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!

References:

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Unpublished videotaped lecture presented to T.C. O’Brien’s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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Mathematical Disposition: More than an attitude (using guided math groups to foster the many aspects) Part 4

Posted on October 19, 2010. Filed under: Assessment, Classroom environment, Guided Math Introduction, Mathematical Proficiency | Tags: , , , , , , , , , , , , , |


Much has been written about mathematical dispositions or ways of thinking and being NCTM (National Council of Teachers of Mathematics, 1989, 2000) and others (e.g., Maher, 2005; De Corte, Verschaffel, & Op’T Eynde, 2000: Polya, 1969).  The research tells us that mathematical disposition is much more than an attitude.  It is about ways of thinking, doing, being and seeing math.  It includes confidence, flexibility, perseverance, interest, inventiveness, appreciation, reflection and monitoring (Merz, 2009).

Given that, how do you cultivate each one of these in your class?

  1. What do you do to boost students’ confidence?  Name 2 things.  What could you do? Name 1 more.  How might you do this in a guided math group?  Since you only have a few students in a group, you can attend more individually to each one.  One way to do this is to give problems that they can do.  Success breeds success and confidence.

2. What do you do to help foster flexibility? This idea of thinking in many different ways?  Do you engage in ongoing strategy talk?  Do you have a culture of sharing in your class that goes beyond the answer but talks about how people got the answer or didn’t get it?

3. What do you do to build perseverance?  How do you teach that?  How do you do that?  So that students’ perseverance levels increase over time?

4. What do you do to spark interest?  How do you connect math to their lives? Where is the math in Pokeman or Dragonball Z?

5. What do you do to encourage inventiveness?  Do we publicly celebrate inventive thinking?  How do we get our students to think hard about the math their doing and take risks?

6. What do you do to cultivate appreciation of math?  Do you make connections to real life situations that are important to them so students see that math really does matter?

7. How often do we get them to reflect about the math they are learning?  Do we consistently use entrance and/or exit slips so they can think about their learning? Do we use individual pupil responses like thumbs up, thumbs down or sideways to check in with them?  Do we use red, green, and yellow slips so they can give us immediate feedback about speeding up the lesson, slowing down the lesson or stopping to explain further?  Do we ask them to do oral and or written reflections on their quizzes and tests and make plans to learn what they are still struggling with?  You can do this in small guided math groups! This is an excellent space for these types of discussions.

8. How do we get student’s to monitor their learning?  Do they have action plans that they reflect on?  Who is responsible for knowing where they are?  Just us?  Think about how powerful it would be if they knew too! And if their parents knew, more than just a few times a year.  The more people who know, the more likely the student is to get there!  Think of the power of everybody being on board.  What does a consistent inclusive monitoring system look like?

References:

Alice Merz

Journal of Educational Thought
Vol. 43, No. 1, 2009, 65-78.

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5 Steps to Teaching Math Greatly

Posted on May 29, 2010. Filed under: Uncategorized | Tags: , |


1.  Enjoy it. Find the fun in numbers.  Because if you Don’t, your students NEVER will:)

2. Learn it. (Study, buy the algebra book or the geometry book….by it in cartoons, buy it in the “for dummies” series,but it in the “painless” series, buy it in the middle school version, however you can get through it…but by a content strand at a time and master it).

3.  Find a great, fun, engaging way to teach it.

4.  Go to a math conference (local, regional, state, or national) http://www.nctm.org/meetings/

5.  Commit to “stretching your own pedagogy,” –often.

See some of the books:

http://books.google.com/books?id=nM9aj9wiMSUC&dq=painless+fractions&printsec=frontcover&source=bn&hl=en&ei=#

http://books.google.com/books?id=bFj3ZWxNkgIC&printsec=frontcover&dq=geometry+the+easy+way&ei=f0cBTPL4MYnazQS_x7CmDA&cd=1#v=onepage&q&f=false

http://books.google.com/books?id=sjKR7Rqt12kC&printsec=frontcover&dq=algebra+for+dummies&ei=oUcBTJfXNI7YywTH6fD8DA&cd=1#v=onepage&q&f=false

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Teacher’s Role in Guided Math

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


The teacher puts up a Math Schedule so that students know what they are doing that day during math workshop.  Teachers schedule various groups in different math centers and usually two groups a day for guided math lessons.  During guided math lessons, the children meet in small groups for explicit math instruction based on specific content, strategies or skills.  The teacher introduces the content for the lesson.  The children discuss the content.  The children engage in a mathematical activity around the content. The children then discuss the activity in detail.  The teacher then summarizes the learning for the day and then the children return to their desks.   The teacher scaffolds the lessons so that children become competent, confident, flexible mathematicians.  Teachers need to create a non-threatening, supportive learning environment. 

Guided Math provides the necessary opportunity for teachers to explicitly teach math content, strategies and skills at the students’ individual levels.  During this group time, teachers review, reinforce, reteach and practice mathematical ideas, concepts, strategies and skills.  Developing mathematicians must have multiple opportunities to work with numbers in non-threatening environments and to make sense of their meaning by engaging in scaffolded discussions about them.  Guiding students to think mathematically takes planning, persistence and time to practice.

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