What's Your Math Problem!?! Book Study Chapter 8

Have you read the book, What's Your Math Problem!?! This is a brief review of chapter 8.

Questions form The Field

In the final chapter, the author answers some commonly asked questions about problem solving.  The first question answered is one that I think would be asked by most teachers:

How do I find time to fit problem solving into an already full curriculum? 

This is a question that I myself have wondered.  With the Common Core, it seems like more and more is being asked of teachers.  But, with the problem solving component, it is actually asking teachers to do less.  By giving students one complex rich problem instead of multiple easy operational problems, we are killing two birds with one stone so to speak.  We are not only teaching the skill, but we are teaching problem solving.

Where Can I find Rich Problems:

The author suggested NCTM Illuminations as one possible resource.

Some other sources I have used include:

Math Landing

NRich

I am linking up with 
                                                     Jennifer Smith-Sloane from 4mulaFun
                                                     Meg Anderson  from Fourth Grade Studio
                                                    Jamie Riggs from MissMathDork
                                                    and Jennifer Findley from Teaching to Inspire 5th Grade

for this book study on What's Your Math Problem!?!



 If you missed my previous posts you can find them here:

Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7

What's Your Math Problem!?! Book Study Chapter 7

I am linking up with
                                                     Jennifer Smith-Sloane from 4mulaFun
                                                     Meg Anderson  from Fourth Grade Studio
                                                    Jamie Riggs from MissMathDork
                                                    and Jennifer Findley from Teaching to Inspire 5th Grade

for this book study on What's Your Math Problem!?!



 If you missed my previous posts you can find them here:

Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6

Assessing Problem Solving

As we all know, we need to use assessment to drive our instruction, but how do you assess problem solving?  The author suggests throwing away any preconceived notions of using assessment for grading purposes, but instead as a way to analyze the student's thinking.  How does the student organize their work?  What strategies did they use?

Gojak suggests having the students involved in the assessment process by teaching them to ask the following questions:

• Am I making progress with the strategy I am using or should I try a different one?
• Does my work make sense? (I always have my students ask themselves, Does my answer make sense?)
• Can I explain my work and justify it to someone else? (This really ties into the Common Core)

The book also contains rubrics which can be used by both teachers and students.

What's Your Math Problem!?! Book Study Chapter 6

I am linking up with
                                                     Jennifer Smith-Sloane from 4mulaFun
                                                     Meg Anderson  from Fourth Grade Studio
                                                    Jamie Riggs from MissMathDork
                                                    and Jennifer Findley from Teaching to Inspire 5th Grade

for this book study on What's Your Math Problem!?!



 If you missed my previous posts you can find them here:

Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5

Chapter 6 - Advanced Thinking Strategies

This chapter focuses on four new thinking strategies:

Solve a Simpler Problem - This is one of my favorite strategies that I have used in my classroom for years.  I tell my students to plug in smaller numbers to see if they can figure out how to solve a problem.  The author also addresses a second form of this strategy by beginning with a simpler case of the problem.  The example they give is:

Find the sum of the first 50 odd numbers.

The author suggests first finding the sum of the first 2 odd numbers, and then moving on to the sum of the first 3 odd numbers and so on.  You would keep track and see if a pattern appears.

Account for All Possibilities- In real world situations and problems, we often find that there may be more than one possible solution.  The key part of this strategy is systematically accounting for all possibilities. 

Work Backwards -In this type of a strategy, the student starts with the answer and works their way backwards.  This might be a strategy to teach using multiple choice questions.  If you worked backwards, would that particular answer work?

Change Your Point of View- This is one of the more complicated strategies to use, because it involves stepping away from the problem and trying to solve it a different way.  I think in the classroom it might be helpful to teach students how to use this strategy by seeing examples of how other students solved a problem differently.  You could ask, could anyone else use so and so's strategy in another way?

What's Your Math Problem!?! Book Study Chapter 5

I am linking up with
                                                     Jennifer Smith-Sloane from 4mulaFun
                                                     Meg Anderson  from Fourth Grade Studio
                                                    Jamie Riggs from MissMathDork
                                                    and Jennifer Findley from Teaching to Inspire 5th Grade

for this book study on What's Your Math Problem!?!



 If you missed my previous posts you can find them here:

Chapter 1
Chapter 2
Chapter 3
Chapter 4

Chapter 5 - Visualizing Strategies

This chapter focus on the following four visualizing strategies:

• Make a Model
• Draw a Picture or Diagram
• Act it out
• Make or Use a Graph

I think these strategies are pretty self-explanatory, so I'm not going to go too in depth with the descriptions of each. 

I definitely use the first two strategies in class all of the time.  If my kiddos are not understanding, I will pull out blocks or other manipulatives to give them a model.  I also tell them to draw out problems, especially multiplication and division problems.  The two strategies that I don't use very often are acting it out or making or using a graph. 

Have you used these two strategies in your class?  Any advice on implementing them in mine?

What's Your Math Problem!?! Book Study Chapter 2

I am linking up with

Jennifer Smith-Sloane from 4mulaFun

Meg Anderson  from Fourth Grade Studio

Jamie Riggs from MissMathDork

and Jennifer Findley from Teaching to Inspire 5th Grade

for this book study on What's Your Math Problem!?!



 If you missed my posting for Chapter 1 you can find that here.

Chapter 2 - Planning for Problem Solving in the Classroom

What Does it Mean to Plan for Problem Solving?

Students have difficulty solving problems in part because they do not have the necessary framework to approach these tasks.  They have been taught to compute and follow procedures. Solving problems involves much more than simply following procedures. In order to help students to learn to solve problems, you must plan for instruction that will help your students to become problem solvers.

Step 1: Finding a Good Problem - You need to find problems that both  involve the mathematical concepts that you are planning on teaching, but are also "doable" for your students. The author suggests building a library of rich problems.

 4mula for Fun has this freebie form to help you plan.  Visit her site to access it as well as to see an example of how she would use it in her classroom.

Step 2: Provide Your Students With A Problem Solving Framework

Gojak recommends using George Polya's 4 principles of problem solving:

1. Understand the Problem

2. Devise a Plan

3. Carry out the Plan

4. Look Back

Gojak continues on to describe a new model of problem solving called the Launch, Explore and Summarize Instructional Model.

The Launch stage engages the students in the problem they are about to solve.

 

 

The next stage, Explore, is where the students work as a class, in small groups, with a partner, or individually to solve the problem. 

 

The final stage, Summarize, is the area that I most overlook, and yet it is where the main teaching should occur according to Gojak. 

 

My main takeaways from this chapter:

 

1. I definitely need to plan my math lessons differently.

 

2. Gojak provides some question stems at the end of this chapter that I need to incorporate into my lessons.  Jennifer at 4mula for fun mentioned printing them out and putting them on a ring to use throughout the lesson, and I definitely think that is something I am going to do as well.

 

What's Your Math Problem!?! Book Study Chapter 1

I am linking up with

Jennifer Smith-Sloane from 4mulaFun

Meg Anderson  from Fourth Grade Studio

Jamie Riggs from MissMathDork

and Jennifer Findley from Teaching to Inspire 5th Grade

for this book study on What's Your Math Problem!?!



I missed posting for Chapter 1 last week, so this post will include  my thoughts on Chapter 1 and I will post my thoughts for Chapter 2 tomorrow - then I should be back on track.

Chapter 1 - The 5 Ws and and H of Problem Solving

Gojak opens the book with a quote from Van de Walle, "Problem solving develops the belief in students that they are capable of doing mathematics and that mathematics makes sense."  I agree - it does seem that half the battle is getting past the mental blocks that students have put up against math.

What is Problem Solving?

She then discusses what problem solving is and what it isn't.  What you and I might have come to know as problem solving (think word problems at the end of a lesson in a textbook) are actually routine problems.  The kind that we really don't have to think about.  They match the lesson, so we already know what formula we are using, we just have to plug in some numbers.

Real problem solving is what we deal with in real life.  The type where we have to go beyond the procedure, the type where students do not immediately know what equation to plug the numbers into. 

Why teach Problem Solving?

Not only does the National Council of Mathematics recognize that problem solving should be "an integral part of all mathematics learning.." but, problem solving is everywhere.  We do it each and every day in almost every career.  If we want our students to be college and career ready, they need to be problem solvers.

Who should solve problems?

Short answer - EVERYONE!

When should we solve problems?

According to Gojak, problem solving should be a part of every mathematics class. EVERY?  I definitely need to work on this next year.  Did you include problem solving in every class?

How should we teach problem solving?
The author suggests beginning lessons with rich problems as a context to help students understand the context behind the mathematics for that day's lessons.

Where can you find good problems?

The million dollar question right?  A variety of resources were given including problem solving books, and websites such as Illuminations and PBS Mathline.

My main takeaway from this chapter - I need to incorporate a lot more problem solving in my lessons!