Math & Teaching Ideas I might use
- I want to show this to my pre-calc class as part of their intro to trig: sailboat leans to get under bridge
- Wild Maths has a lovely collection of questions with photos: Move it to prove it
- Snug angles, from Sam Shah. He's doing it with a geometry class. I'm wondering if it might be good at the beginning of the trig unit.
- As I prepared for Math Jam, our 3-day pre-semester math boost, I found lots of cool ideas here: Math Assessment Project (assessment doesn't sound promising, but these activities have lots of open-ended questions)
- I just learned that if you start with the harmonic series, which diverges, and take out all the terms with 9s in the denominator, you'll get a converging series. Too weird. I don't understand it yet, but I sure want to. (for Calc II)
- Geometric construction on sciencevsmagic.net. (I knew about this site, but reading this post made me decide to use it in Math Jam to get them playing around.)
- Mobius Hearts. Too fun not to do. (I didn't use it, though. Too overwhelmed this past month to do anything new...)
- Sam Shah made this fabulous website, Explore Math, that pulls together gobs of cool math resources from the web. He has his students pick one (or was it a few?) to play around with and report on. I believe I'm going to do this in pre-calc.
- What is proof? Here's a good conversation about proving the Pythagorean Theorem with visuals. Includes the best video I've ever seen, on my favorite proof.
- Trig Fairy Tales (having students write them)
- Infinity is so weird! (infinite ping pong balls in, infinite ping pong balls out, how many left in?)
- Infinite sums and China's demographics
- Algebra Aerobics Stick Figure in Geogebra
Problem Solving
- Finding out how far you can drop an egg without breaking it
- Systems of equations, using a problem with no solution
- On problem solving, with videos. I might give the absolute value problem in precalc, as a challenge.
- Doubling surface area, a good question
- What's the longest time you've ever spent solving a problem?
- Flipping pancakes
Using Desmos
- An introduction to desmos
- Linearization in Calculus, an amazingly detailed lesson using desmos, with commentary about how students did with it
- I do a unit in trig called Days Of Our Lives, using minutes of daylight on each day of the year as data, and getting students to construct an equation for it. This Moon Illumination project someone made on desmos using the activity builder looks like something I could imitate. (Where did they get their data? Who made this?)
- Desmos art project
On Teaching
- Michael Pershan, on writing about teaching
- How to help people remember what they learn (using retrieval practice)
- How do you respond to wrong answers? This post helps me think about that.
- A good summary of Dweck's Mindset research
- Ben Blum-Smith on the strategies used at PCMI. "when students are talking to the room it is always students that Bowen
and Darryl have preselected to present a specific idea they have already
thought about. They never ask for hands, and they never cold-call. This means they already know more or less what the students are going to say." And then Elizabeth responded. I loved her katamari.
- Using sentence starters for math conversations with 4th and 5th grade students
- Fraction talks
- Getting students talking to each other
- Getting students not to fear confusion
- Physical activity during lessons improves learning (research with elementary students, but I imagine it would help my college students too. Yikes! I don't like this perspective: "the researchers found no differences on reading scores. They think activity works better for subjects with a lot of memorization and repetition." Math should not have lots of memorization!)
- More movement and math...
- If I were a high school teacher, I'd seriously consider this. Metacognition and homework
- On Metacognition (download pdf, interesting part for me is sections 3 and 4)
Science
- Simulation, mathematically modelling how chemistry and growth work together
Statistics
Estimation & Elementary
- How many blocks will equal an apple? (3-act lessons, with video)
- Number Talks
- Pre-algebra: Working with signed numbers
Math for Parents
- Parents’ Math Anxiety Can Undermine Children’s Math Achievement
- Fractions may be elementary (previous topic), but the idea of fractions is also the first math concept that messes a lot of people up. Here's James Tanton's new collection on fractions.
- When did you stop playing around with mathy ideas?
- A video about what kids learn in the early grades about addition and subtraction (Please let me know what you think!)
- Finding the Beauty in Math
Social Justice
- On responding to people's surprise that I'm a math teacher
- How affirmative action makes for a better physics education
- "Why Black kids don't like math..."
- The master's tools... (Dr. Danny Martin's talk at NCTM conference)
Playing with Math
- As usual, this game (called this game is about squares) is more about logic than about math. What I'm finding interesting is how impossible it seems, and then when I (and others) go away and come back, it can suddenly seem so easy.
- Tracy Zager wrote a great post on evaluating math fact apps. Lots of good ones are mentioned in the comments. [My comment: I would really love to be able to find this app online so I can recommend it. I have this game on my phone. It seems to be called 1 Whole. There are rectangular shapes that fill with liquid. You push one toward another and they go together if the sum is less than or equal to one. You watch the liquid rise. If it’s 1, it goes away and you get points. You keep going until the screen is full of things that won’t combine (sum > 1). There is no time pressure, the conceptual basis seems strong to me, and mistakes aren’t allowed. No penalties, no bad sounds, it just won’t work. I think it’s pretty good. I wish I could find it online. Cna anyone help me?]
- Kids like doing the simple math involved in thinking about the Collatz Conjecture. [Start with any number (whole, >1). If odd, triple it and add 1. If even, cut in half. Repeat. Does this always end up at 1? Conjecture is 'yes'.] Mathematicians don't know the answer, but they like to explore the question in sophisticated ways. Here's a post on what sorts of functions come close to modeling the number of steps it takes to get to 1 from each number.
- This game would have made it into my book, I think. Cross Over looks like it has enough strategy to entertain us jaded adults, and it's for addition and subtraction practice. Coolo.
- Not math. Go. Learning to play go.
- New game for iphone (really, it's logic not math), Ringiana
- I love surreal numbers. I need to come back and read this more carefully when I have more time to play with it.
- A silly little game. Totally violates Tracy's criteria (nothing timed). But mathy folk may like it. How many primes can you identify in a minute (with no mistakes)? (Use y and n for y and no.)
Books
- Here's a great list of fun math books, compiled with a 14-year-old in mind, but almost all good for adult mathophiles too. I think this list came from the same question and has a different set of books.
- My publisher is having a sale. All 5 books published by Natural Math for $50 total. What a great way to expand your playful math collection.
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