Developing Our Problem Solving Skills

As the dreaded testing season looms closer and closer, the need to get my students actively problem solving every day has become almost an obsession for me!

 

 

Depending on the complexity of the task, and the ability of my students, I introduce each problem differently.  Sometimes, I give all of the students the task with little to no instruction, and let them plug away at it.

 

 

 

 

 

 

Other times I will provide a warm-up small group lesson for my struggling learners.

 

 

For this particular challenge, I introduced them to modeling with manipulatives.  They were then able to provide support to their whole group in using manipulatives to solve the problem.  This always gives them a big boost of confidence when they are able to be the "experts".

 

 



 

 

When the problem appears to be challenging for all of the students, I often display a similar problem on the Smart Board and we problem solve it together.  I then give them the problem to work in small groups.

 

 

 

Problem solving is always better with popcorn isn't it??

 

 

I will be creating a larger product this summer using these problems and more, but for now, I have a freebie for you that includes ALL of these problems.  You can download it from my TpT store here.

 

 

 

 

If you download the freebie, I would love any feedback or suggestions you have for the final product.

 

Thank you!

 

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! 

Problem of The Day

Every day I put a problem of the day on the board for my kiddos to solve.  I usually use real world problems and examples using either the students or my family.  My fifth grader noticed that I did this the other day, and asked why?  I told him that my students are always curious about my family, so they enjoy these little problems. 

Today I had collaboration in the morning and my kids usually hang out in my classroom before school.  When I came back in, I noticed this on the board.  My fifth grader had written a problem of the day for the students!  While it was a little too challenging for my third graders - I thought it was a great way to stretch my 5th grader.  I think I might have him come up with problems more often!

It also made me think that it might be fun to ask some of my students to come up with problems as well.

Do you incorporate problem solving into your daily lesson? What things do you do?