Friday, February 28, 2014

Math and Inequality

Got this email, and I'm wondering how a math educator should respond:
Dear Colleague,

A teach-in is being planned for the purpose of mutual education among students, faculty and staff of the GVSU community.  The teach-in is designed to address topics related to inequality and systems of oppression, as well as social justice and liberation.  Recognizing the multi-faceted dimensions of these topics, we are planning this teach-in as a day-long event.

The details are as follows:
Date:                     Wednesday, March 26th
Time:                     8am – 10pm
Location:              Exhibition Hall, Mary Idema Pew Library  (Room 040)

The learning objectives of the teach-in are to raise awareness, share knowledge, and create dialogue.  Therefore, in an effort to involve as many students, faculty and staff as possible, we will be adhering to the MWF class schedule, with the possibility of fourteen 50-minute sessions, each starting on the hour. 

We hope that you will attend as many sessions as your schedule allows and encourage your students to attend.

If you’re interested in taking a more active role, you’re encouraged to work with other colleagues around campus to propose a 50 minute session. Please keep in mind that a teach-in is practical, participatory and action oriented. We especially encourage contributions with an intersectional framework (race, class, gender, sexuality, religion, ability, etc.).  Sessions may include student leaders as co-presenters or panelists.
I love that the university is doing this. Will you help me brainstorm how to participate?
I have an intro to math class, and a grad class on secondary math education issues that meet during this time.

Thanks for any ideas!

Lucky Duck is a recurring character
in Tom the Dancing Bug by Ruben Bolling

Tuesday, February 25, 2014

Capstone Book Club

One of the courses I'm teaching this semester is a capstone course for our majors. Rather than me picking the book, I let them choose from a list that the Math-Twitter-Blog-o-Sphere helped me put together. Last summer, The Mαth Book and Joy of X were the big hits, this semester, they made some very different choices. (Here's the list and their choices.) Having them choose makes me feel a little less like this:

My notes of the discussion, with links to some of their blogposts. Since they're notes of a discussion, pretty terse. Also, not my point of view, this is the students'. The people who got the most new students interested in their book were those reading The Mathematician's Lament and e: the Story of a Number.

Euler: Master of Us All. History at HS level, proofs at graduate school. Felt outclassed reading it. Simplify or explaining the proofs would have helped. Averaged a paper per week. Very dense.
Review: Alex

Visions of Infinity. Each chapter is a different idea, then has history and the author explains the important proofs about the idea. How mathematicians think vs what they thought about. Eg. squaring the circle, explained why you couldn't do it. Was advanced, but not frustrating. Recommend it to someone who knows about math. Last two chapters… where math is going. Strongly the author's point of view.
Review: Kristine, Emily

The Math Book: one discovery per page. Good if you like quick little synopsis of many topics. Different big discoveries. Learned a lot of little things, but so rudimentary in some places. There were some over your head, too. I would recommend it. Gives sources to dig deeper. Easy to make connections. Biased towards white Christian males.
Pro reviews: Kenton, Erin. Con review: Brittney
Journey through Genius: history, picks important results and proves them. No non-western mathematics. Tries to justify why no islamic mathematicians but comes across as a cop out. The Greeks asked why, but the Egyptians were satisfied with just working. Did give a personal view of the mathematicians. Recommended to people who want to get to know the mathematicians well.
Review: Biz looks at it from a multicultural perspective.

Accessible Mathematics: 10 instructional shifts. Works with field experience, works with math ed classes, what happens when you don't use these. Multiple representations, number sense. Good to examples and non-examples. Recommended to anyone going in to teaching or to teachers who need to change.
Review: Danielle, Becky, Keegan

Concepts of Modern Mathematics: overview of the math classes you have to take here. Like 310, statistics, history on those areas. People who have made significant work in that area. Some new to us, like topology. Pretty dry and boring. First chapter was the peak, then funniness ran out. Long lines of equations. Not a bad book for someone in 210, to know what's coming, but then it would be hard to understand. Examples are pretty simple - maybe even dumbed down. Pretty dull read. Good at explaining ideas like 1 to 1 and onto. Large scale review.
Review: Bryce. Killer line: "Mr. Stewart slowly became less of my friend who I wanted to hang with and more of a dreaded professor whose class you have to sit through every week."

Godel Escher Bach. It's about cognitive science, psychology, computer science, math. The Godel part is the most on math. You think because you are, but you have to be to think. Need a lot of time to dig in. Hurts to read, in a good way. Challenges the way you think. Connections with taoism and Buddhism. Isomorphisms and symbols… uses all these metaphors. Kind of like A Brief History of Time by Hawking or The Elegant Universe by Brian Green.
The Joy of X. Goes from things people have been told is true to why they're true. Negative times a negative, infinity… goes further at the end.
Short review but long notes: Jennifer
Sensible Mathematics, sister to Accessible Mathematics. Written more to administrators than to math teachers. Why it's good to have students explore more. Convinces teachers and parents to go with modern views of learning and teaching mathematics.
Review: Kerry
Love and Math. Hard to understand because it's so into physics. His life story is interesting, discrimination against Jews in Russia as a backdrop.
Kate's review says that you should like physics and math to pick up this book.
The Mathematician's Lament. Talked about how math is an art. It's about discovery, and we need a big do over in education. We're just handed formulas, not told where they're from or who made them. Can't teach teaching. Recommend to any future teacher.We take away the art of math.
Powerful review from Sara.
e: the Story of a Number. I didn't know where e came from. That's why… the math amazes me more. Everything I learn unites math more. This book did that and combined it with physics, through the number e. Pascal's triangle, derivative of e^x is itself. My optics class is about that. The challenging thing the author had to face. Pi could fit in a few pages, but e, there's no place where it came from. Napier and his tables, and how logarithms require e; when you extend to continuous cases… Book does a good job of balancing history, different contributions. His jumps are really strange and don't make sense until you finish reading. Balances history with math, saves all the proofs for the appendix. Bernoulli's conversation with Bach about the space between notes, a logarithmic increase... that was amazing.
Review: Duncan
There wasn't a whole lot of discussion in the whole class setting, but the individual discussions among students who read the same books were deep and intense. Even the group of people who all had read unique (in our class) books.

What do you think of their reactions? Any disagreements? Is there a new book in which you're interested?

Wednesday, February 19, 2014

Followers Beware

Smarter Balance has released several items for the fast approaching Common Core assessments. One really caught my eye as a dynamic context: safe following distance. I can't find a way to link to the specific item, but it is #43060 at (CCSS: F-BF.1a, F-LE.1b). The sketch is on GeoGebraTube, as well.

How far should you drive behind the car in front of you?

GeoGebra notes: With the spirit of Jennifer Silverman hanging over my shoulder, I got real car images to use. The trickiest thing was sizing the images to look right since the scale was not 1:1. I like the flexibility of looking for feet (sigh, USA) or for car lengths or for time separating the vehicles.

The actual assessment question:
 Pretty complex problem, as illustrated by the rubric:
Just a quick post to encourage you to think about using some dynamic visualization with your math work. Many of the released items have a little gif like animation instead of text.

Sunday, February 16, 2014

Fibonacci Week: Spiral Curriculum

We were discussing Leonardo of Pisa, Filius Bonacci, this week in class, and despite it being the least of his accomplishments, THE sequence always comes up. I finally wised up and, rather than fight it, separated out the sequence stuff into a day of its own.
Our Agenda:
  • The original puzzle
  • And Pascal, too?
  • Spirals & Golden Ratio: what is going on?
    • Vi Hart awesomeness: Part 1 of 3. WATCH at least part 1.
  • Extensions

The puzzle appeared in Fibonacci's momentous The Book of Calculation. In addition to lots of fine mathematics, examples of calculation algorithms, and applications, it has entertaining puzzles and activities. One of these was deeper than he could know.
“A certain man put a pair of rabbits in a place surrounded on all sides by a wall. How many pairs of rabbits can be produced from that pair in a year if it is supposed that every month each pair begets a new pair which from the second month on becomes productive?”
The students were awesome with this. They knew the sequence already, of course, but did a nice job fitting the sequence to the situation. What impressed me were their objections. What if the rabbits weren't split males and females? What about mortality? What about that rabbits can be pregnant with to litters at once? (Impressive. Turns out they can conceive the day they give birth, also impressive, and giving credence to LoP's 1 litter per month.) Also a student who tried to think about all possible pairs. Just good math thinking. The emphasis I tried to convey was making sense of the two representations: the tree diagram that helped most make sense, and the usual expression of the sequence summing two terms to get the next.

I love that the sequence shows up in diagonals of the other mystical math favorite: Pascal's Triangle.I challenged the students with the more important question: why? They both have the add two to get one idea - is that related?
(This image from mathispun.) Does anyone know ow to phrase a probability question that brings up this relationship?

Ever since Susan Walborn and I did this with 5th graders for the Math in Art festival (art connection: Mondrian) I have loved this. It so naturally ties in with the near similarity, and then the fabled Golden Ratio.

One of the things I love is how fast the sequence converges even if you don't start with a square. Start with a very non-square 1x10 and ... well, just look. You can play with the spreadsheet on Google docs.

If you're talking Fibonacci Spirals, you have to watch some Vi Hart. They were properly amused and impressed.

Explore on your own, of course. Ideas:
  • explore one of the connections
  • look into closed form generation of the numbers
  • explore golden ration connections
  • make Fibonacci themed art (Jennifer Silverman or a skyscape)
  • Prove a Fibonacci Proposition


People tried more with the spiral, including on isometric dot paper.  Some played with the sequence and ratios.

Some tried to prove the provided propostions:  (senior math majors)
My extension
I was interested in the spiral, too. (It's a minor obsession.) One interesting thing is that it is an approximation of the Golden spiral (the logarithmic spiral built on Φ), but it has a beginning. However the Fibonacci sequence extends backwards, ...8, 5, 3, 2, 1, 1, 0, 1, -1, 2... so what would that look like for the Fibonacci spiral?

I made a tool in GeoGebra for adding arcs and the center of the next arc for a spiral growing counter clockwise without too much trouble. But it was hard to find a way to do the backwards step that was robust. I wound up going with a vector approach instead of geometric, to better simulate those alternating terms going backwards. It made for some pretty interesting curves!
This gif is showing the same curve depending on the starting ratio of the first two steps. 1:1 to 2:1. Sometimes you get cycles - that's what those four petal flowers are: like 0, 2, 0, 2, ... If you want to play with it yourself, the tools are in this sketch on GeoGebraTube. (Sometimes tools don't work well in the student worksheet and you have to download the .ggb file.)

I also fooled around to make some art for myself. That's in a Tumblr post.