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.

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.

Improving Middle School Teachers' Reasoning about Proportional Reasoning

2003 ◽  
Vol 8 (8) ◽  
pp. 398-403
Author(s):  
Charles S. Thompson ◽  
William S. Bush
Keyword(s):  
Professional Development ◽  
Middle School ◽  
Middle School Teachers ◽  
Middle Grades ◽  
Proportional Reasoning ◽  
Development Project ◽  
School Teachers

Article describes a professional development project to increase teachers' understanding of proportional reasoning, the thinking patterns associated with proportional reasoning, and the applications of proportional reasoning across the middle-grades curriculum.

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.

Examining What Elementary School Teachers Take Away from Mathematics Professional Development

2016 ◽  
pp. 62-84
Author(s):  
Drew Polly
Keyword(s):  
Professional Development ◽  
Elementary School Teachers ◽  
Professional Learning ◽  
Mathematical Knowledge For Teaching ◽  
Educational Leaders ◽  
Development Project ◽  
Mathematical Tasks ◽  
Mathematics Standards ◽  
Knowledge For Teaching ◽  
Arduous Task

The process of providing effective ongoing professional development to teachers is an arduous task for educational leaders. In areas, such as mathematics, professional learning opportunities must deepen teachers' knowledge of content, pedagogy, and other skills connected to teaching. This chapter provides an examination of what teachers learned during a professional development project that was designed based off of principles for Learner-Centered Professional Development and addressed components of the Mathematical Knowledge for Teaching framework. The project included 3 half-day meetings with classroom-embedded activities completed between workshops. An inductive, thematic analysis of workshop evaluations indicated that teachers' learning related to: a) a deeper understanding of the Common Core Mathematics Standards, b) exploring mathematical tasks, and c) planning lessons that start with mathematical tasks instead of direct teaching.

Mathematics Teachers' Enactment of Cognitively Demanding Tasks: Investigating Links to Teachers' Knowledge and Conceptions

2014 ◽  
Vol 45 (5) ◽  
pp. 636-674 ◽  
Author(s):  
Anne Garrison Wilhelm
Keyword(s):  
Middle School ◽  
Mathematics Teachers ◽  
Mathematical Knowledge ◽  
Teaching And Learning ◽  
Mathematical Knowledge For Teaching ◽  
Middle School Mathematics ◽  
Knowledge For Teaching ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Cognitively Demanding Tasks

This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. The author found that teachers' mathematical knowledge for teaching and conceptions of teaching and learning mathematics were contingent on one another and significantly related to teachers' enactment of cognitively demanding tasks.

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 

Examining What Elementary School Teachers Take Away From Mathematics Professional Development

2018 ◽  
pp. 237-260
Author(s):  
Drew Polly
Keyword(s):  
Professional Development ◽  
Elementary School Teachers ◽  
Professional Learning ◽  
Mathematical Knowledge For Teaching ◽  
Educational Leaders ◽  
Development Project ◽  
Mathematical Tasks ◽  
Mathematics Standards ◽  
Knowledge For Teaching ◽  
Arduous Task

The process of providing effective ongoing professional development to teachers is an arduous task for educational leaders. In areas, such as mathematics, professional learning opportunities must deepen teachers' knowledge of content, pedagogy, and other skills connected to teaching. This chapter provides an examination of what teachers learned during a professional development project that was designed based off of principles for Learner-Centered Professional Development and addressed components of the Mathematical Knowledge for Teaching framework. The project included 3 half-day meetings with classroom-embedded activities completed between workshops. An inductive, thematic analysis of workshop evaluations indicated that teachers' learning related to: a) a deeper understanding of the Common Core Mathematics Standards, b) exploring mathematical tasks, and c) planning lessons that start with mathematical tasks instead of direct teaching.

Mathematical Knowledge of Middle School Teachers: Implications for the No Child Left Behind Policy Initiative

2007 ◽  
Vol 29 (2) ◽  
pp. 95-114 ◽  
Author(s):  
Heather C. Hill
Keyword(s):  
Middle School ◽  
No Child Left Behind ◽  
Middle School Teachers ◽  
Mathematical Knowledge ◽  
Mathematical Knowledge For Teaching ◽  
Teaching Experience ◽  
School Teachers ◽  
Knowledge For Teaching ◽  
School Teaching ◽  
Nationally Representative

This article explores middle school teachers’ mathematical knowledge for teaching and the relationship between such knowledge and teachers’subject matter preparation, certification type, teaching experience, and their students’ poverty status. The author administered multiple-choice measures to a nationally representative sample of teachers and found that those with more mathematical course work, a subject-specific certification, and high school teaching experience tended to possess higher levels of teaching-specific mathematical knowledge. However, teachers with strong mathematical knowledge for teaching are, like those with full credentials and preparation, distributed unequally across the population of U.S. students. Specifically, more affluent students are more likely to encounter more knowledgeable teachers. The author discusses the implications of this for current U.S. policies aimed at improving teacher quality.

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.

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