Tag Archives: mental math

Number Talks

In my last post, I talked about the importance of fostering mental math strategies in class.

A great resource for how to think about doing this in your class is Sherry Parrish’s book Number Talks: Helping Students Build Mental Math and Computation Strategies, Grades K-5.   I highly recommend taking some time to read the book over the summer.   It even includes a DVD with videos of model number talks.

So what is a number talk?

It’s a 10-15 minute conversation about a computation problem that is purposefully designed to allow students to communicate and justify their thinking.

What might it look like?

In the early grades, it might involve asking students for different pairs of numbers that add up to 10.

In the later grades, it might involve asking students for different ways to solve a multiplication problem like 25 x 16.

After sufficient wait time, students share their strategies, including justification for why a particular strategy works.

What I love about number talks is that they can easily be incorporated into a class.  Often, as teachers, we are bound to a particular curriculum that is beyond our control.  However, most of us can find 10 or 15 minutes to add in a number talk, even if it’s not every day.

I also love that they challenge different students.  Higher-level students can think of more complex solutions or multiple solutions while lower-level students can access the problem with a simpler solution.  And all students can benefit from hearing alternative methods.

Finally, I love that they allow for rich discussions to take place.  Students can talk about which solutions are mathematically correct or which may be more efficient.

Have you tried number talks in your class?  How have they worked?

Want to know more?

Check out this article:

Parrish, S. D. (2011). Number Talks Build Numerical Reasoning. Teaching Children’s Mathematics, 18(3), 198-206.

Mental Math

My sister gets nervous sometimes when we are at the store together.   She is afraid (rightfully so) that she may have to witness me give a math lesson at the cash register.   I can see why it might be embarrassing to her and I can also see why it infuriates people behind me in line, but sometimes I just can’t help myself.     As a math teacher, it frustrates me that the cashier can’t figure out the change when I give her a twenty, a one and a nickel for a bill that is $11.05.

Now, one could argue that the reason why the cashier can’t do this is because he or she did not receive enough instruction on the traditional algorithm for subtraction.  Maybe he or she used calculators too much in class instead of doing lots of “drill and kill” exercises.

But I don’t think that having lots and lots of practice with the traditional subtraction algorithm would help in this case.

The truth is, I don’t often use traditional algorithms when solving math problems in real life.  I do use a lot of mental math.

I count up or I count down when adding or subtracting.  I break numbers apart when multiplying.  I rarely think about multiplying 25 times 6 in my head using a traditional algorithm. Instead, I think of 20 x 6 plus 5 x 6 or I think about 25 x 4 plus 25 x 2.  It is just easier.  To figure out a 15% tip, I usually find 10% and then half it and add the two together.   Or most of the time I double it because waiters and waitresses really deserve that 20%.

I bet a lot of you operate the same way.  You don’t take out a pen and paper in the store or restaurant.

Yet as I mentioned in a previous post, some people still think that traditional algorithms are the only way to teach math.

As you may expect, I disagree.  How much more valuable is it to work flexibly with numbers? To be able to calculate things in your head quickly.  To have a sense of whether an answer is way off base.  I think this is the way we should approach math in the early grades.  It certainly would make my experiences at the grocery store less traumatic.

So what does the research say? Two researchers (Fosnot and Dolk, 2001) reported on a program called “Mathematics in the City” in which teachers fostered mental math computation strategies in children between the ages of 4 and 8.  They showed how these students developed a deep understanding of number and the operations of addition and subtraction.

Now is there a place for learning traditional algorithms?  I think there is.  But I think it’s often more valuable to do after students have had experience working flexibly with numbers.

So how do we begin to do this in our classrooms?    That I’ll talk about in my next post.  But feel free to write any suggestions you have in the comments below.

Want to know more?

Check out the Mathematics in the City site here.

Check out Fosnot and Dolk’s book: Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction.