Mathematics

CAREER: Designing Learning Environments to Foster Productive and Powerful Discussions Among Linguistically Diverse Students in Secondary Mathematics

Award Number: 
1553708
Funding Period: 
Mon, 02/01/2016 to Sun, 01/31/2021
Full Description: 

The project will design and investigate learning environments in secondary mathematics classrooms focused on meeting the needs of English language learners. An ongoing challenge for mathematics teachers is promoting deep mathematics learning among linguistically diverse groups of students while taking into consideration how students' language background influences their classroom experiences and the mathematical understandings they develop. In response to this challenge, this project will design and develop specialized instructional materials and guidelines for teaching fundamental topics in secondary algebra in linguistically diverse classrooms. The materials will incorporate insights from current research on student learning in mathematics as well as insights from research on the role of language in students' mathematical thinking and learning. A significant contribution of the work will be connecting research on mathematics learning generally with research on the mathematics learning of English language learners. In addition to advancing theoretical understandings, the research will also contribute practical resources and guidance for mathematics teachers who teach English language learners. The Faculty Early Career Development (CAREER) program is a National Science Foundation (NSF)-wide activity that offers awards in support of junior faculty who exemplify the role of teacher-scholars through outstanding research, excellent education, and the integration of education and research within the context of the mission of their organizations.

The project is focused on the design of specialized hypothetical learning trajectories that incorporate considerations for linguistically diverse students. One goal for the specialized trajectories is to foster productive and powerful mathematics discussions about linear and exponential rates in linguistically diverse classrooms. The specialized learning trajectories will include both mathematical and language development learning goals. While this project focuses on concepts related to reasoning with linear and exponential functions, the resulting framework should inform the design of specialized hypothetical learning trajectories in other topic areas. Additionally, the project will add to the field's understanding of how linguistically diverse students develop mathematical understandings of a key conceptual domain. The project uses a design-based research framework gathering classroom-based data, assessment data, and interviews with teachers and students to design and refine the learning trajectories. Consistent with a design-based approach, the project results will include development of theory about linguistically diverse students' mathematics learning and development of guidance and resources for secondary mathematics teachers. This research involves sustained collaboration with secondary mathematics teachers and the impacts will include developing capacity of teachers locally, and propagating the results of this work in professional development activities.

Researching Science and Mathematics Teacher Learning in Alternative Certification Models

This research is examining science and mathematics teacher learning in the context of an alternative certification program employing two different models of field-based preparation. The project will inform the research community about science and mathematics teacher learning and will aid in the design and implementation of alternative certification programs and field-based internships in science and mathematics teacher preparation, as well as potentially impact policymaking concerning teacher certification.

Lead Organization(s): 
Award Number: 
0553929
Funding Period: 
Thu, 06/01/2006 to Mon, 05/31/2010

A Task Force on Conceptualizing Elementary Mathematical Writing: Implications for Mathematics Education Stakeholders

The Elementary Mathematical Writing (EMW) Task Force was made up of educators with unique perspectives about elementary mathematical writing and with the goal to reach a consensus about and priorities for the types of and purposes for elementary mathematical writing. The EMW Task Force met in October 2015, analyzed elementary writing prompts and samples, standards documents, and recommendations, and identified four types of mathematical writing and their associated purposes: Exploratory, Informative/Explanatory, Argumentative, and Mathematically Creative.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1545908
Funding Period: 
Tue, 09/01/2015 to Wed, 08/31/2016
Full Description: 

Communicating about mathematical ideas by talking and writing is central to the teaching and learning of mathematics as it can help students learn concepts at a deeper level. More specifically, according to the Common Core State Standards (CCSS), students should develop their ability to construct viable arguments and critique the reasoning of others in mathematics and write across content areas. However, there is limited guidance about how to teach students to write mathematically, how to evaluate students' mathematical writing, and the kinds of mathematical writing tasks to include in curriculum resources. This may mean that students do not experience the benefits from writing about their mathematical ideas.

The Elementary Mathematical Writing (EMW) Task Force was made up of educators who bring unique perspectives about elementary mathematical writing. It included practitioners and academics from the fields of mathematics education, mathematics, and writing education and who are knowledgeable about students who have special needs, are English language learners, and have been identified as gifted. With the ultimate goal of reaching consensus about and priorities for the types of and purposes for elementary mathematical writing, the task force reviewed student work, writing prompts, curriculum standards, and other items. They also suggested recommendations for future work in this area.

The EMW Task Force meth the goals of identifying, describing, and recommending productive types of and purposes for mathematical writing by elementary students. The four types of mathematical writing are:

  • Exploratory – with the purpose of personally making sense of a problem, situation, or one’s own ideas.
  • Informative/Explanatory – with the purposes of describing or explaining mathematical ideas.
  • Argumentative – with the purposes of constructing viable arguments and/or critiquing the reasoning of others.
  • Mathematically Creative – with the purposes of documenting original ideas, problems, and/or solutions; conveying fluency and flexibility in thinking; and elaborating on ideas.

The work and recommendations of the EMW Task force highlights the necessity of a comprehensive line of work related to mathematical writing at a critical juncture in the history of the field of mathematics education. The intellectual merit of this project, therefore, is in its potential to transform the field of mathematics education. The broader impacts include the facilitation of collaboration among and across disciplines and stakeholders.

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

Building Assessment Items and Instructional Tasks to Build Intercommunity Capacity to Develop Teachers' Mathematical Knowledge for Teaching

The infrastructure to improve mathematics education in the US requires building human resources in mathematics and mathematics education into a professional community that can respond to the critical needs in the field. This project seeks to build a professional community with shared understanding of the specialized content knowledge (SCK) - the special forms and ways of reasoning about mathematical knowledge used in teaching (MKT). 

Lead Organization(s): 
Award Number: 
1502778
Funding Period: 
Tue, 09/01/2015 to Sat, 08/31/2019
Full Description: 

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. The infrastructure to improve mathematics education in the US requires building human resources in mathematics and mathematics education into a professional community that can respond to the critical needs in the field. This project seeks to build a professional community with shared understanding of the specialized content knowledge (SCK) - the special forms and ways of reasoning about mathematical knowledge used in teaching (MKT). This community will help increase the capacity for further research and development on teachers' SCK in mathematics, which has been shown to relate to student achievement. Building on the professional community's shared knowledge, the project will also work to collaboratively develop an item bank of MKT/SCK items and tasks using the platform developed by the Illustrative Mathematics group for similar task and item development for K-12 students. Better measures, with a larger item bank, will help support both the learning and assessment of teachers' MKT/SCK.

Based on theories of communities of practice, this project will bring together mathematicians and mathematics educators to build a professional community with a shared understanding of the SCK in mathematics through engaging in efforts to develop items to measure SCK and the development of a task bank. Based on the "item camps" they engaged with to develop prior measures, the project will host twelve 4-day camps with varying themes for pairs of faculty and teachers or graduate students, ensuring a mix of mathematicians and educators. This work will lead to a certification for MKT/SCK. They will also develop approximately 60 items and have a mechanism for the future review and publishing of items. Using case-study methodologies, the project will study the development of these partnerships and the professional communities within and across the camps.

Mathematical and Computational Methods for Planning a Sustainable Future II

The project will develop modules for grades 9-12 that integrate mathematics, computing and science in sustainability contexts. The project materials also include information about STEM careers in sustainability to increase the relevancy of the content for students and broaden their understanding of STEM workforce opportunities. It uses summer workshops to pilot test materials and online support and field testing in four states. 

Lead Organization(s): 
Award Number: 
1503414
Funding Period: 
Wed, 07/15/2015 to Sun, 06/30/2019
Full Description: 

The project will develop modules for grades 9-12 that integrate mathematics, computing and science in sustainability contexts. The project materials also include information about STEM careers in sustainability to increase the relevancy of the content for students and broaden their understanding of STEM workforce opportunities. It uses summer workshops to pilot test materials and online support and field testing in four states. Outcomes include the modules, tested and revised; strategies for transfer of learning embedded in the modules; and a compendium of green jobs, explicitly related to the modules. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. The STEM+Computing Partnerships (STEM+C) Program is a joint effort between the Directorate for Education & Human Resources (EHR) and Directorate Computer & Information Science & Engineering (CISE). Reflecting the increasing role of computational approaches in learning across the STEM disciplines, STEM+C supports research and development efforts that integrate computing within one or more STEM disciplines and/or integrate STEM learning in computer science; 2) advance multidisciplinary, collaborative approaches for integrating computing in STEM in and out of school, and 3) build capacity in K-12 computing education through foundational research and focused teacher preparation

The project is a full design and development project in the learning strand of DRK-12. The goal is to enhance transfer of knowledge in mathematics and science via sustainability tasks with an emphasis on mathematical and scientific practices. The research questions focus on how conceptual representations and the modules support students' learning and especially transfer to novel problems. The project design integrates the research with the curriculum development. It includes a mixed methods data collection and analysis from teachers and students (e.g., interviews, content exams, focus groups, implementation logs). Assessment of student work includes both short, focused problems in the content area and longer project-based tasks providing a range of assessments of student learning. The investigators will develop a rubric for scoring student work on the tasks. The curriculum design process includes iterations of the modules over time with feedback from teachers and using data collected from the implementation.

Retention of Early Algebraic Understanding

The project will use a quasi-experimental design to explore students' knowledge of core algebraic concepts in middle grades (grade 6), one year after their completion of 3-year, grades 3-5 early algebra intervention. The research questions are: (1) how well students who received a specific intervention retain their understanding of algebraic concepts in future years; and (2) whether and how the intervening year of regular classroom instruction in grade 6 influences the algebra understanding of both intervention and comparison students.

Lead Organization(s): 
Award Number: 
1550897
Funding Period: 
Tue, 09/01/2015 to Wed, 08/31/2016
Full Description: 

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by prek-12 students and teachers through research and development of innovative resources, models and tools. While national and state standards provide important benchmarks for algebra learning beginning in kindergarten, they do not provide rigorously tested models by which these algebra standards might be attained in elementary grades classrooms in ways that will ensure further mathematics achievement. This work will addresses this need by closely documenting the effectiveness of models and tools, developed in our previous work, for early algebra education

The proposed project will use a quasi-experimental design to explore students' knowledge of core algebraic concepts in middle grades (grade 6), one year after their completion of 3-year, grades 3-5 early algebra intervention. The project will also study the algebraic knowledge of a comparison group of students. The research questions are: (1) how well students who received a specific intervention retain their understanding of algebraic concepts in future years; and (2) whether and how the intervening year of regular classroom instruction in grade 6 influences the algebra understanding of both intervention and comparison students.

Collaborative Math: Creating Sustainable Excellence in Mathematics for Head Start Programs

This project will adapt and study a promising and replicable teacher professional development (PD) intervention, called Collaborative Math (CM), for use in early childhood programs. Prepared as generalists, preschool teachers typically acquire less math knowledge in pre-service training than their colleagues in upper grades, which reduces their effectiveness in teaching math. To address teacher PD needs, the project will simultaneously develop teacher content knowledge, confidence, and classroom practice by using a whole teacher approach.

Lead Organization(s): 
Award Number: 
1503486
Funding Period: 
Tue, 09/01/2015 to Sat, 08/31/2019
Full Description: 

This project was submitted to the Discovery Research K-12 (DRK-12) program that seeks to significantly enhance the learning and teaching of science, technology, engineering, and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models, and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects. The project will adapt and study a promising and replicable teacher professional development (PD) intervention, called Collaborative Math (CM), for use in early childhood programs. CM content will focus on nine topics emphasized in preschool mathematics, including sets, number sense, counting, number operations, pattern, measurement, data analysis, spatial relationships, and shape. These concepts are organized around Big Ideas familiar in early math, are developmentally appropriate and foundational to a young child's understanding of mathematics. The project addresses the urgent need for improving early math instruction for low-income children. Prepared as generalists, preschool teachers typically acquire less math knowledge in pre-service training than their colleagues in upper grades, which reduces their effectiveness in teaching math. To address teacher PD needs, the project will simultaneously develop teacher content knowledge, confidence, and classroom practice by using a whole teacher approach. Likewise, the project will involve teachers, teacher aides, and administrators through a whole school approach in PD, which research has shown is more effective than involving only lead teachers. Through several phases of development and research, the project will investigate the contributions of project components on increases in teacher knowledge and classroom practices, student math knowledge, and overall implementation. The project will impact approximately 200 Head Start (HS) teaching staff, better preparing them to provide quality early math experiences to more than 3,000 HS children during the project period. Upon the completion of the project, a range of well-tested CM materials such as resource books and teaching videos will be widely available for early math PD use. Assessment tools that look at math knowledge, attitudes, and teacher practice will also be available. 

The project builds on Erikson Institute research and development work in fields of early math PD and curriculum. Over a 4-year span, project development and research will be implemented in 4 phases: (1) adapting the existing CM and research measures for HS context; (2) conducting a limited field study of revised CM in terms of fidelity and director, teacher/aide, and student outcomes, and study of business as usual (BAU) comparison groups; (3) a study of the promise of the intervention promise with the phase 3 BAU group (who offered baseline in phase 2) and (4) a test of the 2nd year sustainability intervention with phase 3 treatment group. The teacher and student measures are all published, frequently used measures in early childhood education and will be piloted and refined prior to full implementation. The project is a partnership between Erikson, SRI, and Chicago Head Start programs. Project research and resources will be widely disseminated to policy makers, researchers, and practitioners.

Conceptual Model-based Problem Solving: A Response to Intervention Program for Students with Learning Difficulties in Mathematics

This project will develop a cross-platform mathematics tutoring program that addresses the problem-solving skill difficulties of second- and third-grade students with learning disabilities in mathematics (LDM). COMPS-A is a computer-generated instructional program focusing on additive word problem solving; it will provide tutoring specifically tailored to each individual student's learning profile in real time. 

Lead Organization(s): 
Award Number: 
1503451
Funding Period: 
Tue, 09/01/2015 to Fri, 08/31/2018
Full Description: 

The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

The 3-year exploratory project, Conceptual Model-based Problem Solving: A Response to Intervention Program for Students with Learning Difficulties in Mathematics, will develop a cross-platform mathematics tutoring program that addresses the problem-solving skill difficulties of second- and third-grade students with learning disabilities in mathematics (LDM). While mathematics problem-solving skills are critical in all areas of daily life, many students with LDM do not acquire key math concepts such as additive and multiplicative reasoning in a proficient manner during the early school years. In fact, about 5-10% of school-age children are identified as having mathematical disabilities which might cause them to experience considerable difficulties in the upper grades and experience persistent academic, life, and work challenges. Despite the proliferation of web-based mathematical games for early learners, there are very few programs or tools that target growth in the conceptual understanding of fundamental mathematical ideas, which is essential in enabling young students with LDM to perform proficiently in mathematical and everyday contexts. COMPS-A is a computer-generated instructional program focusing on additive word problem solving; it will provide tutoring specifically tailored to each individual student's learning profile in real time. COMPS-A will also make the reasoning and underlying mathematical model more explicit to them, and the tool's flexibility will facilitate group or one-on-one instruction in regular classroom settings, in other sessions during or after the school day, and at home. COMPS-A addresses a significant practical issue in today's classrooms by providing individualized and effective RtI intervention programs for students with LDM.

COMPS-A program represents a mathematical model-based problem-solving approach that emphasizes understanding and representation of mathematical relations in algebraic equations and, thus, will support growth in generalized problem-solving skills.COMPS-A will achieve the following objectives: 1) Create the curriculum content, screen design, and a teacher's manual for all four modules in the area of additive word problem solving; 2) Design and develop the cross-platform computer application that can be ported as a web-based, iPad, Android, or Windows app, and this flexibility will make the program accessible to all students; and 3) Conduct small-scale single subject design and randomized controlled trial studies to evaluate the potential of COMPS-A to enhance students' word problem-solving performance. The following research questions will be resolved: (1) What is the functional relationship between the COMPS-A program and students' performance in additive mathematics problem solving? (2) What is the teacher's role in identifying students' misconceptions, alternative reasoning, and knowledge gaps when students are not responsive to the intervention program? (3) What are the necessary instructional scaffolds that will address students' knowledge gaps and therefore facilitate the connection between students' conceptual schemes and the mathematical models necessary for problem solving in order to promote meaningful understanding and construction of additive reasoning? A functional prototype of the COMPS-A will be developed followed by a single-subject design study with a small group of students with LDM to field-test the initial program. Finally, a pretest-posttest, comparison group design with random assignment of participants to groups will then be used to examine the effects of the two intervention conditions: COMPS-A and business as usual. An extensive dissemination plan will enable the project team to share results to a wider community that is responsible for educating all students and, especially, students with LDM.

 

TRUmath and Lesson Study: Supporting Fundamental and Sustainable Improvement in High School Mathematics Teaching (Collaborative Research: Schoenfeld)

Given the changes in instructional practices needed to support high quality mathematics teaching and learning based on college and career readiness standards, school districts need to provide professional learning opportunities for teachers that support those changes. The project is based on the TRUmath framework and will build a coherent and scalable plan for providing these opportunities in high school mathematics departments, a traditionally difficult unit of organizational change.

Award Number: 
1503454
Funding Period: 
Wed, 07/01/2015 to Sun, 06/30/2019
Full Description: 

Given the changes in instructional practices needed to support high quality mathematics teaching and learning based on college and career readiness standards, school districts need to provide professional learning opportunities for teachers that support those changes. The project will build a coherent and scalable plan for providing these opportunities in high school mathematics departments, a traditionally difficult unit of organizational change. Based on the TRUmath framework, characterizing the five essential dimensions of powerful mathematics classrooms, the project brings together a focus on curricular materials that support teaching, Lesson Study protocols and materials, and a professional learning community-based professional development model. The project will design and revise professional development and coaching guides and lesson study mathematical resources built around the curricular materials. The project will study changes in instructional practice and impact on student learning. By documenting the supports used in the Oakland Unified School District where the research and development will be conducted, the resources can be used by other districts and in similar work by other research-practice partnerships.

This project hypothesizes that the quality of classroom instruction can be defined by five dimensions - quality of the mathematics; cognitive demand of the tasks; access to mathematics content in the classroom; student agency, authority, and identity; and uses of assessment. The project will use an iterative design process to develop and refine a suite of tool, including a conversation guide to support productive dialogue between teachers and coaches, support materials for building site-based professional learning materials, and formative assessment lessons using Lesson Study as a mechanism to enact reforms of these dimensions. The study will use a pre-post design and natural variation to student the relationships between these dimensions, changes in teachers' instructional practice, and student learning using hierarchical linear modeling with random intercept models with covariates. Qualitative of the changes in teachers' instructional practices will be based on coding of observations based on the TRUmath framework. The study will also use qualitative analysis techniques to identify themes from surveys and interviews on factors that promote or hinder the effectiveness of the intervention.

TRUmath and Lesson Study: Supporting Fundamental and Sustainable Improvement in High School Mathematics Teaching (Collaborative Research: Donovan)

Given the changes in instructional practices needed to support high quality mathematics teaching and learning based on college and career readiness standards, school districts need to provide professional learning opportunities for teachers that support those changes. The project is based on the TRUmath framework and will build a coherent and scalable plan for providing these opportunities in high school mathematics departments, a traditionally difficult unit of organizational change.

Award Number: 
1503342
Funding Period: 
Wed, 07/01/2015 to Sun, 06/30/2019
Full Description: 

Given the changes in instructional practices needed to support high quality mathematics teaching and learning based on college and career readiness standards, school districts need to provide professional learning opportunities for teachers that support those changes. The project will build a coherent and scalable plan for providing these opportunities in high school mathematics departments, a traditionally difficult unit of organizational change. Based on the TRUmath framework, characterizing the five essential dimensions of powerful mathematics classrooms, the project brings together a focus on curricular materials that support teaching, Lesson Study protocols and materials, and a professional learning community-based professional development model. The project will design and revise professional development and coaching guides and lesson study mathematical resources built around the curricular materials. The project will study changes in instructional practice and impact on student learning. By documenting the supports used in the Oakland Unified School District where the research and development will be conducted, the resources can be used by other districts and in similar work by other research-practice partnerships.

This project hypothesizes that the quality of classroom instruction can be defined by five dimensions - quality of the mathematics; cognitive demand of the tasks; access to mathematics content in the classroom; student agency, authority, and identity; and uses of assessment. The project will use an iterative design process to develop and refine a suite of tool, including a conversation guide to support productive dialogue between teachers and coaches, support materials for building site-based professional learning materials, and formative assessment lessons using Lesson Study as a mechanism to enact reforms of these dimensions. The study will use a pre-post design and natural variation to student the relationships between these dimensions, changes in teachers' instructional practice, and student learning using hierarchical linear modeling with random intercept models with covariates. Qualitative of the changes in teachers' instructional practices will be based on coding of observations based on the TRUmath framework. The study will also use qualitative analysis techniques to identify themes from surveys and interviews on factors that promote or hinder the effectiveness of the intervention.

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