Preparing prospective secondary teachers to teach mathematical reasoning and proof: the case of the role of examples in proving

被引:6
作者
McCrone, Sharon [1 ]
Buchbinder, Orly [1 ]
机构
[1] Univ New Hampshire, Durham, NH 03824 USA
来源
ZDM-MATHEMATICS EDUCATION | 2023年 / 55卷 / 04期
基金
美国国家科学基金会;
关键词
Reasoning and proving; Mathematical Knowledge for Teaching Proof; Prospective secondary teachers; PEDAGOGICAL CONTENT KNOWLEDGE; FUTURE TEACHERS; ARGUMENTATION; COMPETENCE;
D O I
10.1007/s11858-023-01493-4
中图分类号
G40 [教育学];
学科分类号
040101 ; 120403 ;
摘要
Mathematics teacher education programs in the United States are charged with preparing prospective secondary teachers (PSTs) to teach reasoning and proving across grade levels and mathematical topics. Although most programs require a course on proof, PSTs often perceive it as disconnected from their future classroom practice. Our design research project developed a capstone course Mathematical Reasoning and Proving for Secondary Teachers and systematically studied its effect on PSTs' content and pedagogical knowledge specific to proof. This paper focuses on one course module-Quantification and the Role of Examples in Proving, a topic which poses persistent difficulties to students and teachers alike. The analysis suggests that after the course, PSTs' content and pedagogical knowledge of the role of examples in proving increased. We provide evidence from multiple data sources: pre-and post-questionnaires, PSTs' responses to the in-class activities, their lesson plans, reflections on lesson enactment, and self-report. We discuss design principles that supported PSTs' learning and their applicability beyond the study context.
引用
收藏
页码:779 / 792
页数:14
相关论文
共 53 条
  • [1] Alvarez J. A., 2022, PRIMUS, V32, P685
  • [2] [Anonymous], 2009, Focus in High School Mathematics: Reasoning and Sense Making
  • [3] Indirect proof: what is specific to this way of proving?
    Antonini, Samuele
    Mariotti, Maria Alessandra
    [J]. ZDM-MATHEMATICS EDUCATION, 2008, 40 (03): : 401 - 412
  • [4] Australian Curriculum Assessment and Reporting Authority (ACARA), 2022, CRITICAL CREATIVE TH
  • [5] Pedagogical context and proof validation: The role of positioning as a teacher or student
    Baldinger, Erin E.
    Lai, Yvonne
    [J]. JOURNAL OF MATHEMATICAL BEHAVIOR, 2019, 55
  • [6] Content Knowledge for Teaching What Makes It Special?
    Ball, Deborah Loewenberg
    Thames, Mark Hoover
    Phelps, Geoffrey
    [J]. JOURNAL OF TEACHER EDUCATION, 2008, 59 (05) : 389 - 407
  • [7] Future teachers' competence to plan a lesson: first results of a six-country study on the efficiency of teacher education
    Bloemeke, Sigrid
    Paine, Lynn
    Houang, Richard T.
    Hsieh, Feng-Jui
    Schmidt, William H.
    Tatto, M. Teresa
    Bankov, Kiril
    Cedilllo, Tenoch
    Cogan, Leland
    Il Han, Shin
    Santillan, Marcella
    Schwille, John
    [J]. ZDM-MATHEMATICS EDUCATION, 2008, 40 (05): : 749 - 762
  • [8] Blomeke S., 2015, Assessment of Competencies in Higher Education
  • [9] Blomeke S., 2014, International perspectives on teacher knowledge, beliefs and opportunities to learn: TEDS-M results, DOI DOI 10.1007/978-94-007-6437-8_2
  • [10] Buchbinder O., 2021, Journal of Technology and Teacher Education, V29, P279