My Mother and ‘The Number Talk’

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.

Creating Safe Places to Take Risks for Learning

What messages will you give your students about the value of mistakes as we learn?

Mistakes, fertile ground for growth.

Live on the learning edge – don’t be afraid to make a mistake.

The path of learning is littered with mistakes – thank goodness!

Mistakes are the stepping stones to learning.

If you can’t make a mistake you can’t make anything.

How to grow new pathways in your brain:

1. Take on a tricky problem.

2. Never fear mistakes.

4. Persist till you meet success.

Parents and teachers, what messages do you give your kids to encourage risk taking as they learn?

Taking on the Challenge

And the moral of the story is….

Ugh!  A didactic tale can fall flat. With little meaningful connection to the story the message is seldom remembered or lost to the reader.  You may identify with this.  I for one, recognize this didactic interaction not only in books but in my classroom.

Lesson 4  of How to Learn Math with Jo Boaler  describes the didactic contract in the classroom.  See if you recognize it.

The Didactic Contract  identified by by Guy Brouseau, states that there are certain expectations for both the student and the teacher in a learning setting.  Teachers are to demonstrate and guide their pupils, and students are to learn with ease.

Here is how it happens in my classroom.  During a math class I quickly step in to clarify, add to a student’s math explanation, or demonstrate the next step. Students on the other hand, are quick to ask for help  when faced with uncertainty because they do not necessarily believe that learning involves struggles or challenges. Together we fall into this unspoken contract. This way of interacting in the classroom becomes a barrier to learning.

Jo Boaler describes it well: We empty the interaction of learning and reduce the cognitive demand for the student.

As a teacher responsible for student learning, it is too easy to take ownership of something that belongs to the learners. Instead of this didactic interaction I need to allow mistakes, reflection, redirection, and meaning making, as students develop math skills.  My goal as a teacher is to have an engaging classroom where students  pursue questions and discuss their thinking about mathematical processes.  This dynamic interaction would promote deeper thinking and meaningful problem solving.

It is critical in this setting to ask the kinds of questions that promote meaningful engagement.  What is a good math question? Here is a challenge I love!  I am building on what I know and will share more with you in a future post.