MATHEMATICS

Rabu, 17 November 2010

To Understand, Book Club 3

Ellin Oliver Keene
Today my preservice K-8 teachers are discussing Chapters 5 and 6 in To Understand.  I gave them four focus questions to try and help guide discussion:
  1. What is the author's main point in the chapter?
  2. How does she support that point?
  3. How does this idea apply in mathematics?
  4. What's your reaction or connection with this.
Chapter 5 - To Savor the Struggle
Mentor: Reynolds Price, author and poet who has written and spoken eloquently about his response to an inoperable spinal tumor, as well as just been more artistically productive than he was before.  (Sample of his poetry available at Google Books: The Collected Poems.)  What enables some people to flourish in adversity?

  • Greatest gift to a student is the experience of struggle leading to understanding.  We don't do it in younger grades; students may not experience struggle till college.  
  • Intentional struggle for students requires time and modeling.
  • Teaching kids how to learn to think more critically requires struggle, versusthe students just doing without reflection.  In math, struggle leads you to know why you're solving, and where the answer comes from.
  • Part of conceptual understanding is problem solving.  If it's too easy there's no problem solving.  Struggle requires problem solving.
  • How do you motivate students to struggle?  They'll sit there until someone else does it.  One student, or the teacher, or.. (several stories to back this up).
  • Once you get them willing to struggle, then they can gain understanding.  They will know why they got that answer.
  • A lot will blow off the work b/c of the struggle.  They didn't have a need to struggle until college.
  • When you conquer through struggle you're more likely to remember how, remember your process, and be able to use it again.
  • Does more struggling now mean less struggling later?  It means you will be less frustrated with struggle later.  Got through it, rather than going through it.  
  • Frustration is a problem.  You have to continue to struggle to add new understanding.  My elementary struggles make me able to struggle for a long-time now.  
  • With struggling comes a work ethic.  It was a shock in college to have to learn to do the work.
  • Struggle motivates me to want to figure it out.  
  • How much is too much struggle?  Different for every student.  Know your students and differentiating.
  • Mixed emotions.  Why don't we want to find a way to prevent struggle, for them to get it without struggle.  What happens in real life?  Remember waiting for others to solve and just get this lab done; later on, on my own, I had to do it for myself.  Want our students to get content, but more so to be able to solve their real problems in life.  They will have struggles, I want first struggles to be in the safety of my classroom.  Help them now or help them later?
  • Isn't a struggle enough now? Some of the kids struggling will ask, but some just shut down.  Do nothing.  How motivated is each student? 
  • Why don't we have leveled math problems like leveled readers?
  • How does it happen - when a student moves from resisting to engaging struggle? 
  • If you create struggle, what about that 10% that cannot even begin.  Everyone's different. 

She discusses these systems in literacy instruction, and I think it would be worth investigating in math.
  • Semantic System - word meaning and use
  • Schematic System - process focus on what it means to read
  • Pragmatic System - what do you do with the content

Leonardo's horse at Meijer Gardens, Grand Rapids

Chapter 6 - A Renaissance of Understanding
Mentor: thinkers and artists of the renaissance.  Considering the idea of intellectual liberation.  What conditions are necessary for a renaissance?
  • Allow the students to go beyond your expectations.  Challenge my students.  A teacher who designed tests so no one could get an A - that's not challenge.
  • Be interesting to see reading levels transferred to math.  A math corner... and then science.  Time and effort from teachers too much?  Maybe they don't have the background to do it.
  • Choice is a part of the answer to this.
  • The title renaissance: something new.  The testing is a problem because it's based on a norm.  Students should be awarded for original thinking.  Writing you can imagine this.  What is it like in math - original thinking?
  • Grading is fear inducing, restricts creativity.  Especially when it rewards conformity.
  • Are you going to take the classes where you struggle, or where you can get an A.  It looks good on your GPA.  Could grade technical difficulty and performance.

In this chapter she considers the importance of text and genre in literacy instruction.  What are these things in mathematics?  Is it our content areas?  Problem types?  Different processes?  Different uses like investigation, homework, tests?

The Chapter 5 discussion was energetic and purposeful.  Definitely one of the reasons to use this book.

Photo by cliff1066 @ Flickr

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