Mathematics

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.

 

Ramping Up Accessibility in STEM: Inclusively Designed Simulations for Diverse Learners

This project brings together leaders in simulation design and accessibility to develop and study interactive science simulations for diverse middle school students including those with sensory, mobility, or learning disabilities. The resulting simulations and research findings will help to address the significant disparity that exists between the achievement in science by students with and without disabilities.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1503439
Funding Period: 
Wed, 07/15/2015 to Fri, 06/30/2017
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.

This project will bring together leaders in simulation design and accessibility to develop and study interactive science simulations for diverse middle school students including those with sensory, mobility, or learning disabilities. The resulting simulations and research findings will help to address the significant disparity that exists between the achievement in science by students with and without disabilities. The Physics Education Technology (PhET) Interactive Simulations project (University of Colorado Boulder) will develop and research interactive science and math simulations used by teachers and students around the world. The Inclusive Design Research Centre (OCAD University, Toronto, Ontario) is an international leader in inclusively designed technology, with the goal of designing for the full range of human diversity including those with and without disabilities. Together, the project team will engage in an iterative design process to develop innovative solutions for making the highly interactive environment of an educational simulation simultaneously intuitive, accessible, and supportive of exploration and discovery practices in science. Development efforts will focus on three inclusive simulations and optimize the design and implementation of several inclusive simulation features, including keyboard navigation, auditory descriptions for screen readers, the use of non-speech sounds to provide feedback (sonification), and the ability to control the simulation with assistive technology (AT) devices. For each simulation, professional development materials for teachers, including classroom activities and user guides, will be developed to support teachers in effectively using the inclusively designed simulations in their classrooms. 

Through new research, this project will seek to understand: 1) how inclusive simulations can support students with disabilities to engage in science practices, 2) how students with and without disabilities utilize inclusive simulations for learning STEM content, and 3) how students can engage in collaborative learning between students with and without disabilities - with an inclusive simulation. Researchers will use individual interviews with diverse students to closely examine these questions. The resulting resources, models, and tools will provide exemplars and important building blocks for an inclusively designed interactive curriculum, educational games, and assessment tools. Resulting simulations, research findings, design guidelines, and exemplars will be disseminated through the project team and advisor partner networks, education resource websites, and educator professional organizations.

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.

Student-Adaptive Pedagogy for Elementary Teachers: Promoting Multiplicative and Fractional Reasoning to Improve Students' Preparedness for Middle School Mathematics

The project develops a teacher professional development intervention to support student-adaptive pedagogy for multiplicative and fractional reasoning. The idea is that classroom instruction should build on students' current conceptions and experiences. It focuses on students from urban, underserved and low-socioeconomic status populations who often fall behind in the elementary grades and are left underprepared for middle grades mathematics.

Lead Organization(s): 
Award Number: 
1503206
Funding Period: 
Wed, 07/15/2015 to Sun, 06/30/2019
Full Description: 

The project develops a teacher professional development intervention to support student-adaptive pedagogy for multiplicative and fractional reasoning. The idea is that classroom instruction should build on students' current conceptions and experiences. The context for the study is grades 3-5 teachers in Aurora Public Schools. It focuses on students from urban, underserved and low-socioeconomic status populations who often fall behind in the elementary grades and are left underprepared for middle grades mathematics. It includes a summer workshop and academic year follow-up including teacher collaboration. The project provides tools for capitalizing on successful, school-based research for promoting teachers' buy-in, adoption, and sustaining of student-adaptive pedagogy. The project also includes measurement of student understanding of the concepts. An extensive plan to share tools and resources for teachers and instructional coaches (scalable to district/state levels) and of research instruments and findings, will promote sharing project outcomes with a wide community of stakeholders (teachers, administrators, researchers, parents, policy makers) responsible for students' growth. This is a Full Design & Development project within the DRK-12 Program's Learning Strand. 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 project aims to implement and study a professional development intervention designed to shift upper-elementary teachers' mathematics teaching toward a constructivist approach, called student-adaptive pedagogy (AdPed), which adapts teaching goals and activities based on students' conceptions and experiences. The project focuses on multiplicative and fractional reasoning--critical for students' success in key areas of middle school mathematics (e.g., ratio, proportion, and function). The project seeks to design an instrument for measuring teachers' implementation of AdPed, a clinical interview rubric for students' multiplicative reasoning and then an analysis of teachers' content knowledge and the implementation of AdPed following the professional development. The research design is rooted in an innovative, cohesive framework that integrates four research-based components: (i) a model of mathematics learning and knowing, (ii) models of progressions in students' multiplicative and fractional reasoning, (iii) a model of teaching (AdPed) to promote such learning, and (iv) a mathematics teacher development continuum. Capitalizing on successful preliminary efforts in the Denver Metro area to refine a PD intervention and student-adaptive tools that challenge and transform current practices, the project will first validate and test instruments to measure (a) teacher growth toward adaptive pedagogy and (b) students' growth in multiplicative reasoning. Using these new instruments, along with available measures, the project will then promote school-wide teacher professional development (grades 3-5) in multiple schools in an urban district with large underserved student populations and study the professional development benefits for teacher practices and student outcomes. The mixed methods study includes classroom-based data (e.g., video analysis, lesson observations, teacher interviews) and measures of students' multiplicative reasoning specifically and mathematical understanding generally.

Visual Access to Mathematics: Professional Development for Teachers of English Learners

This project addresses a critical need, developing professional development materials to address the teachers of ELLs. The project will create resources to help teachers build ELLs' mathematical proficiency through the design and development of professional development materials building on visual representations (VRs) for mathematical reasoning across a range of mathematical topics.

Award Number: 
1503057
Funding Period: 
Sat, 08/01/2015 to Wed, 07/31/2019
Full Description: 

The demands placed on mathematics teachers of all students have increased with the introduction of college and career readiness standards. At the same time, the mathematics achievement of English Language Learners (ELLs) lags behind that of their peers. This project addresses a critical need, developing professional development materials to address the teachers of ELLs. The project will create resources to help teachers build ELLs' mathematical proficiency through the design and development of professional development materials building on visual representations (VRs) for mathematical reasoning across a range of mathematical topics. The project will study how to enhance teachers' pedagogical content knowledge that is critical to fostering ELLs' mathematical problem solving and communication to help support fluency in using VRs among teachers and students. To broaden the participation of students who have traditionally not demonstrated high levels of achievement in mathematics, a critical underpinning to further success in the sciences and engineering, there will need to be greater support for teachers of these students using techniques that have been demonstrated to improve student learning. 

The project will use an iterative design and development process to develop a blended learning model of professional development on using VRs with a 30-hour face-to-face summer institute and sixteen 2-hour online learning sessions. Teachers and teacher-leaders will help support the development of the professional development materials. A cluster randomized control trial will study the piloting of the materials and their impact on teacher outcomes. Thirty middle schools from Massachusetts and Maine serving high numbers of ELLs, with approximately 120 teachers, will be randomly assigned to receive the treatment or control conditions. Using a two-level random intercepts hierarchical linear model, the study will explore the impact of participation in the professional development on teachers' mathematical knowledge for teaching and instructional practice. The pilot study will also explore the feasibility of delivering the professional development model more broadly. It builds on prior work that has shown efficacy in geometry, but expands the work beyond a single area in mathematics. At the same time, they will test the model for feasibility of broad implementation.

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.

Strengthening the Quality, Design and Usability of Simulations as Assessments of Teaching Practice

Ensuring that beginning teachers are "classroom-ready" requires assessments that efficiently and validly evaluate proficiency in teaching. This project explores assessments involving simulated students as a way to assess teaching practice, which could provide an important complement, or alternative, to directly assessing teaching practice in classrooms.

Lead Organization(s): 
Award Number: 
1502711
Funding Period: 
Tue, 09/01/2015 to Thu, 08/31/2017
Full Description: 

Ensuring that beginning teachers are "classroom-ready" requires assessments that efficiently and validly evaluate proficiency in teaching. This project explores assessments involving simulated students as a way to assess teaching practice, which could provide an important complement, or alternative, to directly assessing teaching practice in classrooms. This form of assessment has the potential to provide a way to avoid onerous expense, logistics, and other difficulties of assessments happening in classrooms. The project will address questions about the development of performance expectations for elementary mathematics teachers, the extent to which the performance of the "student" role can be standardized across different performance contexts, and different approaches for generating teaching scenarios. The assessments will focus on the teaching practices of eliciting and interpreting students' mathematical thinking. The project will support: (1) establishing the validity of the assessment as a means to assess readiness to teach elementary mathematics and (2) providing the necessary foundation for scaling research and the use of simulation assessments. 

The goal of this project is generating, calibrating, and studying standardized simulations of clinical performance of mathematics teaching. The strategy is to investigate three components of the simulation assessment that will enable its broader use in the field. One component will focus on approaches that use different foundations (wisdom of practice, interactions with children, and learning trajectories research) for the design of simulations that are authentic and provide robust information about teaching. Data on the ways in which each approach supplies resources needed for assessment development will be compared. Another component will focus on the degree to which the role of the student can be standardized given the dynamics of teaching. Data on the responses of standardized students, who have similar initial training, to different situational categories will be analyzed. A final component will be establishing a basis for calibrating performance expectations for simulations linked to key points in a teacher's career trajectory (early career teachers, experienced teachers, "accomplished" teachers). Data on the performance of teachers at different points in their careers on the same assessment simulations will be compared. This study of components impacting assessment design will result in a more robust foundation for further development of, and further research on, teaching simulation assessments. 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.

Thirteenth International Congress on Mathematical Education (ICME-13) Travel Grant

This project will support the participation of 55 U.S. K-12 mathematics teachers or supervisors, graduate students, community college/university mathematics teachers, mathematicians, mathematics teacher educators and mathematics education researchers to attend the Thirteenth International Congress for Mathematical Education (ICME-13) to be held in Hamburg, Germany, July 24-31, 2016. The project will also prepare an educational status report (called the Fact Book) for the United States.

Lead Organization(s): 
Award Number: 
1503277
Funding Period: 
Mon, 06/15/2015 to Wed, 05/31/2017
Full Description: 

This project will support the participation of 55 U.S. K-12 mathematics teachers or supervisors, graduate students, community college/university mathematics teachers, mathematicians, mathematics teacher educators and mathematics education researchers to attend the Thirteenth International Congress for Mathematical Education (ICME-13) to be held in Hamburg, Germany, July 24-31, 2016. The project will also prepare an educational status report (called the Fact Book) for the United States. The research team will report on the state of U.S. mathematics education in 2016, through a Fact Book that builds from those published for ICMEs 9, 10, 11, and 12.

Through participation in the conference, American math educators will interact with mathematics educators from many countries and learn about their current math education practices concerning curriculum development, the use of technology in learning mathematics, strategies for reaching all students, teacher education and ongoing teacher professional development. The project is supported major national mathematics research and professional societies including the National Council of Teachers of Mathematics, Association of Mathematics Teacher Educators, United States National Commission on Mathematical Instruction, Mathematical Association of America, American Mathematical Society and American Mathematical Association of Two Year Colleges. Participants will disseminate information and resources from the conference through these mathematics organizations, math education journals, and social media.

The Discovery Research K-12 (DRK-12) program 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. This conference will advance the understanding of the U.S mathematics community regarding current international research and development in mathematics education, addressing the Teaching and Learning strands of the DRK-12 program.

Teaching and Learning Algebraic Thinking Across the Middle Grades: A Research-based Approach Using PhET Interactive Simulations

This project addresses three central challenges: 1) the tendency for students to not engage in real mathematical thinking as they use technologies; 2) the tendency for teachers to not enact pedagogically-effective approaches; and 3) the lack of adoption of effective technologies by teachers due to a variety of barriers. This project will use rich, exploratory, interactive simulations and associated instructional materials as a pathway for making rapid progress and focusing on advancing algebraic thinking in Grades 6-9.

Lead Organization(s): 
Award Number: 
1503510
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.

Widespread, high-quality use of technology has great potential to transform today's mathematics classrooms and enable all students to develop a robust conceptual understanding of mathematics. Critical challenges are currently limiting the realization of this potential, and 69% of US Grade 8 students are scoring below proficient in national studies. In this 3-year Discovery Research K-12 Full Research and Development project, Teaching and Learning Algebraic Thinking Across the Middle Grades: A Research-based Approach Using PhET Interactive Simulations, the PhET Interactive Simulations group at the University of Colorado Boulder is partnering with mathematics education researchers at the University of South Florida St. Petersberg and Florida State University to address three central challenges, as follows: 1) the tendency for students to not engage in real mathematical thinking as they use technologies; 2) the tendency for teachers to not enact pedagogically-effective approaches; and 3) the lack of adoption of effective technologies by teachers due to a variety of barriers. This collaborative effort uses rich, exploratory, interactive simulations and associated instructional materials as a pathway for making rapid progress and focuses on advancing algebraic thinking in Grades 6-9.

This project seeks to enable teachers to fully-leverage the benefits of interactive simulations to advance student engagement and learning of mathematics, moving technology from the margins to a core part of instruction. The project will answer critical research questions, such as: how the design of an interactive simulation can generate pedagogically-productive use; how instruction with simulations can be best structured to support learning of mathematical concepts and engagement in mathematical practices; how sim-based instruction can be made attractive, feasible and effective for teachers; and finally, how student learning is impacted by sim-based instruction. At the same time, this project will produce a collection of open educational resources for teachers and students. These resources will include 15 research-based, student-tested simulations for teaching and learning of algebraic thinking, associated instructional support materials, and teacher professional development resources for effective implementation. Based on the 75 million uses per year of PhET?s science simulations, we expect these resources to transform mathematics instruction for millions of students and thousands of teachers.

This project will employ a variety of research methods to approach these questions. Researchers will use individual interviews from a diverse group of Grades 6-9 students as they use the 15 new simulations to examine usability, engagement, and achievement and to identify design approaches that stimulate productive use. In parallel, classroom-based studies in Colorado and Florida will investigate ways in which simulations can be combined with instructional materials and teacher facilitation to engage groups of students in inquiry, promote rich discussions of important mathematical ideas, and advance achievement in the Common Core State Standards for Mathematics. The project will employ an iterative design and development process involving qualitative and quantitative analysis of diverse measures including the quality of mathematical instruction. Finally, a pilot study and an evaluation of teacher PD supports will examine the feasibility and fidelity with which teachers implement the innovation, and the impact on student learning.

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