Making Data and Stats Matter More in K-6, Part 2

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.  This post is Part 2.  In my first post, I wrote about how 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…and a solution to this practice.  (If you missed Part 1, click here.)

In this post, I’ll outline another troubling practice and my attempt to help to teachers work around this obstacle.

Making Desmos Elementary: A 1st Grade Card Sort

Hello math geeks!  Welcome back!

I’ve been an advocate for using dot images and visuals as problems for number talks in the elementary classroom.  (You can find a great bank of visuals here.)  I’ve also been an advocate for using Desmos as an instructional tool for letting student thinking drive the classroom discourse.

Traditionally, Desmos has been used mostly by middle and secondary teachers as a teaching tool.  But recently they’ve introduced Card Sort as a way to make Desmos a useful instructional tool for elementary teachers and students as well.  I wrote a bit more about this on my post here.  Annie Forest made some brilliant screencast videos about how to use Desmos here.  Check them out!  She also has a bank of activities (small but growing!) here.

Here’s a link to my card sort activity. 

How Much Sugar in a Soda? A 3rd/4th Grade Division Problem

I conducted a lesson study with some elementary teachers.  We used Dan Meyer’s engaging lesson called Sugar Packets to get students talking about an interesting problem, sharing their thinking, showing what they know about division strategies.  Dan has the lesson listed as 6th grade ratio and proportional reasoning activity, but we found this problem to be suitable for both 3rd and 4th graders and possibly as a review for 5th graders.  There is a remainder in the solution.  And we found that this lesson works best if students haven’t had many opportunities to learn about remainders.  It’s a wonderful introduction to thinking about the contextual and mathematic meaning for the remainder.  (If you teach 3rd grade, I think you’ll find that your students will dig it!  Don’t let the remainder spook you off!)

This lesson addresses many of the Operation and Algebraic Thinking standards for 3rd and 4th grade.  It is also a rich opportunity for students to reason abstractly and quantitatively and to communicate their reasoning with each other.

So, give it a read and give it a go!  Let us know what you learn.  Let’s get better together.

Making Desmos Elementary

For the past few weeks, I’ve had the fun opportunity to write for the Global Math Department newsletter.  Haven’t heard of the Global Math Department?  It’s great tool to find out what’s going on in the online math world about math teaching and watch professional development webinars.  Check the site out here and read about some of the fine folks that coordinate the work here.

In the last newsletter, Bridget Dunbar (@BridgetDunbar), Anna Bornstein (@Borschtwithanna), and I (@mathgeek76) wrote separately about the importance of grade level teachers sharing and learning from teachers at other grade levels.  Teachers of all levels have a lot to learn from each other.  You can find the complete newsletter here.  (If you sign up, you’ll get weekly newsletters straight to your inbox!)

Here’s what I wrote about using Desmos as an instructional tool in the elementary classroom.  While historically used by secondary teachers, several elementary teachers are creating a lot of useful stuff.  Give it a read.  Share your thinking.  And I invited you to a call to action.

Punch-A-Bunch: A 3-Act Math Lesson on Probability

Welcome back math geeks!  I need your help making a lesson better.
I love Price is Right because many of the games require contestants to make predictions.  This often involves estimating prices of products.  But sometimes contestants have to make choices of a different nature, and these choices are ripe opportunities to think about probability and expected value.  And I love when a fruitful 3-Act Math opportunity presents itself.  (I’ve written about one before here.)

The example I want to share now doesn’t seem to fit a 3-Act format.  Maybe that’s because it’s not truly a 3-Act Math lesson.  But I don’t know what else to call it.  I’m curious about your thoughts on how to make it better. 

Some questions I’m asking: 

Is it too clunky? 
What grade levels will find this lesson useful? 
What concepts/standards does it best target? 
What opportunities did I miss? 
What extensions can be made?

I’m inviting your feedback in the comment section.  Thanks for helping me get better!

What is Argument? And Emerging from the Rabbit Hole

Welcome back math geeks!  Last week, I was preparing for a workshop facilitating the learning of a dozen elementary teachers as they prepared for a 6-week interdisciplinary math/science summer academy.  I chose to focus their thinking on “argument.”  More specifically, I wanted teachers to internalize how making arguments based on reason and evidence is a […]

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.

We’d like to share with you what we learned about using Numberless Data Problems and crafting an open investigation into bar graphs that is engaging for all students. As always, feedback welcome. Let’s get better together.

Numberless Word Problem 2: Data Exploration in 1st Grade

Have you seen the amazing visuals over at Number Talk Images? These pictures are ideal for any teacher looking to get all students talking about numbers and mathematical reasoning, regardless of ability levels. We used this image as a number talk to launch a lesson that focused on first grade students making statements about a data display. Inspired by the work by Brian Bushart and Regina Payne, we used a numberless word problem approach to build and structure discourse about a data display.

I hope that there are other 1st (and 2nd) grade teachers out there that might find this analysis useful if they are looking for strategies to get students talking about their mathematical thinking. We wanted students to produce mathematical thinking, not just consume it. Here’s what we created.

The Objectives of Objectives, Part Three: Joy

One of the reasons why we teach is because we want our students to experience the JOY of mathematics. Mathematics should be about questioning, wondering, and the joy of discovery…and math classes should leave students wanting to know more math and do more math thinking. We cannot build an appreciation of math through content standards alone. Math classes should be filled with opportunities for students to have voice and a choice. At the very least, they need a voice in making meaning of problems and a choice in how they go about seeking a pathway to a solution.

But sometimes we (or our textbooks) squash all the joy out of a math lesson. We rob them of their right to notice math things, wonder about math ideas, or do messy math stuff. And lessons that focus on “measurable outcomes” with “explicitly defined objectives” often euthanize mathematical curiosity.

The Objective of Objectives, Part Two: Headache First

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.

Dan Meyer has written extensively about the importance of 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 suggests, if math is the aspirin, then how do we create the headache?