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Focus on Teacher and Student Mathematical Understandings

Improvement in teachers' practices requires a greater understanding of mathematics content. Recently, some have made the case for pedagogical content knowledge; that is, it is important that what the mathematics teachers learn is intimately connected to the mathematics they are teaching to their students (Ball & Bass, 2000; MA 1999). Two processes for teacher change that have been shown to be effective in mathematics education will play a central role in the professional development model (Ball, 2000; Ball, 2003). The first is the opportunity for teachers to do mathematics themselves where the emphasis is on learning with understanding. Thus, institutes and teacher meetings were structured in ways that asked teachers to be learners. The second is the opportunity to conduct close examination and discussion of student work. Regular teacher meetings and postings to a discussion board provided vehicles for this examination and discussion.

Pedagogical Goals of TIAN
  • Work collaboratively on open-ended investigations
  • Share strategies and understandings orally and in writing
  • Justify answers in multiple ways
  • Use contexts that are meaningful to adults
  • Encourage various ways for entering and solving problems
What Happened in the Classroom

Work Samples from TIAN Participants

In both the pilot test in Massachusetts and Ohio and the field test in Arizona, Kansas, Louisiana, and Rhode Island, the 20 teachers from each state developed work samples from their students' work in their classrooms in Data and Graphs and Algebra. The Work Sample is a tool for helping bring together in a meaningful, coherent way planning, instruction, and assessment that fosters student learning. It represents the kind of planning, implementation and assessment that should be ongoing in the classroom, although it may not always explicitly detail the teacher's actions.The work sample includes: 1) description of the classroom context and students being taught; 2) description of the classroom activity; and 3) the collection, interpretation, and reflection upon evidence of student progress toward attainment of the desired learning outcomes.


TIAN Participant Work Samples

(click each lesson to open)

Data and Graphs Lessons in the Classroom

Algebra Lessons in the Classroom