What+is+great+math+teaching?

=Please give your opinions about what great math teaching is. This will help ensure that when we have a webinar or telephone discussion that we've thought carefully about what we want to see in our schools.=

__Again, a few of Marcy's ideas just to start:__ I usually look at what the students can do after a lesson as much as what the teacher does during the lesson. Are the students able to read math contexts and problems by themselves? Can students discuss - and even argue - about math in small groups? Are students capable of estimating with ease, using basic "facts" fluently, and able to handle a variety of math tools, i.e. compass, ruler, protractor, calculator, computer programs?

Please add your ideas here: (Just hit "edit this page" and when you're done be sure to hit "save.")

I've been focusing a lot on culture in my thoughts, currently, and on paper soon. How do you describe a classroom environment that celebrates the //process// of learning math in terms of feeling free to think about patterns and solutions rather than celebrating the "right answer?" In my mind, this question sums up the culture of the classroom place in the terrain we are creating and addresses the flow of events leading to the learning outcomes outlined in Marcy's previous statement. Many things are included in this one question, such as safe space, collaboration, engagement, and the list can probably go on...How is this summarized in a comprehensible manner for a single-page terrain document? stef

Stephanie -- Thanks for sharing some of your thoughts. There is, indeed, so much packed into this one little question -- yet this is the question that I believe truly needs to be answered -- at least from an ELS perspective. When big rifts occur between & among groups working to improve math, I've found that the factions often have very, very different ideas about what "great math teaching" is! Marcy

Hi, ALL! I've been thinking about the nature of mathematics and what implications that has for the way math is taught. Do we need to define/clarify our own thinking about mathematics? Some of what I'm reading says mathematics is the science/art of patterns, relationships, order in our universe. Mathematics gives use the tools to think, examine, explore, reason --to dissect, describe, define, explain, connect, manipulate, find parameters --about phenonena that occur in our world. Moreover, mathematics gives us a language to talk about absractions within mathematics. So, do we need to look at mathematics wholistically -- provide a working definition for our teachers -- before we take it apart and chunk it into stands, steps, processes, etc.? Somehow what we frame has to overcome misunderstandings, misrepresentations, and cultural stereotypes and fears about math -- for teachers, School Designers and students. More than any other discipline, we seem to have a culture to overcome as well as to build. BIG TASK! Nan _________________________________________________________________________________________________ Somemore Terrain thoughts from Nan having looked at the other terrains: Possible catagories (boxes) we need: Definition of Nature of Mathematics...................... Ways of thinking/reasoning -- Logical, visual, spatial, inductive, deductive, connectional.... process+ product!................ Disciplinary techniques -- inquiry tools: read write draw model experience explain discuss defend clarify: use comprehension stategies........................ Teaching structures -- 5 Es. workshop model inquiry.................. Strands -- number and operations, algebra, geometry, measurement and data analysis, probability and statistics Culture of the Classroom -- safe, collaborative, challenging, open for discussion and exploration................... Character Traits needed for success -- perseverance, collaboration, having of wonderful ideas, success, failure, tolerance........ Assessment FOR/OF -- see assessment terrain...................... Nan _____________________________________________________________________________________________

MORE THOUGHTS: another way of looking at what great teaching will give to students. -- Tom Post uses this way to describe success in mathematics "Mathematical proficiency has five components or strands:	1. conceptual understanding—comprehension of mathematical concepts, operations, and relations	2. procedural fluency—skill in carrying out procedures flexibly, accurately, efficiently, and appropriately	3. strategic competence—ability to formulate, represent, and solve mathematical problems       4. adaptive reasoning—capacity for logical thought, reflection, explanation, and justification	5. productive disposition—habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in     diligence and one’s own efficacy. These strands are not independent; they represent different aspects of a complex whole." He talks about "braiding" these together as Hyde does with comp. strategies.

Nan