Numberless Word Problem 3: Data Exploration in 2nd Grade

I worked with a team of amazing 2nd grade teachers this week as a part of an ongoing lesson study.  They were in the latter chapters of their curriculum where the Measurement and Data content is often stuffed away as an afterthought because they aren’t “Focus Standards.”

And it’s a drag too because there’s so many rich opportunities for meaningful student discourse about data.  That is, if it’s done right.  Most textbooks suck all the life out of the content.  Students need to understand that data tells a story; it has contextual meaning that is both cohesive and incomplete.  Students need to learn how to ask questions about data and to learn to identify information gaps.  In other words, students need to learn to be active mathematical agents rather than passive mathematical consumers.

Here’s a quick snapshot of how their GoMath curriculum laid out some of the lessons.

I don’t see a lot of opportunities for students to make any meaning of the mathematics.  There’s no pop, no life, no intellectual need to think.  Furthermore, there’s no discussion about why we show data in bar graphs.  The essential question shouldn’t be “How do bar graphs show data?” but “Why are bar graphs useful?”  Only the latter question drives at the “story-telling” quality that data sometimes possesses.

So, inspired by the work by Brian Bushart and Regina Payne, we used a numberless word problem approach to create information gaps that sparked student conversation and brought more life in to the lesson.  We’d like to share our learning with you.

I hope that there are other teachers (2nd grade and otherwise) out there that might find this analysis useful if they implement strategies to inspire students to produce and talk about their mathematical thinking, not just consume math from a textbook.

Please feel free to plagiarize and make it your own as you see fit.  I’d love to hear from you if you use it so we can get better together.  (Special thanks to Brian Bushart and Regina Payne for their amazing resources.  I encourage all readers to check them out.)

Some background:

I conducted this lesson study with a team of 2nd grade teachers.  It was taught to 3 classrooms, and each lesson was a unique experience with its own twists and turns and choices.  What we show here is the result of how we revised the lesson throughout the day based on our observations of student learning.  The lesson pathway below shows the main flow of the learning experience and took about 60 minutes.  Further analysis and takeaways can be found at the end of this post, but I’ve tried to embed a lot of our thinking within the flow of the lesson plan.

The content of this lesson centers around creating and interpreting bar graphs (2.MD.10).  Specifically, we wanted students to ask questions, make statements about graphs, and share their thinking.  The lesson allowed students to apply their previously learned skills in the chapter as they were getting ready to review for assessment.

You can find our slide deck here and the student handout here.

Our objectives (as teachers):

• We wanted students to ask questions, participate in making conjectures, and share their thinking.  We wanted a lot of student talk as they wondered, made estimations, and shared their ideas.
• We wanted to see what students know and what meaning they’re making about the content they’ve been studying as they prepare for a summative assessment later in the week.

Learning objectives (for students):

• We will make sense of data by asking questions and writing sentences. This will help us understand the story about what the data says.

Into:

(Note:  We did not focus on the objectives at the start of the lesson, but just stated that we were interested in how they communicated their thinking and how they listened to each other.  We used the Into portion of the lesson as an opportunity for students to internalize the objective about making comparisons between numbers.)

We gathered the students on the carpet for a Numberless Data exploration.  We set a “number talk” tone by telling students we were interested in their thinking and how well we could communicate and listen to each other.  Here’s our first slide.

 

We gave students some silent think time then had them turn and talk before having some group discussion.  Students are immediately engaged.  They begin to describe what they see (“It’s a graph!”) before going deeper.  Many students noticed a “going down then going up” pattern and also noticed that it was missing a title and labels.  They didn’t know what the graph was about, but they wanted to.

So you’re wondering what this data is about.  You’re trying to figure out what the story is but you don’t have enough information.

Heads nod.

Here’s the next slide.  (Note:  We often skipped the “What do you wonder?” slide because student inquiry got us to where we needed to be.)

More silent think time before some pair-sharing.  Students are point to the screen and making conjectures about what the data might mean without even being asked.  During group discussions, students are already trying to come up with examples about the story behind the data.

As a result, we sometimes skipped the next slide and jumped right to…

We kept a strong “number talk feel” throughout this exploration focusing on constructing arguments and critiquing reasoning.  At no time did we as teachers go in to “direct instruction mode”.

We concluded the Into part of the lesson by covering the objectives for the day.  We kept this part brief and short and simple.

Today, you’re going to ask questions and make statements about data.  You’ve already just done that and in a moment, we’re going to do more at our desks with a different graph.  

Through (part one):

Students move back to their desks.  In the lesson, we had a much more structured handout (that you can see in some of the images below).  Our original intent was to make sure students used words like “total,” “more,” and “fewer” in their sentences to address the language in the standard asking students to add to, take apart, and compare categories.  In the handout here, we removed a lot of that structure up front because we discovered that the prompts constricted student thinking too much.  We found that we could strive toward this language by facilitating group discussion around selected student statements.  We gave students about 10-15 minutes to do this task.

Here’s the graph we displayed.

Here’s some of what some students wrote.

(Student concludes with “And that’s what I think!”  I love it!)

While students worked alone and in pairs, we monitored the room looking for students samples.  We typed up student responses in the slide of the graph and displayed them for students to analyze.

Does this statement appear to be true?  What evidence do we have?

Students are naturally thrust into Math Practice 3 as they make arguments (in this case statements) and critique their accuracy.  Furthermore, after students shared some insightful sentences, we were able to use their sentences as sentence frames for other students to help further their writing.

Through (part two):

We extended the lesson with an activity that asked students to write questions for given answers.  This was the first time students had been asked to think about data in this way.  They had spent over a week being conditioned to answer a textbook questions.  We knew that this might be a challenging task, but we wanted to see how they would respond and try to keep their thinking flexible.

Here’s the back side of our handout:

And here are two samples of what some students wrote.  As you read, notice how the openness of this activity allows these students to make different, but valid arguments.

At this point, some students were pretty gassed and started to lose steam, but they all were able to achieve some success.

We closed the lesson by asking students to share their “make your own” examples of answers and questions.  Then we reflected about what they had learned and connected their thinking back to the lesson objective.  We then asked them to tell us what their favorite part of the lesson was and why.

Reflections, Takeaways, Analysis:

At the end of the day, we reflected on our objectives and student learning.  We looked at what the students had produced and examined the structure of the lesson in the GoMath text.  We had gotten them to the same outcome, but had done so in a way that focused on students producing the learning rather than consuming it.  In this model, the GoMath text becomes useful for practice, formative assessment, and extensions as a way to follow up lessons like these.

I can’t stress how important it is for us as teachers to reclaim the vitality of instruction from lifeless textbook structures.  This lesson study is one example of how teachers can collaborate, risk, experiment, and engage in meaningful professional development together as a way to achieve that goal.

Some things we noticed and wondered and a few professional goals moving forward.

• We need to give students more choice and voice about how they make meaning of problems and which problems they choose to solve.  Numberless Data problems like these can be be a tool for that.
• Openness in lesson plans creates more engagement.  It naturally differentiates for all learners.
• “Productive struggle” is a difficult zone to achieve.  It’s a fine line between “too open” and “too directed,” but that’s where student learning happens best.
• Students responded well and embraced the freedom to come up with their own answers and justifications.
• The missing information in the graph created more engagement.
• It’s important to find the right amount of talk time with class discussion (more listening) time.
• Some things we wondered:  How do we find the balance between openness and also structure to maximize student learning and autonomy?  How do we structure objectives and questions on the fly in response to what students share?
• It’s important to embed the objectives continually throughout lesson.

An invitation:

As always, feedback and comments are welcome.  What inspired you?  What opportunities did we miss?

Help us get better together.

Oh!  And I created a Desmos lesson for this activity as well.  Try it out here and let me know what you think!