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Mathematics

Leveraging MIPOs: Developing a Theory of Productive Use of Student Mathematical Thinking (Collaborative Research: Leatham)

The core research questions of the project are: (1) What is the nature of high-leverage student thinking that teachers have available to them in their classrooms? (2) How do teachers use student thinking during instruction and what goals, orientations and resources underlie that use? (3) What is the learning trajectory for the teaching practice of productively using student thinking? and (4) What supports can be provided to move teachers along that learning trajectory?

Lead Organization(s): 
Award Number: 
1220141
Funding Period: 
Mon, 10/01/2012 - Fri, 09/30/2016
Full Description: 

Leveraging MOSTs (Mathematically Significant Pedagogical Openings to build on Student Thinking) is a collaborative project among Brigham Young University, Michigan Technological University and Western Michigan University that focuses on improving the teaching of secondary school mathematics by improving teachers' abilities to use student thinking during instruction to develop mathematical concepts. The core research questions of the project are: (1) What is the nature of high-leverage student thinking that teachers have available to them in their classrooms? (2) How do teachers use student thinking during instruction and what goals, orientations and resources underlie that use? (3) What is the learning trajectory for the teaching practice of productively using student thinking? and (4) What supports can be provided to move teachers along that learning trajectory? The project is developing a theory of Productive Use of Student Mathematical Thinking (PUMT Theory) that articulates what the practice of productively using student mathematical thinking looks like, how one develops this practice, and how that development can be facilitated.

Design research methodology underlies the work of four interrelated phases: (1) Student thinking - testing and refining a preliminary framework by expanding an existing data set of classroom discourse video to include more diverse teacher and student populations; (2) Teachers' interactions with student thinking - assessing teachers' perceptions of using student thinking and how they make decisions about which thinking to pursue; (3) Teachers' learning about student thinking - using a series of teacher development experiments to improve teachers' abilities to productively use student mathematical thinking during instruction; and (4) Shareable products - creating useful products that are in forms that encourage feedback for further refinement. Data include video recordings of classroom instruction (to identify MOSTs and teachers' responses to them), teacher interviews (to understand their decisions in response to instances of student thinking), and records of teacher development sessions and the researchers' discussions about the teachers' development (to inform the teacher development experiments and future professional development activities). Project evaluation includes both formative and summative components that focus on the quality of the project's process for developing a PUMT Theory and associated tools and professional development, as well as the quality of the resulting products.

Leveraging MOSTs provides critical resources - including a theory, framework, and hypothetical learning trajectory - for teachers, teacher educators, and researchers that make more tangible the often abstract but fundamental goal of productively using students' mathematical thinking. The project enhances the field's understanding of (1) the MOSTs that teachers have available to them in their classrooms, and how they vary in diverse contexts; (2) teachers' perceptions and productive use of student thinking during instruction; and (3) the trajectory of teachers' learning about student thinking and how best to support movement along that trajectory. Using student thinking productively is a cornerstone of effective teaching, thus the PUMT Theory and associated supports produced by the project are valuable resources for those involved in mathematics education as well as other fields.

Leveraging MIPOs: Developing a Theory of Productive Use of Student Mathematical Thinking (Collaborative Research: Leatham)

Enhancing Mathematics Teaching and Learning in Urban Elementary Schools: A Cluster-Randomized Efficacy Trial of a Novel Professional Development Approach

This project is working with all teachers in grades three through five in the Portland, OR Public Schools in order to test the feasibility and efficacy of the Mathematics Studio Model of professional development. The model requires professional development to occur at the school level involving both teachers and principals. The goal of the project is to improve students' engagement and learning in mathematics by fostering effective instruction.

Lead Organization(s): 
Award Number: 
1223074
Funding Period: 
Sat, 09/15/2012 - Wed, 08/31/2016
Full Description: 

The Enhancing Mathematics Teaching and Learning in Urban Elementary Schools project is working with all teachers in grades three through five in the Portland, OR Public Schools in order to test the feasibility and efficacy of the Mathematics Studio Model of professional development. The model requires professional development to occur at the school level involving both teachers and principals. The professional development is conducted at the school and is integrated with instruction. The goal of the project is to improve students' engagement and learning in mathematics by fostering effective instruction. Partners in the project include Teachers Development Group, Portland State University, Portland Public Schools and Horizon Research.

The researchers are identifying the key ingredients that make the professional development successful. They are using a cluster-randomized research design to examine the efficacy of their model. They are using observational measures to identify successful teaching practices as well as student discourse patterns. They are studying the fidelity of implementation of the model and are looking for specific variables that may be particularly helpful for students who have not been successful in learning mathematics.

It is difficult to implement professional development at a large enough scale to make a significant difference in student achievement within a district. This research is important because it tests the use of a practice-based, professional development model within a large, public school system, and documents the challenges of implementation as well as the variables that contribute to student learning of mathematics.

Enhancing Mathematics Teaching and Learning in Urban Elementary Schools: A Cluster-Randomized Efficacy Trial of a Novel Professional Development Approach

Learning Trajectories to Support the Growth of Measurement Knowledge: Pre-K Through Middle School

This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This research project tests, revises and extends learning trajectories for children's knowledge of geometric measurement across a ten-year span of human development. The goal will be to validate all components of each learning trajectory, goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments.

Lead Organization(s): 
Award Number: 
1222944
Funding Period: 
Wed, 08/01/2012 - Sun, 07/31/2016
Full Description: 

This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This four-year, mixed methods research project tests, revises and extends learning trajectories (LTs) for children's knowledge of geometric measurement across a ten-year span of human development. Specifically, research teams from Illinois State University and the University at Denver are working with children in urban and suburban schools to (1) validate and extend prior findings from previous NSF-funded research developing measurement learning trajectories with children in pre-K to Grade 5, and (2) generate and extend portions of trajectories for geometric measurement for Grades 6-8.

The project employs a form of microgenetic studies with 24-50 children per grade from pre-K through Grade 5 representing a stratified random sample from a specific set of suburban schools. These studies will test the validity, replicability and generalizability of the LTs for length, area, and volume. The goal will be to validate all components of each learning trajectory, goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments. Analysis of variance measures with pre/post assessments in an experimental/control design will complement the repeated sessions method of microgenetic analysis.

To explore and extend LTs for children in Grade 6-8, the project employs teaching experiments. This design is used to generate and extend portions of trajectories for geometric measurement, and to explore critical aspects of measurement in clinical and classroom contexts. This work is coordinated with the teaching and learning standards issued by the Council of Chief State School Officials/National Governors Association, the National Council of Teachers of Mathematics, the National Science Teachers Association, the American Association of the Advancement of Science, and the National Research Council with cognitive and mathematics/science education literature. Emerging constructs for the hypothetical LT levels in relation to relevant frameworks generated by other researchers and those implied by standards documents to establish ongoing sequences of the experimental interventions for grades 6-8 are being compared, critiqued and evaluated.

This project provides a longitudinal account of pre-K to Grade 8 children's ways of thinking and understanding mathematical and scientific concepts of measurement based upon empirical analysis. The resulting learning trajectory will represent state of the art integrated, interdisciplinary, theoretically- and empirically-based descriptions of increasingly sophisticated and complex levels of thinking in the domain of measurement (albeit, more tentative for Grades 6-8). This account will be used to verify and/or modify existing accounts of children's development of reasoning from short-term analyses of learning or cross-sectional studies. There are not yet integrative longitudinal studies describing this cognitive domain for area or volume measurement. This trajectory-based analysis of development and instruction supports the design and testing of integrative, formative assessment of individuals and groups of children. Such learning trajectories will be useful in implementing the standard-focused curriculum described in the Common Core State Standards Mathematics and in supporting the multiple large assessment projects currently underway

Learning Trajectories to Support the Growth of Measurement Knowledge: Pre-K Through Middle School

Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Sword)

This collaborative project is developing instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement.

Award Number: 
1222426
Funding Period: 
Wed, 08/15/2012 - Sun, 07/31/2016
Full Description: 

Boston University, Education Development Center, Inc., and St. Olaf College are collaborating on Assessing Secondary Teachers' Algebraic Habits of Mind (ASTAHM) to develop instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. MHoM is a critical component of mathematical knowledge for teaching at the secondary level. Recognizing the need for a scientific approach to investigate the ways in which MHoM is an indicator of teacher effectiveness, the partnership is researching the following questions:

1. How do teachers who engage MHoM when doing mathematics for themselves also bring MHoM to their teaching practice?

2. How are teachers' engagement with MHoM and their use of these habits in teaching related to student understanding and achievement?

To investigate these questions, ASTAHM is developing two instruments: a paper and pencil (P&P) assessment and an observation protocol that measure teachers' knowledge and classroom use, respectively, of MHoM.

The work is being conducted in two phases: (1) an instrument-refinement and learning phase, and (2) an instrument-testing and research phase. Objectives of Phase 1 are to gather data to refine the project's existing instruments and to learn about the bridge factors that impact the relationship between teachers' knowledge and classroom use of MHoM. Specific research activities include: administering the pilot P&P assessment to 40 teachers, videotaping Algebra instructions of 8 teachers, performing initial testing and refinement of the instruments, and using the data to analyze the bridge factors. Phase 2 is a large-scale study involving field-testing the P&P assessment with 200 teachers, videotaping 20 teachers and studying them using the observation protocol, collecting achievement data from 3000 students, and checking P&P content validity with 200 mathematicians. With these validated instruments in hand, the project will then conduct an investigation into the above research questions. Lesley University's Program Evaluation and Research Group (PERG) is the external evaluator. PERG is assessing ASTAHM's overall success in developing valid and reliable instruments to investigate the extent to which a relationship exists between teachers' MHoM and their classroom practice, as well as student achievement. Evaluators are also investigating whether users' coding guides for both instruments enable field-testers to effectively use and adequately score them.

This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement. The MHoM construct is closely aligned with the Common Core State Standards-Mathematics (CCSS-M); especially its Standards for Mathematical Practice. For example, both place importance on seeking and using mathematical structure. Thus the instruments this project produces can act as pre- and post-measures of the effectiveness of professional development programs in preparing teachers to implement the CCSS-M. Mathematics teacher knowledge at the secondary level is an understudied field. Through analyses of the practices and habits of mind that teachers bring to their work, ASTAHM is developing instruments that can be used to shed light on effective secondary teaching.

Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Sword)

Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Matsuura)

This collaborative project is developing instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1222340
Funding Period: 
Wed, 08/15/2012 - Sun, 07/31/2016
Full Description: 

Boston University, Education Development Center, Inc., and St. Olaf College are collaborating on Assessing Secondary Teachers' Algebraic Habits of Mind (ASTAHM) to develop instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. MHoM is a critical component of mathematical knowledge for teaching at the secondary level. Recognizing the need for a scientific approach to investigate the ways in which MHoM is an indicator of teacher effectiveness, the partnership is researching the following questions:

1. How do teachers who engage MHoM when doing mathematics for themselves also bring MHoM to their teaching practice?

2. How are teachers' engagement with MHoM and their use of these habits in teaching related to student understanding and achievement?

To investigate these questions, ASTAHM is developing two instruments: a paper and pencil (P&P) assessment and an observation protocol that measure teachers' knowledge and classroom use, respectively, of MHoM.

The work is being conducted in two phases: (1) an instrument-refinement and learning phase, and (2) an instrument-testing and research phase. Objectives of Phase 1 are to gather data to refine the project's existing instruments and to learn about the bridge factors that impact the relationship between teachers' knowledge and classroom use of MHoM. Specific research activities include: administering the pilot P&P assessment to 40 teachers, videotaping Algebra instructions of 8 teachers, performing initial testing and refinement of the instruments, and using the data to analyze the bridge factors. Phase 2 is a large-scale study involving field-testing the P&P assessment with 200 teachers, videotaping 20 teachers and studying them using the observation protocol, collecting achievement data from 3000 students, and checking P&P content validity with 200 mathematicians. With these validated instruments in hand, the project will then conduct an investigation into the above research questions. Lesley University's Program Evaluation and Research Group (PERG) is the external evaluator. PERG is assessing ASTAHM's overall success in developing valid and reliable instruments to investigate the extent to which a relationship exists between teachers' MHoM and their classroom practice, as well as student achievement. Evaluators are also investigating whether users' coding guides for both instruments enable field-testers to effectively use and adequately score them.

This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement. The MHoM construct is closely aligned with the Common Core State Standards-Mathematics (CCSS-M); especially its Standards for Mathematical Practice. For example, both place importance on seeking and using mathematical structure. Thus the instruments this project produces can act as pre- and post-measures of the effectiveness of professional development programs in preparing teachers to implement the CCSS-M. Mathematics teacher knowledge at the secondary level is an understudied field. Through analyses of the practices and habits of mind that teachers bring to their work, ASTAHM is developing instruments that can be used to shed light on effective secondary teaching.

Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Matsuura)

Supporting the Emergence of a Professional Teaching Community Through Collective Knowledge-Building in Assessment and Feedback of Mathematical Thinking (Collaborative Research: Brandt)

This collaborative project is developing an online, professional teaching community that addresses issues of assessment in mathematics classes. The developers are building on the success of the NSF-supported Math Forum's Problem of the Week program to create a community that works to increase students' mathematics learning by helping teachers stimulate student thinking, assess that thinking, and provide useful feedback to students.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1221351
Funding Period: 
Sat, 09/01/2012 - Wed, 08/31/2016
Full Description: 

This collaborative work involves Drexel University and Temple University where they are developing an online, professional teaching community that is addressing issues of assessment in mathematics classes. The developers are building on the success of the NSF-supported Math Forum's Problem of the Week program to create a community that is working to increase students' mathematics learning by helping teachers stimulate student thinking, assess that thinking, and provide useful feedback to students. The teachers are working together to create rubrics for assessing the progress of students as they solve challenging mathematics problems. The program is structured so that the teachers are learning mathematics and assessment strategies in addition to establishing a research-based model for online, professional communities.

Researchers are studying how specific activities (e.g., discourse, active participation, use of rubrics, feedback, and reflection) and an online community support teachers' engagement in authentic and generative assessment. Researchers are using ethnographic methods to understand the development of the community, and conducting focus groups and individual interviews to determine the impact of participation in the community on mathematics teachers. In addition, they are collecting data through discourse analysis, student work analysis, and rubric analysis to determine the optimal design of the products. The intentional structure of the online community builds on research findings on creating professional communities and research on assessing mathematics learning.

Online professional teaching communities offer new venues for communication, professional development, and shared work among mathematics teachers. The Math Forum provides an optimal, online context for expanding the popular Problem of the Week into a productive discussion of assessment of problem solving, the building of specific rubrics, and the related reflection on how to encourage student thinking. This collaborative work will offer rubrics for assessing mathematical problem solving, a new model for online professional development, and extensive information on building an online mathematics community.

Supporting the Emergence of a Professional Teaching Community Through Collective Knowledge-Building in Assessment and Feedback of Mathematical Thinking (Collaborative Research: Brandt)

Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Stevens)

This collaborative project is developing instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1222496
Funding Period: 
Wed, 08/15/2012 - Sun, 07/31/2016
Full Description: 

Boston University, Education Development Center, Inc., and St. Olaf College are collaborating on Assessing Secondary Teachers' Algebraic Habits of Mind (ASTAHM) to develop instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. MHoM is a critical component of mathematical knowledge for teaching at the secondary level. Recognizing the need for a scientific approach to investigate the ways in which MHoM is an indicator of teacher effectiveness, the partnership is researching the following questions:

1. How do teachers who engage MHoM when doing mathematics for themselves also bring MHoM to their teaching practice?

2. How are teachers' engagement with MHoM and their use of these habits in teaching related to student understanding and achievement?

To investigate these questions, ASTAHM is developing two instruments: a paper and pencil (P&P) assessment and an observation protocol that measure teachers' knowledge and classroom use, respectively, of MHoM.

The work is being conducted in two phases: (1) an instrument-refinement and learning phase, and (2) an instrument-testing and research phase. Objectives of Phase 1 are to gather data to refine the project's existing instruments and to learn about the bridge factors that impact the relationship between teachers' knowledge and classroom use of MHoM. Specific research activities include: administering the pilot P&P assessment to 40 teachers, videotaping Algebra instructions of 8 teachers, performing initial testing and refinement of the instruments, and using the data to analyze the bridge factors. Phase 2 is a large-scale study involving field-testing the P&P assessment with 200 teachers, videotaping 20 teachers and studying them using the observation protocol, collecting achievement data from 3000 students, and checking P&P content validity with 200 mathematicians. With these validated instruments in hand, the project will then conduct an investigation into the above research questions. Lesley University's Program Evaluation and Research Group (PERG) is the external evaluator. PERG is assessing ASTAHM's overall success in developing valid and reliable instruments to investigate the extent to which a relationship exists between teachers' MHoM and their classroom practice, as well as student achievement. Evaluators are also investigating whether users' coding guides for both instruments enable field-testers to effectively use and adequately score them.

This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement. The MHoM construct is closely aligned with the Common Core State Standards-Mathematics (CCSS-M); especially its Standards for Mathematical Practice. For example, both place importance on seeking and using mathematical structure. Thus the instruments this project produces can act as pre- and post-measures of the effectiveness of professional development programs in preparing teachers to implement the CCSS-M. Mathematics teacher knowledge at the secondary level is an understudied field. Through analyses of the practices and habits of mind that teachers bring to their work, ASTAHM is developing instruments that can be used to shed light on effective secondary teaching.

Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Stevens)

Learning Mathematics of the City in the City

This project is developing teaching modules that engage high school students in learning and using mathematics. Using geo-spatial technologies, students explore their city with the purpose of collecting data they bring back to the formal classroom and use as part of their mathematics lessons. This place-based orientation helps students connect their everyday and school mathematical thinking. Researchers are investigating the impact of place-based learning on students' attitudes, beliefs, and self-concepts about mathematics in urban schools.

Lead Organization(s): 
Award Number: 
1222430
Funding Period: 
Sat, 09/01/2012 - Mon, 08/31/2015
Full Description: 

Learning Mathematics of the City in The City is an exploratory project that is developing teaching modules that engage high school students in learning mathematics and using the mathematics they learn. Using geo-spatial technologies, students explore their city with the purpose of collecting data they bring back to the formal classroom and use as part of their mathematics lessons. This place-based orientation is helping students connect their everyday and school mathematical thinking.

Researchers are investigating the impact of place-based learning on students' attitudes, beliefs, and self-concepts about mathematics in urban schools. Specifically, researchers want to understand how place-based learning helps students apply mathematics to address questions about their local environment. Researchers are also learning about the opportunities for teaching mathematics using carefully planned lessons enhanced by geo-spatial technologies. Data are being collected through student interviews, classroom observations, student questionnaires, and student work.

As the authors explain, "The use of familiar or engaging contexts is widely accepted as productive in the teaching and learning of mathematics." By working in urban neighborhoods with large populations of low-income families, this exploratory project is illustrating what can be done to engage students in mathematics and mathematical thinking. The products from the project include student materials, software adaptations, lesson plans, and findings from their research. These products enable further experimentation with place-based mathematics learning and lead the way for connecting mathematical activities in school and outside of school.

Learning Mathematics of the City in the City

Developing Principles for Mathematics Curriculum Design and Use in the Common Core Era

This project is developing principles for supporting middle school mathematics teachers' capacity to use curriculum resources to design instruction that addresses the Common Core State Standards for Mathematics. These principles are intended for: (1) curriculum developers; (2) professional development designers, to help teachers better utilize curriculum materials with respect to the CCSSM; and (3) teachers, so that they can use curriculum resources to design instruction that addresses the CCSSM.

Award Number: 
1222359
Funding Period: 
Wed, 08/15/2012 - Sun, 07/31/2016
Project Evaluator: 
Horizon Research
Full Description: 

This project is developing principles for supporting middle school mathematics teachers' capacity to use curriculum resources to design instruction that addresses the Common Core State Standards for Mathematics (CCSSM). These principles are intended for: (1) curriculum developers to help in the design of curriculum materials; (2) professional development designers and local instructional leaders, to help teachers understand and better utilize curriculum materials with respect to the CCSSM; and (3) teachers, so that they can use curriculum resources to design instruction that addresses the CCSSM. The study addresses the following research questions:

1. What design features of materials support effective instructional design?

2. What teacher and district characteristics support effective instructional design?

3. How do teachers use materials to design instruction that addresses the new CCSSM?

4. What design practices lead to instruction that addresses the progressions and practices in the CCSSM?

A sample of teachers across grades 6 - 8 and their instructional leaders will be selected, up to a maximum of 72 teachers. The sample of teachers is purposefully diverse in terms of demographic, geographic, and curriculum contexts. The curricula include NSF-funded programs as well as commercially-developed programs. The ways teachers understand and access curriculum resources in fully digital environments as well as more conventional media will be studied. Partnering institutions include the University of Rochester, Michigan State University, Western Michigan University, and Washington State University Tri-Cities.

The data collection includes surveys, assessments of teachers' mathematical knowledge for teaching, observations of teachers' use and enactment of curriculum materials, analyses of student text and associated teacher resource materials, and teacher logs. These data are used to test conjectures about: (1) how curriculum materials, particularly the teacher resources, can be better designed to help teachers productively design instruction, especially with regard to incorporating the mathematical practices in the CCSSM; and (2) how teachers can be better supported to understand and use curriculum resources. The project evaluation includes formative and summative components, providing information and assistance to ensure that the project addresses its stated goals and employs rigorous methodology. Multiple methods are being used to collect evaluation data, including observations, interviews, and document review.

The deliverables are aimed at audiences who can impact large numbers of teachers and students, such as curriculum developers, designers of professional development, and researchers. The deliverables include: (1) guidelines for curriculum developers that are intended to make curriculum resources more transparent and accessible; (2) guidelines for instructional leaders to support teachers to use curriculum materials to design instruction that addresses the rigorous features of the CCSSM, and (3) refined instruments for studying teachers' curricular practices.

Developing Principles for Mathematics Curriculum Design and Use in the Common Core Era

Supporting the Emergence of a Professional Teaching Community Through Collective Knowledge-Building in Assessment and Feedback of Mathematical Thinking (Collaborative Research: Silverman)

This collaborative project is developing an online, professional teaching community that addresses issues of assessment in mathematics classes. The developers are building on the success of the NSF-supported Math Forum's Problem of the Week program to create a community that works to increase students' mathematics learning by helping teachers stimulate student thinking, assess that thinking, and provide useful feedback to students.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1222355
Funding Period: 
Sat, 09/01/2012 - Wed, 08/31/2016
Full Description: 

This collaborative work involves Drexel University and Temple University where they are developing an online, professional teaching community that is addressing issues of assessment in mathematics classes. The developers are building on the success of the NSF-supported Math Forum's Problem of the Week program to create a community that is working to increase students' mathematics learning by helping teachers stimulate student thinking, assess that thinking, and provide useful feedback to students. The teachers are working together to create rubrics for assessing the progress of students as they solve challenging mathematics problems. The program is structured so that the teachers are learning mathematics and assessment strategies in addition to establishing a research-based model for online, professional communities.

Researchers are studying how specific activities (e.g., discourse, active participation, use of rubrics, feedback, and reflection) and an online community support teachers' engagement in authentic and generative assessment. Researchers are using ethnographic methods to understand the development of the community, and conducting focus groups and individual interviews to determine the impact of participation in the community on mathematics teachers. In addition, they are collecting data through discourse analysis, student work analysis, and rubric analysis to determine the optimal design of the products. The intentional structure of the online community builds on research findings on creating professional communities and research on assessing mathematics learning.

Online professional teaching communities offer new venues for communication, professional development, and shared work among mathematics teachers. The Math Forum provides an optimal, online context for expanding the popular Problem of the Week into a productive discussion of assessment of problem solving, the building of specific rubrics, and the related reflection on how to encourage student thinking. This collaborative work will offer rubrics for assessing mathematical problem solving, a new model for online professional development, and extensive information on building an online mathematics community.

Supporting the Emergence of a Professional Teaching Community Through Collective Knowledge-Building in Assessment and Feedback of Mathematical Thinking (Collaborative Research: Silverman)
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