# Author Archives: Darrell Blanks

### Games That Promote Mathematical Thinking, Part 2

Before Christmas our team developed a game to work with students on building the concept of equal size groups. We named the game “The Great Wall.” Students are given the task of building the Great Wall of China for the emperor. They are directed to build sections of the wall, each a certain number of squares long and then report three things to the emperor: the number of sections they made, the number of squares long for each section, and the total number of squares long the entire part of the wall was. They made their report without looking at the drawing of the wall they had previously made. This requires the student to imagine the wall and begin to build the ideas associated with multiplication. Afterward, they could look at the wall they drew, count the squares that made the wall, and check the answer they gave for the total length to get a bonus from the emperor for having a correct report.

As we tried the game with the students, we saw some interesting things. One was that students had a more difficult time counting the squares to make the sections of the wall than we expected. This was problematic when we had them check their answers. In one case, a student figured out the correct number of blocks used to make x number of y blocks each and got confused when he counted the blocks in the drawing and ended up with a different number.

Another interesting behavior we saw was how some students would make a section of wall with, say, six blocks by counting each block at a time while other students would sweep along the blocks until it was six blocks long. The students that swept along the blocks seemed to have an easier time remembering the number of sections and the number of blocks in each section than the students who counted each block.

Through the development and use of the game as an independent activity, we found that the students took more time learning how to think about the mathematics during the game than we originally intended. If the game is designed for students to construct new mathematical ideas, then how realistic is it to have them work without a teacher monitoring? Does that mean that games in classrooms should be used only for reinforcing the mathematics students have already constructed? Or can they serve another purpose as well?

We want to engage students in activities that relate to their enjoyment of games. Doing so means creating a balance between two elements: the thinking energy spent on the game playing versus the energy spent on mathematical thinking. The best games accomplish both of these things.

I would enjoy hearing your experiences trying to make games out of mathematics. Where have you found success in gamifying mathematics?

### Top Lessons Learned in 2017

I would like to take a small detour for this entry and use the start of the new year reflect on the previous year. Reflecting on the past as a teacher can help us to think about what we might consider for the future. So what were the top lessons learned at AIMS in 2017?… Continue Reading

### Games That Promote Mathematical Thinking

A few years ago, I went to a conference where I was able to listen to Keith Devlin, a noted mathematician from Stanford, talk about using technology, particularly computer games, to help students think mathematically. He made the case that the symbols we use to represent mathematics, like numerals, operation signs, etc. create a barrier… Continue Reading

### What Every Student Needs to Know for Multiplication (Part 4)

***This is part 4 of a series. Click the links to go back and read part 1, part 2, and part 3*** In this series, we have been discussing a progression of tasks that give students the opportunity to construct meaning for working with two types of units, the towers and the cubes that make… Continue Reading

### Same Task, Different Situation

When I taught middle school, I always found it interesting that my students could do this task: Johnny rode 34 miles on Tuesday and on Wednesday he rode 27 miles. How far did he ride over the two days? Yet they often had no idea what to do when I gave them this task: Johnny… Continue Reading

### How much knowledge is enough knowledge?

The semester has started and I am confronted with the same question the AIMS Center is currently wrestling with: How much knowledge is enough for a teacher to know to make effective decisions with students? We read research by researchers who have been spending years if not decades studying how students come to learn to… Continue Reading

### Lesson From Mexico: Pan De Mujer

Every day on the way to our work site in Mexico, we passed a small sign on the side of a similarly small building that said, “Pan de Mujer, 5 pesos.” I speak Spanish but I was still a little unsure what this meant. I knew the words, but “woman’s bread” didn’t make sense, so… Continue Reading

### Building Understanding in Mathematics

This week I’m writing from Mexico. Every year, my church travels down to build houses for families in need. We work with local churches to supply building materials and manpower to build simple homes. The work could not occur without the help of local pastors, who help by identifying the families and local contacts we… Continue Reading

### Small Misunderstanding, Big Difference in Meaning

After one month as a missionary in Argentina I was ready to raise the dead. Or at least that is what the woman at the door must have thought. Let me explain. As we were proselyting door to door, it was my turn to talk to whoever answered the door. A woman happened to answer… Continue Reading

### Ill Fitting Brakes and Ill Fitting Instruction

Yesterday, my daughter called me and told me there was a horrible scratching sound coming from her car. It was her brake pads. I have replaced brake pads on lots of cars, but not hers. The bolts came off easily and the pads came out without much effort and so I thought everything was going… Continue Reading