Transition to a concept-based classroom
Teachers often mention to me that it’s difficult to visualize how the new concept-based approach for MYP will fit into teaching plans. Colleagues can easily ensure learners grasp and explore the mathematical objectives, but it can be hard to know how to integrate all the key and related concepts across a whole scheme of work.
Myself and my co-authors are currently developing new MYP Mathematics resources that incorporate all the mathematics needed for the new e-assessment and the prior learning for the Diploma courses. These resources are organized by the related concepts and progress by level of difficulty. This enables you to autonomously plan the mathematical units you want to teach in the order that you want, but with a clear, flexible structure for linking them to both the key concepts (like relationships or form) and related concepts (like simplification and change).
For example, if you’re teaching a unit on algebraic expressions, you might dip into the chapters on simplification, system and equivalence to cover the required mathematical objectives in your unit, and synergistically incorporate the key concept of form.
I’ve given an example of how this could work practically below.
How could this work in the classroom? For example, in a unit on algebraic expressions you could introduce the unit by having the students look at the key concept of form to understand why algebraic expressions are presented in a particular format. More specifically, in the related concept of simplification, students will understand that there are different ways of writing equivalent algebraic expressions. By using certain rules of algebra they will discover the related concept of system, and they can simplify expressions to make better sense of these rules, or be able to use the rules in real world settings. This process of simplification in algebra is seen as a way of changing the form of an expression while at the same time making sure that the equivalence of the expressions is maintained.
So, a unit on algebraic expressions strongly emphasizes the related concepts of simplification, equivalence and system. These related concepts can then be tied back to the underpinning key concept of form; you can conclude by examining students’ findings and discussing the implications of form.
Progressing through this unit leads us directly into linear equations where we heavily rely on the concept of equivalence to understand fully the equivalence transformations in simplifying and solving the equations. Systems of equations naturally follow, leading into linear programming. This lends itself to a whole range of real life examples where the concepts of equivalence, simplification and system can be fully comprehended.
Try this example
Try the following to link in the global context of Globalization and Sustainability with the key and related concepts.
A small island in the Caribbean imports and exports a variety of products. For the years 1995 to 2012 the island’s total exports and imports can be modelled by the following system of equations, where y represents the total exports or imports in millions of dollars, and x represents the time in years, and x=0 corresponds to the year 2000:
Exports: y = 1310x + 5165
Imports: y = 725x + 7430
- By analyzing the system of equations both algebraically and graphically, describe the island’s balance of trade between 1995 and 2012
- Explain what is meant by the term system of equations in the context of this problem.
- Describe the form of these equations.
- Explain what it means to say that both equations are presented in the same form.
- Explain how the form of these equations has helped you represent them on a graph and hence obtain a solution.
- How does the gradient of the lines determine the pattern in imports and exports?
Here are some examples of how to cover a mathematical objective in algebra through the related concepts. The key concepts can change depending on the context of the unit.
How your resources can help
Resources that are organized by related concept help students learn the mathematical objectives in a different way and encourage them to form stronger connections. This creates a framework for learners to embrace three-dimensional instruction where one of the goals is increased conceptual understanding supported by factual knowledge and skills, and the transfer of understanding across global contexts to assimilate information (Erickson 2008). It also establishes a base for subsequently linking in more mathematical objectives in later units.
Very much in line with the MYP: Next Chapter aims, this approach also builds the foundations for cross-curricular understanding, helping learners to recognize and manipulate mathematical ideas as they encounter them in other disciplines.
Rose Harrison is an MYP workshop leader with nearly 20 years' experience of teaching in international schools. She is an MYP Community and Service Leader, in addition to consulting on IB curriculum review.