*This week we are proud to introduce our first guest blogger for the 2013-2014 school year, Principal Mark Koller, from Pleasant Hill Elementary! Principal Koller and his staff are working hard to transform math instruction and they know that it begins with action steps and trying a few things different. Let's learn from this principal as he begins his journey with Number Talks...*

There are many benefits to being a campus administrator. You
get a sweet walkie-talkie, maybe an extra nugget or two in the cafeteria, and
most importantly, the joy of working with hundreds of students on a daily
basis. I love my job, but as an administrator, I do miss the interaction,
academic conversations and relationships built in the classroom setting that
thousands of teachers across our district experience each day. Luckily for me,
my staff allows me to pop in from time to time and teach.

Recently, I was able to work with my fourth grade team facilitating
Number Talks in six different classrooms on six consecutive days. If you’ve
read this blog before, you are probably very familiar with the basics of Number
Talks. We were fortunate enough to have our math curriculum department on
campus this week, and I also had the fortune of hearing from them in my
district admin meeting. The point that hit home with me, and what I tried to
model in my lessons this week, was the three pronged approach to math:

1: Make
Sense of the Math

2: Do the
Math

3: Use the
Math

According to
Cathy L. Seeley, author of __Faster Isn’t Smarter__, students
must have a “conceptual understanding,” while utilizing “facts, skills, and
procedures,” when problem solving. (Seeley, 2009) This to me, reiterated the
make sense of, do, and use the math approach.
Equipped with this information, I felt ready to get into the classroom
and work with the students.

I started my
Number Talks journey in Mrs. Lukes’ class. The students and I discussed 27x5.
As with every Number Talk, I ask if anyone had a way to solve that problem.
Hands went up or really hands went to their chest and they started gesturing to
me in a sort of Number Talk sign language that took a second to decipher.
Each student held up the number of ways they could solve the problem.

- The first student I called on started to talk to
me about friendly numbers and why it’s easier to count in ones, 2’s, 5’s, and
10’s She encouraged me not to look at the problem as 27x5, but more as 20, 5, and 2 multiplied by 5.
This way I could literally count by 20 five times, 5 five times and 2 five
times. I was super excited. I could hear Yoda saying, “Conceptual Understanding
this one has.” (Star Wars reference)
- A second student made the point that
multiplication was repeated addition and I should just add 27+27+27+27+27 to
get to our eventually goal of 135. I was pumped.
- A third student said to just multiply the
numbers using the traditional algorithm to solve it. When I asked this student
to walk me through this, he stumbled on some steps. While participating in a
Number Talk all answers are valued and validated. The conversation with the
students is the basis of the mini lesson. This particular student was on the
right track but just was not sure how to move the numbers around in the algorithm
to bring him to ultimate success, and could not explain the reasoning behind
it. My advice to him and the student in the second class I worked with that
wanted to write out 27 dots, five times and then count up all the dots was
similar; When choosing the best strategy it is important to pick one that you
understand and will ultimately bring you reasonable and efficient success. I
found myself reiterating this point over and over in all six classes: make sure
you can make sense of what you are doing first.

When asked
how you came up with your strategy, a student’s answer shouldn’t be my teacher
showed me. It should be based on the numbers and how they can manipulate their
thinking with them. Algorithms are great in some instances. They should be used
as a tool for doing the math only after we can make sense of it. Reasonable, efficient
strategies are ones in which we are not setting ourselves up for failure before
we even start. Putting 27 dots on the paper five times in a row is a recipe for
miscounting and frustration. They may start there, but encourage the
progression from dots, to tally marks, to numbers, and then finally the
friendly numbers that will help them succeed in an efficient manner.

Encourage
your students to look for the friendly numbers that the first student I
encountered encouraged me to do. Think in numbers that are easy to manipulate
and don’t settle for 13 to be 13. Let it be a 10 and a 3 or two fives and three
ones.

Bridging the
conversations from the Number Talk to the application or the “Use the Math” portion
of the classroom is the key for ultimate learning target success and the recipe
for cooking up mathematical thinkers. I look forward to revisiting these
classrooms and others in the coming weeks and Tweeting out the evidence of
great Number Talks and math conversations. You can follow me, @KollerTX, on
Twitter.