(This is the second post in a five-part series on this topic. You can see Part One h.)
The new question-of-the-week (and the first one in this column鈥檚 sixth year!) is:
There鈥檚 a lot of talk about how we should 鈥渃elebrate鈥� and 鈥渆ncourage鈥� mistakes and failures. How can teachers do that in the most effective way?
in this series featured guest responses from experienced educators Doug Lemov, Danny Woo, Kathleen Neagle Sokolowski, Bena Kallick, Allison Zmuda, Jen Schwanke and Mike Janatovich.
You can listen to a I had with Doug, Danny and Kathleen on . You can also find a list of, and links to, .
Today鈥檚 post includes answers from Warren Schnack, Jenny Edwards, Michael Thornton, Annie Ward, and Cathy L. Seeley.
Response From Warren Schnack
Warren Schnack has taught at Luther Burbank High School in Sacramento and at the International School Ho Chi Minh City. He enjoys travel, fatherhood, and all dairy products:
The first standard for mathematical practice asks students to 鈥渕ake sense of problems and persevere in solving them.鈥� Of course we want to guide students on how to approach and understand problems. But it鈥檚 the second half of the SMP that really hits home for me. To persevere implies continuing to tackle something after repeated failure. And that may be the most important lesson we can teach students in our short time together.
Mathematics is unique in that, with the correct guidance, it can be figured out. The teacher becomes the coach, directing students toward their own discoveries. Much of the figuring out time is messy, and mistakes are made. And that is when the learning happens.
I try to emphasize to my students early in the school year that interesting wrong answers are often better than obvious right answers. Similar to highlighting the correct parts of a wrong answer both validates students鈥� effort and creates an environment where mistakes are not only tolerated, but encouraged. Stanford professor of mathematics education Jo Boaler has championed research which shows that , and that students work harder in a mistakes-friendly environment. In fact, guessing answers to a question or problem, even when answers are nowhere near correct, seems to prime our minds for learning the content and .
My Algebra II class (or Math 2 class) fills in a t-chart for y=x2 and plots the points on a coordinate plane. After we talk a bit about the shape of the parabola, I ask how the graph of y=3x2would be different. After some wait time to give everyone a chance to ponder, the ideas shared range from a graph which has been moved up to a graph that is much wider, and I make it a point to praise these thoughtful (incorrect) answers, without letting on what the correct answer looks like. Then Veronica adds, 鈥渋t won鈥檛 be any different at all.鈥� 鈥淲hy?鈥� I ask. She explains that since exponents are more 鈥減owerful鈥� than just multiplying, merely multiplying won鈥檛 do much.
I praise Veronica鈥檚 great interpretation of the difference between multiplying and raising to a power, and make sure other students understand her argument. Then the class makes another t-chart and figures out that y=3x2actually stretches the parabola vertically, thus making it looking 鈥渢hinner.鈥� Not necessarily intuitive, but discoverable and verifiable. Students can then compare that answer with their guess, which also helps retention.
Yet Veronica鈥檚 (wrong) answer is an amazing way to show a deeper understanding of the relationship between multiplying and raising to a power. She understands the difference between these two things, but did not apply this understanding correctly. Even though it wasn鈥檛 correct in this case, her statement is the kind of idea that we can return to throughout our time exploring exponents to see how the it can be applied. When simplifying rational expressions, when discussing exponential growth, or when we need to review the power rules, I can now ask: 鈥淚s this an example of what Veronica was talking about when she said that exponents are more powerful than multiplying?鈥� That wrong answer gave the class a way to describe the underlying concept in a way I wouldn鈥檛 have thought to present, and it was offered by a peer. Such practices reinforce that we鈥檙e all exploring the content, and sometimes the students are the ones to lead everyone鈥檚 understanding; even, or especially, through their mistakes.
The bottom line is that it鈥檚 OK to ponder out loud, to go down a path which may not lead to the right answer, but will lead to thinking. Because that鈥檚 what we鈥檙e trying to get our students to do, right? Think. Figure things out. Try something else when they fail. That is how we build lifelong learners.
Response From Jenny Edwards
Jenny Edwards teaches doctoral students in the School of Educational Leadership and Change at Fielding Graduate University in Santa Barbara, Calif. Edwards is the author of the ASCD books and :
How can we celebrate and encourage mistakes and failures with our students? We can change our vocabulary when we talk with them. When we make mistakes, it is 鈥渓earning in action,鈥� according to C. Hall (personal communication, April 14, 2016) because students are learning what doesn鈥檛 work, and they are one step close to learning what does work. 鈥淢istakes can also be called 鈥渕iss-takes.鈥� Actors and actresses do not always do things correctly the first time. That is the reason that film crews say, 鈥淭ake 1,鈥� 鈥淭ake 2" when filming.
We can remove the word 鈥渇ailure鈥� from our vocabulary. What might be another word to use? How about 鈥渓earner?鈥� Someone who is not yet doing something correctly is in a wonderful place to learn. According to Dilts and DeLozier (2000), 鈥淭here is no failure, there is only feedback鈥� (p. 393).
How could we ever learn if we didn鈥檛 make mistakes? If students already knew how to read at a 5th grade level when they entered first grade, they would not need to read first grade books. We want them to be a level where they make mistakes so that they can learn and advance to the next level. A pilot who is flying from Los Angeles to New York City is not always completely on course and is continually calibrating between being slightly off course to being on course in order to arrive at the destination.
If students say that they cannot do something, we can say, with a lilt in our voice, 鈥淵et,鈥� 鈥淯ntil now,鈥� 鈥淏ut not for long鈥� (Hall, 2006). A colleague of mine shared that her son, who had special needs, was experiencing a great deal of frustration and saying, 鈥淢ommy, Mommy, I can鈥檛 do this!鈥� She smiled and said, 鈥淵et.鈥� He paused a moment and broke out in a big grin!
When I am teaching something that students might perceive as being difficult, I introduce the material by asking them to think of something they have learned, such as reading or writing. 鈥淲ere you born knowing how to read? Were you born knowing how to write?鈥� Of course, they laugh and say, 鈥淥f course not!鈥� Then, I ask, 鈥淒id you learn to read all in one day? Did you learn to write all in one day?鈥� They respond, 鈥淣o!鈥�
I teach a writing course in higher education. I continually tell students, 鈥淲e aren鈥檛 born knowing how to write in a scholarly manner.鈥� My goal is to point out patterns in students鈥� writing. When students internalize the patterns, they advance to higher levels. One student said that the only thing that kept him from dropping out of school was the statement, 鈥淲e aren鈥檛 born knowing how to write in a scholarly manner.鈥�
Sylvia Rimm (1986) talked about the gift that students receive when they struggle. When they struggle (i.e., make mistakes) and learn from them, they grow stronger. On the other hand, if they learn things easily, they never learn to work hard and have the feeling of accomplishment. I shared this with a mother of one of my students. She said that she never had to work in high school because things came easily to her. When she went to college, she had to study and did not know how. She thought she was not smart because she had to work hard to get good grades, and she dropped out. Her life spiraled down until she finally decided to turn it around.
Think of something that you have learned. Did you do it perfectly the first time? Of course not! What was your experience as you were learning to drive a car? Did you make some mistakes? Of course you did! And did you learn to drive! Of course!
How might we use language to help students to celebrate mistakes?
References
Dilts, R. B., & DeLozier, J. A. (2000). Encyclopedia of systemic neuro-linguistic programming and NLP new coding. Scotts Valley, CA: NLP University Press.
Hall, C. (2006). Language in action. Santa Cruz, CA: The NLP Connection.
Rimm, S. (1986). Underachievement syndrome: Causes and cures. Watertown, WI: Apple Publishing.
Response From Michael Thornton
Michael Thornton has been teaching primary grades for 11 years in and around the Charlottesville, Virginia area. He also writes a on education and can be found on Twitter at . Michael is co-authoring a book, Reimagining Education: A Space for Risk, that will publish in 2017 with Rowman & Littlefield:
Failure is not an option.
This message paints a picture that failing is bad. That people should proceed carefully through life with a fear of failure. It encourages people to become comfortable with what they can do without the challenge of trying something new or different. In the classroom, this is the last message you want shared with your students. In fact, we should be challenging our students to become lifelong learners while fostering a mindset that failing is a natural part of the learning process. Failure is not the end but a stepping stone along the path of learning.
Teachers should model failure and risk-taking to show why it is an important step when learning. I currently teach in a for 117 kindergarten through fifth grade students. The nontraditional setting and multiage instruction provides a great opportunity for growth for the teachers and the students. The students in our space understand that risks should be taken and that mistakes will happen. Together, we understand that learning is a long journey that will inevitably include mistakes. Those mistakes are not reasons to stop learning but merely opportunities for academic and personal growth.
In my experience, this generation of learners have a much better outlook on failure but unfortunately it is often shielded from them in the classroom. Our learners experience failure everyday. For example, building with Legos or crafting in Minecraft increases their endurance with failure while also engaging them in learning. Their ability to translate that to projects or assignments in school is easy if they are given the opportunity to do so. The is an engineering activity I do at the beginning of the year and sporadically throughout the year that demonstrates their ability to endure failure.
Students must have the freedom to make choices in the classroom. If those risk-taking choices are eliminated, how can we expect them to learn from their own mistakes? The more choices students have in the classroom, the more they will take ownership of their learning. In turn, the more ownership they feel, the more invested they will be in the results regardless of any failure along the way. Then students will meet the For this to happen organically in the classroom, educators must step back and relinquish some control. Give the students space to, , and without dictating their every decision and choice. When this happens seamlessly in the classroom, students will proceed not with a fear of failure but an eagerness to succeed and learn no matter the risks being taken along the way.
Response From Annie Ward
Annie Ward has served as the Assistant Superintendent for Curriculum and Instruction for the Mamaroneck Public Schools in Westchester County, New York since 2004. Prior to that, she was a Local Instructional Superintendent for the New York City Department of Education and the Supervisor of Curriculum and Instruction for the Ridgewood, NJ Public Schools. . Annie and Stephanie Harvey are currently co-authoring a professional book to be published by Scholastic, Striving to Thriving Readers: The Best Intervention is a Good Book. Follow Annie on Twitter @AnnieTWard:
First, by watching our language! Celebrating a mistake or a failure sounds oxymoronic, because the terms connote negativity and finality. But if we speak instead of an 鈥渋nitial attempt鈥� or a 鈥渇irst go,鈥� we normalize the iterative process of improvement. Successes typically result from sustained effort over time with feedback and practice. Recently, author J.K. Rowling posted publishers鈥� rejection letters on Twitter to encourage aspiring writers by reminding them that 鈥渘o鈥� is a normal part of the publishing process--even for the creator of Harry Potter!
Comprehension specialist (and my current writing partner) Stephanie Harvey encourages teachers to 鈥渉onor the learning, not the knowing鈥� in order to foster a growth mindset in classrooms. Rather than celebrate the students who are quickest to contribute accurate answers, Stephanie urges us to give the floor to students whose thinking has changed in light of new information from texts or peers. She seizes opportunities to share her own misconceptions and the delight she feels when she learns something new.
How does the celebration of mistakes and failures play out in the realm of reading development? Certainly, emergent readers鈥� miscues and self-corrections provide a valuable window into the reading strategies they are and are not yet using. Also, proficient readers typically experience comprehension challenges in the early pages of a book when they are trying to get their bearings; adolescent literacy specialist Kelly Gallagher has coined the term 鈥渇irst draft reading鈥� to denote readers鈥� initial grasps. As readers encounter and integrate additional information, their comprehension deepens. Rather than clarify students鈥� misunderstandings at the outset by providing established, final-draft interpretations (鈥淣ick Carroway is an unreliable narrator鈥�), we would do better to model and support the authentic, ongoing process of theory construction and revision.
So while miscues and rough-draft comprehension are healthy parts of the reading process, it is vital to understand that excessive mistakes and failures are toxic to striving readers. Unfortunately, the recent emphasis on 鈥渢ext complexity鈥� has given rise to the notion that it鈥檚 good for kids to puzzle over really hard books. In fact, the opposite is true. Decades of research trumpeted by Richard Allington and Stephen Krashen establish that readers develop through voluminous, high-success reading--that is, by turning page after page in books that they love. When readers flounder and abandon assigned books that are too difficult and/or unappealing, we should not be surprised, nor should we hold their noses to the grindstone.
Instead, we should double down on conferring and book-matching. Striving readers thrive through close encounters with compelling books, and it鈥檚 our responsibility to provide continual access and a way in. Book Whisperer Donalyn Miller urges us to create 鈥減review stacks鈥� of books to gauge kids鈥� interest in different topics and formats. We鈥檝e seen reluctant readers reach eagerly for captivating graphic novels like The Dogs of War and Amulet and accessible series like Ricky Ricotta and Knights of the Lunch Table.
In spite of concerns that kids would languish in these genres, we have found that readers acquire meaningful background knowledge and vocabulary from them and naturally gravitate towards more complex books over time (as Nancie Atwell, Donalyn Miller, and Teri Lesesne have suggested they would). 鈥淐hange the book, change the reader鈥� is a mantra that my district embraces as we work to freshen and diversify classroom libraries and connect kids with books they can鈥檛 wait to read.
Failure in reading leads to what Jon Scieszka has termed the 鈥渄eath spiral.鈥� Stalls, interruptions, and gaps in kids鈥� reading lives mean they are not getting the volume of high-success reading that they need to thrive. By providing students with abundant daily access to irresistible books, teachers have the capacity to propel them forward on powerful reading paths. Make no mistake about that!
Response From Cathy L. Seeley
Cathy L. Seeley has worked as a teacher, district mathematics coordinator, Texas state mathematics director for grades K-12, and is a former president of the National Council of Teachers of Mathematics. Her books include (ASCD) and (ASCD):
In mathematics, making mistakes has always been a fear of students. Many have believed that math is all about getting right answers, and that making a mistake means a student isn鈥檛 good at math or maybe just isn鈥檛 a 鈥榤ath person.鈥� Working toward right answers is certainly part of doing mathematics. But today we know that making mistakes--and dealing with them--can serve as a powerful foundation for learning, and can even contribute to a person becoming smarter. And we now know that struggling over challenging problems can contribute to someone growing their mind.
The hottest topic in teaching today may be the importance of adopting a 鈥榞rowth mindset.鈥� In Carol Dweck鈥檚 landmark book, Mindset (2006), we gained new insights into the nature of intelligence, and we learned that intelligence is more malleable than many have believed. From brain scans and related research, we now know that intelligence is not solely determined by genes, but rather can be affected by many factors, including working through hard problems and receiving the right kind of encouragement and support.
Part of the key to using students鈥� mistakes as a step toward learning lies in the way we structure our classrooms. Rather than a teacher showing students rules and procedures, and then asking students to solve word problems where they apply the recently learned procedure, we can turn that model upside down. We can start by asking students to tackle a problem--ideally a rich and somewhat challenging task, and preferably one they don鈥檛 already know how to solve. As students work through the problem, either alone or with others, they wrestle with the underlying mathematical ideas. The resulting classroom discourse allows students to share ideas and solutions, sometimes including incorrect approaches or answers. The richest discussions often arise from a student sharing something that doesn鈥檛 work. The class can discuss with each other why they think an answer or idea may be sound or why they think a different approach might yield positive results. As the teacher facilitates a discussion, students are engaged in thinking and reasoning far more deeply than if they simply try to replicate what a teacher has shown them. In some classes, students are thanked for sharing their wrong answers, noting the rich learning that followed.
This 鈥榰pside-down鈥� teaching model (Seeley, 2015) might be thought of as a shift from an I-We-You model (I, the teacher, will show something; We, the class, will do guided practice together; then You, the students, will be able to do it on your own) to a You-We-I model (You, the students, will mess around with a problem; We, the class together, will discuss what you did and how you thought about the problem; I, the teacher, will make sure you connect what we did with the mathematics of the lesson). This shift not only makes room for mistakes, it builds students鈥� mathematical reasoning and communication skills and sets the stage for long-term learning of concepts and procedures.
Professor Jo Boaler of Stanford, author of 鈥淢athematical Mindsets鈥� (2015), shared on her blog the following sign posted at a summer math camp for middle school students:
In other words, we know mistakes will sometimes happen, even as we strive for correct answers. When mistakes occur, we will take a close look at them and see what led to them and how we might rethink a process or approach. In all cases, we will respect each other and appreciate the sharing of mistakes. What a great sign to post in every classroom!
References:
Boaler, Jo. Mathematical Mindsets: Unleashing Students鈥� Potential through Creative Math, Inspiring Messages and Innovative Teaching. San Francisco, CA: Jossey-Bass, 2015.
Dweck, Carol S. Mindset: The New Psychology of Success. New York: Ballantine Books, 2006.
Seeley, Cathy. Smarter Than We Think: More Messages About Mathematics, Teaching, and Learning in the 21st Century. Sausalito, CA: Math Solutions, 2014.
Seeley, Cathy. Making Sense of Math: How to Help Every Student Become a Mathematical Thinker and Problem Solver. Alexandria, VA: ASCD, 2016.
Thanks to Warren, Jenny, Michael, Annie and Cathy for their contributions!
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Look for Part Three in a few days...
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