This weeks challenge on the Math(s) Twitter Blog ‘o’ Sphere is to check into one of the collaboration projects set up by Maths educators around the world (mostly in the US but at least one of which comes out of the UK), to explore a bit and reflect on what we find.

I’ve been lurking around the edges of Maths education blogs for a long time, so I remember a lot of these projects starting up. I’ve dropped in but for whatever reason I haven’t contributed much – I thought I’d use this as an opportunity to drop back in on one of them, namely 101questions which is a project of Dan Meyer.

Dan has done a lot of work thinking through 3 Act lessons. When I describe that work to others I talk about trying to get a picture or video that poses one key and interesting question that could be used as the launching point for a lesson or series of lessons. I talk about seeing lessons as stories with a beginning, middle and end, with possible sequels. I talk about using the digital projectors in our rooms to share digitally rich materials. I talk about having something beyond the answer key or my decision being the measure of correctness or success.

101questions is an online community set to pose videos and pictures to see what questions come up – to see if other people intuitively jump to the question you have in mind. The people posting the pictures or videos and the people suggesting questions are mostly Maths teachers but given that level of homogeneity, there is a great diversity in the types of answers that are given. You still get different questions in the classroom but this gives a good starting point to make sure you aren’t completely blindsided.

I have taken some of these and used them in the classroom. We’ve watched the video or examined the picture, come up with our questions, asked what information we might need to begin to solve that question and get stuck in doing some mathematics. It takes work to find an Act 2 (the information) or Act 3 for some of these problems which is where I have greatly appreciated the work of others doing this (I’ve benefited a lot from Dan and Andrew Stadel in particular). The site now has functionality to search for those resources that have lessons associated with them. I’m pretty sure this is new and will make it much more likely for me to use these in my lessons more often.

I find that these problems are very engaging but not often fully mathematically rich. They do present problems that can be solved in a variety of ways but as we are aiming toward one key question most students are working to try find out the same thing. Maybe the sequels is where the juicy richness comes in – we could encourage pattern spotting and generalisations as students develop their own problems in our context.

Do you think 3 Act lessons are mathematically rich? Am I way off base here? Are there ways to make them more rich?

I spent some time on 101q last night. There are all levels of pictures that generate questions for me. My ‘first thought’ questions are more about the picture’s context than some math-y question, and I felt silly typing them, as if my q’s needed a bit more substance.

I could see how many of the pictures, with the right guiding instructions for students could fit into very rich tasks. The ‘with instructions’ being the key to the richness. I don’t mean the specific ‘do this, go here, what does this equal’ kind of instructions. Rich tasks need guide-ers of thinking: Oh that path looks interesting, why don’t you look at it from that angle, what would you need to support that, how could we prove/see/make that happen.

I have tagged 101q as one of my resources, and I am looking for contributions. Right now I would love to post the TED talk link to the video I tweeted about yesterday on.ted.com/hrE9 – there were some great math questions: the speaker compared our existence to sand dunes and even posted a picture with an angle mark drawn over it. He talked about the pressure of the wind against the pull of gravity. What would my students be able to pull out of that? Could the find other situations where those forces exist in tandem and calculate?

The other problem arose through his discussion of the weight of a particle. He compared it to the weight of a gram. Could my students find a way to compare everyday things in completely different ways, to foster a new understanding of comparisons in different terminology? Anyway, my point is that for a task to be rich, we must envision, as teachers, how something as simple as a picture or diagram can lead to speculation and present it as a mystery (or puzzle, or paradox) to be examined, discussed and wondered over by our students. We bring these gifts to our students and ask them to open them. And then watch, to see what they make of our gift. (Do you think I could post a whole TED talk, or should I just use screenshots of the two frames I liked?)

I have been following Dan’s work long before he started 101 questions and I think there is so much amazing stuff there. My frustration has always been the fact that I teach first graders. In some ways that means that everything they learn is immediately relevant and all around them in the world. In other ways it means that, because we are working on such basic, foundational skills, I find it hard to create questions as engaging as the ones on 101 questions. It has to be possible, but I haven’t discovered how to make it happen yet. (I was better at it when I taught 4th/5th grades.)

The site you reference, Nrich, states “On its own a rich task is not rich – it is only what is made of it that allows it to fulfil its potential,” when talking about rich tasks. I think that is true of any of the 3Act lessons (and I’m a huge fan of Dan Meyer and these lessons!). It’s how we use the problems in our classes that can make them rich or not. Thanks for reminding me of this!