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Learning from Mistakes: Not Just for Students


by Rob Wieman & James Hiebert - October 10, 2018

Educational researchers and theorists have noted the importance of student experimentation and learning from mistakes. The authors of this commentary argue that teachers need the same kinds of opportunities, calling for a cultural shift that acknowledges the centrality of experimentation, which inevitably includes mistakes, in teaching and teacher learning.

Two diametrically opposed views of school teaching are floating around the educational community, especially among those engaged in policy setting. One is captured by C. Roland Christensen’s claim that “Every good lesson has an experiment built into it” (Simon, 1995). The second is commonly heard from parents who are concerned that their children are being taught using a new method: “Don’t treat our children like guinea pigs.” The first view encourages teachers to try something new, even to take risks. This view accepts the fact that improving teaching necessarily requires teachers to make mistakes. The second view assumes that a teacher’s job is to use the best practices we know, to avoid mistakes by using proven methods. To do otherwise would be akin to malpractice. Clearly, one cannot hold both views.


EXPERIMENTING AND LEARNING FROM MISTAKES


Our goal in this essay is to explain why we believe Christensen is right. Our primary argument is drawn from what educators know, and continue to learn, about the consequences of making mistakes. Our argument begins more than a century ago when John Dewey published his remarkable analysis, How We Think (1910). One of Dewey’s many fertile themes in this book, still timely today, is that experimenting and making mistakes is a rich and sometimes essential path toward learning. Dewey’s sweeping claim applied to all of human learning. This dramatic theme appeared again in Sir Ronald Fisher’s 1949 ground-breaking descriptions of using statistical methods for testing the likelihood that hypotheses are true. In The Design of Experiments, Fisher said that people have always learned from experience, and that “experimental observations are only experience carefully planned in advance” (p. 8). In other words, the kind of learning that accumulates to improve practices is built on planned experience, or “experimental observations.”


More recently, Shulman (2004) elaborated Dewey’s and Fisher’s ideas to argue for the value of teachers experimenting with teaching methods and learning from their mistakes. In fact, for Shulman, this is not really an option. Teaching, said Shulman, is such a complex practice that it is unrealistic to think that teachers will not make mistakes. The key is that teachers learn from their mistakes.


We are struck by the fact that learning from mistakes has been considered, for some time, a productive way for students to learn, but this same insight has not so often been applied to teachers. Research has provided consistent, powerful evidence that students learn from mistakes (National Research Council, 2000). Take mathematics as an example. For years, teachers were asked to plan instruction so that students would learn smoothly, with a minimum of errors. But we now know that helping students reflect on mistakes, and understand the reasons for them, is one of the most effective ways to develop deep understanding (Hiebert & Grouws, 2007).


THE NEED FOR TEACHER LEARNING


But here is the problem. The methods of teaching known to support deeper student learning, the methods that make good use of student mistakes, are quite different than those found in the average U.S. classroom today. Ambitious teaching probes students’ thinking, uncovers misconceptions that could yield valuable learning opportunities, and treats student errors as opportunities for all students to learn (NRC, 2000). Not only are these methods of teaching more complex and demanding, they are new to most teachers. This means teachers must learn how to use them.


If we apply accepted views of student learning to teachers, we see that teachers learn by experimenting with teaching methods that are new to them. All the best current evidence on learning says that this kind of planned experience, which inevitably leads to mistakes, is the best way for teachers to learn what they need to know to teach in more ambitious ways.


But teachers in many schools work under a view that sees mistakes only as a sign of poor teaching. Making mistakes is a red flag of incompetence. Teachers caught making mistakes during evaluations are frequently scored lower. As we have argued, this is shortsighted for two reasons: (1) teaching is such a complex practice that mistakes are inevitable and, most importantly, (2) making mistakes while experimenting, while trying to learn from planned experience, is a powerful way for teachers to learn and improve.


HOW TEACHER EDUCATORS CAN TREAT TEACHER LEARNING: THE METHODS CLASS ASSIGNMENT


Believing that teachers should avoid experimenting and avoid making mistakes is baked into the educational culture in the U.S. Changing a culture often requires breaking into a systemic perspective from multiple entry points. There is some indication that one entry point currently being attempted is how teachers are evaluated (e.g., Caposey, 2017; Ferretti & Hiebert, 2018). We want to highlight the entry point of teacher preparation. If teachers are prepared with an understanding that improving requires experimenting, and learning from mistakes, perhaps they will enter the field with a new perspective and help to transform the culture.


How could learning from mistakes play out in teacher preparation? Pre-service teachers are typically asked, in their methods classes, to plan a lesson and teach it in a practicum setting. Consider the experience one of us had with Gail, Petra, and Maria (Wieman, in press). These three pre-service teachers planned a lesson for their sixth-grade practicum students in which teams of two players decide which whole number (0, 1, 2, or 3) is closest to the sum of two cards chosen at random. In sharing their strategies with their partner and then with the whole class, students were supposed to develop a deeper understanding of fractions and decimals, while developing their ability to make and critique mathematical arguments.


Although Gail, Petra, and Maria planned this lesson in great detail, including specific directions, students spent much of the time confused about how to play the game. Many of them disengaged, chatting about non-mathematical topics. The key learning opportunity was the culminating discussion, when students would share their solution strategies. But, Gail, who taught the lesson, did not get this far. Students had not developed any strategies to talk about.


From the perspective of “avoiding mistakes while teaching,” Gail’s performance would be judged harshly; she had not demonstrated an ability to provide meaningful learning opportunities or to manage a classroom. Based on the serious mistakes in this lesson, it is hard to imagine how Gail could receive a good grade for this assignment, or even how the pre-service teachers could find it a positive learning experience.


TEACHING MISTAKES AS SITES FOR LEARNING TO IMPROVE


The kinds of mistakes most likely to provide powerful learning for teachers are mistakes that arise from trying to propel students forward in their understanding, mistakes that result from trying more ambitious teaching and then analyzing what happens. This means planning for, and implementing new techniques that have good reason to improve students’ learning. Inevitably, teachers will fail to anticipate what will happen at each point in the lesson. This creates risky situations that lead to mistakes. But if the mistakes are coupled with collecting and analyzing student data from lessons, and comparing actual student performance to predicted performance, teachers can see if the methods they used were effective, or what methods might have worked better.


Fortunately for Gail, Petra, and Maria, the failed first lesson was not the end of the story. They had a chance to meet together with their methods instructor, share what they had observed, make revisions to their lesson and reteach it to a new group of students later that day. For the second lesson, they created a new opening to the lesson during which the teacher would play a round of the game with one student while the rest of the class watched. This simple revision resulted in a drastically different lesson. The second class of students engaged in the game more quickly and developed a variety of strategies. The teacher of the second lesson spent less time correcting off-task behavior, and more time assessing student thinking and facilitating a culminating discussion about strategies. Gail’s “failed” enactment was recast, not as a red flag signaling her ineptitude, but as an opportunity for the pre-service teachers to learn about teaching. Without this failure, the pre-service teachers would not have learned to analyze teaching in this way, a skill that they can apply throughout their careers.   


We can imagine some readers asking why Gail, Petra, and Maria had to make this mistake. Surely, their instructor could have told them to demonstrate the game, thus enabling them to enact a better lesson from the start. However, this critique misses the mark in two important ways. First, it is not clear when giving directions or demonstrating a game would be better; there is no one best way to introduce a game. For these students in this context, demonstration proved more effective. Also, as Dewey wrote over a century ago, and many researchers have since verified, the kind of deep learning that can be applied flexibly in complex contexts, exactly the kind of knowledge that teachers need, is best learned through experimenting, and analyzing why these experiments sometimes do not turn out as planned.


We can also hear some readers asking about the fate of the students in the first lesson, or about students in any lesson where teachers make mistakes. Aren’t mistakes unfair to students who experience them? We have three responses. First, most U.S. students now experience unambitious teaching and low-quality learning opportunities. In fact, most U.S. students are recipients of a long-running failed experiment in teaching (Schoenfeld, 1994). These are the students being treated unfairly. Second, if teaching mistakes lead to presenting students with incorrect ideas and information, these experiences are not indelible. The problem teachers constantly face is that human beings don’t remember very well; if students remembered well, they would perform perfectly on most tests of facts and procedures. Third, in the long run, all students will experience more ambitious learning opportunities if their teachers are encouraged to experiment with promising methods. Ultimately, when teachers do not improve their teaching by learning from mistakes, students get the short end of the stick.


As noted, we are asking for a huge cultural change. But teachers already realize that their teaching is imperfect, and that many students are not receiving the learning opportunities they need. Making public what every teacher already knows in private, that we learn from our mistakes, can unleash a powerful tool for teacher learning. No proven methods of teaching exist. But teachers can continuously improve the methods they use if they build an experiment into each lesson.



References


Caposey, P. J. (2017). Making evaluation meaningful: Transforming the conversation to transform schools. Thousand Oaks, CA: Corwin Press.


Dewey, J. (1910). How we think. Boston, MA: DC Heath.


Ferretti, R.P., & Hiebert, J. (Eds.). (2018). Teachers, teaching, and reform: Perspectives on efforts to improve educational outcomes. New York: Routledge.


Fisher, R. A. (1949). The design of experiments (5th ed.) New York: Hafner.


Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students' learning. In F. K. Lester, Jr., (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Charlotte, NC: Information Age Publishing.


National Research Council. (2000). How people learn: Brain, mind, experience, and school (Expanded edition). J. D. Bransford, A. L. Brown, & R. R. Cocking (Eds.). Committee on the Developments of Science in Learning, Commission on Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.


Schoenfeld, A. H. (1994). What do we know about mathematics curricula? The Journal of Mathematical Behavior, 13(1), 55–80.


Shulman, L. S. (2004). Forgive and remember: The challenges and opportunities of learning from experience. In L. C. Solman & T. W. Schiff (Eds.), Talented teachers: The essential force for improving student achievement (pp. 89–7). Greenwich, CT: Information Age Publishing.


Simon, J. (Producer/Writer/Director) (1995). The art of discussion leading: A class with Chris Christensen (VHS tape). Cambridge, MA: Harvard University, Derek Bok Center for Teaching and Learning, as cited in Hiebert, Morris, and Glass, (2003). Learning to learn to teach: An “experiment” model for teaching and teacher preparation in mathematics. Journal of Mathematics Teacher Education, 6, 201–222.


Wieman, R. (in press). Scaffolding ambitious instruction: Teaching and re-teaching in a methods practicum. In T. Hodges & A. Baum (Eds.), Handbook of research on field-based teacher education. Hershey, PA: IGI Global Publishing.




Cite This Article as: Teachers College Record, Date Published: October 10, 2018
https://www.tcrecord.org ID Number: 22527, Date Accessed: 1/27/2022 10:21:37 AM

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About the Author
  • Rob Wieman
    Rowan University
    E-mail Author
    ROB WIEMAN is an associate professor in the Department of STEAM Education at Rowan University. He began his career as a math teacher and instructional coach in the New York City Public School system, and now works with in-service and pre-service math teachers and researches efforts to improve mathematics instruction. He is the author, with Fran Arbaugh, of Success from the Start: Your First Years Teaching Secondary Mathematics.
  • James Hiebert
    University of Delaware
    E-mail Author
    JAMES HIEBERT is the Robert J. Barkley Professor of Education at the University of Delaware, where he researches mathematics teaching, learning and teacher education. He co-authored Making Sense: Teaching and Learning Mathematics with Understanding and The Teaching Gap: Best Ideas from the World’s Teachers for Improving Education in the Classroom.  
 
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