We are sooooo very excited to welcome each of you to what, we hope, will become a regularly occurring event!
First things first, let me explain how this will work. Each week, on Wednesday, you can stop in at one of the blogs listed below. That blog will have a post up with a link for you to click to take you to that week’s discussion. We decided that would be the easiest way to keep all the discussion happening in one place and cause the least bit of confusion for all involved (I hope!) I’ve also listed the dates for each chapter below as a reminder!
Each week one of us will write a quick summary of the chapter and post the questions that NCTM President, Linda Gojak poses in her book to start the discussion. Then, it’s your turn! Jump right in and leave your thoughts! Make sure to use the reply option when replying to a specific person’s thought so that it is easier to follow who is saying what. The author also suggests keeping a problem-solving journal, or notebook with you as you read, to jot down thoughts and to solve different problems.
Jennifer Smith-Sloane from 4mulaFun
Meg Anderson from Fourth Grade Studio
Jamie Riggs from MissMathDork
and Jennifer Findley from Teaching to Inspire 5th Grade
Okay, here we go! Chapter 1:
What is problem solving?
Gojak begins the chapter by discussing what problem solving is and is not. What many of his have grown to know as problem solving, both as teacher and as students, is considered routine problem solving. Routine problem solving is when we, as learners, know how to solve the problem, and really the problem is more an application of a past experience. Non-routine problem solving, on the other hand, is when learners are given a new task in which they cannot immediately apply something from a past experience to solve the problem. They MUST make connections to multiple experiences AND extend their thinking and reasoning in order to develop an appropriate answer. Gojak gives an example of the 2 types of problem solving on page 17. Gojak speaks about students struggling with the non-routine problems. The struggle is what makes it a true problem, rather than just a task. (As a teacher, I find that it’s hard to let your students struggle, but if you tell them in advance, “hey you’re going to struggle with this and THAT’S OKAY”, I find that they handle it a bit better)
Why teach problem solving?
Gojak, being the NCTM President, uses the NCTM process standards as her biggest argument for teaching problem solving . If you are not familiar with the process standards go HERE to read more about them
Who should problem solve?
Gojak also states that students should begin problem solving as early as pre-school! I love this idea! By the time the kiddos get to me in middle school they are scared of problem solving… why? because they haven’t done enough of it! Page 27 has a great table of strategies to use for your kiddos!
When should we problem solve?
All the time in every math class, every day! Pages 29 -33 suggest various activities and examples for implementing more problem solving in your classroom.
Where can you find good problems?
And finally, Gojak leaves us with some great website resources! NCTM’s Illuminations is a personal favorite of mine! Check out page 35 and 36 for more problem solving websites (also, feel free to leave your own favorites in the discussion below!)
So, there you have it! Chapter 1, in the books! Now, let’s “reflect and act!” Here are 4 discussions questions that Gojak leaves us with on page 37. The four of us are looking forward to joining in on a lively discussion with you! (Also, we are working on a wiki page where we can merge all the information together as a great resource for all of us in the end!)
- How is problem solving an important part of your professional growth as a mathematics educator?
- How can you convince your students of the importance of problem solving when learning mathematics?
- Think about problems you solved in this chapter that involved quantitative reasoning. Write a description of how you went about approaching and determining a reasonable solution
- How has your perspective of problem solving changed after this chapter?