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.

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.

Making Data and Stats Matter More in K-6, Part 1

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.  There are two curriculum practices that trouble me 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.

Beyond the Blame Game

A friend and I were reflecting over a beer at Twitter Math Camp in July about how to get more elementary teachers to attend this amazing conference.  (Click here to know more!)

He’s an inspirational colleague with a background in special education at the elementary and middle school level.  We were talking about content knowledge.  He said, “My ability to teach math has always been limited by my lack of content knowledge beyond middle school.”  After pondering a beat, I replied, “Me too.”  Knowing my teaching experience, he leaned back with a skeptical smirk and looked askance at me.  I continued…

My New Favorite Term: Abductive Reasoning

What is Abductive Reasoning?

I’m going to share my new favorite term:  abductive reasoning.  Maybe you’ve known about it for years and never told me about it.  (If that’s the case, you might be a jerk.)  Or maybe it’s new to you too.  (If that’s the case, let me know because I’m a little embarrassed I haven’t learned about abductive reasoning until recently.)

To recap, deductive reasoning is about making specific conclusions from general statements (like a math proof).  Inductive reasoning is about making generalizations about specific observations (like a science experiment).

By comparison, abductive reasoning is about making your best prediction based on incomplete information.

Abductive reasoning?!?!?!  Where have you been all my life?  Welcome to my lexicon.  Have a seat front and center and let’s talk.

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 […]

Why Lesson Study?

Imagine a football team operating like a faculty at a school site.

Players (teachers) gather at the beginning of the season (school year) for some team-building and some pep talk (fall PD) about goals and visions for improvement from their coach (principal).

The players then study a playbook (curriculum) and some plays (instructional strategies) and maybe they practice them. Maybe they don’t. Once the season starts, they hardly ever observe each other run drills (routines). They definitely don’t scrimmage together. The coach may walk around once or twice, check some boxes on a list, and give that feedback to a player, but rarely does the coach model techniques or facilitate collaboration and discussion between players.

The players practice all year for one single game (student testing) that they don’t even believe is worth playing but everyone makes them prepare for it anyway because how else could we measure our effectiveness except through standardized test data. The players won’t find out until 4 months later how they did and how they compared to other teams (schools) in the league (district). Except by then, the offseason has happened, players have shifted teams, new playbooks have been adopted, perhaps new coaching has been hired, and it’s time to start the whole process again.

The season concludes without any player ever watching another player play.

How stupid is that?

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.