PrBL can be intimidating because it seems like a whole new way of teaching. What one mentor told me, describes it beautifully: just flip to the end of the section and start with the problems there. The whole goal is so that students can apply concepts, so just start there instead of waiting til “the end” (you also run the risk of running out of time and skipping that part which is no good!).
I tend to be someone who researches online for the perfect problem(s) to use and that kind of time commitment is unappealing to teachers trying to try PrBL out for the first time. An approach I learned in college on the research team can work perfectly. They described it as converting word problems to rich problems.
I am going to illustrate the process with a problem I for radian measures and trig ratios this past January.
Step 1: Find a problem in the text book.
If you find a problem in the book you know for sure it will cover the standards you want to teach.
Step 2: Delete the extra words
Many textbook word problems give TOO much direction or too much information. All those extra words take away students’ opportunity to think.
I converted questions (a)-(c) to these instead:
- How wide are the steps?
- Will we get dizzy?
- How long would the railing need to be to go all the way around the staircase?
- How much carpeting would you need to cover the steps?
You need to use the same math in both scenarios but with these, there is more thinking involved. The textbook versions tells you exactly what information you need to use. The rich problem makes you think.
Step 3: Tweak the numbers to make things less neat
If one more child tells me the answer is wrong because it ISN’T a whole number….
Nothing in the real world comes out easy or perfect. Neither should the answers in math class.
I converted the background info to:
Mrs. Pier’s husband, a carpenter/welder/builder, is planning to build a spiral staircase to the add-on loft in their house. Mr. Pier’s initial plan includes 20 steps that are 42 inches long. The angle for each step is pi/6. Mrs. Pier has some questions so she can be sure she and her children will be safe traveling up these stairs. Help him answer her questions below.
because 15 steps makes 1 1/4 a circle while 20 steps makes 1 7/12 of a circle, which is just a little messier and a little more interesting.
Step 4: Review
A good problem should
- allow different ways of thinking
- encourage multiple representations
- give just enough information
- illicit questions and conversation from students
You just want to make sure that students will have struggle time or think time. It should not be immediately obvious what to do but the problem should be solvable. Try converting a word problem from your text book and let me know how it goes!
Here I have attached the problem form for a New Staircase as well as the problem planning form which is the PrBL version of a lesson plan. I will cover that more in a future post.