OK

----------
>From: "Stinson, Mary Jane" <[log in to unmask]>
>To: 'Jim Abrams ' <[log in to unmask]>
>Subject: RE: [MLMATHNET] problem solving
>Date: Tue, Apr 11, 2000, 9:26 PM
>

> Excellent ideas!
>
>Mary Jane Stinson
>Folsom Educational Center
>South Hero
>
>-----Original Message-----
>From: Jim Abrams
>To: [log in to unmask]
>Sent: 4/4/00 4:56 PM
>Subject: [MLMATHNET] problem solving
>
>I am convinced that improving problem is possible within the context of
>virtually any math lesson.  I would like to hear responses to the
>comments
>below from other math teachers.    Sue Abrams, VISMT
>
>At the heart of improving problem solving is providing ALL students with
>opportunities to engage in problem solving on a daily basis.  While we
>all
>recognize the importance of having our children solve rich open-ended
>problems such as those we use as portfolio tasks, we may not recognize
>that
>can help develop problem solving skills in our students EVERY DAY  if we
>create an atmosphere in which ALL students regularly
>
>    * make their own observations, however insignificant (and hear the
>    observations of classmates)
>
>    * probe their own reasoning (and that of others)
>
>    * make and test their own conjectures (and test the conjectures of
>others)
>
>    * synthesize the big math ideas that are at the heart of each lesson
>
>
>Specifically, we classroom teachers can make each day rich in problem
>solving
>if we do the following:
>
>1.  Have students write -- or in some way note -- observations before
>sharing
>with a partner and/or the whole class.
>
>2.  Pause...twice (once after asking the question; then once after an
>answer
>
>is proposed)
>
>3.  Avoid praising correct answers or even saying "right"  (This does
>NOT
>mean letting students think that any answer is OK, however.)
>
>4.  Model problem solving ourselves.  (First I noticed that...; then I
>tried...., but I knew it wouldn't work when....; so I decided....)
>
>5.  Have regular experiences where each child synthesizes his/her
>learning.
>
>(reflective writing, think/pair/share, end of class "mathematicians
>circle")
>
>6.  "Un"scaffold the lesson to create richer problem solving
>possibilities
>(more important in some published programs than others)
>
>
>7.  ASK "GENUINE" QUESTIONS and MAKE COMMENTS THAT INVITE DEEPER
>THINKING
>(Keep in mind that DISEQUILIBRIUM is needed for meaningful new learning
>to
>take place.)
>
>* Why? / Why not?
>
>* Help me understand ...
>
>* Tell me more ...
>
>* Hmm ...
>
>* Convince me ...
>
>* What do you notice / observe?
>
>* I see that you look (puzzled).  What are you wondering about /
>thinking?
>
>* What if...? / What if ... not ... ?
>
>* We have (several) solutions here.  I am confused ...
>
>* When you said / did ..., tell me what you were thinking.
>
>* How is this like / different from...?
>
>* Will that always work?  Why / why not?
>
>* What questions do you have for (John)?
>
>* What are your questions?  (Then answer with a question.)
>
>* Describe what YOU think (Beth) is saying, and ask her if you are
>correct.
>
>* (Jenny), perhaps you can help me understand what (Joey) is saying.
>
>* How many ways can you ...?