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.
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 […]
I went searching for more knowledge about argument. I fell into a rabbit hole. Help me make sense of this. Do you agree? Disagree? What are your thoughts?
“…there is a difference between mathematical arguments and scientific arguments. The difference is that scientific arguments are always based on evidence, whereas mathematical arguments never are. It is this difference that renders the findings of science provisional and the findings of mathematics eternal…Blurring the distinction between mathematical and scientific arguments leads to a misunderstanding of what science is about.” -NGSS Appendix L
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.
Have you seen the amazing visuals over at www.fractiontalks.com? They’re ideal for any teacher looking to get all students, regardless of ability levels, talking about equivalent fractions (4.NF.1), comparing the value of fractions (4.NF.2), and expressing mathematical reasoning. This activity could also work for 3rd grade students that are exploring fraction equivalence (3.NF.3). We used one of images to introduce 1/2 as a benchmark fraction to some 4th grade students. We learned a lot and the students did too! We’d like to share our learning with you.
I had the opportunity to work with several K-5 instructional coaches last week during a one-day workshop on increasing student engagement and discourse in the math classroom. (My favorite workshop to lead!) Leadership in the district is making a focused effort to support teachers in their practice of creating classrooms where Math Practice 3 thrives and students are […]