My brother nodded in agreement and chuckled, “Yes our mother was great with numbers.” She had the ability to use numbers fluently, a skill we we both easily acknowledged.
How well I remember standing next to my mother in a grocery store or bank as she quickly and easily calculated totals. I would line up the digits mentally in my head, carry or borrow if needed, and try to remember the numbers as I worked. What a cumbersome procedure! She, on the other hand, already had the answer and cheerfully let the clerk know the amount required. I recognized her skill and longed to have it. It wasn’t speed I wanted, it was the ease with which she worked. Why couldn’t I do that?
Was it the education my mother received during the 1920’s in the Netherlands? Or was it as a young, single woman when she worked for Unilever that she developed proficient number sense? It was not until later in my mathematical life that I learned her secret. Perhaps I would have benefited from a motherly ‘Number Talk‘.
A Number Talk? Yes, the kind of talks I plan to use with students this year. Parents certainly can engage their children in number talks. They’re fun! And teachers of math will find them a best practice for developing number sense in students.
I observed a number talk as part of my summer math course. Here are my observations.
How Number Talks Work
The instructor sets the students up for the number talk telling them they are to figure out a math question.
1.The question is written on the board and students are asked to solve it. No pencils, no paper, they are to calculate their answers mentally. No comment is given on how to approach the problem.
2. Students are given lots of thinking time and respond with a thumbs up once they have the solution. A low key way to respond so that everyone can take the time they need.
3. Students then share their answers and explain how they arrived at the solution.
4. Through the discussion students are led to see the interesting variety of approaches used to solve the question.
Open ended questions such as these spur the discussion on.
“Anyone try something different?”, “Anyone else do that?” These questions give everyone a chance to explain their process.
“I think I heard you say.” or “How did you know you should have…..” These statements give the student opportunity to clarify thinking and communication. The teacher does not add to the student’s explanation she only repeats what she hears. The onus is on the student to ensure that the explanation is clear.
“Where do you think your mistake came from?” Helps the student clarify logic and identify the error. Mistakes are part of the solution process both acceptable and interesting as part of the learning.
5. The process students use to solve the problem is written on the board so that it is easy for everyone to follow. This is important. Everyone needs to understand how the numbers are manipulated.
6. All solutions are represented on the board and students are asked to draw a picture of their solution and someone else’s solution. Another important step as it makes the learning more concrete and helps students see how they can work flexibly with numbers.
Screen shot from XEDUC115N How to Learn Math
Number talks are one way to help students develop insight, ability and willingness to to break numbers apart and regroup them as they observe and discuss different ways to solve math problems.
Yes, the answer is important but it is not the most interesting part of a mathematical question. As we show students that problems can be solved in different ways we teach them the very, very important building block of number sense, a skill that is foundational for the rest of math.
Ahhh yes, a number talk would have given me insight into the skillful mind of my mathematician mother but I think I am on to her secret now.