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.

Friday Two Cents: Funny How Life Works In Mysterious Ways.


For the past month I have not been posting many Friday Two Cents. To be honest I have been preoccupied with finishing assignments and lesson plans for my practicum in teacher’s college to have the time for posting. This week I finished off my first practicum / semester and last assignment and now I have settled in to just relax for the holidays.

Yet I was privileged to go to my staff’s Christmas party at the after school program I work in. The students had finished their last play of the holiday celebration for their parents and the staff always goes out for their Christmas celebration dinner. There we exchange gifts and relax in a more social atmosphere.

After the dinner and the gift exchange the director did something different this year.   She asked us to reflect on the past four months and tell the group, “How would you describe these past four months of the school year?” This question got us all thinking but all of us had to say it was hard work but in the end the students and teachers are beginning to understand one another and everyone was enjoying their time at the school.

For me though I have a more unique perspective. I only can go in once or twice a week because of teacher’s college so my experience of the first four months is quite different. Yet I described that going in to the school for those few days was like an anchor for me. No matter how difficult or chaotic my life got with assignments of lesson plans, I knew going to the school was like a safe harbour in a storm that has been my life so far. The director and the other staff appreciated me saying that and I meant every word.

Thinking about my reflection I have to admit that the school truly has been a comforting anchor that has kept me on course these past four months. Not only with the ECE staff, whom I work with, but also the teaching staff at the school. They have been a constant reminder of why I went into teaching. Their constant well wishes and support has given me the strength and determination I needed at some trying times.

I thought that once I got into teacher’s college I would not see or spend time with people from the school, that my studies would consume all my time. Then when I was asked to return for at least one day a week and I was not sure I could handle the extra pressure of another school, staff and students to my already busy schedule. Yet it has been this extra school, staff and students that have been my rock, my anchor in a sea of turmoil. Funny how life works in mysterious ways.

Friday Two Cents: This Above All: To Thine Own Self Be True


This week started off pretty bleak. Not just from the weather, though I think that it may have been a contributing factor, but I was beginning to not enjoy my practicum placement. It had nothing to do with my students, mentor teacher (MT) or the school, it everything to do with myself.

I felt that I was not succeeding in my practicum because I had a couple of not so successful lesson plans. I followed the curriculum and the students understood the lesson but I thought that they were bored or uninterested in what I had to say. Yet when I reflected on my performance I looked inside myself and said, “That was not you. You were not acting like yourself, or being yourself.” It was true on soo many levels.

You see I made a conscious effort not to bring my Early Childhood Education (ECE) background or baggage with me into practicum. I wanted to take a fresh approach to teaching and learning, to not come into the classroom thinking I know everything there is to teaching, because in truth I do not. Yet after reflecting on what had happened I said, “This is it. I have to be myself. If I am going to be condemned than let them see the real me.”

Therefore I began with my attire. The school has a dress code that male teachers wear collared shirts. I do that but I was wearing dress pants each day and did not like it. It wasn’t me, so I started wearing my dressier looking designer jeans and right away I felt better. Next I consciously reminded myself to have a positive attitude, so I began smiling. It is a small thing but if you do it, others will follow you and soon everyone is smiling. Lastly and the most significant was reminding myself that I am an ECE and that has value.   I should not dismiss this part of me so easily. Therefore I began looking at the lesson plans as an ECE and the ideas of how to implement them became easier.

Play is so Important in a child’s learning development

My ECE philosophy is that children learn through play and self-exploration. So in my math lesson I brought in manipulatives and turned the lesson into a game. I did something similar in a kindergarten program but I made it more advanced for the older grade 6s. I even brought in an activity for the special needs child based on a kindergarten activity too.   Right away the students got right into it and it was fun to teach them. It was a tremendously positive experience.

I expanded that positive lesson into my Art lesson with them in the afternoon. They had not had art this year and this was to be their first lesson. I started with lines, shapes, 3 dimensional shapes, shading and light. They all know how talented and how much I love art that they were eager to have art with me.   I did the lesson and they were so enthusiastic, especially when I turned the 3D shapes into real world objects. I told them that to get to draw 3D objects and images they need to know this first and they loved it. They were expressing themselves through their art and I loved it. Now I am doing the art lesson for a while and I am very excited.

No matter what the age, kids need play.

In the end I learned two extremely important lessons about teaching and more importantly, myself. Teaching is engaging the students through none traditional means. If you can play a game with blocks while they learn about expressions and equations then do it. Children are children, whether they are kindergarten or grade 6, they are all kids at heart. The second is to be yourself. I am an ECE teacher, that will never change. I just have to remember this and use the tools and skills I developed becoming an ECE. For in the end I have to remember that famous quote from Shakespeare’s Hamlet, “This above all: to thine own self be true.

Friday Two Cents: Their Heart’s Are In The Right Place


This week was an exciting one because I was able to do my first two lesson plans with the students. I was so excited to begin that I could feel my heart racing while I did them.  At one point I noticed I needed to calm down when I was printing on the board. When I get excited or nervous my handwriting is, to put it mildly, terrible. But if I am calm and focused on the task I have pretty good penmanship, so I have been told. My mentor teacher noticed my enthusiasm and said that it was good to see and for me to keep it up. But back to the lesson plans.

Tubes - A Cooperative Game to help with motion, teamwork skills and strategy

Tubes – A Cooperative Game to help with motion, teamwork skills and strategy

The first was a physical education lesson centred on cooperative games to foster teamwork and strategy. The activity starts in one corner of the gym and the students needs to get a Ping-Pong ball into the bind at the centre of the gym. However, you have to do this by rolling it through pipes or tubes that are about 30 cm or 1 foot long and cut in half. The team only gets 5-6 of these tubes and that is only about 1.5 m. They still have 3-4 m to go so the first person must go to the end and continue the tube system and the next person and so on. The team must work together to achieve their goal of getting the ball into the bin. I have to tell you they were excited to do the activity and their enthusiasm was amazing to see.

The next plan was a read-a-loud to the children in the class. I selected “How Full is Your
Bucket” to read to the class. It is about a boy who is told that everyone has an invisible bucket above his or her head. When their bucket is empty they feel terrible. But when it is full they feel great. Every time you feel badly because of what some says or does to you, you lose a drop from your bucket. But if someone does something nice to you, a drop will fall into your bucket. The trick also is if you do something nice for someone else you not only drop into his or her bucket, but you also drop one into yours.

I read the book to the class but I added the sound effect of water drops dripping with my mouth. This little effect added so much to their interest in the book. They enjoyed the story and I also had a reflection question for their religion lesson. “What can you do to fill someone else’s bucket?” They came up with some great ideas such as, sharing with others, caring, helping, giving compliments but I really enjoyed one sentence a student wrote. “We can pray for others to help them feel better.” That is what’s so amazing about children; they have their hearts in the right place.

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