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.
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.
I hope that there are other 6th (and 7th) grade teachers out there that might find this analysis useful if they are looking for ways to increase student engagement, thinking, and discourse around percents, fractions, and proportional reasoning standards. This engaging learning opportunity can be used at the beginning of a unit as an inquiry-based exploration and pre-assessment. It can also be used as a way of assessing student learning in the middle or the end of a unit. It’s a low-floor opportunity that allows for students at all levels to participate. It also allows for rich discussion and sense-making because solutions can be reached via multiple strategies.
This lesson write-up is for any 5th or 6th (or 7th) grade teacher who wants students to explore decimal concepts and refine decimal operations while exploring a compelling task that is engaging and accessible to all learners. Using an image from Andrew Stadel’s Estimation 180 page, students estimate, investigate, and then calculate the value of a bowl full of coins and demonstrate learning for 5.NBT.2, 5.NBT.7, and 6.NS.3. The write-up contains a lesson pathway with specific questions and instructional moves to consider, analysis of the opportunities for student learning, and other wisdoms and insights we learned from teaching this lesson as a part of a lesson inquiry.
Give it a try with your own students. And then tell me how it went. Let’s get better together.