Welcome back Math Geeks! I’ve been thinking a lot about the objectives of lesson objectives, and I’m committing to writing a series posts to spark a conversation. I’m curious about how you frame lesson objectives to maximize student thinking, and I invite you to tell me. If you missed my first post about ways to make the learning objective an invitation and not a mandate, I encourage you to check it out here.
Why we teach must align with how we teach.
If you’re a regular reader, you know about my belief that alignment between our purpose and our practice is essential for healthy teaching, inspired learning, and engaging classrooms. Our professional identity (the reasons why we became teachers in the first place) must be congruent with our choices and our practices in the classroom. When purpose and practice are not aligned, both teachers and students waste energy fighting needless friction in the classroom and learning suffers.
An Objection about Objectives
One habit where I continue to see a misalignment between purpose and practice centers on how we post, frame, communicate lesson objectives to our students. All teachers want students to be inspired, motivated, engaged, and curious, yet I’ve witnessed a lot of teachers euthanize student intellect by spending the first 5 minutes of a lesson reading aloud and unpacking a lesson objective that is written on the board. The objective often uses robust (intimidating?) language that is not accessible to students. Furthermore, the objective sits there devoid of any context, meaning, or inspirational value.
Let me be clear, every practice we do as teachers should have clear and intentional objectives. Without objectives, we have no way to measure the effectiveness of our instructional choices as teachers. It’s our practice of how we communicate and frame those objectives to students that has my feathers ruffled. I hope that you’ll join me in the conversation on Twitter or in the comment section below.
The Textbook Approach: Offer the Objective before the Need
Dan Meyer has written extensively about the importance of (and the research behind) creating intellectual need in the mathematics classroom. If we are going to ask students to use mathematics to solve problems, we need to let students internalize problems through inquiry and exploration BEFORE we teach them the mathematics. As Dan says, if math is the aspirin, then how do we create the headache?
Let me offer an example. I was facilitating a lesson inquiry with some 3rd grade teachers who were about to start a unit on data and graphs. Here’s the full language of the CCSS standard:
3.MD.3: Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.
Here’s how their GoMath curriculum wanted to start the unit:
I don’t know about you, but the thought of teaching this lesson this way makes me professionally queasy for a variety of reasons. A few things that stand out to me:
- The curriculum aims to cover the entire standard in one page by having students creating a graph and using it to solve a problem (which I’m guessing is to determine just how awesome chocolate yogurt is).
- It wants to accomplish this by giving students a tool (the frequency table) without creating an intellectual need for that tool first.
- The essential question is a thinly veiled “objective as a mandate.” The lesson tells students that they will use tables to organize data and solve problems. There’s no opportunity to invite students in to the problem.
- Students are doing NO MEANINGFUL MATH. There is no headache, no authentic need to use a table. Furthermore, they are learning that math is something that happens to them and not something that can usefully help us understand and describe the world around us. How can a teacher possibly make this lesson (as written) engaging and meaningful to my students?
This is what happens when we offer students the lesson objective without first offering them a chance to discover the intellectual need.
A Different Approach: Offer the Need before the Objective
In our lesson preparation for the lesson inquiry, we were dismayed out how structured the curriculum was throughout the unit. So we stepped back, and I asked Dan’s question to the group: “If graphs are the aspirin, what’s the headache?”
In the end, we concluded that graphs are only useful if visualizing patterns in the data helps us answer a meaningful question.
So the headache is a meaningful question that generates a need for data. The aspirin becomes the graph that usefully organizes that data. As written, the lesson prevents students from internalizing a question and therefore prevents them for appreciating the usefulness of graphs.
This was our solution. At the beginning of class, we gave each student a sticky note. We posted this question on the board: What do you like to do most at recess? (Not the most intriguing question, but we went with it because it was simple and easy to answer and would generate useful categorical data: swings, kickball, talk to friends, etc.) Students wrote their answers silently. Then we quickly scribed their answers on the board in the order that we received them.
With all the class data fully displayed, we asked: What do you notice? Talk time in pairs then a classroom share. Then we asked: As a class, what do you like to do the most at recess?
We let students work on this question for about 10 minutes and watched what they did. Sure enough, students start trying to count and organize the list on the board. Some students came to the board because they wanted to color code the answers to make counting easier. Others started making tally marks counting the activity that seemed to appear the most.
After a few minutes, we paused the class and asked them to share and reflect on their thinking. What are you doing as you try to answer this question? Students told us (in their own words) that an unorganized list of data is not useful if we want to answer questions. Furthermore, it’s hard to count the number of each response when things are all jumbled together. As teachers, we also shared with them some of the things we observed them doing.
So what you’re saying is: We need to find ways to organize data.
Well, math offers us several tools (graphs) that can help us do that. In the next week or so, we are going to explore those tools.
It was at this point that we introduced what a frequency table was and had the students work together to fill in the tally marks so that we could answer our questions. With the graph created, we asked: What other patterns do you see? What other questions can we answer?
We then concluded with an exit ticket that asked: What did you learn about math today? Almost all students gave a response that showed they internalized our objective: that graphs help us answer questions about data.
The second approach to the lesson allows students to think mathematically. Students develop an understanding for the need to organize data and how graphs are useful. But the lesson is a boring failure if we post on the board and begin class with: Today you will use frequency tables to organize data to solve problems.
This is why we need to rethink the practice of posting lesson objectives on the board without first creating the intellectual need for the math. And most curriculum doesn’t encourage this kind of lesson preparation. So help me continue the conversation by sharing your experiences.
In what ways do you create intellectual need in your lessons before sharing your lesson objectives? What resonates with you (or irks you) the most about this post? Help us further the conversation.
Find Part Three here.