The Effects of Teachers' Knowledge and Understanding of Addition and Subtraction Word Problems on Student Understanding

Open Access
Author:
Lunt, Jana
Graduate Program:
Curriculum and Instruction
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
December 14, 2009
Committee Members:
  • Glendon Wilbur Blume, Dissertation Advisor
  • Glendon Wilbur Blume, Committee Chair
  • Rose Mary Zbiek, Committee Member
  • James F Nolan Jr., Committee Member
  • Bernard Joel Badiali, Committee Member
Keywords:
  • teacher knowledge
  • student understanding
  • cognitive demand
  • word problems
Abstract:
This study examines the influence of teacher understanding on student understanding through teacher practice. Three elementary school teachers participated in a university course that discussed mathematical and pedagogical knowledge regarding addition and subtraction word problems. Data were gathered from the course, teacher interviews, classroom observations, and student interviews. The data from this exploratory study were analyzed qualitatively to describe the nature of the teachers’ understandings, the ways teachers used their understandings in their practice, and the nature of their students’ understandings. This study reveals that there were aspects of student understanding directly influenced by teachers’ understandings, such as an expanded understanding of mathematical operations, the nature and quality of written and verbal representations of students’ understanding, the ability to progress to more sophisticated levels of problem solving, and students’ understandings of mathematical concepts that are more pervasive in mathematics than solving word problems. In addition there were aspects of teacher practice influenced by teachers’ understandings that may have led to student understanding, such as, creating new tasks, the ability to comprehend and implement the lesson objectives, the ability to understand and address specific students’needs, the ability to purposefully target questions asked of students, requiring students to solve problems in multiple ways, providing examples with detailed explanation and interpretation, and allowing students to solve problems using their own valid interpretations. This study hypothesizes that teachers used their understanding to create and implement tasks at a high level of cognitive demand, maintaining that demand while the students implemented the tasks, which affected student understanding.