How often do learners get a chance to look for patterns in order to discover a larger concept?
What does inductive learning look like at different stages of cognitive development?
Will the future we are preparing kids for demand that they think inductively more, or deductively more?
I remember it so very well. The lightbulb that went off was so powerfully bright, that it continues to shine for me today.
It was my first exposure to learning through inductive reasoning in a classroom setting – from the teacher’s point of view.
I was in my post-baccalaureate mathematics education program at Nazareth College, and my teacher, Prof. Susan Riegle, was modeling a sample lesson for us using a “Construct-A-Concept” activity. She had a worksheet with approximately 20 paired images, each of them numbered. She explained to us that we were trying to determine what the special relationship was between the pairings. However, some of the pairings on the page did not possess the relationship. She then said, “As I look at the images on this page, I have a relationship in mind that I see. Number 7 is an example of it, but number 18 is not. If you think you know the relationship, give me the number of a pairing that is an example and the number of a non-example.” My classmates and I remained silent because we didn’t know the relationship. “Number 12 is an example, but number 3 is not. If you think you know it, give an example and a non-example.” We still didn’t know, but after the next round, we felt enough confidence to at least venture a guess – a conjecture really. We weren’t correct, but upon hearing that we hadn’t identified the correct relationship, that response – being wrong – gave us enough new information to be able to declare that number 20 was an example, but number 15 was not.
It was powerfully simple, like most realizations usually are. Prof. Riegle didn’t first tell us what the relationship was, and then ask us to find examples. Instead, she gave us examples and asked us to determine the relationship. In a teaching context, the lesson script had been completely flipped. This wasn’t the standard mathematics lesson where the students are given a formula and then asked to crank out five or six “problems” that utilize that exact formula.
I couldn’t remember a time when I was asked to think inductively (examples —> formula) in a mathematical context. Deductively (formula —> examples) had always been the norm.
In our small class at Nazareth, I could tell that I wasn’t the only one sitting there in wonder and amazement. All of my classmates were there with the same facial expression that said, “I didn’t know math could be learned this way. Mind. Officially. Blown!”
But what Prof. Riegle told us at the end of the activity’s debrief is what really made that light bulb glow with incredible intensity. She said something to the effect of, “The world you are preparing your students for will require them to learn in ways that you yourselves never experienced when you were students. You cannot teach the way you were taught because that isn’t what they will need to be successful. You will need to learn new ways of learning, to prepare them for their world.”
This single experience changed by teaching philosophy before I even had a teaching philosophy. If I can take a moment to make a confession, when I was in my undergraduate program at Nazareth, I tried a number of different majors to see if any of them struck a chord of interest with me. When education was presented as a possibility, I can remember saying to my advisor that I didn’t want to become a teacher because, “I didn’t want to spend my days explaining things to people.” This tells me so much about what my educational experience as a student had been, and reinforces what a mind-opening revelation Prof. Riegle’s lesson had been for me.
That revelation, that students could inductively reason their way to powerful conceptual understanding, totally informed my practice as a math teacher – I found as many opportunities as I could for students to learn inductively (besides just the required work on inductive mathematical proofs 🙂 It informed my practice as a technology integrator, and as a college professor. It informed my practice as a “maker teacher”. And it has informed my professional learning work with other educators as well.
Prof. Riegle was telling me about the need to find better ways of helping students learn in those methods classes of 2002; New York’s Math A and Math B programs were just beginning and were touted as asking students to have to “think in new ways.” She also told us that we would be responsible for helping to blaze new educational trails because the resources for inductive heaving pedagogies were not in ample supply. Fortunately, that is no longer the case today. The ASCD book Core Six, for example, has a chapter dedicated to inductively learning. They cite the work of Robert J. Marzano, PhD. in the book: “Marzano (2010) identifies inference as a foundational process that underlies higher-order thinking and 21st Century Skills.”
Inductive learning is a vital building block in any pedagogical approach that falls under the umbrella* of inquiry-based learning: constructivism; design thinking; PBL; constructionism; the Project Approach; plus others, including tinkering! Inductive learning is how authentic discoveries in the real world are made, and have been made throughout history. From the craftsmen in the guilds learning through experience what works and doesn’t work, to the polymaths that observed the guildsmen to create the defining formulas that made it into our textbooks. Inductive reasoning is one of the many ways of how we got to now. (*HT to Meghan Cureton for the mental visual of an umbrella.)
And if you are talking about deeper learning and the transfer that it asks of the learner, Core Six’s definition of inductive learning makes it pretty apparent how it can aid in those efforts:
“In an Inductive Learning lesson, students examine, group, and label specific “bits” of information to find patterns. […] Inductive Learning does not stop at categorization, however; it also asks students to use their labeled groups to develop a set of working hypotheses about the content to come. Then, during the learning, students collect evidence to verify or refine each of their hypotheses.”
But despite all of this researched evidence on the importance of incorporating inductive learning, it still doesn’t happen in all classrooms. Yet I’m not entirely sure it would have happened in my classrooms had it not been for the experience I had with Prof. Riegle. She showed me a different way that I would have otherwise never known, and I added that understanding to my own. But what about teachers that don’t have that understanding? What are the experiences – keyword right there – that school leaders can create to help turn more of the light bulbs on? And in turn, the light bulbs of their students?
Author’s Note: For those that are interested, you can download a few of the artifacts that I made in that Mathematical Methods class way back when… my answer key to the handout above, my lesson plan, and the homework I would have assigned for the lesson – all in PDF formats.
By Jim Tiffin Jr. (Cross-posted on my personal blog, Building Capacity)
Images in this post, but not shown in the Image Credits section, are my own.