Inviting Prospective Teachers to Share Rough Draft Mathematical Thinking

2016 ◽  
Vol 4 (2) ◽  
pp. 145-163 ◽  
Author(s):  
Eva Thanheiser ◽  
Amanda Jansen
Keyword(s):  
Elementary Teachers ◽  
Prospective Teachers ◽  
Mathematical Thinking ◽  
Comfort Level ◽  
Prospective Elementary Teachers ◽  
Class Discussions ◽  
Academic Settings ◽  
Rough Draft ◽  
Mathematics Content Course ◽  
Mathematics Content Courses

Engaging prospective elementary teachers (PTs) in participating productively by making their exploratory (rough draft) thinking public during class discussions remains a constant challenge for instructors of mathematics content courses for teachers, in part because of perspectives incoming PTs may hold about interacting in academic settings. In this article, we share the effects of an intervention designed to confront PTs' incoming perspectives. PTs were provided with opportunities to label the level of completeness and correctness of their thinking before they displayed and discussed their written work publicly during a mathematics content course for teachers. Results indicated that labeling their work increased PTs' level of comfort with sharing their thinking and awareness of the value of doing so. PTs also reported that the label served as a reflection tool. The label increased the PTs' productive disposition in terms of comfort level with taking intellectual risks when doing mathematics and reflecting on their work.

scholarly journals Formatively assessing prospective teachers’ skills in leading mathematics discussions

2021 ◽  
Author(s):  
Meghan Shaughnessy ◽  
Nicole M. Garcia ◽  
Michaela Krug O’Neill ◽  
Sarah Kate Selling ◽  
Amber T. Willis ◽  
...  
Keyword(s):  
Elementary Teachers ◽  
Formative Assessment ◽  
Conceptual Understanding ◽  
Prospective Teachers ◽  
First Year ◽  
Teacher Education Programs ◽  
First Year Teachers ◽  
Education Programs ◽  
Prospective Elementary Teachers ◽  
Making Sense

AbstractMathematics discussions are important for helping students to develop conceptual understanding and to learn disciplinary norms and practices. In recent years, there has been increased attention to teaching prospective teachers to lead discussions with students. This paper examines the possibilities of designing a formative assessment that gathers information about prospective elementary teachers’ skills with leading problem-based mathematics discussions and makes sense of such information. A decomposition of the practice of leading discussions was developed and used to design the assessment. Nine first-year teachers who graduated from a range of different teacher education programs participated in the study. The findings reveal that our formative assessment works to gather information about teachers’ capabilities with leading discussions and that the associated tools support making sense of the information gathered. This suggests that such tools could be useful to support the formative assessment of the developing capabilities of prospective teachers.

Lived Moments of Shift in Prospective Elementary Teachers' Mathematical Learning

2019 ◽  
Vol 50 (4) ◽  
pp. 436-463
Author(s):  
Keri D. Valentine ◽  
Johnna Bolyard
Keyword(s):  
Elementary Teachers ◽  
Lived Experience ◽  
Prospective Teachers ◽  
Critical Role ◽  
Single Event ◽  
Prospective Elementary Teachers ◽  
Phenomenological Inquiry ◽  
Teachers Experiences ◽  
Past Experiences ◽  
Time Frames

Past experiences as mathematics learners play a critical role in the way mathematics teachers consider what it means to know, do, and teach mathematics. Thus, understanding past experiences and ways to work with them in teacher education is a critical concern. Using phenomenological inquiry, we investigated moments of shift that occur along one's mathematics journey. The study draws on 30 prospective teachers' experiences in the form of lived-experience writing and interview data. Findings show that prospective teachers' shifts manifest in relations with others, across different time frames, and through material relations with mathematics. Most salient was the tentative and mutable nature of shifts, showing that shift might be better viewed as a possibility rather than a single event.

Supporting Teacher Learning: Shaping Prospective Teachers' Justifications for Computation: Challenges and Opportunities

2007 ◽  
Vol 14 (2) ◽  
pp. 112-116
Author(s):  
Theresa J. Grant ◽  
Jane-Jane Lo ◽  
Judith Flowers
Keyword(s):  
Elementary Teachers ◽  
Prospective Teachers ◽  
Teacher Educators ◽  
Sense Making ◽  
Major Focus ◽  
Prospective Elementary Teachers ◽  
Difficult Time ◽  
Whole Number ◽  
Challenges And Opportunities ◽  
Mathematical Justification

This article discusses the challenges and opportunities that arose in attempting to support prospective elementary teachers in developing mathematical justifications in the context of wholenumber computation. Justification for whole-number computation is important for three reasons. First, this is the introductory topic in the first of three mathematics courses for prospective elementary teachers. Second, the number and operations strand is a major focus in elementary school. Third, in our experience as teacher educators, prospective elementary teachers have a difficult time considering how and why to teach whole-number computation in a conceptual manner. If prospective teachers' reasoning and justifications can be shaped in this area of mathematics, sense making and mathematical justification in other areas of mathematics can be shaped as well (Simon and Blume 1996).

scholarly journals Caracterización del significado de múltiplo por maestros en formación

2016 ◽  
Vol 10 (2) ◽  
pp. 111-134
Author(s):  
Ángel López ◽  
Encarnación Castro ◽  
María C. Cañadas
Keyword(s):  
Elementary Teachers ◽  
Elementary School Teachers ◽  
Prospective Teachers ◽  
Teaching Experiment ◽  
Practice Session ◽  
School Teachers ◽  
Prospective Elementary Teachers ◽  
Structure Representation ◽  
Representation Systems ◽  
Multiple Product

Este trabajo forma parte de una investigación centrada en la divisibilidad en Z+. Los sujetos participantes son maestros en formación. Uno de los objetivos de la investigación consiste en caracterizar los significados que muestran los maestros en formación sobre el concepto de múltiplo. Este artículo recoge los resultados obtenidos en relación con dicho objetivo. Analizamos las producciones escritas de 37 maestros en formación obtenidas en una sesión práctica de aula, diseñada y desarrollada en el contexto de un experimento de enseñanza. Realizamos la caracterización de los significados a través de los elementos del análisis didáctico: estructura conceptual, sistemas de representación y fenomenología. Los maestros en formación mostraron mayoritariamente tres significados de múltiplo: producto, relación y dividendo en una división exacta. Characterizing the meaning of multiple by pre-service elementary school teachers This paper is part of a wider study focused on divisibility. Participants were prospective elementary teachers. One of the aims of the research is to characterize the meanings of multiple shown by prospective teachers. In this paper, we present the results concerning this aim. We analyse the productions of 37 prospective elementary teachers collected in a practice session, designed and developed in the context of a teaching experiment. We characterize the meanings through the following elements of the didactic analysis: conceptual structure, representation systems and phenomenology. Prospective teachers showed mostly three meanings of multiple: product, relationship and dividend in an exact division.Handle: http://hdl.handle.net/10481/39495WOS-ESCI

Prospective Elementary Teachers' Knowledge of Division

1993 ◽  
Vol 24 (3) ◽  
pp. 233-253 ◽  
Author(s):  
Martin A. Simon
Keyword(s):  
Elementary Teachers ◽  
Prospective Teachers ◽  
Real World ◽  
Conceptual Knowledge ◽  
Prospective Elementary Teachers ◽  
Research Results ◽  
Individual Interviews ◽  
The Relationship ◽  
Mathematical Preparation ◽  
Real World Problems

Prospective teachers' knowledge of division was investigated through an open-response written instrument and through individual interviews. Problems were designed to focus on two aspects of understanding division: connectedness within and between procedural and conceptual knowledge and knowledge of units. Results indicated that the prospective teachers' conceptual knowledge was weak in a number of areas including the conceptual underpinnings of familiar algorithms, the relationship between partitive and quotitive division, the relationship between symbolic division and real-world problems, and identification of the units of quantities encountered in division computations. The research also characterized aspects of individual conceptual differences. The research results suggest conceptual areas of emphasis for the mathematical preparation of elementary teachers.

Research, Reflection, and Practice: Writing for an Audience in a Mathematics Methods Course

2004 ◽  
Vol 10 (9) ◽  
pp. 480-486
Author(s):  
Alfinio Flores ◽  
Carmina M. Brittain
Keyword(s):  
Elementary Teachers ◽  
Prospective Teachers ◽  
Teacher Educators ◽  
Methods Course ◽  
Mathematics Methods ◽  
Prospective Elementary Teachers ◽  
Knowledge And Attitudes ◽  
Mathematics Methods Course ◽  
First Time ◽  
Natural Way

During their first mathematics methods course, many prospective elementary teachers confront their previous conceptions about mathematics and its teaching for the first time. This juncture makes the course important in their evolution as teachers of mathematics. Prospective teachers in a mathematics methods course must develop the ability to reflect on their actions, beliefs, knowledge, and attitudes. Writing in a mathematics methods course fosters reflection in a natural way; it serves as a tool for documentation, analysis, and discussion to help prospective teachers internalize what they learn and reach new levels of comprehension. At the same time, what teachers in training write gives teacher educators a window into their reflection and growth process.

Make Up Your Own Mazes

1975 ◽  
Vol 22 (8) ◽  
pp. 650-652
Author(s):  
Edward T. Ordman
Keyword(s):  
Elementary Teachers ◽  
Prospective Teachers ◽  
Grade Level ◽  
Euclidean Geometry ◽  
Classroom Teacher ◽  
Inservice Teachers ◽  
Prospective Elementary Teachers ◽  
Grade Levels ◽  
Elementary Classes ◽  
Theorem Proof

A few years ago I showed a class of prospective elementary teachers a theorem that I had always assumed to be part of the folklore of topology. Apparently, however, it is little used today, either by teachers or by mathematical researchers. It was so well received by the class of prospective teachers that I then showed it to inservice teachers, and finally I visited a few elementary classes to try it on the pupils firsthand. It was regularly a success—in one instance pupils were so excited they showed it to fri ends during lunch and disrupted school for much of the afternoon. Even at the third-grade level, some pupils were able to follow the reasoning well enough to convince another classroom teacher (who had not seen the material in advance) of the truth o f the theorem. At higher grade levels, the theorem continues to be appropria te for any pupils who have not yet had exposure to the “theorem-proof” arguments of the sort common in Euclidean geometry.

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