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Dec 03

What does it mean to be done?

Posted by Bank Street in Math Leadership on Dec 03, 2015

by Michael P. Cassaro
Posture Educational Consultants
Metamorphosis Teaching Learning Communities

 

What does it mean to be doneYou’ve heard this before. Someone across the room finishes the fact sheet, solves the problems, gets the answers and - SLAM. Done!

While we could chalk this comment up to a person’s lack of impulse control, a more patient questioning might reveal a deeper source. What if we consider that a person’s behaviors may reflect a set of belief systems? What belief systems underlie this pencil slamming behavior? In what ways is this behavior unproductive for learning? And what can we do about such unproductive behaviors?

It’s not just our students who slam their pencils and proclaim, Done! We teachers do it, too. What are some of the student- and teacher-held beliefs that underlie this behavior? That’s not entirely clear, but it probably has something to do with the person’s beliefs about learning and about learning math in particular.

  • The best way to learn math is through practice and drill. Arthur Baroody’s 2006 article from Teaching Children Mathematics suggests otherwise. His work follows Constance Kamii and the Dutch work out of the Freudenthal Institute. Developing a network of relationships amongst numbers and facts promotes durable fluency and an understanding of the properties of operations that can be applied to computation with larger numbers. Memorization of facts is the outcome of a long process of learning.
  • Math is about calculating sums quickly using memorized facts. Ann Dowker’s 1992 research on computational fluency has shown this to be patently false among mathematicians. Jo Boaler of Stanford and her public campaign (www.youcubed.org) echo these ideas. Fosnot and Dolk have written extensively on the topic and have collaborated to publish curriculum that supports a different type of mathematical learning.
  • Being smart and being a good learner means knowing the answers. I could not do justice to the volumes of brain and learning research that discount this belief. Lauren Resnick at the University of Pittsburgh and Carol Dweck at Stanford are some of the leaders in this field as it relates to education. Intelligence is not fixed. Learning is a process that involves failure. Learning outcomes are most durable when they relate to the journey.

This behavior, slamming a pencil and proclaiming doneness, is unproductive for learning. In addition to communicating unproductive beliefs about learning mathematics, this behavior impacts others in real ways.

  • What does it mean to be doneFor some, the goal of completion has been achieved and there is no longer any desire to work.
  • Others may now worry that everyone else too will soon finish, leaving me last.
  • Many are disheartened: I’ll never finish first.
  • Hopefully some are relieved. That’s over with. Now I can actually think without all that pressure in the room.
  • Ultimately, it’s the emotions that get stirred up. When the fact sheets come out the sorting begins. Unless that’s already been decided.

So these behaviors don’t come up only with fact sheets. Because if you’re reading this blog you probably don’t use timed fact sheets, anyway. These behaviors come up always, thought they might look differently. What can we do in our everyday practice to counter-model unproductive beliefs such as fixed-mindset, hierarchical learning structures, and emphasis on speed?

  • Respond neutrally, whether the answer is right or wrong.

Student: 3 x 16 is 36.
Teacher: How do you know? How did you figure it out?

Student: 3 x 16 is 48.
Teacher: How do you know? How did you figure it out?

  • Turn it back to the class.

Student: 3 x 16 is 36.
Teacher: Did anyone get a different product? Do you agree or disagree?

Student: 3 x 16 is 48.
Teacher: Did anyone get a different product? Do you agree or disagree?

  • Slow it down. Explicitly communicate to students that you value understanding.

Student: 5 x 30 is 150. 5 x 3 is 15 and then add a zero.
Teacher: Wow. That’s cool. Most of you seem to know about this trick. 150 is the Product of 5 x 30. [Writes 150.] But something doesn’t sound right to me. 5 x 3  is 15 and then add a zero, that’s still 15. Let’s take some time to explore and understand what is really happening here. 

Small classroom behaviors are often indicative of deep-rooted mindsets about learning, especially when it comes to learning mathematics. Addressing behaviors without understanding and addressing belief systems is like putting a band-aid on a broken leg. I’ve suggested a few ways that teachers can counter-model unproductive beliefs about teaching and learning mathematics. In the spirit of not being done, I invite you to share your thoughts and ideas…

  • Maybe you use some of these techniques. What impact do these teaching moves have on student thinking in your classroom?
  • Maybe you have some classroom-tested teaching moves that counter-model unproductive belief systems. How do you use these techniques? What is the impact on student thinking?

References

Baroody, A. (2006). Why children have difficulties mastering the basic number combinations and how to help them. Teaching Children Mathematics, 13(1), 22-31.

Dowker, A. (1992). Computational estimation strategies of professional mathematicians. Journal for Research in Mathematics Education, 23(1), 45-55.

Dweck, C. (2006). Mindset: The new psychology of success. New York: Random House.

Fosnot, C. & Dolk, M. (2001). Young mathematicians at work: Constructing addition and subtraction. Portsmouth, NH: Heinemann.

Kamii, C. (2000). Young children reinvent arithmetic: Implications of Piaget’s theory (2nd Ed.). New York: Teachers College Press.

Resnick, L., and Hall, M. (2005). Principles of learning for effort-based education. Pittsburgh, PA: University of Pittsburgh.

tagged fact sheet, math
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