the Max Ray Blog

Problem-solving Journal

by Max

June 20th, 2011

I’ve been meaning to start a problem-solving journal and write about actual problem-solving experiences. I’d been putting it off but now that it’s the summer I have no excuse… and then this blog post at Infigons, etc. inspired me!

I just picked out a possible Algebra Problem of the Week for next year that asks, “A point is chosen at random from within a circular target board. What is the probability that the point will be closer to the center of the board than to the boundary of the region?”

Infigon’s problem changes the circular dart board to a square. To which I say, “Yikes!”

My first thought is to solve the simpler problem first. I’m going to start with the circular board. My first idea is we need to find a circle that takes up half the area of the dart board. I know every point on the boundary of the circle is as close to the boundary of the dart board as every other point on the circle…

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Any Questions?

by Max

June 12th, 2011

I’m playing Dan Meyer’s “Any Questions?” game.

What questions come to mind looking at these photos? What questions might come to mind if you were in math class in 6th, 7th, or 8th grade?

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WCYDWT: Building Columns

by Max

March 28th, 2011

My first multi-media math mystery!

I made a What Can You Do With This video of the investigation that launches Core Plus Mathematics Book 1, Unit 6, Lesson 3.

Video 1 is the set-up of the experiment.

Column Strength Video 1: The Set Up from max ray on Vimeo.

Video 2 is a faster version of the experiment (the paper was a little thicker in Video 1) with a question.

Video 3 answers the question.

Video 4 tests a circular column. Read More→

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Pseudoteaching & Lesson Planning

by Max

March 16th, 2011

I’m a math coach, and one major point of contact I have with teachers is around their lesson planning process. Sometimes, we get to talk about implemented lessons and revise them, but way more often the revision process is focused on drafting lessons and improving how they are planned.

So… if I want to help teachers engage in Teaching (as opposed to pseudoteaching), how can I help them structure the planning process to plan against pseudoteaching and for Teaching.

Some first-pass gleanings:

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Bitten by the WCYDWT Bug

by Max

March 4th, 2011

Dan Meyer’s “What Can You Do With This?” idea for creating and presenting multimedia math scenarios for kids to explore has got me totally intrigued. I’ve shared his videos with so many people…

And, I’ve been looking for some kind of hand’s-on, building things project for a while now. I haven’t built enough stuff and played with enough tools and toys since leaving the classroom to work online.

And then Dan blogged the following, “I don’t trust myself to be an effective inquiry-based teacher if I’m not living an inquiry-based life. I don’t trust either of us.

What about your discipline has caught your eye this week? What has prompted you to pull out a notebook or your cameraphone or a video camera?”

I realized it’s been a while. So, I am committing to make a WCYDWT video a month this year. And yikes, I’m already 2 months behind!

Ideas for videos you’d love to see produced? Leave suggestions in the comments, please. My partner is a lovely and talented videographer who knows her way around cameras and editing software, and she’s on board!

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Problem-Solving Strategies and the Common Core Practice Standards

by Max

January 31st, 2011

I just attended an AMTE session on the Common Core State Standards and math teacher education. The panelists and audience listed many immediate needs as we plan how to implement the standards; the one that caught my ear was the need to align the Mathematical Practice Standards to the work that’s already been done, like the NCTM practices and the “Adding it Up” strands.

I figured that I could at least align the work I’ve already been doing about developing activity structures for teaching problem-solving and problem-solving strategies to the process standards. Here’s my first attempt at that.

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Travels

by Max

January 28th, 2011

I am in Irvine, CA right now for two really cool reasons.

1) To visit a long-time Math Forum Problem of the Week (PoW) user, Doug Compton. If you follow the AlgPoW and read the solutions and commentary regularly, you see Rancho San Joaquin Middle School quite regularly. That’s because Doug has his nearly 70 algebra students submit to the PoW each week. They focus on writing detailed explanations of their problem-solving and why their answers make sense. They also reflect each week on where they got stuck and how they got unstuck, if needed, or what they thought of the problem’s relative difficulty. Reading their thinking is one of the highlights of my week; picking just one or two to highlight is one of the hardest parts!

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Putting the “Fun” back in Exponential Functions

by Max

December 22nd, 2010

The teachers I coach are beginning their investigation of exponential functions. They are using Core Plus Math, and are working really hard to do increasingly problem-based, student-centered teaching. I’m helping the teachers with pacing, lesson-planning, and formative assessment, as well as coaching them on facilitating student-teacher and student-student interactions.

So… my project over the break is to put the “fun” back in exponential function (and maybe put a little “expo” back in there too). “Why do we have to learn this? What matters? What does this have to do with what we already know?” are valid questions I hope students ask and I can help them answer. (By the way, I just learned that exponential functions can help us predict when everyone on earth will be following Lady Gaga on Twitter (October 2025), but I don’t think we even need such fascinating applications to help make sense of exponential functions. Source: http://www.youtube.com/watch?v=51AhdTj-irQ&feature=youtu.be)

What’s the big idea behind exponential functions? And what experiences help kids ask the big idea questions themselves?

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Threshold Math Concepts

by Max

December 3rd, 2010

This morning’s water-cooler topic here at the Math Forum: threshold concepts. I’m not sure if it’s a phrase we just coined or not, it’s definitely not original, I think Erik Meyer and Ray Land coined the term, but it led to really interesting conversations and storytelling, more of which I hope will continue in the comments.

Our working definition of a threshold concept: something that changes the way you understand mathematics, which after you understand it, you can’t go back to previous ways of thinking, and you find yourself interpreting and understanding math through the lens of that concept.

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How I’d Want to be Evaluated

by Max

November 16th, 2010

More musing on the coaching relationship… I thought it might be worthwhile to imagine how I would assess myself and how I’d want observers to assess my classroom. Here’s what I’ve got so far. I hope that observers would see:

Classroom Culture:
- Students looking to themselves, their text, and other resources as much as they look to me for mathematical expertise.
- Students checking to see if any mathematical claim made (by me, themselves, each other, a text, etc.) makes sense & is reasonable.

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Problem-solving Journal

Any Questions?

WCYDWT: Building Columns

Pseudoteaching & Lesson Planning

Bitten by the WCYDWT Bug

Problem-Solving Strategies and the Common Core Practice Standards

Travels

Putting the “Fun” back in Exponential Functions

Threshold Math Concepts

How I’d Want to be Evaluated

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