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PhotoMath came out a few weeks ago and it has given me a lot to think about. It’s funny how a new technology can force you to look inward and re-evaluate what your role is as a Math teacher.
My first thought was, of course, “How cool is this!”. An app that lets you take a picture of an equation, and it shows you not only the answer, but the step-by-step process to solve it. I showed some of my students and they had a similar response. It was also followed by the question “isn’t using this cheating?”. That’s a great question. As I told my students, I don’t think it is cheating at all.
We have to design our courses and learning goals to be valuable in the context of the 21st century. The actual solving is more efficiently done by computers in the modern world, especially when the equations get more complicated. The next logical question is: What can people do that computers can’t? This is what I could come up with:
- People can think critically and interpret solutions to equations in the real world in order to solve real problems.
- People can use their understanding of mathematics to program computers to automate processes.
- People can use their understanding of mathematics to develop new processes to solve a broader scope of problems.
This is what I hope to be training my students to be prepared to do.
I have been planning a project (with a lot of help from fellow BSS teachers Joseph McRae and Cassandra Arsenault) with the goal of facilitating this type of learning. They will use the Scratch environment to write a program that allows the user to solve simple equations instantly from a pre-set list. Examples:
This can be done fairly easily from a coding perspective. Hopefully the students end the project with not only a better sense of how to work with and rearrange equations without substitution of numbers, but also a better understanding of what the role of a 21st century mathematician is.
The computer should be doing the heavy lifting, but people should be doing the thinking.
WoW! This is great stuff Andrew – and certainly lots to think about. There are a few posts from Cohort 21 members that ask the question: what is the role of technology in the classroom. I think that you’ve started down the path to an answers (NB “an” answer, not “the” answer:)).
I encourage you to reach out to them: Tia, Melissa and Danny Neville to start. You could point them back to your blog and start a great conversation!
Thanks, I’ve already tweeted this out and shared it with my math teachers!
garth.
Fabulous post! I am intrigued by the prospect of using Scratch in Math. What age group are you using this program with? Do they have any previous coding experience?
Thanks for sharing,
Su A
Thanks very much Susan. I am using it with Grade 8 students right now and it seems to be at the “sweet spot” where the challenge is developmentally appropriate but the interface isn’t too “childish”. There is also a Scratch Junior for younger students that I haven’t really played with yet. My degree is in math, but I took 3 or 4 computer science courses and i’ve had a few jobs where I was programming.
Great post Andrew, I have spent many years teaching math and science. Though I love teaching math, it was always hard to get students (especially in grade 10) to see the value in what they were learning. The App sounds great but certainly is just another tool. The ‘What can you do with this?’ questions is much more valuable and the way that you have framed these ‘Essential Questions’ is perfect.
I’m late to join the discussion, but I am intrigued by this idea and app also… I teach Grade 11 Functions right now, and I just finished reading an article on word problems (found it through Twitter) that talked about starting with word problems, and finishing with numerical equations. I think your idea for your project really emphasizes the thinking as opposed to memorization of steps alone, much like the argument from the article! Here’s the link, and thanks for sharing! http://www.edweek.org/ew/articles/2014/11/19/13mathwords.h34.html
Thanks for the link! You made me realize I should think of how these ideas work in the context of a problem-based learning lesson.