Reasoning Skills

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.

PBS NewsHour STEM Student Reporting Labs: Broad Expansion of Youth Journalism to Support Increased STEM Literacy Among Underserved Student Populations and Their Communities

The production of news stories and student-oriented instruction in the classroom are designed to increase student learning of STEM content through student-centered inquiry and reflections on metacognition. This project scales up the PBS NewsHour Student Reporting Labs (SRL), a model that trains teens to produce video reports on important STEM issues from a youth perspective.

Award Number: 
1503315
Funding Period: 
Sat, 08/01/2015 to Wed, 07/31/2019
Full Description: 

The Discovery Research K-12 program (DR-K12) 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 scales up the PBS NewsHour Student Reporting Labs (SRL), a model that trains teens to produce video reports on important STEM issues from a youth perspective. Participating schools receive a SRL journalism and digital media literacy curriculum, a mentor for students from a local PBS affiliate, professional development for educators, and support from the PBS NewsHour team. The production of news stories and student-oriented instruction in the classroom are designed to increase student learning of STEM content through student-centered inquiry and reflections on metacognition. Students will develop a deep understanding of the material to choose the best strategy to teach or tell the STEM story to others through digital media. Over the 4 years of the project, the model will be expanded from the current 70 schools to 150 in 40 states targeting schools with high populations of underrepresented youth. New components will be added to the model including STEM professional mentors and a social media and media analytics component. Project partners include local PBS stations, Project Lead the Way, and Share My Lesson educators.

The research study conducted by New Knowledge, LLC will add new knowledge about the growing field of youth science journalism and digital media. Front-end evaluation will assess students' understanding of contemporary STEM issues by deploying a web-based survey to crowd-source youth reactions, interest, questions, and thoughts about current science issues. A subset of questions will explore students' tendencies to pass newly-acquired information to members of the larger social networks. Formative evaluation will include qualitative and quantitative studies of multiple stakeholders at the Student Reporting Labs to refine the implementation of the program. Summative evaluation will track learning outcomes/changes such as: How does student reporting on STEM news increase their STEM literacy competencies? How does it affect their interest in STEM careers? Which strategies are most effective with underrepresented students? How do youth communicate with each other about science content, informing news media best practices? The research team will use data from pre/post and post-delayed surveys taken by 1700 students in the STEM Student Reporting Labs and 1700 from control groups. In addition, interviews with teachers will assess the curriculum and impressions of student engagement.


Project Videos

2019 STEM for All Video Showcase

Title: How Video Storytelling Reengages Teenagers in STEM Learning

Presenter(s): Leah Clapman & William Swift

2018 STEM for All Video Showcase

Title: PBS NewsHour's STEM SRL Transforms Classrooms into Newsrooms

Presenter(s): Leah Clapman & William Swift

2017 STEM for All Video Showcase

Title: PBS is Building the Next Generation of STEM Communicators

Presenter(s): Leah Clapman, John Fraser, Su-Jen Roberts, & Bill Swift


Science Teachers Learning from Lesson Analysis (STeLLA): High School Biology

This project will develop and test a biology teacher professional model that employs analysis of videotaped lessons to promote increased biology content knowledge and pedagogical content knowledge among practicing biology teachers. The content of the professional development activities will focus on the crosscutting concepts of stability and change that link core ideas in three areas of biology: cell biology, heredity, and evolution.

Lead Organization(s): 
Award Number: 
1503280
Funding Period: 
Sat, 08/01/2015 to Wed, 07/31/2019
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. This project will develop and test a biology teacher professional model that employs analysis of videotaped lessons to promote increased biology content knowledge and pedagogical content knowledge among practicing biology teachers. The content of the professional development activities will focus on the crosscutting concepts of stability and change that link core ideas in three areas of biology: cell biology, heredity, and evolution. These are content areas that have been shown to be difficult for students to learn, and difficult for teachers to teach. The professional development model will include: a) a summer institute where teachers gain new knowledge and skills in biology and learn to analyze videotaped lessons; b) opportunities to teach project-developed lessons during the academic year; and c) study group sessions during the academic year where participating teachers analyze videoclips of their own teaching.

The project will design, develop, and test a teacher professional development model that is based on a previously developed approach that has been shown to be effective among elementary school teachers. It is hypothesized that the newly developed program will have a positive impact on the science achievement of high school students, that it will improve teacher science content knowledge and classroom practice, and that the effects on student outcomes will be equitable across student demographic variables. To test thee hypotheses, the project will employ a quasi-experimental research approach in which teachers will serve as their own comparison groups in a cohort control design. Hierarchical linear modeling will be used to differentiate the effects of variances in teacher content knowledge and pedagogical content knowledge, student demographic variables, and school factors. It is anticipated that the project will find evidence that the proposed approach to biology teacher professional development has the potential to close the achievement gaps among student populations.

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.

SimScientists Games: Development of Simulation-Based Game Designs to Enhance Formative Assessment and Deep Science Learning in Middle School

This project will focus on understanding how educational games, designed according to research-based learning and assessment design principles, can better assess and promote students' science knowledge, application of science process skills, and motivation and engagement in learning.

Lead Organization(s): 
Award Number: 
1503481
Funding Period: 
Sat, 08/01/2015 to Wed, 07/31/2019
Full Description: 

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 project is a four-year design and development study submitted to the assessment strand of the program. It will focus on understanding how educational games, designed according to research-based learning and assessment design principles, can better assess and promote students' science knowledge, application of science process skills, and motivation and engagement in learning. The project will develop a new genre of games to serve as formative assessment resources designed to collect evidence of science learning during gameplay, provide feedback and coaching in the form of hints, and reinforce middle grade (6th-8th) students' life science concepts and investigation practices about ecosystems described in the Next Generation Science Standards (NGSS) (Achieve, 2013). The games will build on the designs of the simulation-based, curriculum-embedded assessments developed in previous NSF-funded efforts, which include student progress reports and reflection activities that allow teachers to provide feedback to students and adjust instruction. The design of the games will draw from multiple lines of research, such as cognition, particularly model-based learning; principled assessment design; and motivation. Intended to provide engaging activities for understanding and investigating the system components, roles, interactions, and population dynamics of ecosystems, the project will produce two sets of comprehensive games: (1) Organisms and Interactions, and (2) Emergent Population Levels: Managing an Ecosystem. Each game will consist of progressively advanced mini-games. Twenty-four California Bay Area middle school teachers will participate in the study. Teacher professional development (PD) will include face-to-face sessions and an online platform that permits a wide range of interactions among participants and the facilitators. The PD will emphasize the alignment of the ecosystem simulation-based curriculum modules with their state standards, instructional materials, and the new games. 

The project will address six research questions: (1) How well do the games align with the ecosystem crosscutting concepts, core ideas, and inquiry practices in the NGSS?; (2) How well do game components meet quality standards?; (3) How well do the games integrate with the existing simulation-based curriculum modules and the teachers' existing instructional sequence?; (4) What effect does the use of the games have on students' understanding of the science concepts, scientific practices, and collaboration skills?; (5) How does success in gameplay relate to improved performance on the external outcome measures comprised of the simulation-based benchmark and the pre/posttest?; and (6) How does the use of the games affect students' engagement in science learning? In a Year 1 usability study, the project will test, analyze, and revise alpha versions of the games. In Year 2, a classroom feasibility study of beta versions will inform further revisions. In Year 3, six teachers will pilot-test the games. A second pilot test in Year 4 will examine the effectiveness of the games by comparing student performance in classes using the existing simulation-based curriculum-embedded assessments and reflection activities with classes using the curriculum-embedded assessments plus the new games. Data collection and analysis strategies include: (a) alignment reviews; (b) focus groups and usability testing; (c) cognitive labs for construct validity and usability; (d) game reports (badges); (e) pre/posttest of American Association for the Advancement of Science (AAAS) items; (f) benchmark assessment data; (g) student interest in the games and science; (h) teacher surveys; (i) case studies; (j) game quality analysis; (k) differential item functioning; (l) analysis of covariance; and (m) analysis of variance on posttest scores (outcome variable) to compare the means across student groups (by intervention mode) and their prior science achievement levels.

SmartCAD: Guiding Engineering Design with Science Simulations (Collaborative Research: Xie)

This project investigates how real time formative feedback can be automatically composed from the results of computational analysis of student design artifacts and processes with the envisioned SmartCAD software. The project conducts design-based research on SmartCAD, which supports secondary science and engineering with three embedded computational engines capable of simulating the mechanical, thermal, and solar performance of the built environment.

Lead Organization(s): 
Award Number: 
1503196
Funding Period: 
Mon, 06/15/2015 to Fri, 05/31/2019
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. 

In this project, SmartCAD: Guiding Engineering Design with Science Simulations, the Concord Consortium (lead), Purdue University, and the University of Virginia investigate how real time formative feedback can be automatically composed from the results of computational analysis of student design artifacts and processes with the envisioned SmartCAD software. Through automatic feedback based on visual analytic science simulations, SmartCAD is able to guide every student at a fine-grained level, allowing teachers to focus on high-level instruction. Considering the ubiquity of CAD software in the workplace and their diffusion into precollege classrooms, this research provides timely results that could motivate the development of an entire genre of CAD-based learning environments and materials to accelerate and scale up K-12 engineering education. The project conducts design-based research on SmartCAD, which supports secondary science and engineering with three embedded computational engines capable of simulating the mechanical, thermal, and solar performance of the built environment. These engines allow SmartCAD to analyze student design artifacts on a scientific basis and provide automatic formative feedback in forms such as numbers, graphs, and visualizations to guide student design processes on an ongoing basis. 

The research hypothesis is that appropriate applications of SmartCAD in the classroom results in three learning outcomes: 1) Science knowledge gains as indicated by a deeper understanding of the involved science concepts and their integration at the completion of a design project; 2) Design competency gains as indicated by the increase of iterations, informed design decisions, and systems thinking over time; and 3) Design performance improvements as indicated by a greater chance to succeed in designing a product that meets all the specifications within a given period of time. While measuring these learning outcomes, this project also probes two research questions: 1) What types of feedback from simulations to students are effective in helping them attain the outcomes? and 2) Under what conditions do these types of feedback help students attain the outcomes? To test the research hypothesis and answer the research questions, this project develops three curriculum modules based on the Learning by Design (LBD) Framework to support three selected design challenges: Solar Farms, Green Homes, and Quake-Proof Bridges. This integration of SmartCAD and LBD situate the research in the LBD context and shed light on how SmartCAD can be used to enhance established pedagogical models such as LBD. Research instruments include knowledge integration assessments, data mining, embedded assessments, classroom observations, participant interviews, and student questionnaires. This research is carried out in Indiana, Massachusetts, and Virginia simultaneously, involving more than 2,000 secondary students at a number of socioeconomically diverse schools. Professional development workshops are provided to familiarize teachers with SmartCAD materials and implementation strategies prior to the field tests. An external Critical Review Committee consisting of five engineering education researchers and practitioners oversee and evaluate this project formatively and summative. Project materials and results are disseminated through publications, presentations, partnerships, and the Internet.

Scientific Data in Schools: Measuring the Efficacy of an Innovative Approach to Integrating Quantitative Reasoning in Secondary Science (Collaborative Research: Stuhlsatz)

Lead Organization(s): 
Award Number: 
1503005
Funding Period: 
Wed, 07/15/2015 to Fri, 05/31/2019
Project Evaluator: 
Kristin Bass
Full Description: 

The goal of this project is to investigate whether the integration of real data from cutting-edge scientific research in grade 6-10 classrooms will increase students’ quantitative reasoning ability in the context of science. Data Nuggets are activity-based resources that address current needs in STEM education and were developed by science graduate students and science teachers at Michigan State University through prior support from the NSF GK-12 program and the BEACON Center for the Study of Evolution in Action. The goal of Data Nuggets is to engage students in the practices of science through an innovative approach that combines scientific content from authentic research with key concepts in quantitative reasoning. Partners from Michigan State University and BSCS will adapt the materials to address current science and mathematics standards, create a professional development program for teachers, and test the efficacy of the materials through a cluster-randomized trial in the classrooms of 30 teachers in Michigan, Colorado, and California.

The project will study whether short, targeted interventions of classroom activities embedded within a typical curriculum can impact student outcomes. Prior to the study teachers will participate in professional development. Classrooms of the teachers in the study will be randomly assigned to either a treatment or comparison condition. Student outcome measures will include understanding of quantitative reasoning in the context of science, understanding of the practices and processes of science, student engagement and motivation, and interest in science.

In order to adequately train the next generation of citizens and scientists, research is needed on how quantitative reasoning skills build upon each other throughout K-16 science education Students need to experience activities that emphasize how science is conducted, and apply their understandings of how scientists reason quantitatively. Establishing the efficacy of Data Nuggets could provide the field with information about supplementing existing curriculum with short interventions targeted at particular scientific practices. By facilitating student access to authentic science, Data Nuggets bridge the gap between scientists and the public. Scientists who create Data Nuggets practice their communication skills and share both the process of science and research findings with K-12 students (and perhaps their families), undergraduates, and teachers, improving the understanding of science in society.

Fostering STEM Trajectories: Bridging ECE Research, Practice, and Policy

This project will convene stakeholders in STEM and early childhood education to discuss better integration of STEM in the early grades. PIs will begin with a phase of background research to surface critical issues in teaching and learning in early childhood education and STEM.  A number of reports will be produced including commissioned papers, vision papers, and a forum synthesis report.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1417878
Funding Period: 
Mon, 06/15/2015 to Tue, 05/31/2016
Full Description: 

Early childhood education is at the forefront of the minds of parents, teachers, policymakers as well as the general public. A strong early childhood foundation is critical for lifelong learning. The National Science Foundation has made a number of early childhood grants in science, technology, engineering and mathematics (STEM) over the years and the knowledge generated from this work has benefitted researchers. Early childhood teachers and administrators, however, have little awareness of this knowledge since there is little research that is translated and disseminated into practice, according to the National Research Council. In addition, policies for both STEM and early childhood education has shifted in the last decade. 

The Joan Ganz Cooney Center and the New America Foundation are working together to highlight early childhood STEM education initiatives. Specifically, the PIs will convene stakeholders in STEM and early childhood education to discuss better integration of STEM in the early grades. PIs will begin with a phase of background research to surface critical issues in teaching and learning in early childhood education and STEM. The papers will be used as anchor topics to organize a forum with a broad range of stakeholders including policymakers as well as early childhood researchers and practitioners. A number of reports will be produced including commissioned papers, vision papers, and a forum synthesis report. The synthesis report will be widely disseminated by the Joan Ganz Cooney Center and the New America Foundation.

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 project.

CAREER: Proof in Secondary Classrooms: Decomposing a Central Mathematical Practice

This project will develop an intervention to support the teaching and learning of proof in the context of geometry.

Lead Organization(s): 
Award Number: 
1453493
Funding Period: 
Wed, 07/15/2015 to Tue, 08/31/2021
Full Description: 

This project, funded as part of the CAREER program, would add to the knowledge base on the teaching and learning of proof in the context of the most prevalent course/topic in which proof is taught in the K-12 curriculum, geometry. Given the centrality of the role of proof, and the persistent difficulties in teaching proof in the K-12 and undergraduate curriculum, the topic is of vital importance. The work is novel, focusing on an area of proof that is understudied, the introduction of students to the topic of proof. While building on prior work in proof, the project will tackle an important area of beginning to teach proof, which may lead to broader innovations at both the K-12 and undergraduate level. The project will produce a resource, a set of lessons, which can be used widely and are likely to be broadly disseminated based on the PI's previous NSF-supported work, which has been broadly disseminated to practitioner audiences. 

The goal of the project is to develop an intervention to support the teaching and learning of proof in the context of geometry. This study takes as its premise that if we introduce proof, by first teaching students particular sub-goals of proof, such as how to draw a conclusion from a given statement and a definition, then students will be more successful with constructing proofs on their own. The 5-year design and development study builds on the researcher's prior work from a Knowles Science Teaching Fellowship (KSTF) grant to study how teachers introduce proof to students. This study will build on the prior work to refine a framework for introducing proof developed in the KSTF study. Using this framework the researcher will work with five high school geometry teachers to develop lessons via Lesson Study methods to introduce sub-goals of proof. The PI will study the impact of the use of these lessons on students' ability to perform proofs, and compare to students of ten teachers who will not have participated in the intervention.

 

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