This is great and I absolutely agree! Problem solving skills need to be
developed in all content areas and many of these tips and strategies
would apply to other types of problem solving( as applies to other
content).. science inquiry, investigation of community social issues,
mediation of social issues at school on the playground, etc. At Oxbow
high School we are in the beginning stages of designing a cross content
area problem solving program and your comments will be useful as we
think and design what might work. Any other suggestions would be
greatly appreciated. Any schools that are designing programs and
professional development around cross content problem solving
strategies, I'd love to hear from you. It seems to me that we should be
able to connect some of the evidence of math problem solving, science
investigation etc. so that we have some common language and criteria to
help keeps see the connections between these processes.
Jim Abrams wrote:
> I am convinced that improving problem is possible within the context
> virtually any math lesson. I would like to hear responses to the
> below from other math teachers. Sue Abrams, VISMT
> At the heart of improving problem solving is providing ALL students
> opportunities to engage in problem solving on a daily basis. While we
> recognize the importance of having our children solve rich open-ended
> problems such as those we use as portfolio tasks, we may not recognize
> can help develop problem solving skills in our students EVERY DAY if
> 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
> • synthesize the big math ideas that are at the heart of each
> Specifically, we classroom teachers can make each day rich in problem
> if we do the following:
> 1. Have students write -- or in some way note -- observations before
> with a partner and/or the whole class.
> 2. Pause...twice (once after asking the question; then once after an
> is proposed)
> 3. Avoid praising correct answers or even saying "right" (This does
> 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
> (reflective writing, think/pair/share, end of class "mathematicians
> 6. "Un"scaffold the lesson to create richer problem solving
> (more important in some published programs than others)
> 7. ASK "GENUINE" QUESTIONS and MAKE COMMENTS THAT INVITE DEEPER
> (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 /
> • 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
> • (Jenny), perhaps you can help me understand what (Joey) is saying.
> • How many ways can you ...?