Reshaping Teachers' Mathematical Perceptions: Analysis of a Professional Development Task

2015 ◽  
Vol 3 (2) ◽  
pp. 116-129 ◽  
Author(s):  
Gwyneth Hughes ◽  
Jonathan Brendefur ◽  
Michele Carney
Keyword(s):  
Professional Development ◽  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Knowledge For Teaching ◽  
Guided Reinvention ◽  
Solution Methods ◽  
Development Course ◽  
Multiple Solution Methods ◽  
Representative Task

As the focus of mathematics education moves from memorization toward reasoning and problem solving, professional development for in-service teachers must model these activities while simultaneously increasing participants' mathematical knowledge. We examine a representative task from a mathematics professional development course that uses rational number operation as an opportunity for problem solving and modeling. Transcripts exemplify the growth teachers make in deeply understanding the content–division of fractions–while engaging in guided reinvention and classroom discourse. We propose 4 interconnected qualities of this task that allow participants to engage in and reflect on the process of guided reinvention: (1) authentic context with multiple solution methods, including visual; (2) cognitive dissonance; (3) deep engagement; and (4) impact on mathematical knowledge for teaching.

Measuring Mathematical Knowledge for Teaching Fractions With Drawn Quantities

2012 ◽  
Vol 43 (4) ◽  
pp. 391-427 ◽  
Author(s):  
Andrew Izsák ◽  
Erik Jacobson ◽  
Zandra de Araujo ◽  
Chandra Hawley Orrill
Keyword(s):  
Professional Development ◽  
Item Response ◽  
Mathematical Knowledge ◽  
Middle Grades ◽  
Mathematical Knowledge For Teaching ◽  
Knowledge For Teaching ◽  
Irt Models ◽  
Psychometric Modeling ◽  
Teaching Fractions ◽  
Development Course

Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study investigated the utility of an alternative called the mixture Rasch model that allows for subgroups. The model was applied to middle-grades teachers' performance on pretests and posttests bracketing a 42-hour professional development course focused on drawn models for fraction arithmetic. Results from psychometric modeling and evidence from video-recorded interviews and professional development sessions suggested that there were 2 subgroups of middle-grades teachers, 1 better able to reason with 3-level unit structures and 1 constrained to 2-level unit structures. Some teachers, however, were easier to classify than others.

scholarly journals Mathematical knowledge for teaching: Adding to the description through a study of probability in practice

Pythagoras ◽  
2006 ◽  
Vol 0 (63) ◽  
Author(s):  
Mercy Kazima ◽  
Jill Adler
Keyword(s):  
Problem Solving ◽  
Mathematical Knowledge ◽  
Mathematical Problem ◽  
Mathematical Knowledge For Teaching ◽  
Mathematical Work ◽  
Mathematical Problem Solving ◽  
Knowledge For Teaching ◽  
Scaling Down ◽  
Multilingual Classroom ◽  
Everyday Knowledge

In their description of the mathematical work of teaching, Ball,  Bass & Hill (2004) describe the mathematical problem solving that teachers do as they go about their work. In this paper we add to this description through our study of teaching of probability in a grade 8 multilingual classroom in South Africa. We use instances of teaching to highlight the mathematical problem solving that teachers might face as they work with learners’ ideas, both expected and unexpected. We discuss  the restructuring of tasks as an inevitable feature of teachers’ work, and argue that in addition to scaling up or scaling down of the task as Ball et al. (2004) describe, restructuring can also entail shifting the mathematical outcomes from those intended. We also point out how well known issues in mathematics education, for example working with learners’ everyday knowledge, and the languages they bring to class, are highlighted by the context of probability, enabling additional insights into the mathematical work of teaching.

Mentor-Guided Lesson Study as a Tool to Support Learning in Field Experiences

2015 ◽  
Vol 4 (1) ◽  
pp. 20-31 ◽  
Author(s):  
Kristen N. Bieda ◽  
Jillian Cavanna ◽  
Xueying Ji
Keyword(s):  
Professional Development ◽  
Teacher Preparation ◽  
Lesson Study ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Student Thinking ◽  
Practicing Teachers ◽  
Knowledge And Skills ◽  
Knowledge For Teaching ◽  
Intern Teachers

Field experience can be a rich site for intern teachers to develop the knowledge and skills they need for effective teaching. Lesson study has been shown to be a powerful form of professional development that enhances practicing teachers' mathematical knowledge for teaching through collaborative inquiry with their peers. In this article, we discuss the use of mentor-guided lesson study to support mentor and intern collaboration in the field and share what we have learned about its potential to support interns' attention to student thinking. We will also share insights from the field for those interested in implementing this activity in teacher preparation coursework.

scholarly journals LEARNING TRAJECTORIES BASED INQUIRY UNTUK MEMBANGUN MATHEMATICAL KNOWLEDGE FOR TEACHING GURU ANAK USIA DINI

PRISMA ◽  
2018 ◽  
Vol 7 (2) ◽  
pp. 123
Author(s):  
Merry Novianty
Keyword(s):  
Professional Development ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Development Program ◽  
Professional Development Program ◽  
Learning Trajectories ◽  
Knowledge For Teaching ◽  
Teaching Professional Development ◽  
Teaching Professional

Guru mempunyai peran penting dalam meningkatkan kemampuan matematika anak. Oleh karena itu, Mathematical Knowledge for Teaching (MKT) harus dibangun dan ditingkatkan agar dapat melakukan kegiatan pengembangan dengan baik.  Untuk meningkatkan kualitasnya, para guru diharapkan terlibat dalam pengembangan profesional atau Professional Development Program (PDP). PDP merupakan sarana untuk menigkatkan dan mempertahankan pengetahuan dan keterampilan yang berkaitan dengan kehidupan profesional guru. Dalam pengembangan program tersebut, diperlukan sebuah model pembelajaran sebagai pedoman pelaksanaannya. Model tersebut diharapkan dapat memancing logika dan pengetahuan guru dalam mengajar matematika. Learning Trajectories Based Inquiry (LTBI) merupakan lintasan belajar dengan menekankan kepada proses mencari dan menemukan. Dalam hal ini, pengetahuan dibangun melalui proses pencarian, serta proses berpikir kritis dan analitis untuk merumuskan kesimpulan. Makalah ini akan membahas apa yang dimaksud dengan Learning Trajectories Based Inquiry (LTBI), bagaimana merancang model LTBI dalam pelaksanaan Professional Development Program (PDP). Serta bagaimana pelaksanaan PDP dengan model LTBI dapat membangun MKT. Keywords:  Learning Trajectories Based Inquiry, Mathematical Knowledge for Teaching, Professional Development Program 

Fostering Middle School Teachers’ Mathematical Knowledge for Teaching via Analysis of Tasks and Student Work

2020 ◽  
Vol 9 (1) ◽  
pp. 50-62
Author(s):  
S. Asli Özgün-Koca ◽  
Jennifer M. Lewis, ◽  
Thomas Edwards
Keyword(s):  
Professional Development ◽  
Middle School ◽  
Mathematical Knowledge ◽  
Proportional Reasoning ◽  
Mathematical Knowledge For Teaching ◽  
Development Project ◽  
Student Work ◽  
Knowledge Domains ◽  
Knowledge For Teaching ◽  
Knowledge Of Content

Mathematical knowledge for teaching is a complex web of knowledge domains. In this article, we share findings from an 18-month professional development project that aimed to improve middle school mathematics teachers’ mathematical knowledge for teaching (MKT) of proportional reasoning by focusing on the critical analysis of mathematical tasks and student work. Although multiple studies have shown that professional development can contribute to teachers’ MKT globally, little is known about how this knowledge grows and how specific domains of MKT can be targeted through professional development. Findings in this study show how professional development positively influenced participants’ knowledge of content and teaching and knowledge of content and students, two domains of MKT, through teachers’ twinned analyses of tasks and student work in proportional reasoning.

scholarly journals Mathematical Modeling and teachers’ formation: a discussion on mathematical knowledge for teaching

2019 ◽  
Vol 16 (21) ◽  
pp. 5-17
Author(s):  
Rogério Marques Ribeiro ◽  
Arthur Belford Powell
Keyword(s):  
Mathematical Modeling ◽  
Professional Development ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Continuing Professional Development ◽  
Early Years ◽  
Public Education System ◽  
Knowledge For Teaching ◽  
Video Recordings ◽  
School Based

This study discusses the utilization of Mathematical Modeling for the continuing professional development of Mathematics teachers in the early years of primary school based on studies and investigations by Ball and her collaborators, in which they broached mathematical knowledge for teaching. We started to study such approach during an extension course developed with seven teachers from the São Paulo public education system. For data collection, we applied the triangulation of methods, which is characterized by the use of different instruments, like the use of quizzes, interviews and audio and video recordings of our meetings. Through the analyses of the collected data, we observed that the utilization of Mathematical Modeling as a learning environment provided us with a highly favorable scenario, so that we were able to foment the necessary discussions in order to study the knowledge harnessed by teachers throughout their continuing professional development and discuss the necessary mathematical knowledge for teaching.

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