Learning to Teach Hard Mathematics: Do Novice Teachers and Their Instructors Give up Too Easily?

1992 ◽  
Vol 23 (3) ◽  
pp. 194-222 ◽  
Author(s):  
Hilda Borko ◽  
Margaret Eisenhart ◽  
Catherine A. Brown ◽  
Robert G. Underhill ◽  
Doug Jones ◽  
...  
Keyword(s):  
Teacher Education ◽  
Knowledge Base ◽  
Mathematics Teaching ◽  
Mathematics Teacher Education ◽  
Learning To Teach ◽  
Methods Course ◽  
Mathematics Methods ◽  
Division Of Fractions ◽  
Good Mathematics Teaching ◽  
Mathematics Methods Course

This article analyzes from several vantage points a classroom lesson in which a student teacher was unsuccessful in providing a conceptually based justification for the standard division-of-fractions algorithm. We attempt to understand why the lesson failed, what it reveals about learning to teach, and what the implications are for mathematics teacher education. We focus on (a) the student teacher's beliefs about good mathematics teaching, her knowledge related to division of fractions, and her beliefs about learning to teach; and (b) the treatment of division of fractions in the mathematics methods course she took. The student teacher's conception of good mathematics teaching included components compatible with current views of effective mathematics teaching. However, these beliefs are difficult to achieve without a stronger conceptual knowledge base and a greater commitment to use available resources and to engage in hard thinking than she possessed. Further, the mathematics methods course did not require the student teacher to reconsider her knowledge base, to confront the contradictions between her knowledge base and at least some of her beliefs, or to reassess her beliefs about how she would learn to teach. These findings suggest that mathematics teacher education programs should reconsider how they provide subject matter knowledge and opportunities to teach it, and whether and how they challenge student teachers' existing beliefs.

scholarly journals Creative Character Education in Mathematics for Prospective Teachers

2019 ◽  
Vol 11 (6) ◽  
pp. 1730
Author(s):  
Dong-Joong Kim ◽  
Sung-Chul Bae ◽  
Sang-Ho Choi ◽  
Hee-Jeong Kim ◽  
Woong Lim
Keyword(s):  
Teacher Education ◽  
Preservice Teachers ◽  
Character Education ◽  
Prospective Teachers ◽  
Teacher Education Program ◽  
Mathematics Teacher Education ◽  
Methods Course ◽  
Mathematics Methods ◽  
Mathematics Methods Course ◽  
Teachers Perspectives

This study examines preservice teachers’ perspectives of creativity and character education in mathematics through a university-based teacher education program. We developed a curricular unit on creative character education in a mathematics methods course and investigated participants’ (n = 56) emerging perspectives of teaching creativity and character by the integration of content and process in mathematics. Data were collected through pre- and post-questionnaires and transcribed course discussion and presentation sessions. A quantitative analysis of the questionnaires through a t-test confirmed key changes in participants’ perspectives, while the qualitative context of data illustrates the participants’ emergent views on creative character education in mathematics. Overall, findings suggest that a mathematics teacher education curriculum integrating mathematical creativity and character education has the potential to prepare future educators to implement pedagogy that bridges between process and content in school mathematics for the next generation of learners.

Critical Thinking and Mathematics Teaching and Learning

2019 ◽  
pp. 234-253
Author(s):  
Kelli Thomas ◽  
Douglas Huffman ◽  
Mari Caballero
Keyword(s):  
Critical Thinking ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Methods Course ◽  
Teaching Behaviors ◽  
Mathematics Methods ◽  
Mathematics Classrooms ◽  
Mathematics Methods Course ◽  
Mathematics Teaching And Learning ◽  
And Mathematics

The purpose of this chapter was to investigate pre-service teachers' noticing of children's critical thinking and views towards eliciting and using students' critical thinking in mathematics teaching. A mixed method study was used to provide a range of perspectives on pre-service teachers' views towards mathematics. The results indicated that the pre-service teachers initially held beliefs that mathematics teaching and learning consist of transferring information and students absorbing and memorizing information. The pre-service teachers based their instructional responses on experiences they had as students in elementary mathematics classrooms. The pre-service teachers described what they had observed about teaching mathematics as the ideal without regard for how the teaching behaviors they observed might influence children's critical thinking about mathematics. After completing a mathematics methods course, the pre-service teachers held beliefs more consistent with a reform-oriented classroom and demonstrated growth in their ability to notice children's mathematics thinking.

Conceptual Knowledge Falls through the Cracks: Complexities of Learning to Teach Mathematics for Understanding

1993 ◽  
Vol 24 (1) ◽  
pp. 8-40 ◽  
Author(s):  
Margaret Eisenhart ◽  
Hilda Borko ◽  
Robert Underhill ◽  
Catherine Brown ◽  
Doug Jones ◽  
...  
Keyword(s):  
Student Teacher ◽  
Conceptual Knowledge ◽  
Procedural Knowledge ◽  
Teacher Education Program ◽  
Learning To Teach ◽  
Methods Course ◽  
Mathematics Methods ◽  
National Goal ◽  
Mathematics Methods Course ◽  
Teaching Pattern

In this article we focus on two interrelated aspects of the process of learning to teach mathematics for understanding: (a) ideas and practices for teaching procedural knowledge and (b) ideas and practices for teaching conceptual knowledge. We explore one student teacher's ideas and practices, together with the messages about teaching for procedural and conceptual knowledge that were presented by the teacher education program in which the student teacher was enrolled and the placement schools in which she student taught. We reveal a pattern in which the student teacher, her mathematics methods course instructor, her cooperating teachers, and the administrators of her placement schools expressed a variety of strong commitments to teaching for both procedural and conceptual knowledge; but with these commitments, the student teacher taught, learned to teach, and had opportunities to learn to teach for procedural knowledge more often and more consistently than she did for conceptual knowledge. We find that the actual teaching pattern (what was done) was the product of unresolved tensions within the student teacher, the other key actors in her environment, and the learning-to-teach environment itself. We hypothesize that situational supports constructed to emphasize more consistently teaching for conceptual knowledge might help resolve at least some of the tensions, and we suggest that such supports should be developed if the national goal to increase the teaching of mathematics for understanding is to be achieved.

Developing an Online Mathematics Methods Course for Preservice Teachers

2014 ◽  
pp. 308-317
Author(s):  
Drew Polly
Keyword(s):  
Preservice Teachers ◽  
Graduate Students ◽  
Online Courses ◽  
Theoretical Background ◽  
Methods Course ◽  
Mathematics Methods ◽  
Mathematics Pedagogy ◽  
Design Based Research ◽  
Mathematics Methods Course ◽  
Online Mathematics

This chapter presents the theoretical background and overview of the design of an asynchronous online mathematics pedagogy course taken by graduate students who are seeking their initial teacher certification. The authors provide the theoretical underpinnings for the design of the course, and then using design-based research, describe the refinement of the course over three iterations of designing and implementing the course. Lastly, implications for the design and delivery of asynchronous online courses are discussed.

Evaluation of a Hybrid Mathematics Methods Course for Novice Teachers

2016 ◽  
pp. 1228-1247
Author(s):  
Christopher J. Johnston
Keyword(s):  
Novice Teachers ◽  
Discussion Board ◽  
Methods Course ◽  
Learning Activity ◽  
Mathematics Methods ◽  
Course Structure ◽  
Face To Face ◽  
Mathematics Methods Course ◽  
The Rich ◽  
Online Format

This paper reports the evaluation of a hybrid mathematics methods course for novice teachers. During a fifteen-week semester, participants met face-to-face for approximately 60% of the semester and took advantage of an online format for the other 40% of the semester. Online activities included asynchronous discussion board postings, synchronous chats as an entire class, synchronous chats in small groups, evaluation of technology tools, and electronic surveys. The researcher used participants' feedback to evaluate the effectiveness of this hybrid format. In addition, the researcher reflected upon his own experiences as instructor to inform future course structure decisions. Within the context of the Rich Environments for Active Learning (REAL) framework, results suggest that cooperative support was a key component of the effectiveness of the experience. Further, participants emphasized one particular generative learning activity as an effective component of this course. Finally, this paper discusses implications for mathematics professional development facilitators.

Adding a New Dimension to Teaching Mathematics Educators

2019 ◽  
pp. 390-412
Author(s):  
Anna Wan ◽  
Jessica Ivy
Keyword(s):  
3D Printing ◽  
Digital Fabrication ◽  
Secondary Mathematics ◽  
Self Report ◽  
Methods Course ◽  
Fabrication Technology ◽  
Mathematics Methods ◽  
Mathematical Content ◽  
Mathematics Methods Course ◽  
Post Assessment

Technology has the potential to transform the classroom, build access to new mathematical content, and provide access to students through unique representations. For this study, the authors considered the transformational promise of digital fabrication technology, specifically 3D printing, in a setting comprised of pre-service teachers. An introduction to digital fabrication session was implemented in a secondary mathematics methods course. Participants were assessed both prior to the experience and after, using an adapted TPACK developmental self-report survey to consider TPACK themes and subthemes. In this chapter, the authors describe ideas that emerged from narratives provided by participants, patterns of change noted from pre- to post-assessment, and three cases that emerged representing students who experienced the most positive changes, most negative changes, and least amount of change on self-perceived levels.

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