data and statistics – In Pursuit of Great Mathematics Teaching

A Nice Activity for Statistics and Data Representation: Estimating One Minute

My year 8 students were learning about working with grouped data. I used an activity that I pull out regularly when I need some data from the class to work with.

Students worked in pairs and one partner timed the other while they were estimating one minute. I asked the estimating student to close their eyes, say start, and then sit quietly until they think one minute has passed. Their partner used a stopwatch (on their iPad this time) to time the duration.

We recorded on the board all the times from the class. In my year 8s we took several tries each since we are a small group and I wanted to have about 30 pieces of data.

Then we went on with our lesson about grouped data. We got to consider all the authentic data questions–for example, how broad should the classes be to record this data? Also our outliers seemed very far from the bulk of the data. Students naturally asked about these. I like it when there is less need for me to point out these things. Because it is their own data they are intensely interested.

a mathematics lesson that worked

We had a bit of a giggle because one of the biggest outliers was my own estimate for one minute. Once I had my eyes closed I vastly overestimated how long one minute was. My teaching & learning assistant said I was having a nap for 114 seconds!

What data collection activities do you like to use?

Make Your Own Normal Distribution Questions

Today we were building our familiarity with the normal distributions. I had a scan of a textbook page with lots of normal distribution sketches, like the one below. I copied them onto yellow card and cut them out, discarding the textbook’s instructions and numbering.

Each student got a sketch and I asked them to make up a normal distribution question to go with it. Here are my instructions. Students were working on their mini whiteboards.

The students got out of their seats to solve other their classmates’ problems. There was a lot of collaboration and those who found writing the question hard got plenty of input from their peers. I was free to circulate and able to clarify some important ideas about continuous distributions and the appropriateness of the normal distribution as a model.

I was impressed by the questions’ variety and ingenuity.

I don’t think I emphsized thoroughly enough that students need to specify that the data they have chosen to write about is normally distributed. However, students were able to solve a wide range of questions, some more difficult than others.

This was definitely much more successful than a page of textbook questions!

Collaborative Talking in Math Class

For the next eight weeks I am participating in Exploring the MathTwitterBlogosphere, a project designed to help math teachers meet others in the cyber community we call home. (It is still a good time to join in, if you haven’t yet.)

Mission 1 is to write about what makes my classroom my very own. One thing I prize and make sure I develop in my students is their ability to communicate with each other about their math. I have been doing more and more discussion-based activities in lessons. I want them to talk about their conjectures and developing ideas. It is rare that my students are sitting in silence. They are usually discussing with the person next to them. Often they are moving around the room, talking to others. Even when we are doing “boring” practice questions they are talking.

Here two grade 12 students are discussing probability statements that may be never true, sometimes true, or always true. They had to go meet as many others as they can, discussing the statements on their cards, and each time trading cards. Then they go off and meet another person. (This is a quiz-quiz-trade activity.)

To help students communicate with each other, I have mini whiteboards (MWBs) and pens on each group of tables. Students love using them because they can quickly explain their thinking. They feel more free to make mistakes on the MWBs and to help and comment on each other’s work. Since having them always available, I have noticed a big increase in how much students help each other and talk about their thinking.

With the MWBs it is also easy to share the thinking of one or two students with the rest of the class. In another probability lesson, I asked students to visualize and then draw what they thought a certain probability distribution would look like. Then I brought six of the MWBs up to the front to discuss with the class their common and distinctive features. In the end, our discussion focused on just two of the graphs made by students.

All this constant discussion helps my students clarify and solidify their developing ideas. This makes my classroom unmistakably mine.

What makes your classroom unique?

Mean, Median, and Mode: Sorting Cards

I have a set of cards with statements like these:

Some of the statements are always true, others are never or sometimes true. I give each pair of students a set of these cards and a laminated board (below). The students have to discuss and sort the statements.

Next, I ask students for feedback and I will often lead a whole class discussion highlighting some of the common misconceptions. This activity always leads to good discussion, both between the pairs and as a class. Here are pdf documents: the cards and the board. If you try it, please leave a comment telling me how it goes.