Friday, November 12, 2010

Response to "Creativity, flexiblity, adaptivity, and strategy use in mathematics" by Christoph Selter

When my children were toddlers, my mom (a wise grandma) would always complement them whenever they are able to take one basic skill and apply it to another area of life.    She used the term "ban jia",  which means in Chinese "move to a different home".    Now that I am in teacher education,  I look back and recognize that this ability is a nice thing to complement a child for ... well, most of the time.

Once my 3-year old son saw a gorilla standing all alone in the corner of the zoo compound.   He said sympathetically,  "Look Mama,  that grandpa monkey is having a time-out!".     For my son,  he was learning how to  adapt  his knowledge of the "time-out" strategy (someone standing in the corner alone) to describe that gorilla in the zoo.  At the same time, he was trying to describe the gorilla based on his previous knowledge of what a monkey and a grandpa looks like.

Using "creativity",  "flexiblity",  and "adaptivity" to learn is a natural part of how human beings shape their understanding of the world.     We often see that in young children.     I guess you can call it a form of educated-trial-and-error.    When children make mistakes whereby the strategy they have chosen does not "solve the problem",   adults think it's cute and laugh about it.   However when adults make mistakes we are in danger of not being able to reverse out of a certain mental mode,  which could lead to frustrations of being unable to solve the problem.  

I was talking to a grade 9 math student recently who said he does not like substitute teachers.    So naturally,  I asked him "why?".      One reason is that substitute teachers might show them how to do a problem using another technique that is different from what his teacher has used.     Maybe he was so focussed on his old method,  that a new method disturbed him.   That's too bad.

As teachers,  we should frequently emphasize to students that are are many ways to approach a problem.    If we can illustrate the value of being open to adapting different strategies,  our students will be able to extend their problem solving skills far beyond the classroom.     Our mathematical training should equip us to solve not just text-book, but real-life problems.

In our UBC math education class,  I have come to appreciate the way we examine different ways of solving the same puzzle on the board.    It has illustrated to me the incredible value of being creative, flexible, and adaptive when chosing a strategy to solve problems.


  1. I like your perspective as it relates to children and have noticed that in my own children as well. They make amazing connections between the new things they see and what they already know. It is a natural part of making sense of the world. However, like your 9th grader, it does seem as kids get older, they are more rushed to just get to an answer. Maybe it is because they are afraid of looking stupid or being wrong OR maybe they always feel in a hurry. As teachers, we need to try and find ways to make more space and time for making connections and also provide a safe environment where they can freely express themselves.

  2. Thank you Carly for this insightful response. The funny thing is that the skill I need to work on the most in my teaching I feel, is my ability to see solving a problem in a variety of ways. I am a result of this school system. Through reflection I realize I am scared of the unknown and veering of my solution path. Math learning has been so structured to be a commitment to finding the right answer, and thus I feel the value of getting to the answer has been lost. As teachers we need to stop, listen and be less afraid of being wrong, so that students can have an example to follow. I see the grade 9's difficult with the Substitute Teacher in two different ways. The students can not see a new way of thinking, and also the substitute can't show a different way of thinking. Thus in a way to change students attitudes we have to be careful as what we portray as teachers.

  3. Hi Carly,

    Your story about the grade 9 student really got me thinking. I hear this type of comments a lot, too. In fact, it makes me realized that when I used to tutor math I often would ask my students how their teachers do something. I did because some teachers prefer to do things a certain way, but this seems to contradict with the idea of encouraging multiple ways of thinking. Also, the learning of mathematics in our school system is so curriculum driven, and students usually just want to find the right answer. It will be a challenge for all of us to promote creativity, flexibility and adaptivity, but it's a worthy goal.


    P.S. I love your personal story about your son! :)