Fix Those Problems (Math Teaching 101)

http://wronghands1.files.wordpress.com/2013/06/math-problem.jpg

First, and foremost, I am a student of instruction.  My resume says I have taught math from 6th grade to college algebra; I taught middle school science; I taught introduction to engineering design and digital electronics at the high school level. And, I facilitate teachers in using project based and problem based instruction (PBL).

What I enjoy most is reflecting on my practice and pursuing better ways to perfect instruction in the classroom.

During the last 6 years I have tried to figure out how to best teach mathematics in a PBL environment. As a practitioner I tried differing ways of providing inquiry while including repeated practice. Then I was introduced to problem based instruction where the depth of inquiry was constrained so that the time frame could be reduced from the normal project length. This worked better in math, for me, and yet I have seen teachers who were still able to keep the longer project settings.

In recent years I have been working as an instructional coach and I have started working for the Buck Institute for Education, BIE. Through these I have been able to offer ideas to many math teachers and I have listened to their concerns.  The common thread between these teachers is the difficulty of following the guidelines for project based instruction while dealing with students who have math skills that are as many as 5 years lower than the class they are sitting in. This is true whether they were teaching in California or Maine.

In Texas we now have state exams that are "more rigorous" (gag me - hate that word, rigor) and with the common core (CCSS) standards you are expected to think logically and to demonstrate concepts. No longer do we just show basic mathematical manipulation of numbers. We expect that students will read a scenario and then apply mathematics to reach a conclusion about a numerical relationship.

Teachers keep asking me to give them good examples of problems with the "proper rigor" (there's that word again). My answer is that all you have to do is look at any, yes ANY, math problem in any math book and take the root problem and embellish it.  The following is an example from a Glencoe Pre-Algebra book. I took it from the 5th chapter and it is question 5 from the chapter test: "Trish bought a CD player for $37.58. The price she paid included a discount of $6.63. How much did the CD player cost before the discount?"

Now let's make it better and bring it up to 2014: "Trish wanted to buy a used iPhone at Best Buy and had saved $50 to buy it.  She searched online for savings coupons and found 3 that said they were the "best buy at Best Buy." The first was for $6.63 off of any used phone marked $40 or less. The second was for 15% off of any used phone costing more than $30. And the last was for "any phone in stock" and was for 12.5% off of the list price.  Which coupon should she use so that she spends less than her $50. Explain to her why she should choose that one. Also assume there is a 6% sales tax in this state that will be applied to the final cost."

In this problem students still need to look at percent increase and percent decrease, which was the main skill being tested in problem 5. But now they have to do some thinking. And, if you let them work in pairs they can have discussions about which is the best answer. That took me about 10 minutes to get it into the post. I looked at problems on the Glencoe website, picked the problem, and then I upgraded it.

What if you did that with one problem every day? What if every summative assessment had problems like that and your students could work in pairs to get the right answer - but each person had to write the correct answer and the reasoning of why it is correct? Need another example? Here you go...

"You are carpeting a rectangular room that is 3.5 yards by 4.5 yards. The carpet costs $15 per square yard. How much will it cost to carpet the room?" This is from Big Ideas Math. Now let's make it better.

"Mr. Smith wants to put carpet down inside of the doors that lead out to the playground so students can wipe their feet when they come in. He wants the area covered to be rectangular and be as wide as the doorway but extend at least 3 yards into the room.  Explore 3 stores for prices of carpet and determine how much it will cost to buy the needed carpet. If you can not measure the width of the doorway assume that it is exactly 2.5 yards wide. Be ready to explain to Mr. Smith which store has the best price and why it is the best price"

It's time to take back your classrooms. Give your students opportunities to work together and analyze situations. The infamous "they" want your students working on rigorous math problems. You have math problems all over the place! Use them, improve them, and then let your students get to work on them. It's not rocket science - but with the right guidance your students might just become rocket scientists.