Encouraging Mathematical Thinking


 Abstract
 Introduction

 Discourse
 Interventions
 Decisions

 Cylinder Problem
 Lesson Reflections
 Student Predictions

 Project Reflections
 Conclusion

 References
 Acknowledgments
 Teacher Resources



Authors'
Biographies

Table of Contents


VIDEO CLIPS: Internet access via modem may mean very long download times for video clips. If you are not on a fast line, you may want to read this paper without viewing the clips.

 
Biography


 Susan Stein       [Project Reflections]

School type independent Quaker school
Student population mostly white; upper middle- and upper-SES.
Grade level I teach seventh grade and one section of eighth grade.
Subjects Math 7 and Eighth Grade Algebra 1 (This was the class video taped.)
Student ability range Students are admitted partly based on test scores, so most students are above the 50th percentile. In addition, students are grouped into advanced and regular sections for mathematics. The Algebra 1 class was a "regular" section.
Class sizes 20 students
Administrative support The administration has been consistently interested in learning more about mathematics education and how it has changed in the last 10 or 15 years. As most of them are former History or English teachers, they are particularly excited when they recognize that mathematics education is becoming more interested in developing a student's ability to make sense of mathematical ideas and connections between ideas by explaining their reasoning orally and in writing. What seems to constrain us is that a need to communicate to our wider community how changes in curriculum and pedagogy will still provide our students with superior skills and knowledge of procedures in addition to any problem-solving and higher order reasoning skills they may acquire.
Curricular reforms I use CMP (Connected Math Project) in seventh grade & we're using a combination of CMP, CORE PLUS and a traditional text (McDougal Littell) in the Algebra 1 course. We may be moving to greater use of CORE PLUS or CMP next year, but those decisions have not been made yet.
Technology used in class TI 83 calculators are introduced in 8th grade. There is just about no computer use in class. Students are expected to work on several Math Forum PoWs per year as out-of-class assignments.
No. years teaching
experience
I began teaching in 1968, and teaching mathematics in 1984. (Before that I taught English and Social Studies, grades 9 - 12). I've taught Middle & Upper School math (one year) and I was a Lower School math coordinator for two years. I am currently Mathematics Department Head at Wilmington Friends.
Internet experience I use email and have been known to use the Internet for information searches, but I don't like to surf. I get lost in and frustrated by its non-linearity.
Professional goals I would like to help the wider community - not just the school community, but others -- understand that demanding that our students make sense of mathematical ideas does not replace the basics as we were taught them when we were children. Rather, it expands those basics to include more than facts and procedures, to include an ability to solve complex problems based in real contexts, make connections between mathematical ideas, and communicate mathematical reasoning using words, symbols and other mathematical models.

On a personal-professional level, I always want to improve my teaching. One goal I have for my classes is to find ways to support my students as they make a bridge from mathematics as the discipline of the "give me the rule and I'll give you the right answer," to the "problem-solving, reasoning, and explaining how I make sense" course. In addition, I would love to be able to work with pre-service teachers more than I do now.


   


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