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**!

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Lottie O. Knapp says

The problem with not being challenged sufficiently goes well beyond not learning math (or whatever) as quickly as you can. I think a lot of what we do at AoPS is preparing students for challenges well outside mathematics. The same sort of strategies that go into solving very difficult math problems can be used to tackle a great many problems. I believe we’re teaching students how to think, how to approach difficult problems, and that math happens to be the best way to do so for many people.

Pamela Smith says

I really enjoyed this chapter and how well the steps of Polya’s principles and the Launch, Explore, Summarize Instructional Model were detailed and explained.

In my classroom we use problem solving and it has some of the components of each approach and my students enjoy it up to the point where they get stuck. I am excited to use the questions listed throughout the process in the section Effective Questioning in chapter two.

Perhaps the most challenging aspect for me is creating an effective launch. This is an area I need better understanding myself. The questions in Launch section are very helpful and I am encouraged to read the part that assures me I will gain confidence with experience.

In my classroom I enjoy the steady-hum of students engaged in small groups or pairs and using manipulatives to solve problems. Sometimes the “hum” stops before students have explored and put together the mathematical ideas. I would like have more effective exploring and summarizing happening in the classroom.

Jennifer Smith-Sloane says

I will be honest that my first few years Launches were non-existent when I was self-contained. I was good to transition smoothly from one subject to the next. Now that I am doing a lot of Exit Tickets and other types of wrap-ups, I can definitely see a difference in how I am able to determine the depth of my student’s knowledge on the subject.

Mandy Casto says

I’m like you, Jennifer, in that my launches were lacking and my summarizing was very “one-dimensional” (due to asking basic follow-up questions and not digging deeper). The questions that Gojak provides in both phases of this prob-solving framework can help us deepen our students’ understanding and our assessment of their knowledge.

Fourth Grade Studio says

I agree that the launch is so critical…it takes a great deal of time and thoughtful planning to create a climate for risk taking, questioning, and idea sharing. The time invested in setting the stage pays off a thousand-fold! I am taking notes as to ways to deepen my practices in this area next year! It’s a delicate dance of scaffolding for strugglers, providing challenge for “thinkers”, and observing how students handle the tasks we give them!

Jennifer Findley says

The Launch, Explore, and Summarize way of teaching is the way we were being trained to teach math last year. I found it to be huge for the kids! However, there was a misconception at my school that this is the only way to “teach” math. Some teachers would spend the entire math on this and nothing else. I still believe some good old fashioned teaching (and re-teaching) needs to take place in addition to this type of instruction. My kids did better than they have ever done this year in Math and I know it was because I attempted a healthy balance of the Launch, Explore, and Summarize and attempted to really foster those mathematical habits.

Ana says

A little late but I have caught up with the reading. This group is amazing and I am learning and getting ideas from all the posts. Thank you.

I like the way the author has broken down the process that we must use for effectively teaching problem solving, however in the Launch stage we are supposed to introduce new material? Do you suggest doing this in the form of another rich word problem? I agree with Jennifer F. that a balance is needed. I think last year I was doing Launch ( a review, and intro lesson) but it was more first making sure they understood the math and then relating it to a word problem. I am looking forward to reading more examples to help with problem solving.

B. Hensley says

Wow! I have been “superficially” launching by altering names,(motivating), etc., yet I did not go deeper into helping them understand. On page 57(top) I plan to explicitly teach my 6th graders that there may be other questions to answer prior, may need an outside source (definitely, limited backgrounds require clarifying the context, real world math), and some that cannot be solved. It has been a huge missing piece of the puzzle for me. In the Explore phase, I will implement the problem solving journals. Thanks to page 164-165 for being my springboard. A bulletin board display that lists the strategies will help me , as well as the students, stay on the right track. I loved the idea of purposeful summarizing: to refine or revise thinking. I have had students orally discuss their revised thinking only to have it confused or forgotten later during assessments. I knowing writing the summary will help. I feel like I’ve found the fountain of mathematical youth!

Kathy says

I am a fan of Polya’s work because I think he simplified the problem solving process (where students often get lost). I like that the Launch, Explore, Summarize Instructional Model is based on Polya’s process and remains simplistic. What I found especially helpful was the lists of effective questions at the end of the chapter. I am going to keep those questions close by for me as I questioning is an area that I need to work on.

Another idea that came up in this chapter that i utilize and like it having the students present their problem on large chart paper. Displaying these problems so that students can see a variety of ways to solve one problem is important. In the age of technology I feel like sometimes these paper displays are forgotten but I feel they are an important aspect of student learning.

Mandy Casto says

Not sure about anybody else, but I never “planned” for problem-solving before. I guess I really appreciated this chapter because it provides teachers the framework (both mental and materialized) to teach problem-solving.

The Launch/Explore/Summarize model seems simple enough until you look at all of the questions that teachers must consider in each step of the process. I agree with Jennifer that putting these questions on bound, laminated index cards is probably the way to go.

The greatest thing that I took away from this chapter? Truthfully, it was the very first sentence: “A teacher’s goal must be to help students understand mathematics…they cannot make students understand.” I must remember this going forward!

Carrie says

I also like the way the chapter is laid out laying the foundation for launch, explore, summarize to teach math. I struggle with the students who want to be spoon fed the strategies and answers. There is always a percentage of students who can solve any problem, and a certain percentage that sit back and wait for others to solve the problems. I am hoping to find the balance to motivate the students who wait for others to solve the problems.

Along with having a meaningful launch, I want to work on making the summary portion more meaningful. I think the exit tickets and classroom wrap up are important to bring additional meaning to the student and allow the teacher a chance to assess understanding.