This term in our math class we were challenged to pick a math SLO and research the difficulties kids have when learning about the concepts in that particular SLO. Then we had to create a lesson that addressed those difficulties and try it out with some kids. ACK, all sounds a bit complicated but, turns out it’s a pretty interesting way to go about things.
Because I am in a grade four classroom this year for my practicum and will be teaching a division unit in March I chose to research kids difficulties with division (shocking I know). Incase you were wondering that falls within the SLO 4.N.7 of the Manitoba Math Curriculum. Riffling through technical research papers is something I haven’t had to do since my undergrad work in Biology and it brought back vague memories of the Chi squared test and correlation coefficients *shudder*. Luckily along the way I learned some interesting things:
- Kids have a pretty good sense of division even in the very early grades (Think sharing cookies) and struggle when it all gets taught in a formal way at school (think old school division problems).
- Young students have a number of fascinating intuitive models that they employ when solving division problems.
- Language matters! Kids get lost when the problem aren’t clear!
- Many students fail to see the connection between multiplication and division.
(I could go on with the list but I wont. If you are curious here is the full list of references I used in my research adventure check them out if you’re looking for some more info!)
Being someone who never really got the concept of division when it was first taught to me the last point stood out to me the most! From the fist time I learned how to do division up until now, I use multiplication to work out and check my answers. So as you can guess, I decided to design a lesson around the connections between multiplication and division.
A few thing to keep in mind before I go ahead and explain the lesson 1) it was designed to be done with a small group of students whom I had never met before 2) I had no idea if they were strong or struggling with math and 3) I only had 40 minutes to complete the lesson! On the day of the lesson I had 3 students in my group, a great number for a test run!
Phase 1 of the lesson consisted of playing around and organizing manipulatives into arrays to show and discuss how multiplication is related to division and vice versa. The purpose of this was just to refresh students memories about the proccesses involved in solving division and multiplication problems.
After their brains were all ready to go I gave them the option between being ‘Mathamagicians’ which involved playing a card game or being ‘Mathtronauts’ who had to escape a math wormhole. Yes, I am a complete sucker for amusing names when doing activities. It almost seems the more ridiculous the better. Both games required students to practice using all four operations, so either choice had them practicing the skills I wanted them to practice.
Anyways they chose to be ‘Mathtronauts’, the one I was secretely hoping for! The game is called “Through the Wormhole” and can be found at www.MathPickle.com. Here’s a quick video to explain what it’s all about:
Since finding Math Pickle in early October I have been itching to try out one of the puzzles with kids. As the video explained this particular puzzle requires that you work systematically to multiply, subtract and divide in order to solve for each blank space. I was a bit apprehensive about doing this puzzle with a group of new kids but I took things slowly and worked with the students to solve the first ring of blanks and we slowly moved up onto the next row. I kept the manipulatives available help the group/individual students concretely work out the multiplication and the subsequent division problems if needed. (Nothing like knowing if you can’t do it your head you can work it out right in front of you step by step).
At first they were a bit scared by the complexity of the puzzle, but as we kept working at it, they loved it! It was difficult, it was tricky but they soon found shortcuts and gained confidence as they moved through the puzzle. My head hurt a little bit from working so systematically and slowly but in the end it was worth it and totally cool to see kids in action solving the puzzle! To all of our dissapoinment we ran out of time before we could finish the whole puzzle, so more than 40 minutes is definitely needed! I was asked if I was coming back to do math with them again so you know, that’s a good sign! I will definitely be trying out the rest of the puzzles on Math Pickle and will be reusing this lesson come March!
www.learnalberta.ca (Great resources on how to teach multiplication and division)
If you want the full copy of the research paper I wrote and the accompanying lesson plan let me know and I will send it to you!