Tuesday, 18 June 2013

More problem solving please!

We've had about 8 weeks of flipped learning in maths now in Year 7,8 and 9. As mentioned in my previous post, not all classes have been running smoothly, however I'd have to say that my classes have pretty much accepted that this is the way we do things now. As you'd expect some students have adapted better than others, and those that consistently watch the videos, write good summaries and try to ask interesting questions are benefiting the most. The culture of the classroom is slowly changing.

I mentioned at the start that in terms of class work I've pretty much stuck to what the students are familiar with, which are questions from the text book. I do try to find more interesting worksheets (usually from the old SMILE resources used in England before I was even a teacher, or some of the CIMT activities), but it's not always inspiring stuff. Now that the structure of flipped learning is in place I want to spend more time designing interesting activities for the students to do in lessons.

The issue that needs tackling is that currently our students are not great problem solvers (as a whole, of course there are exceptions to this!) I've taken problem solving to mean "any task for which the solution method is not known in advance".

In a recent department meeting we discussed reasons that might stop students from attempting complex problem:
  • They don't understand the problem
  • They are unsure of how to get started
  • They don't know any strategies to solve the problem
  • They feel they are not good at maths
  • The problem is not interesting to them
  • They are unwilling to take risks or experience failure
All of these issues are things that we can do something about as teachers. The one that is most obvious for us to tackle is to actually teach the students strategies for solving problems in a structured way. Sometimes as teachers we are very quick to complain about lazy students who don't try, but if we've never tried to help them improve their strategies than who's fault is it really??

So, in Term 3 we will start a Problem Solving programme with Year 7, 8 and 9 classes. We have based this around George Polya's 4 Principles of Problem Solving:

1. Understand the Problem
2. Devise a Plan
3. Carry out the Plan
4. Reflect on the Solution

Currently the students are mostly doing questions that only use Step 3: That is they are given a method to use to answer questions and the carry out the computation. But the other 3 steps are what are going to be most useful to them not only in a maths classroom, but in other subjects and beyond the classroom into the "real world".

We will teach each of these 12 heuristics:
1. Guess and improve
2. Make an organized List
3. Draw a diagram
4. Make a table
5. Look for a pattern
6. Solve a simpler problem
8. Act it out
9. Work backwards
10. Use deduction
11. Change your point of view
12. Write an equation

The idea is to teach one of these strategies each week over 12 weeks. We will spend about 20 minutes each week on this, no more, and continue with the "regular" curriculum at the same time. At the end of the 12 weeks students will be presented with a variety of problems and have to start to make decisions about what strategies to use. They will be formally taught to use the 4 Principles each time they tackle a problem. Hopefully, students will start to  naturally use these strategies with their textbook questions as well. 

As mentioned before, we will use this with Year 7, 8 and 9, with the aim that in the future we will teach it in Year 7 only but constantly refer to the strategies throughout all year groups. 

Our aims for the program are this:

1. Improve students' willingness to try problems and increase perseverance
2. Make students aware of problem solving strategies
3. Make students aware that there is more than one way to solve a problem
4. Improve students' ability to work systematically
5. Improve students' ability to choose and implement a suitable strategy for solving problems

I have high hopes about this program and look forward to reflecting on what is working (and what is not) on the blog in Term 3.

Many thanks to Tom Reardon for his helpful paper on this, accessed here

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