Friday Two Cents: A Problem Solving Model


In it there are four levels to achieve your goal to solve a problem.  The great thing is that you can use this problem-solving model not just for mathematical problems but also other problems in you may face in your life.  Here is my break down of the model…

A couple of weeks ago I wrote several posts about resolutions and making plans to help you beat the winter blues.  I have always thought that planning out things helps to solve the problems that I face on a daily basis, yet I have wanted something tangible that I can see in black and white to help me explain it to others.  I did find such a piece when I took a mathematics additional qualification course a couple of years ago.  It was in the Ontario curriculum, Grades 1–8: Mathematics (revised) document of all places. It is on page 13, figure 1: Problem Solving Model.  

Understand the Problem (the exploratory stage)

This stage should be self-evident.  I cannot tell you how many times I would have students come up to me and say, “I don’t get it.”  Then I would ask, “Did you read the question?”  Most of them would say ‘Ahhh no.’  ‘READ THE QUESTION’ I would say and then look in the question for the pieces you need to answer it.  Others I would rephrase the question to emphasize the important information they may need.  Basically what is the question asking of you: what is the problem?  The best advise I say to people is talk to someone about the problem so you can see it for different angles, especially after you read it several times.  

Make A Plan

Is there another situation that you may have seen a similar problem?  I tell students don’t try and reinvent the wheel.  Or in other words don’t start from scratch look at another situations where you solved a similar problem and try and rework it for this situation.  In essence, “Make a Plan”, think of a strategy you used before and use that plan.  Tweak the plan to fit your needs.  

Carry Out the Plan

Put you plan into motion.  Draw, write, use objects to help you visualize the plan and then implement it. Use different tools to make you plan work, monitor it and make adjustments when needed.  If you planned for something and you don’t need it, don’t use it. Why waste time and energy when you do not need it. 

Look Back at the Solution

Check you results, go back to the question to make sure that it actually answers it.  Does it make sense?  You have to go through the process again from the beginning to refine you answer or correct any mistakes you may have seen.  Could you get the same result another way, perhaps and easier way? This way you can use that revised plan in the future.  

I created this visual to help myself and others try and visualize how to solve a problem.  Maybe it will inspire other teachers and students to think more about how any problem can be solved so long as you have the tools and desire to make the effort in trying.  Remember what Napoleon Hill once said …

‘Effort only fully releases its reward after a person refuses to quit.’ Napoleon Hill

A Problem Solving Model

Ontario Ministry of Education. (2005). The Ontario curriculum, Grades 1–8: Mathematics (revised). Toronto: Queen’s Printer for Ontario. http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

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Art Inspiration: Art and Math in One Lesson


ArtInspirationPaulGLogo

During my practicum I had the opportunity to do the art lessons with the students. They are the younger primary but I wanted to do something that was different and challenging with them. Yet I also taught different lessons though out my stay there. One of the areas was Math. Yes many people do not like to teach or even learn math, but there are ways that you can introduce math concepts that are both fun and educational.

My mentor teacher and I were about to begin the next math unit with the students. It was the unit on 2 and 3 dimensional shapes. We wanted the students to be familiar with the different shapes we were going to use in the unit. Therefore I created a lesson plan for them around this idea. It was also fortunate that I had to use a type of lesson called a Choice Centres for one of my other classes. The Choice Centre strategy allows for a variety of activities providing different modalities and different levels of responses that help students investigate the topic further. Some adaptations can include drama, writing, reading, technology, viewing and experimenting. We were to use this model on a literacy lesson but our professor said we could use it on any subject matter, so long as we stayed true to the model. The model calls for a student to choose a centre and then stay there to explore the subject material. I adapted the lesson so that the students would be rotated to allow all the students an opportunity in each centre. The centres I created are as follows …   Centres (Materials And Instructional Notes)

  1. Blocks 3D shapes / construction toys
    1. Use building blocks and pattern blocks to create structures
    2. Use Kapla Blocks to model real structures
  2. Shape exploration 2D shapes – triangles, rectangles, squares, circles
    1. Use coloured 2D plastic shapes to explore patterns
    2. Different sized triangles, rectangles, squares and circles
  3. Work Sheets with 3D shapes (assessment for learning)
    1. Make the 3D shape into something real (ex. sphere – baseball)
  4. Geoboards – with elastics create different shapes
    1. Students will explore what shapes they can create using the boards and elastics. They can create, rectangles, squares and different shaped triangles.

LiteracyCarocel Important Notes For The Teacher

  • Circulate around the room and observe and listen to what the students are calling the shapes. Are they using the proper terms? What are they calling the 3D shapes? How are they using the material? Is their something you saw that you did not expect?
  • Have a timer (I use an iPad timer displayed on the screen) to allow the students to explore the different stations.
  • Have a class list to write down anecdotal notes of the students for assessment and documentation. (Assessment As during the learning)
Many people may think that this is not Art just a math lesson.  But I say when you create something don’t you use shapes.  When you paint a picutre of a flower doesn’t it start with a circle?  Or when you create Mondrian Art isn’t it divided into geomentric shapes?  Math and Art are a part of each other.  It is a match like ice cream and chocolate fudge.  They are great apart but fantasic together.

Below are some images of the lesson. Who said that art and free expression are not part of learning math?

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