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94 views

References for visualizing numbers in base 10 flats

Base 10 blocks (units, rods, flats and cubes) are a widespread manipulative material for teaching place value. However, piling rods on top of each other is not very stable, so it is not easy to build ...
2
votes
0answers
78 views

Math websites/apps for high school students

I am undergraduate math student who is interested in being a high school math teacher. I have been given an assignment to present to my class (for a total of about 20 minutes) a teaching tool or a ...
2
votes
0answers
140 views

Why are a.e. defined functions rarely mentioned in elementary books?

In any standard development of measure theory in several well-known textbooks, the use of almost everywhere (a.e.) defined functions are first seen in the statement of Fubini's theorem, which states, ...
2
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0answers
98 views

Is There Book on Collection of Theorems? [closed]

For example, there is a book titled "Synopsis of Elementary Results in Pure and Applied Mathematics: Containing Propositions, Formulae, And Methods Of Analysis, With Abridged Demonstrations" (...
2
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0answers
204 views

Online open-course-ware that uses Maclane's book “Algebra”

I am struggling with that book which I find to be more of second-guessing type than a book for self-study: it has cryptically written sections, no examples (and those given, and rarely, are even more ...
2
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0answers
117 views

A compelling example of what complex numbers are for, before teaching them [duplicate]

When talking to kids before they are taught complex numbers, I would really like to give some examples of why it will be exciting to learn them. I am comfortable explaining the intellectual ...
2
votes
0answers
189 views

why don't we do labs in/for math?

(this is in the US and at a high school level) why don't we dedicate a day of the week each week to do a lab for math for exploration? I mean we already do that for Earth Science, Physics, Chemistry ...
2
votes
1answer
139 views

Could this visual explanation of horizontal shift be helpful ? …( if not beautiful…)

With the image below I try to explain in which way substituting (x-a) ( with a> 0) for x in the expression defining a function results in a shift to the right, although " intuition" tells us it ...
2
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0answers
109 views

Tactile Learning Activities in Mathematics

Julie Barnes, Jessica M. Libertini. Tactile Learning Activities in Mathematics: A Recipe Book for the Undergraduate Classroom. 2018. MAA Press. AMS Bookstore link. Can anyone comment / review ...
2
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0answers
110 views

Complex logarithm and $\mathbb{C}/2i\pi \mathbb{Z}$

Is it possible and is it a good idea to introduce the additive group and metric space $\mathbb{C}/2i\pi \mathbb{Z}$ very soon, at the same time as the complex logarithm $\log(r e^{i \theta}) = \ln(r)+...
2
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0answers
322 views

a theorem to simplify continuity in Stewart's calculus: early transcendentals

I'm covering section 2.5 of Stewart (on continuity) and stewarts treatment seems needlessly complicated. It seems like the following theorem would streamline a lot of it: If $f(x)$ and $g(x)$ are ...
2
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0answers
53 views

Geometry sample tests

I am teaching intro to Geometry using Moise and Downs textbook. It is an excellent text but somewhat old. Does anyone know if there are sample tests that are available for use with this textbook?
2
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0answers
112 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 ...
2
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0answers
67 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 ...
2
votes
0answers
108 views

Why does result depend on procedure in my calculation of surface area using Guldin? [closed]

At present, I teach Guldin's rules for surface and volume of rotation, and give an example task from the textbook. The textbook uses procedure 1 (below) for calculation (below), but I advocate that ...
2
votes
0answers
103 views

Which book to use concurrently with each of these mathematics texts?

I'm in search of a good book that I can read --- and recommend to my proteges to read --- along with each one of the following books. Topology by James R. Munkres, 2nd edition Introductory ...
2
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0answers
65 views

Is the annual system still in vogue anywhere in Europe, North America, Australia, or East Asia? And what about the 2-year B.A. / B.Sc. degree?

In Pakistan, we have until now had 2-year B.A./B.Sc. and 2-year M.A./M.Sc. university degrees after our 12th grade F.A./F.Sc. qualifications. Thus the former was a 14-year academic qualification, ...
2
votes
0answers
54 views

App to show exercises solved by students in real time

I'm looking for an app that can be used when the teacher gives a set of exercises to his class to show for each exercise how many students solved it, how many students tried to solve it, etc. The ...
2
votes
0answers
110 views

Strategies for learning proofs

What are the best methods for learning proofs? I'm tasked with learning two dozen proofs about the properties of continuous functions and real numbers in a week well enough to be able to present them. ...
2
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0answers
199 views

Introduction of the power set as a collection of *labels* or *names* for subsets

The way that naïve set theory is usually presented in undergraduate education is via very concrete examples of sets, often involving non-mathematical elements. When power sets are treated, having a ...
2
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0answers
93 views

what is the standard subdivision or classification of calculus related rates problems?

I am working on a project where I have to group/classify calculus problems. Now with most the calculus topics, it's usually obvious how it's divided in various textbooks, but when it comes to related ...
2
votes
0answers
233 views

How many secondary-school students are working on achieving independent understanding?

If mathematicians and math teachers and textbooks in all cultures in all eras say that a certain theorem has been proved, then the reasonable layperson trusts them. At the same time, a student who ...
2
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0answers
82 views

Finding the correct mathmatics based on application as opposed to the other way around?

I just tried to pitch a Math Recommendations site, and it was shot down because it is too broad and that Stack Exchange sites operate on a separation of concerns principle; which makes sense to me but ...
2
votes
0answers
60 views

OP (Overlall Position) Calculations for Queensland's post-secondary-entrance rankings [closed]

I am looking to calculate an OP Score (Overall Position). It is an outdated Queensland system of post-secondary-entrance rankings due to be phased out in 2018. None the less I am looking for specific ...
2
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0answers
180 views

Core-Plus Mathematics: Similar Resources for grades 7-9

I'm looking for rich educational resources similar to core-plus mathematics, for grades 7, 8, and 9. Is there any such material?
2
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0answers
83 views

What should I teach 13 to 15 years old pupils to learn competition mathematics? [closed]

I would like to teach some young and talented pupils basics of competition mathematics. What kind of methods, topics and theorems should I teach to those who are good at school mathematics but have no ...
2
votes
0answers
66 views

Request for IBL Script for Putnam-type Problem Solving Course

One of the major benefits of a good IBL script is that it effectively organizes the experience of students so that their effort does not need to be used on such organization. A good script leads from ...
2
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0answers
183 views

Cognitively Guided Instruction (CGI) for 5th Grade

Are there any schools out there successfully using CGI with a 5th grade curriculum? Our students have poor number sense, and we'd like to remediate using CGI. I'd love to compare sequences of lessons ...
2
votes
0answers
119 views

Is the absence of complex analysis a significant disadvantage in math grad school application? [closed]

I am a junior math major considering math grad school, possibly in probability theory. Would the admission commitee of math grad schools view the absence of complex analysis as a significant ...
2
votes
0answers
118 views

Basic Bayes rule problem [closed]

I was reading this article, and I decided to use the “canonical example” of a “precocious newborn observing his first sunset” as a problem for my students (undergrads in an intro to inductive logic ...
2
votes
0answers
186 views

Minimum preparation to pass advanced functional analysis?

I have made a big mistake by signing up to an advanced functional analysis class, when I do not have the background. This is my first analysis course ever, and aside from that my math background is ...
2
votes
0answers
54 views

Lancasterian/Monitorial system at a secondary level?

While getting stuff ready for the soon-to-be-here school year, I came across Joe Lancaster and the Monitorial system, where older students who have mastered certain content areas are charged with ...
2
votes
0answers
86 views

How can one explain that $(-1) (-1) = 1$ [duplicate]

How could one explain that $(-1)(-1) = 1$? I am trying to avoid arbitrary rules. I suggested to my student to think of it as a reflexion around the 0. putting emphasis on the idea that if you reflect ...
2
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0answers
208 views

Software / hardware for creating Khan Academy style videos? [duplicate]

What software and/or hardware is typically used for creating Khan Academy style math videos?
2
votes
0answers
68 views

Feedback about statistical and numerical illiteracy-examples website? [duplicate]

I have assembled a list of statistical and numerical illiteracy examples in the media, as they appeared in Chance News online (a statistics wiki) between 2005 and 2014. See "Collected Forsooths at ...
2
votes
0answers
172 views

How to choose a good PhD student in pure mathematics? [closed]

I have some personal criterion to choose my graduate students including PhDs. Here I would like to know what my colleagues' criterion are to choose their math PhD/MSc students. I hope this may help me ...
2
votes
0answers
125 views

Searching for an analysis textbook [closed]

Particularly, I'm looking for an undergraduate text with an excellent explanation of $\delta$-$\varepsilon$ proofs, and many example questions related thereto.
2
votes
0answers
75 views

Where to find resources about study skills and strategies of immediate impact? [closed]

Where can research and resources be found, about study skills and strategies for university math of immediate impact? To wit, how do I efficiently find categorical, pragmatic advice about learning/...
2
votes
1answer
215 views

Is derivation based Math a good way to teach my 5 years old daughter addition? [closed]

I love deriving formulas. I am pretty good at Math. Maybe because I have a little asperger syndrome. Most people don't learn Math that way. Why not? I recently taught peano axioms to my daughter. ...
1
vote
5answers
438 views

Proportional density function question

Here is a question I gave on an exam last year. Please let me know what you think of the question (eg: if it is a fair question, easy, difficult, etc). A lot of students were upset for questions like ...
1
vote
6answers
1k views

Can undergraduate math courses be taught at a high school level? [closed]

Can these be taught at a high school level? multivariable calculus linear algebra abstract algebra real analysis complex analysis (non-measure theoretic) probability theory Maybe even other more ...
1
vote
3answers
92 views

Determining sets to show sufficiency of a condition?

$p \to q$ that means (among others) $p$ is a sufficient condition for $q$. To show the sufficiency, I teach my study by determining the set for $p$, the set for $q$ first and comparing their ...
1
vote
2answers
218 views

Is playing and teaching chess appropriate in private lessons?

I am giving tutoring to a high school student since more than one year and half. He is about 17 years old. He has excellent results in mathematics, being best student in his class for the last year ...
1
vote
4answers
315 views

Why is a translated exponential function considered an exponential function?

I am tutoring a student preparing to take Calculus 1 at a university. This student hasn't taken precalculus for a year, so I have been drilling him on definitions, rules, and theorems from a college ...
1
vote
3answers
274 views

Word for the dimension of the vector space in which a vector lives?

The following issue comes up whenever I teach linear algebra: I want to have a quick way to say that a vector $(x,y,z)$ is in $\mathbb{R}^3$. I am tempted to say that it has "length $3$". But then ...
1
vote
5answers
239 views

Practical case for solving with system of 2 equations

When I teach basic math I want to emphasize on it's power (algebraic part for starters) as a tool for solving certain problems you cannot solve with naked brain, so that one models a problem with ...
1
vote
3answers
155 views

Does the “Find” in questions such as “Find the solution” imply the process of finding must be laid out?

I am currently marking a set of math assignment at university, and I am wondering about the following general point: in a question such as "Find the solutions to the equation $x^2 - 3 = 0$", does the ...
1
vote
3answers
191 views

when should we teach basic complex algebra?

I am teaching Differential Equations this semester. The pre-req is Calculus II, not even Multivariable Calculus. I made my peace with that, can't fight with the big-shots of the department. So, I have ...
1
vote
3answers
313 views

Is there a symbol for 'a bit smaller than'?

Im looking for a sign that is the reciprocal of '$\ll$'. Where $a\ll b$ means that $a$ is very much smaller than $b$ (and perhaps may be neglected), im looking for a sign that expresses that $a$ is ...
1
vote
1answer
182 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 ...

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