Learning, Math, Motivation, Uncategorized

Exploration in Mathematics- Allowing Explorers to Flourish

Exploration by it’s very nature is a step into the unknown.  Armed with no map, no set of steps, no set path, the explorer embraces the excitement of discovery with a willingness to get lost in the adventure.  Imagine for a moment exploration that was planned, with every destination known, every step predetermined…it would not be as much fun, it would not belong to the explorer, and it would not be exploration.

Mathematics is a place where exploration is not only possible…it is necessary.  Through exploration and play we can breath life into the learning of mathematics, as we open up opportunities for imagination, creativity  curiosity and wonderment.   These qualities can carry the mathematics beyond the textbook, the worksheet, the drill and practice.  They can make mathematics come alive.  This exploration needs to belong to the explorer and the explorer in every learner needs to be given opportunities to discover and create in mathematics.  There may be  times when we would want to give students the map with the route laid out and support them on reaching the destination but there should also be times where students face a problem or situation and need to reason your way to the other side, without the road map.   In those times it becomes about finding their own way, embracing the different but equally valid paths/solutions of others, and truly discovering not only the science of mathematics but it’s artistry and creativity as well.  This exploration does not need to happen in isolation.  Explorers can join resources and thinking power to help navigate the journey and share in the excitement of discovery.

In this video Dan Meyer‘s describes the problems facing mathematics education when we take all of the exploration out of the subject.

1. Lack of initiative- Translation- I don’t want to do it!

2. Lack of Perseverance- Translation- It’s too hard!  I give up!

3. Lack of Retention- Translation- I don’t know.  Blank look.

4. Aversion to word problems- Translation- Can I just have a sheet of numbers.

5. Eagerness for a formula- Translation- Can you just show me how to do it?

By purposely and deliberately creating an environment where mathematics exploration and discovery flourish we can harness the inner mathematics explorer in our students.

 

Exploration is really the essence of the human spirit.  Frank Borman

Math, Teaching and Instruction

Inquiry in Mathematics

In Saskatchewan our provincial curricula are built around one central core…inquiry.  Inquiry is a philosophical approach to teaching and learning that empowers students to explore and discover.  Through inquiry students are active participants in the creation of understanding and knowledge.   They are asked to be curious, to wonder, to question, to reflect, to share and to think

In Mathematics inquiry is often seen through problem solving.  By collaboratively solving and creating mathematical problems students construct and deepen their understandings of concepts, strengthen their strategic competence, and develop their logical reasoning skills.  As students engage in problem solving they need to attend to 4 important stages in the inquiry/problem solving process:

Stage 1: Understand the Problem–  This very important stage is often overlooked in the classroom.  It is often assume that students understand the problem in front of them but this assumption can by costly.  Without a solid understanding of what they are being asked to do, students are often stumped before they start.  Time spent carefully dissecting a problem and ensuring understanding can be critical to success.

Stage 2: Make a Plan– Just like the construction of a building, the construction of a mathematical solution requires forethought and a plan.  Having a carefully considered plan of attack can help students construct their solution successfully.  Problem Solving plans or strategies can include:

  • Acting it out
  • Using a model
  • Drawing a picture
  • Guessing and testing
  • Looking for a pattern
  • Making a chart or a graph
  • Working backwards
  • Making an organized list
  • Using logical reasoning   

Stage 3: Carry out the PlanIn the words of  Nike – Just Do It!

Stage 4: Look Back –  This stage involves careful reflection, checking to see if your answer makes sense, and considering the solutions of others.  Considering the solutions of others and comparing them to your own provides an opportunity for understanding and learning to be collaboratively constructed in the mathematics classroom.

For more information on Problem Solving in Mathematics check out these great resources:

Making Math Meaningful to Canadian Students by Marian Small

Making Math Meaningful

Introduction to Problem Solving by Susan O`Connell