Teaching staying power, sticktoitness and the right attitude: Mathematical Disposition and Guided Math Lessons (Part 5)

Posted on October 20, 2010. Filed under: Assessment, Classroom environment, Guided math, Mathematical Proficiency | Tags: , , , , , , , , , , , , |

Polya (1969) [the grandfather of problem solving] states: This is the general aim of mathematics teaching – to develop in each student as much as possible the good mental habits of tackling any kind of problem. You should develop the whole personality of the student and mathematics teaching should especially develop thinking. Mathematics teaching could also develop clarity and staying power. It could also develop character to some extent but most important is the development of thinking. My point of view is that the most important part of thinking that is developed in mathematics is the right attitude in tackling problems, in treating problems. (Part II, pp. 5-7) (cited in Merz, 2009).

Polya provokes us to think about what we do everyday.  He says that we are charged with developing in students ” the good mental habits of tackling any kind of problem.”  We have to come up with rich math tasks so students can engage in this type of thinking.  And, dare I say most of those types of problems are not on page 47 in problems 3-10:)  Real problems, with real contexts helps students to see that math is a real subject.

What do you think of his statement that we should “develop the whole personality of the child and math should develop thinking?”  This idea makes math class look very different from many teach, test and move on scenarios.  If we are teaching to develop personality and thinking, then what on earth does that look like?

Polya goes on to state that teaching math is about teaching character, staying power and the right attitude.

Let’s all think about how we write that into our lesson plans!


Merz, A. (2009). Teaching for Mathematical Dispositions
as Well as for Understanding: The Difference Between Reacting to and
Advocating for Dispositional Learning. Journal of Educational Thought
Vol. 43, No. 1, 65-78.

Polya, G. (1969). The goals of mathematics education. Retrieved March 3, 2005, from http://www.mathematicallysane.com/analysis/polya.asp.
Unpublished videotaped lecture presented to T.C. O’Brien’s
mathematics education students

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“Hard fun!”- Guided Math is a Space to Push Thinking!

Posted on June 25, 2010. Filed under: Classroom environment, Elementary math | Tags: , , |

Papert (1996) tells the story of an exchange between two kindergarteners while exiting the computer lab.  One student was exiting with their class and the other was entering. 

        “[Upon exiting the child waiting to enter asked] “What was it like?” The friend replied, “It was   fun.”    Then paused  and added: “It was really hard.”  The relation between “fun” and “hard” may need some interpretation.  Did this mean “it was fun in spite of being hard” or “it was fun because it was hard”?  The teacher who heard the tone of the conversation and knew the children had no doubt.  The child meant it was “fun” because it was “hard.”  Since then I have listened to children with an ear sensitized by this experience and have come to know that the concept of hard fun is widely present in children’s thinking (Cited in Andrews & Trafton, 2002).”

This passage provokes me to think about the type of “hard fun” which we engage children in during math class.  Hard fun is academically rigorous tasks that engage the whole child.  When students are having “hard fun” both their hands and their minds are engaged. When students are having “hard fun” they are doing rich mathematical tasks that push them to reach and learn.  When students are having “hard fun” they laugh, they communicate and they struggle through the difficult parts hanging onto all the scaffolds we set up.

Andrews, A. & Trafton, P. (2002) Little Kids-Powerful Problem Solvers. NH: Heinemann

Papert, S. 1996. The Connect Family: Bridging the Digital Generation Gap. Atlanta: Longstreet.

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What they think

Posted on May 26, 2010. Filed under: Uncategorized | Tags: , |

It ‘s really important what students think about themselves, about us and about each other.  Students should think they can. Really.  Just like the choo choo train did.  The research shows that if they they can, they’ll keep trying until they do.  Resnick (1999)wrote a great article about the conceptualization of “smartness” in America (see reference  below).  If our students really believed they could, with the correct instruction and encouragement, they would.  

Furthermore, the recent  National Math Report (2008) states that what children believe about what they can do matters.  It matters in a big way.  It discusses how when children believe in themselves, they  try harder, they put more effort into learning math and that effort increases their engagement, which in turn raises performance.

They would be able to do so much more than we can even imagine.  Moreover, if they thought that we were really on their side, batting for them, cheering them on, searching every kind of way to help them learn it (whatever “it” might be); if they were truly convinced that we were there to teach them until we reach them, they’d try harder too.  Finally, if they became cheerleaders for each other as well, really concerned about the learning of each other– helping each other and encouraging each other…they’d do better.  I really believe they’d do much, much much better:)






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Student’s Role in Guided Math

Posted on January 18, 2010. Filed under: Guided math | Tags: , , |

Students should come to the group prepared to participate.  They are to pay attention, engage in the discussion with their teacher and their peers.  Do the math.  Try new ways of doing things.  Talk about their learning with their partners and their teachers. Ask questions when they don’t understand.  Explain concepts, strategies and skills to their peers when they do understand. Continue working on the particular concept, strategy or skill, during center time and at home.

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