## Math Debates in Elementary Classrooms

Over the past few months I’ve dedicated a good amount of time to to having math conversations. These math conversations occur when the class is unsure of how to solve a problem or when disagreement ensues over what particular strategy should be used to tackle a problem.  The math conversations (or debates) allow students the freedom to openly discuss logical reasoning when solving particular problems.   These conversations can be sparked by the daily math objective or follow another student’s response to a question.  It’s not necessarily planned in my teacher planner as “math conversation” in yellow highlighter, but I do make time for these talks as I feel that they bring value and encourage student ownership.  The conversations also give insight to whether students grasp concepts and are able to articulate their responses accordingly.  Mathematical misconceptions can also be identified during this time.

During these conversations I have manipulatives, chart paper, whiteboards, iPads and computers nearby to assist in the discovery process.  I emphasize that there’s a certain protocol that’s used when we have these discussions.  Students are expected to be respectful and listen to the comments of their classmates.  To make sure the class is on task I decide to have a specific time limit dedicated to these math conversations.  Some days the conversation lasts 5 minutes, other days they may take upwards to 15-20 minutes.  When applicable, I might use an anchor chart to display the progress that we’ve made in answering the questions.  I should also mention that sometimes we don’t find an answer to the question.  Here are a few questions (from students) that have started math conversations this year:

• Why is regrouping necessary? (2nd grade)
• What can’t we divide by zero? (3rd grade)
• Why are parentheses used in math? (3rd grade)
• Why do we need a decimal point? (1st grade)
• When do we need to round numbers? (2nd grade)
• Why is a number to the negative exponent have 1 as the numerator? (5th grade)
• Why do you have to balance an equation? (5th grade)
• How does the partial products multiplication strategy work? (3rd grade)
• Why do you inverse the second fraction when dividing fractions? (5th grade)
• Why is area squared and volume cubed? (4th grade)

Above is just a sampling of a few of the math conversations that we’ve had.  Afterwards, students write in their journals about their experience finding the solution to the problem.

Of course this takes additional time in class, but I believe it’s time well spent.  The Common Core Standards  focus on depth of mathematical understanding, rather than breadth.  This allows opportunities to have these conversations that I feel are beneficial.  They also emphasize the standards of practice below.

• CCSS.Math.Practice.MP1 – Making sense of problems and persevere in solving them.
• CCSS.Math.Practice.MP3 – Construct viable arguments and critique the reasoning of others