Thursday, 3 April 2014

A Balanced Math Program

There has been a lot of talk about math (at least in the area I am from) lately.  Some talking about going back to basics and others talking about problem solving.  For those that have been reading my blog you know that I tend to lean more to the problem solving approach; however, there is need for fact recall and learning basic arithmetic in a constructive and engaging way.

With this in mind many of us in our board (@mathewolridge, @keriewart) and neighboring areas (@avivaloca @moojean) have been talking a balanced math manifesto (#balancedmathmanifesto).  Thought I would share my thinking in hopes to start the conversation rolling.  Please keep in mind that this is still a work in progress and our only my opinions.  I would love input from any readers.  Hopefully these ideas and all the other collaboration can be added to our Balanced math manifesto.  So please add your voice, would love to hear from you.

Components of a Balanced Mathematics Program

Guided Mathematics: The teacher introduces a selection at the students’ instructional level

  •          Promotes mathematical strategies and offers students the opportunities to practise varying strategies
  •          Links to the problem they will be exploring
  •          Fosnot “String” lessons are great insertion here
  •          Does not need to be a minds-on activity, can be done while other students are solving problem

Contextual/ Rich Task: The teacher introduces an open, or parallel task that encourages thinking of mathematical principals

  •          Rich, truly problematic situation
  •          Authentic to students
  •          Allows students to generate and explore mathematical ideas
  •          Multiple entry points
  •          Supports mathematizing
  •          Important that teachers have anticipated student strategies before students work on a problem

Shared Mathematics: Students work together to “Mathematize”

  •          Students work in homogenously levelled pairs
  •          Allows the teacher to monitor and conference (see the next section)
  •          Provides students opportunities to explore while discussing
  •         Allows for assessment, anecdotal and observations of growth and development
  •          mathematical theories and concepts
  •          Allows students to see themselves as mathematicians.  They feel comfortable and experience fluency when making connections to other problems
  •          Develops fact fluency, patience  problem solving
  •          Students demonstrate their knowledge of mathematical big ideas and concepts
  •          Increase comprehension as students explore related problems

Conferencing/ Monitoring: As students work he teacher is constantly monitoring and conferencing with students

  •         Asking why questions or building varying types of questions
  •          Can sometimes feel like an interrogation
  •          Developing a sense of where the students are mathematically
  •          Comparing student work to learning trajectories or landscapes of development
  •          Planning for “Congress”

Congress: Teachers and students work together to understand the big ideas.

  •          Teachers ask critical thinking questions
  •          3 Types of Questions are: “building upon”, “comparing too” or “going beyond”
  •          Teachers job is to promote thinking and elicit thinking and strategy based mathematics
  •          Students converse and communicate thinking strategies
  •          Solidify understanding

Reflection: Students reflect on the lesson and strategies used. Metacognition in mathematics

Math Games and Math Facts: Student knowledge of basic addition/subtraction/ multiplication/division facts is critical

  •          Teachers give the students a consistent and on-going opportunity to build their knowledge and skills while learning and practising the basic math facts
  •          Math games build communication
  •         Fact recall
  •          Problem solving strategies
  •       Promote further learning of concepts