Tuesday, January 17, 2017

Avoid Hard Work: A Friendly Book of Problem Solving Strategies

Another Natural Math book just came out.  It's called Avoid Hard Work... And Other Encouraging Problem-Solving Tips for the Young, the Very Young, and the Young at Heart.  What is it?

First of all, it contains a lot of tips about how to do math with your kids - there are dedicated Q&A sections at the beginning, middle, and end of the book.  It's aimed at parents who don't necessary feel super confident about mathematics themselves and so makes a big effort to be non-intimidating and easy to use.

The heart of the book is ten chapters, each of which introduces a new problem-solving technique and guides you through a few problems using it.  They even talk about how to adapt the problems to toddlers! While most of the techniques and problems were ones I'd seen before, I was really impressed with the accessible and inviting way they were presented.

The thing that struck me most about this book was that the first step listed in solving each of the problems was "react emotionally to the problem". I've been taking an improv class where the big focus is on reacting emotionally to everything your partner says or does, but I've never before heard that phrase in the context of mathematics.  But mathematicians totally have emotional reactions to mathematics.  There are results and proofs that we find beautiful and ugly.  We develop mathematical tastes, just like musical tastes.  Doing mathematics is like an emotional rollercoaster - there are moments of frustration, sadness, confusion, and hopelessness, but also joy, hope, excitement, and satisfaction.  The high that comes with finally figuring out something that's evaded you for weeks, months, or years is amazing.

You can find another review of the book here. I highly recommend it for parents who want to do mathematics with their children aged 3 - 10 and beyond! It's also great for teachers and math circle leaders.  I plan on using this book to make a "Problem Solving Strategy of the Week" as part of the warmup for my middle school math circle.

Avoid Hard Work

Tuesday, December 13, 2016

Mathematical coloring

Last week, I was looking at mathematical coloring pages to use for math circle's holiday party, and I found this awesome free PDF by the mathematician Marshall Hampton.  The patterns are beautiful and fun to color, but also involve some deep mathematics!

BTW, if you're looking for a mathematical coloring book to give as a gift, I highly recommend buying either Patterns of the Universe (Amazon affiliate link here) or Visions of the Universe (Amazon affiliate link here) by Alex Bellos and Edmund Harriss.

Monday, December 12, 2016

A better way to teach geometry

Today, I saw this blog post by Christopher Danielson entitled "How I Learned to Love Middle School Geometry".  I thought it was super useful for parents, math circle instructors, and math teachers. A few highlights:

- Students spend a lot of time learning how to classify quadrilaterals throughout the years (see example below).  But what if you asked them to do the same thing for hexagons? Suddenly, there's creativity, invention, and discovery! This seems like an awesome idea for a math circle or a school math class.

- His book entitled Which one doesn't belong? (Amazon affiliate link here) also looks awesome. On each page there are four shapes, and any one of them could be the one that doesn't belong - so instead of finding the correct answer, it's all about explaining and justifying your reasoning.  For example, in the cover image below, the bottom right could be the odd one out because it has 5 sides and the rest have 6.  Or the top right shape, because it's the only one that's not convex. Can you think of criteria that make each of the two leftmost shapes not belong?

Clicking the image leads to an Amazon affiliate link

Saturday, October 15, 2016

MouseMatics: Workbooks for Preschoolers

In reading this blog post from Musings of a Mathematical Mom, I found out about an awesome series of math workbooks (or maybe I should call them playbooks?) called MouseMatics for young children (ages 4 - 7) by Jane Kats.  She also has a book of math games called Math for Dessert, and a Christmas Coloring Book. 

These books aim to break the standard conventions:
They know that a picture with dots drawn in the corners of a square is called “four”, and an identical picture with an extra dot in the middle is called “five”. But can they recognize the same number five if it looks different?
Always representing the number of five with the same configuration of dots allows students to memorize the picture instead of counting.  This book makes sure to not let that happen:
In some problems, we have two correct solutions (a pair of friends can split a chocolate bar in different ways); some problems lack an answer (an odd number of objects cannot be divided in two). After all, in mathematics no solution is also a solution. A matching pair of shapes can be found in the same column. We build geometric figures using not only the usual squares, but also diamonds, trapezoids, and triangles. When the child is asked to find a number value, we use a variety of shapes in addition to dots: diamonds, crosses, anything. Also, their arrangements in the boxes are random, unlike the standard dice configurations.
However, the thing I like most about these books is this:
The main purpose of the Mousematics series is not to teach preschoolers to count (this is something every child will inevitably learn sooner or later), but to spark the children's interest, to invite them along on an exciting journey into the world of logics and mathematics. 

Resources for advanced high schoolers

David Zureick-Brown is a math professor at Emory, and as I'm writing this he is in the middle of giving a talk to Atlanta-area undergraduate students.  At the beginning of the talk, he pointed to a page on his website which lists fun math links for undergraduates.  While this blog is not aimed at undergraduate students, many of the resources would also be appropriate for advanced high schoolers. Check it out!

Wednesday, August 24, 2016

YouCubed: Lots of great resources for students, parents, and math teachers

This morning, while scrolling through my Facebook feed, I came across an article entitled "Not a Math Person: How to Remove Obstacles to Learning Math". Being a mathematician, the people I meet are always telling me how impressed they are that I study math, how smart I must be, how they were always bad at math in school, how they just aren't a math person, etc.  It's incredibly frustrating, and I still haven't worked out the perfect response - I usually acknowledge that a lot of people have had bad experiences with math at school, but try to impart that it doesn't have to be that way, that pretty much everyone is capable of learning math.

Through reading this article, I came across YouCubed and the work of Stanford math education researcher Jo Boaler. If you haven't already, take some time to read the article and browse YouCubed. Seriously.  So much good stuff there for parents, students, and math teachers at all levels. After an hour browsing YouCubed, I've already used its Week of iMath to plan my first few middle school math circles.  There are books, online courses, articles, lesson plans, and more.

Monday, August 22, 2016

STEM GEMS: Awesome roll models for girls in STEM

This past Friday, I met Stephanie Espy, the author of the book STEM GEMS. The book tries to combat the lack of women in STEM fields by profiling 44 women who are doing amazing things in science, technology, engineering, and mathematics.

The mission of the book is "to help girls and young women to see their future selves as scientists, technologists, engineers and mathematicians, and to show them the many diverse options that exist in STEM". The book also contains a few chapters at the end giving actionable advice for how to set yourself up for success in a STEM career. The women in the book put a special emphasis on the challenges they faced along the way, helping to debunk myths common in math and other STEM subject like "The Genius Myth" and the "It-Should-Be-Easy Myth".

I was very surprised to find that 12 of the 44 women fall into the broad category of mathematician, and there was even a number theorist (Melanie Matchett Wood) featured!! In many STEM initiatives, the M is not emphasized beyond it's usefulness in S, T, and E.

Stephanie Espy was trained in chemical engineering, and so has experienced first hand what it's like to be one of the only women in the room (and oftentimes, THE ONLY). Luckily, she grew up in a family filled with STEM professionals, and so she had the role models that many young people - especially women and people of color - lack.

On browsing it in person, I found this book to be very visually appealing and not at all intimidating, with big color photos to draw you into the stories of these women.  While there is value to learning about historical women in STEM, like Marie Curie, I think that seeing women in the modern world succeeding at fields like animation, global health, data science, and electrical engineering can have an even bigger impact.