Foran, Alexandra Lair (2018-08). Problem Posing to Promote Cognitive Flexibility in Mathematics Teacher Preparation Programs. Doctoral Dissertation. Thesis uri icon

abstract

  • The purpose of this study was to investigate how prepared teachers are to teach word problems, specifically to connect content to students' real lives, through cognitive flexibility. Four elementary teacher preparation programs in the state of Texas were analyzed through syllabus analysis, instructor and pre-service teacher (PST) interviews, and PSTs' posing of four, original, elementary-level word problems. Four instructors and 18 PSTs discussed assignments and classwork that they felt were helping or hurting the development of PSTs as teachers. Findings indicate that instructors choose coursework and assignments that they feel will build teacher confidence in their students. Instructors do not specifically seek out opportunities to build cognitive flexibility in their students and do not provide many formal problem-posing experiences inside or outside of class. Pre-service teachers' interviews indicated that they had mixed feelings about their confidence to enter an elementary mathematics classroom. Their mathematics education coursework left them feeling prepared in content but not in pedagogy, with little pedagogy at all in geometry. They knew strategies for solving word problems, but not always when or how to teach those strategies to elementary students. Problem posing was not a general practice all of the teacher preparation programs, and the results of the word-problem-posing exercise illuminate the PSTs' relative states of preparation. Writing problems using fractions was particularly challenging. Their programs prepared them to solve problems, but not to write their own. Implications of this study are four-fold. First, PSTs need more interactive word problem experiences in their teacher preparation programs. Second, teacher preparation programs need geometry courses that prepare them to teach elementary geometry. Third, PSTs need field experience in mathematics classrooms to practice what they are learning in courses. Fourth, further studies need to be conducted to evaluate the accuracy and reliability of the first three findings.
  • The purpose of this study was to investigate how prepared teachers are to teach word
    problems, specifically to connect content to students' real lives, through cognitive flexibility. Four
    elementary teacher preparation programs in the state of Texas were analyzed through syllabus
    analysis, instructor and pre-service teacher (PST) interviews, and PSTs' posing of four, original,
    elementary-level word problems. Four instructors and 18 PSTs discussed assignments and
    classwork that they felt were helping or hurting the development of PSTs as teachers. Findings
    indicate that instructors choose coursework and assignments that they feel will build teacher
    confidence in their students. Instructors do not specifically seek out opportunities to build
    cognitive flexibility in their students and do not provide many formal problem-posing experiences
    inside or outside of class.
    Pre-service teachers' interviews indicated that they had mixed feelings about their
    confidence to enter an elementary mathematics classroom. Their mathematics education
    coursework left them feeling prepared in content but not in pedagogy, with little pedagogy at all
    in geometry. They knew strategies for solving word problems, but not always when or how to
    teach those strategies to elementary students. Problem posing was not a general practice all of the
    teacher preparation programs, and the results of the word-problem-posing exercise illuminate the
    PSTs' relative states of preparation. Writing problems using fractions was particularly challenging.
    Their programs prepared them to solve problems, but not to write their own.
    Implications of this study are four-fold. First, PSTs need more interactive word problem
    experiences in their teacher preparation programs. Second, teacher preparation programs need
    geometry courses that prepare them to teach elementary geometry. Third, PSTs need field
    experience in mathematics classrooms to practice what they are learning in courses. Fourth, further
    studies need to be conducted to evaluate the accuracy and reliability of the first three findings.

publication date

  • August 2018