Math teacher friend Bowman Dickson and I presented a session at NCTM in Orlando on Friday. I have never given a public talk about math teaching before. Well, that’s not precisely true. I’ve led a couple of sessions at Math for America on the online math teacher community known as #MTBoS (as part of a larger thing that MfA was doing for new teachers). And at TMC, I have led some workshops. But this felt more official. The program committee for the Orlando meeting contacted me about presenting, and it wasn’t a workshop but a talk. And upon advice from a friend who said “you need to do this because it terrifies you,” I decided to do it. But only if my friend Bowman would do it with me. And of course he did.

This post is going to share the talk. If you scroll to the bottom, you’ll get access to the slides and the handout.

Title: The DIY Math Curriculum: Simple tricks to make creating your own material feel less onerous

Abstract: Don’t like the way the textbook approaches a concept but are intimidated by creating your own content? Bowman and Sam both write their own content from scratch. We’ll share the simple lesson-design tricks we use to write investigations that lead to vibrant discussions and a-ha moments. You will leave ready and excited to write your own content!

Hack #1: Old Problem, New Problem
The Important takeaway: This is the simplest of all the hacks. You might already do this naturally, and textbooks sometimes have questions that switch what students are traditionally given and what they are asked to find. If you’re hankering to see if students have gotten what they’re doing conceptually, mix things up. Just look at a problem and see if you can’t refurbish it by maybe giving them some information and “the answer” and asking them for some other piece of information that they traditionally are given. When you do this, kids will think harder, talk a heck of a lot more with each other (because the problem is more abstract), and you’ll often have many different responses that lead to great whole class conversations.

My favorite slides (one content, one funny):

 

Relevant blogposts:

• Give students right triangles and have them associate the correct trigonometry equation that corresponds with those right triangles: http://bit.ly/NCTMSamTrig
• Come up with the equation for a parabola given a focus and directrix, and the backwards question: http://bit.ly/NCTMSamParabola
• Give students definite integrals and signed areas but missing the function, and see what functions they can draw: http://bit.ly/NCTMSamIntegral
• Play Rational Function Headbandz with students, where students have a rational function (or trig! or logarithm! or whatever!) on their forehead so they can’t see it, but they ask each other yes and no questions to determine the equation of the graph: http://bit.ly/NCTMSamHeadbandz
• Students use protractors to attack forwards and backward questions on inverse trigonometry on the unit circle: http://bit.ly/NCTMSamInverseTrig
• Instead of giving students visual patterns and ask them to come up with the sequence, why not have them come up with their own visual pattern using blocks?: http://bit.ly/NCTMSamBlocks
• Mathematical Iron Chef using group-sized student whiteboards: http://bit.ly/NCTMBowmanIronChef

Hack #2: Thinking Before Mathing
The Important takeaway: Too often, mathematical notation and premature abstractness get in the way of student thinking instead of being the tool for efficiency and communication that it is for those of us that already understand the concept. Let students play around with ideas in their heads, with their own framing, and own vocabulary, before you develop abstract structures. Let them do it their own, inefficient way before you show a better, more efficient, “correct” mathematical way – the right way won’t stick unless they’ve created something in their brain to stick it to!

My favorite slides (one content, one funny):

 

Relevant blogposts:

• Bowman’s blogpost on the fold and cut problem: http://bit.ly/NCTMBowmanFoldCut
• Sam’s blogpost on the fold and cut problem: http://bit.ly/NCTMSamFoldCut
• Fawn Nguyen’s Visual Patters: http://visualpatterns.org
• Kids conceptualize how solids in calculus are formed before learning technical notation and abstract vocabulary: http://bit.ly/NCTMBowmanVolume
• Have kids “notice and wonder” with a single polar equation to generate lots of curiosity about conic sections: http://bit.ly/NCTMSamConicSections
• Kids are asked to find the center of rotation of a figure, and playing with patty paper first makes it more puzzle-like and fun!: http://bit.ly/NCTMSamPattyPaper
• Dan Meyer: If math is the Aspiring, then how do you create the headache? http://bit.lt/NCTMDanAspirin

Hack #3: Make Math Magical Again
The Important takeaway: This hack takes some time, but it is worth it. You are trying to build up a moment of surprise and curiosity for kids – something that will make them want to learn more. (It’s like watching a magic trick. You’re in awe, but you desperately know how the trick was performed because magic isn’t real.) You have to think about something you find interesting and really dig deep to figure out for yourself why it is interesting. That takes some thinking! But once you find the answer, I’ve found it often points directly to a way to get kids to appreciate that thing. Often times, I’ve found that having kids explore uninteresting things is powerful because it gives context for the interesting outcome (e.g. appreciating that the complex solutions to polynomials when plotted aren’t that interesting, but solutions to xⁿ=1 are interesting). Also, like in magic, misdirection can also work. Have kids think they are working on one thing, but actually have them accidentally stumble upon another thing can be powerful (e.g. algebraically finding properties of very different looking trig equations like x-intercepts and vertical asymptotes, but as students work, they find out the very different looking equations actually produce the same graph).

My favorite slides (one content, one funny):

 

Relevant Blogposts:

• A way to motivate trigonometric identities which will make them feel a bit more interesting/magical: http://bit.ly/NCTMSamTrigIdentities
• A way to get kids to be surprised that the perpendicular bisectors of a triangle always meet at a single point: http://bit.ly/NCTMSamPerpBisectors
• A mistake and observation that a student made can be turned into a fascinating lesson: http://bit.ly/NCTMSamMistake
• The moment Sam vowed to change his teaching so that he put a focus on the artistic and creative aspects of mathematics – because he loves the surprise and beauty and wants kids to get that surprise and beauty: http://bit.ly/NCTMSamCreativity
• A simple way to make the joy/magic students feel public and contagious by using a simple $5 hotel bell: http://bit.ly/NCTMSamBell
• Helping students understand the idea of limits by hiding the value of a function at first: http://bit.ly/NCTMBowmanLimit

Hack #4: Toss ‘Em An Anchor
The Important takeaway:  Math instruction doesn’t always need to go from skill to practice to application. Instead, application to some interesting context, whether that be abstract or “real world” can actually drive student learning, and help them learn the more mundane skills and contexts. Great anchors are both natural to the mathematical context, and sticky – tangible, novel, memorable, easy to refer back to.

My favorite slides (one content, one funny):

 

Relevant Blogposts:

• Introducing Inflection with Infection: http://bit.ly/NCTMBowmanInflection
• Modeling Memory with Calculus: http://bit.ly/NCTMBowmanMemory
• Using Income Tax to review piecewise functions: http://bit.ly/NCTMBowmanIncomeTax
• Use inflated balloons to introduce the idea of related rates to make the idea of two rates being connected in different ways “sticky”: http://bit.ly/NCTMSamBalloons
• A series of posts about “pseudocontext” in math textbooks from Dan Meyer: http://bit.ly/NCTMDanPseudo
• An anchor problem for Riemann Sums involving estimating the area of a weirdly shaped object: http://bit.ly/NCTMBowmanRiemann
• When introducing arithmetic series, have every kid in the class fistbump with each other in the most efficient way possible… Kids will constantly be referring to “the fistbump problem” for the rest of the unit:
• http://bit.ly/NCTMSamFistbumpsTwo posts about the concept of letting kids come up with the idea of “Squareness,” basically, inventing a measure for how square a quadrilateral is, one from Avery Pickford, one from Kate Nowak: http://bit.ly/NCTMSquareness1, http://bit.ly/NCTMSquareness2

Photos of Me and Bowman Presenting:

 

 

A photo of Bowman, me, and my colleague who came to support me!

Some Tweets about the Presentation:

 

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Resources: 

NCTM Orlando Handout PDF

Slides (with one taken out…):