NCTM’s Mathematics Teaching in the Middle School, Focus Issue on Fostering Mathematical Reasoning, February 2012 is a direct connection to promoting inquiry, risk-taking, and metacognition where teachers and students alike make their thinking public that were discussed in past blogs. The articles in this focused issue gave examples of how to provide opportunities for mathematical reasoning for younger students so that their conceptual understandings can expand to the high school skill set and more importantly to bridge the concrete to the abstract.
From the article “The Value of Debts and Credits,” on page 335, five suggestions with examples for each are given for fostering mathematical reasoning and I quote, “Encourage students to:
- give conceptual explanations.
- provide efficient solutions.
- make conjectures and prove them.
- create different & sophisticated solutions.”