Components of a Working Mathematically Curriculum

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Reproducible Page ... © Maths300, Curriculum Corporation

• Hands-on Problem Solving Play
  
  • Each task is an invitation to work like a mathematician. Mathematicians don't know the answer to a problem when they start it. If they did, it wouldn't be a problem. They have to play around with it. Each task invites students to play with mathematics.
  • On average this component is one lesson per fortnight and the tasks are often chosen to integrate with the current strand or topic.
  • The Mathematics Task Centre Project provides over 200 of these problem solving tasks and a collection of wisdom about their effective use.
• Skill Development
  
  • A mathematician needs skills to solve problems. Many teachers find it makes sense to students to place skill practice in the context of Toolbox Lessons which help us better use the Working Mathematically Process.
  • On average, Toolbox Lessons are one or two per week.
  • Lesson 9, First Principles Percent, is an example of this component.
• Focus on Process
  
  • This is what mathematicians do; engage in the problem solving process.
  • A balanced curriculum would contain about 20 of these challenges per year, many of which will take more than one session to investigate.
  • Lesson 25, Sphinx, is an example of this component. In the elementary school it can be included within a unit on perimeter and area. In the secondary school it can be included in a unit on patterns and powers.
• Strategy Development
  
  • Mathematicians also make use of a strategy toolbox. These strategies are embedded in Maths300 lessons, but may also have a separate focus. Poster Problem Clinics are a useful way to approach this component.
  • On average a Poster Problem Clinic is one lesson per fortnight.
  • Lesson 14, The Farmer's Puzzle, is an example of this component.
• Concept Development
  
  • There are relatively few major concepts in mathematics. Examples are place value, fractions and probability. Each took centuries for the human race to develop and apply, yet traditionally, students have been expected to understand such concepts after having 'done' them for a two week slot. Often the concepts were not revisited until the next year. A Working Mathematically curriculum identifies such concepts and regularly includes development work.
  • Typically one or two such concepts are visited and revisited (threaded) over a term, perhaps for only a few minutes per session.
  • An example of this component is the threaded use of Lesson 35, Nine & Over, which addresses Place Value.