Math Five Step

The mathematics curriculum in the junior and intermediate grades is organized into five strands consisting of the five major areas of knowledge and skills in which students are expected to achieve desired outcomes based on provincial standards.

The five strands are:

Number sense and Numeration

Measurement

Geometry and Spatial Sense

Patterning and Algebra

Data Management and Probability

As children are being taught the knowledge and skills corresponding to each of the five strands, they are engaged in seven mathematical processes which are designed to help students acquire and apply the knowledge and skills presented in the five strands.

Those seven mathematical processes include:

Problem solving

Reasoning and proving

Reflecting

Selecting tools and computational strategies

Connecting

Representing

Communicating

It is my professional opinion and observation during my 28 years of teaching at the elementary level that problem solving is central to learning mathematics.

I repeat!

Problem solving is central to learning mathematics.

By learning to solve problems, and by learning through problem solving, students are given numerous opportunities to connect mathematical ideas and to develop conceptual understanding.

Most experts and specialists agree with the premise that problem solving must form the basis of effective mathematics programs and should be the mainstay of mathematical instruction.

Once a student understands the basic computational rules and skills, problem solving becomes the tool by which they connect the knowledge they gain in mathematics classes to the real world in which they live. Once this connection is made, a student becomes a master of the mathematics process and begins to make sense of the world in which he/she lives.

It is obvious that many students in the Junior and Intermediate grades have a good understanding of mathematical numeric concepts. In other words, they have little real trouble when it comes to adding, subtracting, multiplying and dividing on simple quizzes or worksheets. Understandably, up until Grade 3, most mathematics programs in school focus on the mastery of basic computational skills.

Once a child enters the Junior grades, the focus shifts to more of a problem-solving approach and this, unfortunately, is where the school system begins to lose a lot of students. From Grades 4 to 6 a child either latches on to mathematics or flounders and gets lost in a world of frustration.

It is not surprising that most of the high achieving students in elementary grades are those who have little trouble with mathematics. Mathematics helps to build confidence and helps students make sense of all other subject areas. On the other hand, students who are just getting by, or who are falling behind, almost always have difficulty with mathematics. For them, nothing makes sense and it shows in everything they do.

Parents sometimes have trouble understanding how their child can be doing so well in mathematics up until the end of Grade 3 and then watch the difficulties mount as the child progresses through the junior grades. There are many theories for this difficulty, but they always stem from the fact that despite the best efforts of teachers, mathematics is not going to make much sense to a great number of students within the confines of modern day classrooms. The connection between mathematics and real life cannot be made inside the four walls of a classroom. You must move beyond the school and help students make the connections so that they can begin to see how mathematics makes sense of life itself. This is precisely why it is so important for parents to take on a "coaching" role at home.

The Greater Sudbury Learning Clinic uses a five-step problem solving model. This is the same five-step model that can be applied not only to the study of mathematics, but also to any other area of life in which one finds him/herself. This is why we contend that if you have a solid foundation in mathematics, you can do just about anything in life.

The five steps are:

            1.         Understand the problem

            2.         Gather all of the available information

            3.         Consider your alternatives

            4.         Solve the problem

5. Communicate the results

The first thing you must do is make sure you understand the problem. If necessary, restate the problem in your own words so that it is clear in your mind.
There is absolutely no point in trying to solve any problem until you clearly understand what it is that must be solved. This may not be as simple as it sounds. Sometimes problems can be a lot more complex than they first appear, so it is critical that you look at the details from all angles before going on.

Once you understand the problem, you must identify all of the information you are given as well as all of the information that you may need to solve the problem.
In most cases you will be given all of the information you need, but there are times when you must draw from outside sources to gather additional information.
When dealing with some problems you may find that you need to do some additional research to come up with the information you need. There are even some problems that simply cannot be solved because you are missing some critical information.

The next thing you do is consider all of the possible strategies for solving the problem.
This is where you draw upon your previous experiences and the knowledge you already have.
You then select the strategy you feel will work best based on the information you have to work with. This is an important consideration, especially in real-life situations. Often times your solution to a problem might have been different had you been aware of different information. Nevertheless, you can only work with what you've got, so you do the best you can with the information you have at hand and decide on the best option.

At this point you go ahead and perform the necessary calculations and actions based on the chosen strategy.
You will use any tools and manipulatives that are necessary, draw diagrams, use words and/or symbols to track your progress.
The Learning Clinic process emphasizes the importance of being able to go back and follow your own work when finished. Therefore, you must record EVERYTHING. I advise that you should write down all of your steps and calculations so that you can go back and check them from time to time.
Once you have come up with your solution, you must check the answer to see if it is reasonable and then even review the method used. For example, once you come up with the answer, you may discover that there was a better strategy that could have been used to arrive at the same answer. Keep this in mind the next time you are faced with a similar problem.

All that is left now is for you to communicate your results appropriately.
Communication is simply the process of expressing mathematical ideas orally, visually, and in writing, using numbers, symbols, pictures, graphs, diagrams, and words. Mathematics has been called a "language" by many people. It is a way of communicating with others.
Communication is an essential process in the learning of mathematics, for what good is solving a problem is you are not able to effectively communicate the results to your intended audience.
In many cases, you require highly refined skills in writing and speaking in order to help your audience understand the mathematical relationship you have just determined.

The Learning Clinic is The Private Practice of
Robert Kirwan, B.A. (Math), M.A. (Education), OCT
4456 Noel Crescent, Val Therese, ON P3P 1S8
Phone: (705) 969-7215 Email: rkirwan@thelearningclinic.ca