flowchart of the relationship of various branches of mathematics - found via twitter (IIRC) but source unknown and unfortunately not listed. If you know the author, please let me know; I’d love to give credit.

I love this, I was just looking for something like this last night. I think it’d be nice to see a couple more branches in here, and have it organized more outwardly so that the center is the core and everything coming out of it builds on that core.

Drawing Transformation.

Inspired by twitter conversations with Andrew Shauver. This sketch views a matrix to see its effect on a point in the plane by matrix multiplication.

Simple, but surprisingly fun.

Can you make the drawing/writing reverse direction? Flip upside down or left to right? Lean left or right?

What effect do different determinants have?

On GeoGebraTube. Have fun!

Regression of Thrones by Geoff Krall.

Geoff cleverly used math to prove you’ll never be satisfied. Play with his graph at Desmos.

Measurement problem.

It was a pretty good problem on the front end, too. Smallest table size was 58”, longest 106”, and the table cloths we were interested in covering went from 70” to 108”.

What other questions could you ask with these images?

For our first night of orientation we, the staff, were asked to describe the word team work by using words or images. This is what I did.

At the base is the word “Frame”. I believe it is important to frame the challenge to a student by giving them information, reminding them of challenge by choice, and inciting them.

Next I have “Ideas”. This is the stage where the students need to come up with possible solutions to the challenge while remembering to honor everyones challenge by choice level.

Third I have, “Communication”. This is the stage where students share their ideas, talk to one another, listen to one another, and discuss personal space.

Fourth I put “Cooperation”. To me cooperation is vital to the success of any challenge. Students need to learn how to be both a leader and a follower, while also compromising to the benefit of the team.

Fifth is “Commitment”. Students need to feel eager to complete the challenge by putting in the effort needed. I wrote ‘fun’ because I believe it is important for the activity to be fun and engaging in order for the students to want to complete it.

Next is “Trust”. Students need to be respectful, loving, and caring towards one another so that trust forms, and people will feel confident about the commitment going forth.

Finally “Completion”. Whether or not the challenge is successful or a failure it is important for there to be some sort of resolution.

Lastly, and most importantly in my opinion, the “Debrief.” Students and facilitator need to discuss and analyze what happened during the challenge in order for it to fully have meaning.

Anyway these are my thoughts. What are yours on team building?

Healthy framework! Love that it culminates in reflection. These frameworks help me by focusing on the transitions. I.e. if someone is in cooperation, what might help them build commitment?

Just a teacher! But that kind of cooperative learning is very strong in my experience.

Differentiation v Integration self assessment.

Substituted in a calc 3 class today, and the teacher gave us review to do. I asked the students to rate their comfort with differentiation and integration as the percentage of those problems they could compute.

Warned them that integration was a lot trickier than they seemed to think!

The second graph is their differentiation comfort - their integration comfort. (Green is negative.)

As a warm up, I asked them to explain integration or differentiation to a non-mathy relative. Turns out that was difficult!

This sketch is inspired by a great story at Pat Bellew’s math history blog.

The theorem (illustrated here for the smallest case) involves Esther Klein, Paul Erdos and George Szekeres, plus the birth of combinatorial geometry,

and the marriage of two mathematicians!

This theorem is also covered at Theorem of the Day. (pdf)

The question is: given 5 points in the plane, can you arrange them so any 4 of them form a concave quadrilateral?

Playing around, you may start to wonder if you can make just 1, 3 or 5 concave quadrilaterals!

This requires play; on GeoGebraTube. This is a rare one that works in Java but not HTML5. Best option: download.

Sperner’s lemmaColor the vertices of a triangulated triangle with three colors such that:

- each vertex of the main triangle has a different color;
- each vertex on an edge of the main triangle is colored with one of the two colors at the end of its edge;
then there exists a small triangle whose vertices are colored with all three different colors. More precisely, there exists an odd number of such triangles.

This result looks playful and innocent but is in fact quite powerful. It is known, for instance, to lead to an easy proof of Brouwer’s fixed point theorem. Its power mainly lies in building bridges between discrete, combinatorial mathematics and continuous mathematics.