Are you ready to discuss Chapter 2 of “What’s Your Math Problem?” What? You haven’t picked up the book yet? Well never fear, there is still time to join us on this weekly excursion. And for anyone joining in after we have finished, feel free to pick up a copy of the book and follow along!
I am so happy to be here with you today to discuss Chapter 2- Planning for Problem Solving in the Classroom.
What does it mean to Plan for Problem Solving?
First, we must remember that students do not always come to use with a background in connecting prior information to use and apply to new problems presented to them. We must teach them how to develop those connections and relationships to be meaningful and therefore sink in for the future. How do we build these connections? How do we decide what is meaningful to each student?
When we are setting up our instruction, it is imperative to keep our students in mind no matter what level we teach. Over the course of my ten years of teaching, I learned that when I incorporated my student’s names as well as their interests into any type of of problem (computation or word problem), it made a connection in their mind and allowed them to understand what was being asked at a different level.
As we are developing and building our bank of problems, we as teachers become more comfortable modifying problems. An example that I would use in my class is shown below.
As you can see the concept being covered is the same for all students, but what is different is how the problem becomes their own. In middle school it is important for students to relate word problem to equation and vice versa so in the beginning of the year I start with an equation and let the students develop the word problem. This easily shows me how deep they are able to go into their problem solving skills as well as who wants to just get the answer.
Gojak continues on to describe a new model of problem solving called the Launch, Explore and Summarize Instructional Model. This is deeply rooted in Poly’as principles of effective problem solving that many of us are familiar with by the name of UPS Check.
The Launch stage is where the teacher prepares the class and reviews prior concepts used within the problem solving process for the day (think intro/mini-lesson). The next stage, Explore, is the all too important stage that I know I have tended to rush and/or not give the crucial amount of time for. We must allow our students to take the necessary time to scaffold their learning without forcing them to answer. This stage is where they are able to connect prior learning with the new concept and formulate a plan to solve. The final step, Summarize, is key for connecting thoughts from students to show progress in reaching their solution.
When you creating problems, you need to look at the possible misconceptions that would arise in the problem that you give students. Where might they make errors? What would steer them off course?
From the problem I stated in the Problem Solving Planner above, which is a FREEBIE for my blog readers by clicking on the picture or here, you can see that extensions are easily made off of this problem. Students can create similar problems with the same equation, new problems with their own equation, etc.
While reading through how to plan the various stages of the Problem Solving Process, it made me look back at the strategies that I ask of my students. We have been using Technical Reading Strategies for the past few years at my prior school and then when I switched schools I brought those strategies with me. You can check out those strategies (and grab an additional FREEBIE) over on my classroom blog.
What are Effective Questions?
Gojak poses quite a few effective questions to use during the Explore and Summarize steps of Problem Solving. Enough so that I am really thinking these would be great to type up and have on a ring to grab at various intervals.
Time to Reflect
1. What does problem solving in your classroom currently look like? What does it currently sound like? What are you doing during problem solving time? What are the students doing during problem solving time?
2. What do you want problem solving in your classroom to look like? What do you want it to sound like? What do you need to change about what you are doing? What do you need to change about what students are doing?
3. What steps can you take to implement the Launch, Explore, Summarize Instructional Model in your classroom?
Feel free to leave comments, link to blog posts that you have written to explore this further, link to examples of what you have tried/want to try to make things different.
And don’t forget to enjoy the freebies!