11 votes

Number theory for self-study students: books and computer languages

I would recommend Python combined with SageMath, as already recommended by Joseph O'Rourke, or rather SageMath and Python comes naturally. Python is a modern, and widely used, interpreted language (...
  • 7,612
8 votes
Accepted

Recommendations for inquiry based/aided discovery textbooks

I am going to copy and paste my answer from another question on this site, because I think one would be hard pressed to beat it in terms of the number of suggestions it covers, and the general quality ...
  • 455
7 votes

Number theory for self-study students: books and computer languages

What computer languages might one recommend for, say, investigations in number theory? I find Mathematica ideal, e.g.: "Mod sequences that seem to become constant; and the number 316" "Does 53 ...
7 votes

How can inquiry-based learning be used in a college classroom?

IBL is a really wide umbrella term, nowadays at least. I strongly suggest browsing the Academy of Inquiry Based Learning website. They have videos for many of the talks at the R.L. Moore conferences,...
  • 5,838
6 votes
Accepted

A role for a non-symmetric equality relation in teaching mathematics?

I believe the answer to this question is "No". Getting students to utilize the equal sign correctly is enough of a headache as it is; they do not understand regular equality. This sounds like a ...
5 votes

Discovery-based and inquiry-based learning

I spent two days sitting in on math classes at Phillips Exeter Academy. It is an outstanding example of inquiry/problem-based mathematics education in practice. Consider their curriculum. Their ...
5 votes
Accepted

In what grade do kids (New York, US) learn common differences?

The linear function component is covered early(ish) in Algebra 1, and quadratic functions are covered towards the end of Algebra 1; so, the former by 7th/8th grade and the latter - if at all - by 8th ...
5 votes

Student Conjectures without Oracular Professor

If you absolutely don't want to introduce your students to proof methods yet, I think you should set a clear timeline. Give them a day or two to work on their conjectures (preferably in groups) before ...
4 votes

How can inquiry-based learning be used in a college classroom?

There are numerous little things you can do to instill an IBL atmosphere in your class; most of them can be found on the AIBL website mentioned earlier. I would also recommend watching this TED talk:...
4 votes

short teaching demo on logs; but by someone who uses active learning

Explain what you explained here to start the interview. Do a 3-5 minute intro that introduces logarithms the way your video would introduce it. Then spend the rest of the time doing whatever else you ...
4 votes

Number theory for self-study students: books and computer languages

Seconding/complementing other answers: Python (and/or Python as a part of Sage) has a command-line interface (on Linux/Unix and on Mac OS) that does allow defining variables, pre-loading files that ...
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4 votes

Number theory for self-study students: books and computer languages

For beginning number theory, Art of Problem Solving has an online course. The textbook used with it, Introduction to Number Theory by Matthew Crawford, can be used alone for self-study. (I have not ...
  • 18.7k
4 votes

Polya's "Nearby Problem" Heuristic and Inquiry Based Learning

(This answer has two parts: The first one is about existing research, and probably relevant, but succinct; the second one is about a problem solved in practice, and possibly relevant, but definitely ...
4 votes

Discovery-based and inquiry-based learning

Here are references directed at teachers more than policy-makers, that analyze teaching from the teacher’s point of view, including the decisions that teachers must make as the lesson unfolds, and how ...
3 votes

Resources for Inquiry-based Projects with Undergraduates

Nice question and I should say Inquiry-based Project is taking my attention. So, I really like these books: Tanton, J.(2001). Solve this: math activities for students and clubs. Cambridge ...
3 votes

Resources for Inquiry-based Projects with Undergraduates

Student Research Projects in Calculus Cameos For Calculus I particularly like the first one because the authors include with each project a description of how long it may take a student, any issues ...
3 votes

In what grade do kids (New York, US) learn common differences?

This is a topic I could imagine not being adequately covered in all U.S. schools, although (as Dave L. Renfro pointed out in a comment), it is listed in the Common Core Mathematics standards under ...
2 votes

short teaching demo on logs; but by someone who uses active learning

I introduce logarithms as answering the question "to what power do I raise this base to get this result?" Ideally I would review exponents beforehand, but 7 minutes is no time at all. ...
  • 788
2 votes

Number theory for self-study students: books and computer languages

Benjamin Hutz has a recent book that could be appropriate: An Experimental Introduction to Number Theory. This book presents material suitable for an undergraduate course in elementary number theory ...
  • 4,536
2 votes

Recommendations for inquiry based/aided discovery textbooks

Combinatorics Through Guided Discovery by the late Kenneth Bogart is a great introduction to combinatorics through a guided set of problems and is freely available for download at the link given above....
2 votes

John Dewey and Educative Mathematical Experience

Not exactly a "study", but you may be interested in a short article I wrote with Deborah Moore-Russo a few years back that touches on issues relating to problem-posing, in particular the last section (...
  • 16.9k
1 vote

Intro to Proof: if $x$ divides $y$, then $ x \leq y$

Let some $k>1$ - since for $k=1$ we have nothing to prove ($x=x$). Starting from the fact that $a<b∧ c<d\Rightarrow a+c<b+d$ we arrive to the fact that for any $x>0$ we have $x+x>0$. ...
1 vote

Using tensegrity structure to teach high school math?

Maybe just do a general unit on solid geometry--it is a bit undercovered in schools. Just have the last class or two be model building and discussion. With the self standing nature of the models ...
  • 1,774
1 vote

Project Based Learning or Applied Math involving modular arithmetics?

I think the idea of check digits is pretty compelling. A bunch of examples of where check digits are used can be found here, including things like government ID numbers in various countries, UPC and ...
  • 2,956
1 vote

Project Based Learning or Applied Math involving modular arithmetics?

Rotations of regular polygons. Start with an equilateral triangle. Label the vertices one, two, three. Define a rotation to be 60° counterclockwise, for example (or you could go clockwise). Note that ...
1 vote

Good apps on the iPad for inquiry-based exploration in a quantitative reasoning course

Mandelpad plots the Mandelbrot set and associated Julia sets in the complex plane, and could spark a few interesting discussions (it has in my class), or even a "fractal art" project. In coordination ...
  • 1,746

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