There seems to be two main, but very different, approaches to teaching problem solving:
- Begin by teaching students how to solve a particular type of problem, and then have students solve a set of similar problems
- Begin by giving students a set of problems to solve, and then respond to individual students’ needs through brief one-on-one and small group conferences
It is the second option that I was told was more effective in teacher school. I was taught that listening to a lecture on how to solve a problem robs the student of the opportunity to discover the solution on their own. I was told that listening at one’s seat is a passive exercise, and that students learn best from activities that require the use of one’s hands. I was told that brains are like muscles and that struggle and failure during problem solving builds these muscles by embedding higher order thinking skills. If someone in my program expressed doubt about these revealed “truths,” they were informed by the lecturer at the front of the room that lecturing from the front of the room was authoritarian. What sort of self-absorbed egotist, we were asked to ponder, would abuse their position as a teacher by choosing to control and indoctrinate students?
My university professors were rather explicit that the best way to get students to solve problems was to have them attempt lots of problems on their own, or in groups, and for the teacher to serve as a guide on the side. As a consequence, this is exactly how I spent the first six years of my career: Trying to facilitate problem solving by asking students to complete math/reading/science/social studies challenges as I circled around the room to see where I was needed. If a particular student still wasn’t getting anywhere with their problem after loads of “productive struggle,” as a last resort I would sit with them and teach them individually how to solve the problem.
I was recently reading Timothy Shanahan’s literacy blog when I came across his list of (hilarious) pet peeves about literacy teaching. While I recommend reading the two-part series in full, it was Pet Peeve #4 that inspired this blog post:
Pet Peeve #4: Teachers who claim that 2-minute individual conferences promote the same depth of thinking as a 20–30-minute group/classroom discussion.
Too many teachers have been led to believe that they can effectively guide students to deep understandings of text or proficient strategy use through brief one-on-one conferences.
There is no research supporting this weird idea. I can’t even understand how anyone might think it could be true.Shanahan on Literacy, read here
The individual conference model that peeves Shanahan, whether it’s in reading or any other subject, is a weird idea indeed. Perhaps it’s not completely necessary, but let’s briefly go into the math of what the individual conference model implies for a 60 minute lesson. Most teachers would be satisfied with a class of “only” 25 students, but some have more. Divide 60 minutes by a class of 25 and you get 2.4 minutes per student for explanation, questioning, feedback, and discussion, provided you are able to get students solving problems immediately. That’s 2.4 for Billy, too, who has lower working memory than his more fortunate peers, and whose parents don’t tutor him after school. Obviously 2.4 minutes isn’t enough time to talk about anything of substance, so we might organize students into small groups to increase that time. Then we’re talking about 7.2 minutes allotted to Billy, Sarah, and Khalid’s small group of three.
No matter how you slice it, a 2.4 minute individual conference or a 7.2 minute small group conference, on average, is a poor substitute for 20-30 minutes of rich explanation, questioning, feedback, and discussion. Perhaps this is one reason why the best teachers have been found to spend more time guiding the learning of the whole group before sending students off to work independently. Here is an excerpt from Rosenshine’s Principles of Instruction (2012), which is a report on how the teachers with the most student achievement gains tend to teach:
The most successful teachers presented only small amounts of material at a time. After this short presentation, these teachers then guided student practice. This guidance often consisted of the teacher working the first problems at the blackboard and explaining the reason for each step, which served as a model for the students. The guidance also included asking students to come to the blackboard to work out problems and discuss their procedures. Through this process, the students seated in the classroom saw additional models.
Teachers who spent more time in guided practice and had higher success rates also had students who were more engaged during individual work at their desks. This finding suggests that, when teachers provided sufficient instruction during guided practice, the students were better prepared for the independent practice (e.g., seatwork and homework activities), but when the guided practice was too short, the students were not prepared for the seatwork and made more errors during independent practiceRosenshine, 2012, pg. 16, para. 7 and 9
It seems unlikely that a series of quick (and often untimely) one-on-one conference would be the best way to provide all students with a healthy diet of guided practice, including modeling, questioning, feedback, and discussion. Individual conferencing during problem solving is too brief, too shallow, too reactive (i.e., putting out fires), and it often comes too late to be anywhere near as effective as whole class instruction in advance of problem solving. This is not to say that individual conferencing is bad, just that it should come after instruction. In fact, an key benefit of beginning a lesson with instruction rather than a problem solving “challenge” is that the teacher is able to check the understanding of all of their students to determine who needs to conference.
While it may be unfairly maligned in education, initial whole class teaching prior to independent problem solving (i.e., I do, We do, You do) should be the default sequence that teachers use to develop their students into expert problem solvers. My regret is that I didn’t realize this sooner.
– Zach Groshell
Rosenshine, B. (2012). Principles of instruction: Research-based strategies that all teachers should know. American Educator, 12–20. https://www.aft.org/sites/default/files/periodicals/Rosenshine.pdf