Monday, October 17, 2016

Mathematical Reasoning: Number Sense

How many people live in Massachusetts?
We used five population statistics today as part of the place value unit students are studying.

Early in the day, I asked students how many students they thought were in the school. They made fairly good guesses that were close to our approximately 400 students.

Then I asked how many people live in the town where our school is located. Their guesses were about 100 or 200 more. Later when discussing this more they added rationale that increased the estimate with points such as the fact that there is more than one school, some students don't go to public schools, students have siblings who aren't in school, students have parents, and there are older citizens too. A few came close to 13,000 which is close to the exact number of people.

After that we estimated the amount of people that live in Boston. Students knew it was bigger than our town with more people and most made guesses that doubled, tripled, and quadrupled the town's population. Only a few used more reasoning and experience to compare Boston with cities they had visited or knew about thus guessing larger numbers. As for the United States and world population similarly only a few could come close to the actual number.

When watching the Presidential election debates, I was struck by the large amount of numbers thrown about--numbers that were difficult to imagine and compare when sharing with just language. I found myself wishing there were reliable infographics to help me understand the comparisons, proposals, and critique. I think the Presidential elections of the future will be blended presentations as the information is simply too sophisticated for words alone, thus the back and forth jabs.

Too often too many of us can't quickly make a numerical comparison or imagine a measurement or value. Yet, it's a very important critical thinking and decision making skill.

Working with numbers that relate to students' lives is a first step towards helping to build number sense, and then allowing students to estimate "how many" and explain their rationale for their estimations is a good way to share and develop mathematical reasoning and explanation.

Tomorrow we'll continue working with these numbers as students learn to write and think about numbers in many ways. Onward