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.