Tuesday, November 2, 2010

Powerful Learning in Math and Science

(This blog today is part of a school assignment)

The book Powerful Learning by Linda Darling Hammond delves into the area of teaching for real understanding.  Chapters 2 and 3 focus on this understanding in math and in science.  Chapter 3, "Mathematics for Understanding" by Alan H. Schoenfeld explains how math needs to be presented to a learner in order for real understanding to happen.  The first, most important thing to happen is for students to begin to make sense of the information.  Students need time to play and manipulate and explore using the mathematical phenomena in order to begin to make sense of the topic being presented.  Schoenfeld calls this an "interaction with the content"  that is very different from the traditional practices of mathematics teaching.  Discourse and questioning, along with writing and proving what they know is imperative for children to develop deeper mathematical understandings.  Rote learning has its place in mathematics for sure.  Knowing basic facts and how to apply them is of great importance.  Students though need a deeper understanding of the rest of the mathematical concepts.  Not having an understanding of the underlying principles, the how and the why in a math concept is like a house not having a foundation.  There is no strong footing to build upon.  It may stand for a while on top of the soil, but when the rains come, the house, (and the knowledge) will be sure to wash away.  If they do have a firm grasp of the underlying principles, then no matter what type of problem is before them, the student will be able to find a way to make it work.

Schoenfeld cites a TIMSS study that countries who place a "greater focus on the conceptual underpinnings of the mathematics"  were higher achieving.  An emphasis on one or two problems during a class period leads students to more in depth thinking.  I have seen this in my classroom.  Student discussion when faced with a multistep, open-ended problem is richer and more focused than when completing a basic word problem.  Students rise to the challenge and relish the opportunity to try and prove they can succeed.

A strong conceptual understanding and opportunities to communicate those understandings in a variety of ways will lead to more improved, confident math students.  These can be taught in tandem with basic skills.  It is our job as teachers to begin to make this not so subtle shift for the benefit of our students.  As a result our teaching will greatly improve, because we are forced to think and teach in new creative ways.  Having the opportunity to work closely with colleagues to develop and implement these new "topic areas" will lead to better teaching.  Having a "continuity of focus" in workshops or Professional Learning Communities on these areas will lead to better practices.

Teaching Science for Understanding apples many of the same principles as teaching math for understanding.  An inquiry based approach is the best, most effective way to teach science for understanding.

Students come to school with some facts that may be accurate or inaccurate.  The need is to help change those misconceptions.  Then making "connections among the facts"  is vitally important to help student understandings.  Deeper questioning and investigation, along with allowing students the opportunity to explore and find information independently creates opportunities for them to be self-directed, self-motivated learners. Working together with peers in science to develop an inquiry investigation helps to increase their scientific knowledge.

As in math, "understanding any concept requires processing prior knowledge and ideas and incorporating them into a broader knowledge base".  Time and deep, rich activities allowing for discourse and student  interaction help foster this powerful knowledge.

As a teacher, science has been the one area I have feared the most.  Teaching in the traditional fact based manner, followed by quizzes and tests if how the past fourteen years of teaching been conducted.  Students have not been learning.  They  learned for the bit of time they needed the information, but that knowledge often evaporated over time.  Attending inquiry training and beginning to teach in a new way has made teaching science fun and exciting.

The four areas that Zimmerman and Stage see as being most important are:

Making Science Accessible

Making Thinking Visible

Helping Students Learn from Each Other

Promote Lifelong Learning Through Reflection

Science teaching needs to change for these important pieces to happen. Unbelievable things will happen as a result.  Students will be more confident, better thinkers, collaborators, writers, and students.  Teachers will be more confident, better questioners, and more reflective in their practice.  Students will then be able to bring this large knowledge base of skills and concepts, not necessarily facts along with them.  Hopefully the successive teachers they encounter will begin to change their practices as well.

I am excited and hopeful that these changes will happen. I am beginning to see this transformation in my classroom...and I like it!


  1. Tim, at this very moment there is a huge controversy brewing over teacher professional development. The superintendent handles it by stating that 3rd grade teachers were recently in-serviced on the distinction between 'your' and 'you're'. Unbelievable! If she had issued a statement similar to your blog post, she would have accomplished so much more. With your permission, I'd love to use some of what you've written for an upcoming Newtown Patch piece. Then maybe the public would understand.

  2. George, that is fine with me. Hope all is well with you!