Over the past few months, Audrey Watters, Dan Meyer, and Keith Devlin have been critical of Silicon Valley, edtech startups, and iPad textbooks which hope to “disrupt” education. In my opinion, the real stumbling block to meaningful change is students’ formal reasoning skills — analytical thinking that cannot be cultivated by pausing and rewinding video or playing Math Blasters.
Here are my 5 points:
- Many of our students are transitioning from concrete to formal reasoning.
- A significant barrier to learning for understanding is students’ own formal reasoning skills.
- Formal reasoning skills (and thus learning for understanding) can be developing when instruction is structured around the Learning Cycle.
- Silicon Valley and edtech startups have been focusing on (often inappropriately) just a small fraction of the learning cycle.
- My Challenge to Silicon Valley: Help students learn for understanding by innovating around the rest of the learning cycle.
1. Many of our students are transitioning from concrete to formal reasoning.
Below are 3 reasoning puzzles, each followed by a video of college students attempting to solve the puzzle while explaining and discussing their logic. It’s a highly illuminating look at students’ reasoning processes.
I. The Algae Puzzle (Combinatorial Reasoning)
II. The Frog Puzzle (Proportional Reasoning)
III. The Mealworm Puzzle (Scientific Reasoning)
2. A significant barrier to learning for understanding is students’ own formal reasoning skills.
You’re probably thinking, “So, what? Just because Johnny can’t figure out all the possible combinations of algae doesn’t mean he can’t learn physics.” But the research strongly suggests that it does, even in interactive engagement classes.
In a previous post, I presented this graph from Hake’s famous six thousand student study:
As you can see, interactive engagement course outperformed traditional courses in learning gains as measured by the Force Concept Inventory (FCI). The FCI is the most widely used test of physics understanding. But why is there such a wide range of FCI gains among the IE courses and (not shown) among the individual students within a particular course? A study entitled “Why You Should Measure Your Students’ Reasoning Ability” (Coletta, Phillips, and Steiner) suggests reasoning ability is strongly correlated with physics success.
In the study, several different physics courses administered both the FCI (to measure physics gains) and the Lawson Test of Classroom Reasoning Skills (to measure formal reasoning ability). The Lawson test contains several items very similar the three puzzles above. Here’s what they found:
The data were split into quartiles based on the Lawson scores. The light green bars represent the average Lawson test score for each quartile and the dark green bars represent the average FCI gain for each quartile. There is clear correlation between reasoning ability and learning gains in physics. I’d wager this correlation extends to other subjects as well.
3. Formal reasoning skills (and thus learning for understanding) can be developed when instruction is structured around the Learning Cycle.
According to Piaget, intellectual growth happens through self-regulation — a process in which a person actively searches for relationships and patterns to resolve contradictions and to bring coherence to a new set of experiences.
In order to get students to experience self-regulation and further develop their reasoning skills, classroom experiences should be constructed around the Karplus learning cycle, which contains the the stages of EXPLORATION, INVENTION, and APPLICIATION. From Karplus’s workshop materials on the learning cycle:
EXPLORATION: The students learn through their own actions and reactions in a new situation. In this phase they explore new materials and new ideas with minimal guidance or expectation of specific accomplishments. The new experience should raise questions that they cannot answer with their accustomed patterns of reasoning. Having made an effort that was not completely successful, the students will be ready for self-regulation.
INVENTION: Starts with the invention of a new concept or principle that leads the students to apply new patterns of reasoning to their experiences. The concept can be invented in class discussion, based on the exploration activity and later re-emphasized by the teacher, the textbook, a film, or another medium. This step, which aids in self-regulation, should always follow EXPLORATION and relate to the EXPLORATION activities. Students should be encouraged to develop as much of a new reasoning pattern as possible before it is explained to the class.
APPLICATION: The students apply the new concept and/or reasoning pattern to additional examples. The APPLICATION phase is necessary to extend the range of applicability of the new concept. APPLICATION provides additional time and experiences for self-regulation and stabilizing the new reasoning patterns. Without a number and variety of APPLICATIONs, the concept’s meaning will remain restricted to the examples used during its definition. Many students may fail to abstract it from its concrete examples or generalize it to other situations. In addition, APPLICATION activities aid students whose conceptual reorganization takes place more slowly than average, or who did not adequately relate the teacher’s original explanation to their experiences. Individual conferences with these students to help identify and resolve their difficulties are especially helpful.
4. Silicon Valley and edtech startups have been focusing on (often inappropriately) just a small fraction of the learning cycle.
Unfortunately, Silicon Valley has been dumping its disruptive dollars almost solely into the INVENTION phase and on the tail-end of the phase at that. It views education purely as a content consumption process and ignores the development of formal thinking and reasoning.
Remember, in the invention phase, “The concept can be invented in class discussion, based on the exploration activity and later re-emphasized by the teacher, the textbook, film, or another medium.” That’s Khan Academy videos, flipclass videos, iBooks, an similar technologies designed to present content via direct instruction. However, “Students should be encouraged to develop as much of a new reasoning pattern as possible before it is explained to the class.” Which means that this type of direct instruction should be as minimal as possible, because it robs kids from reasoning and making meaning. In other words, Silicon Valley is putting its energy into the portion of the invention phase that should be as small as possible!
Now let’s look at the application phase. There has been some development here as well, most notably in apps and exercise software which seek to gamify the classroom. But the application phase isn’t about getting 10 right answers in a row or solving problems to shoot aliens. Remember, “Without a number and variety of APPLICATIONs, the concept’s meaning will remain restricted to the examples used during its definition.“ Real learning with understanding means students can reason about the concepts well enough to use them in new and unique concepts (aka transfer). Applications should require students to examine their own thinking, make comparisons, and raise questions. Great applications examples are open-ended problems, problems which present a paradox, and student reflection on both successful and unsuccessful problem-solving methods. Deep learning does not end when the Application phase begins.
5. My Challenge to Silicon Valley: Help students learn for understanding by innovating around the rest of the learning cycle.
Real disruption isn’t going to come from skill and drill apps, self-paced learning, badges, YouTube videos, socially-infused learning management systems, or electronic textbooks. Students must be continuously engaged in the learning cycle. We need to equip our students with the reasoning skills to learn how to learn anything. Focus on experiences in the exploration phase, meaningful sense making in the invention phase, and worthy problems in the application phase.
But, in reality, we only have ourselves to blame. It shouldn’t come as a surprise to us when students can’t think — the status-quo in education has been to spend most of our time on content delivery while robbing students of exploring and reasoning opportunities. And current edtech trends aren’t fixing this problem; rather, they are making it easier to make the problem worse.
To be fair, a few “good disrutptions” have occurred in the other phases of the learning cycle. Motion detectors allow students to “walk a graph” so they can easily explore position-time and velocity-time graphs. GeoGebra allows students to explore and play with geometry and functions quickly and easily. PhET simulations allows students to conduct open-ended planetary orbit experiments that would be impossible in real life. And VPython programming gets students to apply what they learned to write their own simulations and visualizations.
So when presented with the next great edtech “disruption,” ask yourself: has this innovation actually changed how student think about math and science concepts? Or has it just allowed students to get a few more questions correct on the state exam?
For further reading:
- College Teaching and Development of Reasoning (Fuller, Campbell, Dykstra, Stevens)
- “Can Physics Develop Reasoning?” (Fuller, Karplus, and Lawson)
The next two articles:
- “Promoting Intellectual Development Through Science Teaching” (Renner and Lawson)
- “Physics Problems and the Process of Self-Regulation” (Lawson and Wollman)
are found here: Module 11: Suggested Reading (Workshop Materials for Physics Teaching and the Development of Reasoning)
Action-Reaction 