Meaningful Math

From the desk of Leigh Ann . . .

“The essence of mathematics is not to make simple things complicated, but to make complicated things simple.”  – Stanley Gudder

Math can be a pretty complicated subject, so I am a great believer in math talk in the classroom.  Having a meaningful dialogue about reasoning and problem solving is a great way to move students from passively going through the motions to a deeper understanding of mathematic concepts.  When students have the opportunity to articulate and defend their ideas and analyze the reasoning of others, they activate higher level thinking skills.  Talk about math concepts also offers teachers ongoing assessment opportunities because it allows us to see what our students do and don’t understand.

One of the standards for math practice is to construct a viable argument and critique the reasoning of others and productive math talk is a great way to make this happen.  These discussions open the lines of communication and allow our students to explain, justify, explore, compare, agree and disagree with ideas and processes.  Teachers can facilitate these productive discussions by asking good questions.

Good questions:

• Develop higher level thinking.  They ask more of a student than reciting a simple fact.
• Are open-ended and have more than one answer.
• Use strong math language that develops verbal skills.
• Guide children through next steps and processes.
• Open the door to helping students rethink and reshape strategies.
• Create a spark of wonder and encourage children to ask their own questions.
• Remind students that they can learn through mistakes.

While visiting a 4th grade math class, I watched as the students danced their way through the steps of a 2-digit division problem.  “Divide – Multiply – Subtract – Bring Down – Repeat as needed!”  They followed their song and dance by each solving a written division problem.  Upon completion, volunteers were invited to come to the board to explain their work.  They discussed the procedures step by step and critiqued each others’ explanations and results.  Their teacher intervened when needed with guiding questions and was able to assess who understood the process.  The students were engaged, smiling, and definitely growing in their understanding through this interactive process.  This math talk made a complicated process more meaningful and I left the room singing “Divide – Multiply – Subtract – Bring Down!”  It certainly stuck with me.

“The best way to understanding is a few good examples.”  – Isaac Newton