Authentic Math is a challenge I’ve set myself this year, and I’ve been trying to keep this at the forefront of my teaching. I want students to begin with a conceptual understanding and then transfer that understanding and apply it to familiar and unfamiliar situations. A big part of this is making sure students know why they are learning these math concepts and how people really use Math.
So we discuss a lot and I constantly probe students to communicate their thinking.
Is it real?
This week, we started to talk about data and probability. I asked students to tell me when they had collected data and what kind of decisions they had made with that data. Or, if they hadn’t used the data maybe they knew someone who did.
Everyone’s hands shot up. We collected information about what kind of soft drinks people liked in third grade was one answer I kept hearing. We found out about pets people had was another. When I asked them what kind of decisions they made with that data, they couldn’t figure it out.
We used it to make a graph in class was the common answer. One girl was able to talk about surveying kids about a class party and then playing a certain game because that game had the most votes. Another kid mentioned his family finding out what they liked to eat so they could have more of that.
But that was about it. It was a struggle to pull anything out besides….we did this as part of a project.
Collecting information about pets, beverages, activities, etc… is real and developmentally appropriate but I want students to take it further. I think in our teaching we should be taking it to the next step where students can apply what they know to make real decisions.
Hook them with a game
Games are very real for my 5th grade students, and of course, they’re a great hook. So, in our journey into authenticity, we started in on a game called Skunk, which is a fantastic game. Pig is another game similar to it. It’s a gambling game without money. You roll the dice and collect points. If a “1” comes up, you lose points for that round. If a double “1” comes up, you lose points for all the preceding rounds. What makes it special is that you choose when you stop playing and collect points. You can stay in the round as long as you like and risk getting a “1” or you can duck out and keep the points you gathered. You can find directions online.
Kids love it, but there’s so much learning around it.
We played it several times one day. Kids were calling for it again, so I told them we were going to do an experiment (and taught them terms like experimental probability) that could maybe help us make some decisions to play a better game of Skunk. It was an experiment that might help us win.
In my room full of competitive boys, that excited them immensely. We got in learning partner groups and began to collect data on 100 rolls of the dice. Their job was to record when a “1” appeared and then when a double “1” appeared. Watching them collect data was another pre-assessment of their organization and their ability to collect the right data. Some were starting to write down the numbers that came up on every roll of the dice instead of just marking if a 1 or no 1 came up.
When they finished, they entered information on a class bar graph so we could look at the spread of all 11 groups.
With our data in front of us, we could talk about the mean, median and mode of data and learn those terms. We talked about patterns they noticed, about outliers and in general the shape of our data. We brought in percentages. We created a probability line from impossible to certain and put our results along that. They practiced some computational skills of mean and organizing numbers from least to greatest.
And then the big question: How can this help you play the game Skunk? Which should help inform our decision: the mean, median or mode? They had a discussion with their learning partners about this. This was the application part, which involved them analyzing their data and making some decisions based on it. A few were able to make the connection that 25% (which was the mean of our data) meant that there was a chance that a 1 could be rolled 1 out of 4 times. Some were able to see that 25% was unlikely but still probable so they shouldn’t stay in the Skunk game forever.
They seemed to all have an idea that it wasn’t a random act that brought a “1” to their roll or how hot their hands were that made a 1 come up (some previous thoughts). They were also able to see that rolling a double 1 was very unlikely so that shouldn’t concern them as much. They all seemed to see that collecting some data could help them make decisions in their game.
We of course went back to playing when we were finished their analysis. Although it would have been nice to go into theoretical probability and looking at the possible combinations that could bring up a 1 and the chances of not rolling a 1, we didn’t get there on that day. After all, these are 10 and 11 year olds.
But I think they understood a lot, learned some mathematical vocabulary and are starting to get a feel a feel that we use data to drive decisions, to reflect and to see patterns. We’ll keep working on “making it real” all year.