Welcome back math geeks!
I love teaching young students about data and statistics. And I enjoy finding ways to make data and statistics matter more to young students. But I’m troubled by two curriculum practices about how we teach students to think about data and statistics, especially at the K-6 level. In this post, I’ll outline one of these troubling practices and my attempt to help to teachers work around this obstacle.
Troubling Practice #1
Data is often represented to students in heavily scaffolded textbook pages that rob students of the opportunity to purposely engage in thinking, wondering, and discourse. Graphs are often presented. Questions are asked to the students and the students write in their answers. The questions are usually closed having only one right answer and the answer often only requires DOK1 level thinking. Here’s an example from a textbook.
This textbook presents a straightforward way to teach students how to read graphs, but it doesn’t invite students to engage with the data. There’s nothing to think about, nor is there anything worth talking about. The questions are closed and at the DOK1 level. Students do not explore and reason about concepts tackling more open questions that invite students to make a choice. Furthermore, the thinking is localized to the paper for each student. There is no opportunity to create a public space of thinking like on vertical dry erase boards around the room.
Check out this matrix by Robert Kaplinsky and note the third column, “Interpreting Data.” In what ways do the DOK2 and DOK3 problems invite student choice and voice?
One thing I notice is that the more open the question, the deeper the level of thinking required. Not only that, the more open the question, the more accessible the question becomes for all types of learners. Students have more to wonder and talk about in the DOK2 and DOK3 questions. They can talk about their choices and the teacher can use student thinking to drive lesson flow.
When we remove information, student thinking fills the void. When we open up problems, student choices become interesting things worth talking about.
This is where traditional textbooks (like the one above) fall very short. They can’t do that on a printed page.
A Solution: Numberless Graphs
I’ve written a lot about Numberless Word Problems. They are an effective and efficient routine for restructuring textbook problems so that data and statistics becomes a more inviting concept for students. They ask students to think more deeply, talk about their wonderings, make decisions, and defend their choices.
Imagine starting a lesson with an image like this:
In lessons, students naturally begin to turn their noticings into wonderings and begin asking questions about the context. What is this data about? What could it be about? How do you know? What evidence do you have?
After some discussion, we can add in more structure and allow student responses, choices, and arguments drive the classroom discourse. For example, these are the next two images I show.
I’ve used a sequences of graphs like these in a lesson study with teachers. When I’ve taught lessons using numberless graphs like this, thinking comes alive in the classroom. All students are thinking and wondering more. Students produce rich and interesting work that I can use to scaffold classroom discussion. In these lessons, students do more math than they would doing work out of the textbook.
You can find out more about the lessons here and here. You can find out more about Brian Bushart’s work on Numberless Word Problems with graphs here. You can explore DOK2 and DOK3 problems like the ones in Robert Kaplinsky’s matrix at www.openmiddle.com.
Call to Action
- Read more about these lessons by reading the links in the paragraph above.
- Create your own graph (or use one of ours) as a warm-up one day. Show it and ask students to pair-share about what they notice and wonder. If you make this small 10 minute commitment, you will see how rich the conversation can be for all students.
- Let me know how it goes! Brian and I (and others) are collecting and sharing the work of others. If you want some help, send me an email or post your questions and thoughts in the comment section here.
Let’s get better together.