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Knowing and Learning Mathematics for Teaching Proceedings of a Workshop (2001) / Chapter Skim
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Pages 131-136

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From page 131...
... SUMMARY OF THE MAIN POINTS OF DISCUSSION Recurrent tasks of teaching that require the use of mathematics identified by our group included uncovering students' current base of knowledge and the common base of knowledge shared by the class; assessing the "generality of knowIedge," i.e., knowing where a mathematical concept fits into a sizeable, interrelated body of knowledge; · selecting worthwhile tasks designed to provide experiences with fundamental concepts and techniques, active student participation, and abundant opportunities for students to make (liscoveries. As we began unpacking our own knowledge of recurrent tasks of teaching, we a(l(lresse(1 the question, 'what is a worthwhile task?
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From page 132...
... As we came back together after attending various breakout sessions, we synthesized the ideas and discussions of those various breakout sessions into our small-group discussions. We began to discuss "the mathematics of teaching"how our knowledge of mathematics influences the ways in which we assess our students, evaluate programs, assign gra(les, use a rubric, choose textbooks, envision a course, design a lesson, and select mathematical tasks for investigation.
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From page 133...
... What mathematical content knowledge is needed to make good (recisions? What (lay-to-(lay tasks anti (recisions are (difficult for teachers to make when they lack specific mathematical knowledge?
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From page 134...
... · Remodeling mathematical tasks. · Selecting mathematical tasks that will yield the best results for student learning.
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From page 135...
... Then after using the assessments, discussions could focus on what QUESTION # 1 next steps could be taken to further students' mathematical understanding based on the results. Methods courses and field experiences, as well as content courses, should be examined to determine whether there is a better way to help prospective teachers make a connection between their mathematical knowledge and the recurrent tasks of teaching such as we explored during the sessions.
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From page 136...
... REFERENCE Ma, L (1999~. Knowing and teaching elementary mathematics: Teachers' understanding offundamental mathematics in China and the United States.
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Key Terms

  • mathematical knowledge
  • mathematical tasks
  • content knowledge
  • student learning
  • mathematical content

  • methods courses
  • mathematical topics
  • student thinking
  • knowledge packages
  • various breakout

  • preservice teachers
  • breakout sessions
  • provide preservice
  • assessment strategies
  • worthwhile mathematical

  • analyzing student
  • particular topic
  • assessing student
  • prospective teachers
  • explain subsequent

  • classroom practices
  • preservice teacher
  • specific mathematical
  • examining assessment
  • implied examining

  • managing class
  • mathematics influences
  • strong relationship
  • using information
  • connect mathematical


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