asserted in the standard mathematics curriculum for ...
-4
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0answers
114 views

What would be the advantages and disadvantages of having alternative bases like binary taught primarily in the language department? [closed]

What would be the advantages and disadvantages of having alternative bases like binary, quaternary, octal, hexadecimal, and/or vigesimal taught primarily in the language department? Perhaps using a ...
0
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0answers
21 views

Is a nonzero value of artificial variables in simplex method showing infeasible solution? [closed]

In linear programming we sometimes use artificial variables for the simplex method. After a certain number of iterations of the simplex method we reach a point in which all coefficients are non ...
13
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4answers
203 views

Analyzing an answer to the following problem: Give meaning to $\frac{4}{5} + \frac{2}{3}$

Case: Exam Problem given to student at university: Give a problem/context illustrating the operation $\frac{4}{5} + \frac{2}{3}$ Answer by student: Anna and Beatrice buy flowers for grandpa for his ...
13
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3answers
2k views

How many of “The Seven Laws of Teaching” are still relevant for teaching maths today?

Wikipedia shows that in 1886 John Milton Gregory outlined his "The Seven Laws of Teaching"; asserting that a teacher should: Know thoroughly and familiarly the lesson you wish to teach; ...
1
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1answer
91 views
+50

An intuitive (non rigorous) text book on graph theory which is student friendly with vivid illustrations

Background Hello, I am an undergraduate in CS. I would like to study Graph Theory on my own (self-study) for a competitive examination (named GATE). It is an examination for undergraduates and as such,...
-1
votes
2answers
151 views

What research has been done on the effects of requiring students to learn to count in an alternative number base such a binary or base eight? [closed]

What research has been done on the effects of requiring students to learn to count and do some easy arithmetic in an alternative number base, for example binary, base four, base six, base eight, base ...
0
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0answers
98 views

What are the typical topics of New Math for each age, especially primary school?

A person recalls that he or she: From age six to twelve never saw a slide rule, a table of logarithms, a table trigonometric values, nor an electronic calculator. Did not learn to multiply fractions, ...
6
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7answers
3k views

How do you handle the frustration of having to GRADE student exams / homework?

A math student may write very long and detailed answers, just because he or she does not know what to look for, for example in Geometry proofs. Or - a student may just write an arbitrary step without ...
0
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0answers
79 views

Is it okay If I spend long time on a single question, if the questions are off Jee mains level? [closed]

Is it okay if I spend about 30 mins to 1 hours trying to solve a single math's questions? The Joint Entrance Examination (JEE) is an engineering entrance assessment conducted for admission to Top ...
-1
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0answers
90 views

Which syllabus is harder and more detailed - IB Math AA HL or A level further math? Also, can I take A level further math as an independent person? [closed]

I've two questions that I'd like to ask: I teach IB Math AA HL on a regular basis, but plan to take on some A level further math in near future. I'd like to know how much harder or more detailed A ...
0
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1answer
193 views

in what sense is the subject of finite group theory 'algebraic'?

[cross posted from mse] the class of all finite groups is not closed under produtcs - example: the product over all finite cyclic groups - thus it is not a variety of algebras, ie, it's not ...
7
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7answers
3k views

What is the preferred way to denote the Pythagorean theorem equation?

I am teaching 12-16 year olds. How should I write down the Pythagorean theorem equation? Some alternatives: $a^2 + b^2 = c^2$ $\text{leg}^2 + \text{leg}^2 = \text{hypotenuse}^2$ $\text{leg}_1^2 + \...
3
votes
1answer
64 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 ...
6
votes
3answers
269 views

What is the purpose of “instant” tutoring?

I want to start by sharing my teaching philosophy: I believe in teaching in a way that is primarily student-centered. That is, I prefer to do less talking to give the student(s) more time to practice ...
1
vote
2answers
172 views

Should I do all the proof practice problems in How to Prove It, an intro to proofs book?

Like the title says. I am self studying intro to proofs(How to prove it by velleman) so I can start an introduction to analysis. I am wondering if I should complete all the exercises in the textbook(...
4
votes
7answers
255 views

Should I avoid writing: $ 11:40 - 15 \text{ min} = 11:25$, and what are alternatives to this way of writing?

I want to stress to my students that we should be careful with how we treat the equals sign and that we should always make sure that the units match. However, sometimes I write $ 11:40 - 15 \text{ min}...
3
votes
0answers
133 views

Parkour and Mathematical Practice?

Learning mathematics and learning parkour seem to have a lot in common. Both can be done on varying levels, but to progress in either one needs to overlearn and build basic skills so that these skills ...
5
votes
1answer
109 views

Students reliant on answers provided, but not their own reasoning?

Evidence suggests that even instructional approaches that produce conceptual gains may leave students reliant and expecting to be reliant on guidance from instructors (Redish et al., 1998). Students ...
7
votes
2answers
275 views

Phase shift vs. horizontal shift, and frequency vs. angular frequency in sinusoidal functions

TL;DR version: It seems to me that high school curricula no longer distinguish between "horizontal shift" and "phase shift", or between "frequency" and "angular ...
6
votes
1answer
413 views

“Flipped classroom exercises” resources

I was reading this book: "Dynamics of Particles and Rigid Bodies: A Self-Learning Approach" by Mohammed F. Daqaq In the preface, the author explains of his "flipped classroom ...
0
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1answer
145 views

Matriculation exams like in Europe

I just looked at matriculation exams from Finland. They have both basic and advanced level exams. Most US high school seniors could not pass the basic exam. If each US state were to create its own ...
5
votes
7answers
626 views

What is a good second book in high school geometry?

I have been looking at questions on Math Stack Exchange and I am frequently coming across topics that sound as if they could have been optional chapters in a high school geometry class, but I have ...
1
vote
1answer
174 views

Did Americans, before new math came in to schools, really say, 'three from two is nine carry the one", instead of borrowing ten from the tens column?

Tom Lehrer claims and the audience seems to agree with him that the 'old way', before new math to do subtraction was to say, for example, 'three from two is nine carry the one'. I never heard of this ...
7
votes
1answer
875 views

How to be a good math teacher at a liberal art college?

I am thinking of taking up a position at a liberal art college. I have taught mathematics at large public universities but I have no idea what is it like to work at a liberal art colleges. So what are ...
5
votes
2answers
193 views

Why are most college level math textbooks black and white only?

Why are higher level math textbooks almost completely black and white? I can't think of any math textbooks on a subject more advanced than calculus that uses colors. Edited to add that the comments by ...
15
votes
2answers
185 views

Tension between the most intuitive definition vs. the most common definition of a concept

Many definitions in mathematics are "fully crystalized". Sometimes the form of these definitions might be somewhat baffling to the uninitiated. For example, the definition of a relation ...
22
votes
7answers
3k views

How do you coach students who often make small errors?

Some students are prone to making small calculation errors. Not errors in understanding, but errors like adding or multiplying integers incorrectly, or dropping a negative sign. Unsystematic errors in ...
8
votes
1answer
311 views

Grade on proving |$a_1 +a_2+…+a_n| \le |a_1|+|a_2|+… +|a_n|$

In an Advanced Calculus course, students were asked to prove $$|a_1 +a_2+...+a_n| \le |a_1|+|a_2|+... +|a_n|$$ for $n$ real numbers $a_1,a_2,...a_n$ I am teaching assistant for this course, and one of ...
1
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0answers
56 views

Understanding Modular Arithmetic [closed]

Mathematics Educators. I'm having a difficult time understanding modular arithmetic (particularly its applications for proof writing). I understand very well the basics. I know that $a\equiv b \pmod n$...
1
vote
2answers
171 views

Which works better for learning 6 * 7 = 42: saying “six sevens are forty-two”, or “six times seven equals forty-two”?

When memorizing and recalling the times table, I learned to say "six sevens are forty-two", and always wondered what it would be like to learn to say "six times seven equals forty-two&...
0
votes
1answer
138 views

Which academic subjects examine what the advantages and disadvantages of the various number bases are?

Which academic subjects examine what the advantages and disadvantages of the various number bases are, e.g. besides base ten: base twelve, base sixteen, base eight, base two and the ways that they can ...
1
vote
1answer
172 views

Why do so many people hate math?

I love mathematics and I know pretty much everyone in this community does too! That feeling of being stuck on a mathematical problem for days as you try to unearth the complexity in front of you is ...
2
votes
1answer
56 views

How to do continuous course evaluation and feedback

Typically universities ask students to evaluate each course at the end of semester. "On the scale of 1 to 5 how well did X do Y"-type questions. I rather do a continuous survey, from the ...
1
vote
0answers
62 views

Is there any video lecture series on (UG level) graph theory (might not be specific on any books) but the video/content quality is like that of MIT?

Previously I had asked a question about something similar, but more constrained. But now I ask something more general. I just got hold of the Linear Algebra by Prof Gilbert of MIT and they are just ...
11
votes
3answers
250 views

Are there any applications of $x^x$?

I'm teaching Calculus I. It's time for the derivative of $x^x$. In previous semesters, I've told students we mainly do this just for closure, so that we know that we can find derivatives of every ...
2
votes
3answers
197 views

Why do we typically only teach high-school students affine transformations of elementary functions?

A standard pre-calculus curriculum consists of the study of elementary functions: Polynomials, rational functions, (circular and hyperbolic) trigonometric functions, exponential functions, their ...
5
votes
2answers
159 views

Tabular Fundamental Theorem of Calculus

This semester in first-semester Calculus I've been trying to focus on how to do Calculus calculations when given a table of data since this seems to be of importance to science majors. There are ...
3
votes
1answer
98 views

High school algebra books that encourage creative/novel problem solving

Circumstance Hello, I am looking for books that encourage creative problem-solving at the high school level. I attended secondary school in the United States and I have noticed that there are ...
2
votes
3answers
230 views

History of discrete math curriculum

I will be teaching discrete mathematics. I’m wondering if anyone can tell me a couple topics that were classically in this class (in any undergraduate version) that were probably discarded over time, ...
1
vote
0answers
55 views

History of business calculus/linear algebra curriculum

I will be teaching a combination of business calculus and business linear algebra, two classes that have been around awhile at my school. I’m assuming people are familiar with these types of classes. ...
7
votes
2answers
237 views

Do any tools exist that convert “pretty print” equations into “inline text” equations?

Context: I am an assistant professor of mathematics at a small school in the US. Many of my courses have homework assignments administered by WeBWorK. A small minority of students struggle mightily (...
17
votes
11answers
2k views

Natural occurrences of a to the (b to the c)?

Are there some natural contexts in which a double exponential occurs, $x$ to the ($y$ to the $z$): $$ x ^ {(y ^ z)} \;, \textrm{or} \;, a ^ {(b ^ c)} \; \textrm{?} $$ Of course one can contrive many ...
3
votes
0answers
82 views

Self study curriculum for a working professional who is enthusiastic about mathematics

I had some mathematics education during my high school and Electrical Engineering studies, but I never used any of them during my career as a software professional. Now I am again coming across Linear ...
5
votes
4answers
523 views

Distance Between Curves in First-Semester Calculus

In the optimization section of Calculus 1 a common problem is to find the minimum distance between a curve and a point. I'd like to extend this idea and be able to compute the minimum distance between ...
9
votes
7answers
353 views

Worth introducing a mandatory short module on $\LaTeX$ into a mathematics degree?

On Mathematics StackExchange for a particular instance, it is highly recommended that questioners mark up their questions using $\LaTeX$. A surprising number of mathematicians and student ...
2
votes
0answers
203 views

Which areas of maths should underperforming western countries focus on?

I am not sure which StackExchange to ask this question but I am interested in the relative underperformance of Western countries such as Australia, US, UK compared to other higher performing countries ...

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