My students and I have had much to learn much about how we learn since I started piloting an inquiry-based-learning (IBL) algebra textbook this year. Our context for teaching and learning is drastically different for all of us. From my research into the science of learning, I was confident IBL would be the best improvement I could make for my students’ retention. Not only had my prior observations of IBL confirmed what Daniel Willingham (2009) says about the effects of curiosity, but I could also see the potential for IBL to develop the Common Core State Standards (CCSS) for Mathematical Practice. I placed my faith in our pilot textbook because
- it is highly rated by EdReports for alignment with CCSS.
- most lessons are built upon IBL and modeling activities.
- each homework assignment provides continuous, connected review from prior grades’ learning experiences all the way to the end of the course.
CCSS writer Jason Zimba’s coherence map illustrates the complexity of designing connected concept development. That, and the need for continuous review between and within grades, are the main reasons I sought a textbook to replace materials I wrote on my own. While my students performed very well on standardized tests, I believed it was possible to lift my students to higher levels of analytical problem solving and to build in better retention. I was captivated by CCSS writer Phil Daro’s videos as he explained how to roll low performing students forward while challenging the more accomplished students. However, the key to doing that is having a series of rich problems with low floors and high ceilings that connect the curriculum. The book I’m piloting, College Preparatory Math (CPM) is built on such series, although there are likely others. On the first day of class, my students could see this math class would be unlike any other they had experienced. In order to help my students understand why, I explained how some of their learning challenges relate to the science of learning.
Challenge 1: Retention through Inquiry and Intent
The first CPM lesson required my students to match themselves together using assigned puzzle pieces that connected linear equations, graphs, tables, and scenarios. These students had learned all about linear connections in prior grades, but it became clear they neither recalled nor could apply much from their traditional instruction and practice. I briefly explained the difference between short-term and long-term memory and why I believed our new IBL strategies would help move concepts into long-term memory more efficiently (Prince & Felder, 2017). Instead of learning from Alexa or GPS, well-written IBL is more akin to discussing and interpreting a map. Most students cautiously began to buy in. One illustration that helped them buy in to the importance of intentionally documenting their understanding in the moment came through Legos. The yellow platform represented their brain and I began to drop blocks on it, most of which fell away. But those I anchored by pushing them into place, stayed in place when other blocks dropped off.
Challenge 2: Accuracy
My next challenge was to address an unintended consequence of completion grading: most of my students were in the habit of rehearsing mistakes instead of correcting them. They seemed to understand the importance of spacing out practice (Kang, 2016), but they had no idea that the daily ritual of making homework look done was embedding misunderstandings into long-term memory, resulting in misunderstandings built on misunderstandings. I drew this diagram on my board:
Taking time to correct errors, though, is a hard sell for a generation with so many exciting options. Progress with that continues for my students.
Challenge 3: Capitalizing on curiosity
As my students learn, I encourage dramatization of the ah-ha moments and the great feelings that accompany those (Willingham, 2009). The practice of recognizing learning moments, as identified by New Learning Theory (Chapman, et al. 2007) helps students understand how they learn. I explain that writing has been shown to improve retention (Mueller & Oppenheimer, 2014) and require that they document their learning. Working in teams facilitates this process because they look and listen for each other’s “Oh.” For most of them, the charges of dopamine diminish when they remember they are supposed to log their learning; so I supply glitter and neon pens to appeal to their creative instincts. Appreciating the value of writing is slowly evolving.
Challenge 4: Processing speeds
Carol Dweck and Jo Boaler have moved mountains of progress in establishing the importance of growth mindset in US schools. Yet, many students still hold a negative connotation for slow, associating reflective cognitive processing with not very sharp. My students needed to understand many great thinkers have been slow processors, and both fast and slow processors can have great insights. With low-floor, high ceiling problems, students who want to get to the tougher concepts in their team activities may become frustrated with those who have focus issues or just need more time to think. On the other hand, those who want to carefully consider all options before jumping to conclusions may become frustrated with those who speed ahead based on initial instincts. Students who understand how they fit within a group gain confidence to make contributions and develop patience for each other’s thinking time. A teacher who is skilled at coaching IBL quickly learns how to group students to maximize their learning and minimize frustration.
So far this year my students seem to be retaining far better with deeper understanding of concepts, but the nature of retention will require more than four months to verify. In the interim, they are growing their analytical skills as they discuss and grapple with word problems in their daily learning activities. No doubt, understanding a little about how their brains work will contribute to success in other endeavors as well. Because I was able to convey this information within normal classroom discussions, very little time was diverted from content. Our classroom climate has soared, and my happier learners are also more powerful learners as together we continue to learn how to learn.
Chapman, D. D., Wiessner, C. A., Storberg-Walker, J., & Hatcher, T. (2007). New Learning: a different way of approaching conference evaluation. Knowledge Management Research & Practice, 5(4), 261-270. doi:10.1057/palgrave.kmrp.8500147
Kang, S. H. (2016). Spaced Repetition Promotes Efficient and Effective Learning: Policy Implications for Instruction Policy Insights from the Behavioral and Brain Sciences, Vol. 3(1) 12–19 © The Author(s) 2016 DOI: 10.1177/2372732215624708 bbs.sagepub.com
Mueller, P. A. & Oppenheimer, D. A. (2014). The Pen Is Mightier Than the Keyboard Advantages of Longhand Over Laptop Note Taking. Psychological Science 25(6), 1159-1168
Prince, Michael J., and Richard M. Felder. “Inductive Teaching and Learning Methods: Definitions, Comparisons, and Research Bases.” Journal of Engineering Education 95.2 (2006): 123-38. ProQuest. Web. 27 Dec. 2017.
Willingham, D. T. (2009). Why Don’t Students Like School?: A Cognitive Scientist Answers Questions About How the Mind Works and What It Means for the Classroom. Jossey-Bass