Mathematics

Design and Development of Transmedia Narrative-based Curricula to Engage Children in Scientific Thinking and Engineering Design (Collaborative Research: McGinnis-Cavanaugh)

This project will address the need for engineering resources by applying an innovative pedagogy called Imaginative Education (IE) to create middle school engineering curricula. In IE, developmentally appropriate narratives are used to design learning environments that help learners engage with content and organize their knowledge productively. This project will combine IE with transmedia storytelling.

Partner Organization(s): 
Award Number: 
1813572
Funding Period: 
Sun, 07/15/2018 to Thu, 06/30/2022
Project Evaluator: 
Collaborative for Educational Services (CES)
Full Description: 

Engineering is an important component of the Next Generation Science Standards (NGSS). However, resources for supporting teachers in implementing these standards are scarce. This project will address the need for resources by applying an innovative pedagogy called Imaginative Education (IE) to create middle school engineering curricula. In IE, developmentally appropriate narratives are used to design learning environments that help learners engage with content and organize their knowledge productively. To fully exploit the potential of this pedagogy, this project will combine IE with transmedia storytelling. In transmedia storytelling, different elements of a narrative are spread across a variety of formats (such as books, websites, new articles, videos and other media) in a way that creates a coordinated experience for the user. Once created, the curricula will be implemented in classrooms to research its impact on (1) increasing learners' capacities to engage in both innovative and direct application of engineering concepts, and (2) improving learners' science, technology, engineering, and mathematics (STEM) identity. 

This research will be led by Smith College and Springfield Technical Community College in collaboration with Springfield (MA) Public Schools (SPS). Additional expertise in evaluating the findings will be provided by the Collaborative for Educational Services and an external advisory board of leaders in STEM education and transmedia storytelling. The project will result in the development of a transmedia learning environment that includes two NGSS-aligned, interdisciplinary engineering units and seven lessons that integrate science and engineering. The research study will be implemented in four phases in eight SPS middle schools. Approximately 900 students will participate each year. In Phase 1, the project team will collaborate with SPS teachers to create engineering units, lessons, and standards-based achievement measures. In Phase 2, teachers in the treatment group will participate in professional development (PD) workshops covering IE, transmedia learning environments, structure of the curriculum, and connections to NGSS. In Phase 3 the curricula will be implemented in treatment classrooms and both treatment and control group students will be assessed. In Phase 4, testing and assessment will continue in SPS schools and will be expanded to rural and suburban classrooms. Teachers in these classrooms will use online multimedia PD that will ensure scalability and mirrors the structure and content of in-person PD. Data analysis will provide evidence of whether this imaginative and transmedia educational approach improves students' capacities for using engineering concepts and enhances their STEM identity.


Project Videos

2019 STEM for All Video Showcase

Title: Transforming Engineering Education for Middle School (TEEMS)

Presenter(s): Beth McGinnis-Cavanaugh, Sonia Ellis, & Crystal Ford


Integrating Science with Mathematics and Engineering: Linking Home and School Learning for All Young Learners

This study will investigate the integration of science with mathematics and engineering and develop resources that provide preschool children with integrated STEM learning experiences. The study will also investigate the connection between home and school learning and will develop resources that strengthen children's experiences at school and home.

Lead Organization(s): 
Award Number: 
1813280
Funding Period: 
Sat, 09/01/2018 to Mon, 02/28/2022
Full Description: 

Children in preschool programs have few opportunities to engage meaningfully in science, technology, engineering, and mathematics (STEM) disciplines. This is especially true in programs serving children from low-income communities, where resources are scarce. This study will investigate the integration of science with mathematics and engineering and develop resources that provide preschool children with integrated STEM learning experiences. The study will also investigate the connection between home and school learning and will develop resources that strengthen children's experiences at school and home. This will include investigating the needs of and designing for dual language learners who represent a large (and growing) proportion of the population served in public preschool programs.

Using design based research (DBR), the researchers will: (1) Develop learning blueprints to guide the design of classroom and family learning resources. (2) Co-design resources with teachers and parents from low-income as well as culturally and linguistically diverse communities. (3) Conduct a series of formative pilot studies with partner teachers and parents. (4) Conduct a quasi-experimental field study in preschool classrooms and homes to examine both implementation and learning outcomes. Data sources will include observations in classrooms and homes, surveys and interviews with teachers and parents, and child learning assessments. Analysis will include qualitative approaches to examine patterns of interaction and engagement with resources in classrooms and homes, as well as quantitative approaches to examine children's learning accounting for the multilevel structure of the data. The project involves a collaboration between Digital Promise Global, Education Development Center, WGBH and multiple early childhood programs in California and New York. A total of 28 preschool centers, 56 classroom teachers, 208 families and 560 children are expected to participate. Results from this project are intended to inform understanding of how young children learn STEM, how adults at school and home can support children's early STEM learning, and what supports are useful to diverse learners specifically. Results could also highlight design principles that can inform future early STEM education research and development efforts integrating media and technology.

Developing Preservice Teachers' Capacity to Teach Students with Learning Disabilities in Algebra I

Project researchers are training pre-service teachers to tutor students with learning disabilities in Algebra 1, combining principles from special education, mathematics education, and cognitive psychology. The trainings emphasize the use of gestures and strategic questioning to support students with learning disabilities and to build students’ understanding in Algebra 1.

Project Email: 
Lead Organization(s): 
Award Number: 
1813903
Funding Period: 
Wed, 08/01/2018 to Sat, 07/31/2021
Full Description: 

This project is implementing a program to train pre-service teachers to tutor students with learning disabilities in Algebra 1, combining principles from special education, mathematics education, and cognitive psychology. The project trains tutors to utilize gestures and strategic questioning to support students with LD to build connections between procedural knowledge and conceptual understanding in Algebra 1, while supporting students’ dispositions towards doing mathematics. The training will prepare tutors to address the challenges that students with LD often face—especially challenges of working memory and processing—and to build on their strengths as they engage with Algebra 1. The project will measure changes in tutors’ ability to use gestures and questioning to support the learning of students with LD during and after the completion of our training. It will also collect and analyze data on the knowledge and dispositions of students with LD in Algebra 1 for use in the ongoing refinement of the training and in documenting the impact of the training program.

 

Critical Issues in Mathematics Education 2018

This conference will continue the workshop series Critical Issues in Mathematics Education (CIME). The topic for CIME 2018 will be "Access to mathematics by opening doors for students currently excluded from mathematics". The CIME workshops engage professional mathematicians, education researchers, teachers, and policy makers in discussions of issues critical to the improvement of mathematics education from the elementary grades through undergraduate years.

Award Number: 
1827412
Funding Period: 
Thu, 03/01/2018 to Thu, 02/28/2019
Full Description: 

This conference will continue the workshop series, Critical Issues in Mathematics Education (CIME) on teaching and learning mathematics, initiated by the Mathematical Sciences Research Institute (MSRI) in 2004. The topic for CIME 2018 will be "Access to mathematics by opening doors for students currently excluded from mathematics". The CIME workshops engage professional mathematicians, education researchers, teachers, and policy makers in discussions of issues critical to the improvement of mathematics education from the elementary grades through undergraduate years. Sessions will share relevant programmatic efforts and innovative research that have been shown to maintain or increase students' engagement and interests in mathematics across K-12, undergraduate and graduate education. The sessions will focus particularly on reproducible efforts that affirm those students' identities and their diverse intellectual resources and lived experience.

The CIME workshops impact three distinct communities: research mathematicians, mathematics educators (K-16), and education researchers. Participants learn about research and development efforts that can enhance their own work and the contributions they can make to solving issues in mathematics education. Participants also connect with others concerned about those issues. This workshop will also focus on developing action plans that participants can implement once they return to their institutions. There is also a focus on recruitment of leaders of mathematics departments, teachers, and other leaders in mathematics education across K-12, undergraduate education and graduate education in order to examine systemic changes that can be made to increase access, engagement, and interest in mathematics.

Strengthening Data Literacy Across the Curriculum

This project will develop a set of statistics learning materials, with data visualization tools and an applied social science focus, to design applied data investigations addressing real-world socioeconomic questions with large-scale social science data. This project is designed to promote statistical understandings and interest in quantitative data analysis among high school students and engage students with content that resonates with their interests.

Award Number: 
1813956
Funding Period: 
Sun, 07/01/2018 to Wed, 06/30/2021
Full Description: 

The Strengthening Data Literacy across the Curriculum (SDLC) project seeks to significantly enhance the learning and teaching of Science, Technology, Engineering, and Mathematics (STEM) high school students and teachers through the development of resources, models, and tools. This project is designed to promote statistical understandings and interest in quantitative data analysis among high school students. The project will target students outside mathematics and statistics classes who seldom have opportunities formally make sense of large-scale quantitative data. The population for the initial study will be humanities/social studies and mathematics/statistics high school teachers and their classes. The focus on social justice themes are intended to engage students with content that resonates with their interests. This strategy has the potential to demonstrate ways to provide rich, meaningful statistical instruction to a population that seldom has the opportunity for such learning. By capturing students' imagination and interest with social justice themes, this project has the potential of high impact in today's society where understanding and preparing statistical reports are becoming more critical to the general populace.

This project will build on prior theory and research to develop a new set of statistics learning materials, with data visualization tools and an applied social science focus to design three 2-week applied data investigations (self-contained modules) addressing real-world socioeconomic questions with large-scale social science data. The modules will be aligned with the high school Common Core State Standards for Mathematics and key statistical content for college students. The purpose of the study is to strengthen existing theories of how to design classroom learning materials to support two primary sets of outcomes for high school students, particularly among those historically underrepresented in STEM fields: 1) stronger understandings of important statistics concepts and data analysis practices, and 2) interest in statistics and working with data.  The modules will engage students in a four-step investigative process where they will (1) formulate questions that can be answered with data; (2) design and implement a plan to assemble appropriate data; (3) use numerical and graphical methods to explore the data; and (4) summarize conclusions relating back to the original questions and citing relevant components of the analysis that support their interpretation and acknowledging other interpretations.

The project will employ a Design-Based Implementation Research (DBIR) design using both quantitative and qualitative data to determine results of targeted outcomes (noted above) as well track whether there is any evidence to support the conjectures that key module components directly impact targeted student outcomes. Starting with a well-defined, preliminary conceptual framework for the study, the project team will conduct four cycles of iterative design and testing of the proposed SDLC modules over two academic years, with each cycle occurring during a fall or spring semester.

Investigating Impact of Different Types of Professional Development on What Aspects Mathematics Teachers Take Up and Use in Their Classroom

This project will study the design and development of PD that supports teacher development and student learning, and provide accumulation of evidence to inform teacher educators, administrators, teachers, and policymakers of factors associated with successful PD experiences and variation across teachers and types of PDs.

Lead Organization(s): 
Award Number: 
1813439
Funding Period: 
Sun, 07/01/2018 to Wed, 06/30/2021
Full Description: 

Professional development is a critical way in which teachers who are currently in classrooms learn about changes in mathematics teaching and learning and improve their practice. Little is known about what types of professional development (PD) support teachers' improved practice and student learning. However, federal, state, and local governments spend resources on helping teachers improve their teaching practice and students' learning. PD programs vary in their intent and can fall on a continuum from highly adaptive, with great latitude in the implementation, to highly specified, with little ability to adapt the program during implementation. The project will study the design and development of PD that supports teacher development and student learning, and provide accumulation of evidence to inform teacher educators, administrators, teachers, and policymakers of factors associated with successful PD experiences and variation across teachers and types of PDs. The impact study will expand on the evidence of promise from four 2015 National Science Foundation (NSF)-funded projects - two adaptive, two specified - to provide evidence of the impact of the projects on teachers' instructional practice over time. Although the four projects are different in terms of structure and design elements, they all share the goal to support challenging mathematics content, practice standards, and differentiation techniques to support culturally and linguistically diverse, underrepresented populations. Understanding the nature of the professional development including structure and design elements, and unpacking what teachers take up and use in their instructional practice potentially has widespread use to support student learning in diverse contexts, especially those serving disadvantaged and underrepresented student populations.

This study will examine teachers' uptake of mathematics content, pedagogy and materials from different types of professional development in order to understand and unpack the factors that are associated with what teachers take up and use two-three years beyond their original PD experience: Two specified 1) An Efficacy Study of the Learning and Teaching Geometry PD Materials: Examining Impact and Context-Based Adaptations (Jennifer Jacobs, Karen Koellner & Nanette Seago), 2) Visual Access to Mathematics: Professional Development for Teachers of English Learners (Mark Driscoll, Johanna Nikula, & Pamela Buffington), two adaptive: 3) Refining a Model with Tools to Develop Math PD Leaders: An Implementation Study (Hilda Borko & Janet Carlson), 4), TRUmath and Lesson Study: Supporting Fundamental and Sustainable Improvement in High School Mathematics Teaching (Suzanne Donovan, Phil Tucher, & Catherine Lewis). The project will utilize a multi-case method which centers on a common focus of what content, pedagogy and materials teachers take up from PD experiences. Using a specified sampling procedure, the project will select 8 teachers from each of the four PD projects to serve as case study teachers. Subsequently, the project will conduct a cross case analysis focusing on variation among and between teachers and different types of PD. The research questions that guide the project's impact study are: RQ1: What is the nature of what teachers take up and use after participating in professional development workshops? RQ2: What factors influence what teachers take up and use and in what ways? RQ3: How does a professional development's position on the specified-adaptive continuum affect what teachers take up and use?

CAREER: Mechanisms Underlying the Relation Between Mathematical Language and Mathematical Knowledge

The purpose of this project is to examine the process by which math language instruction improves learning of mathematics skills in order to design and translate the most effective interventions into practical classroom instruction.

Lead Organization(s): 
Award Number: 
1749294
Funding Period: 
Wed, 08/01/2018 to Mon, 07/31/2023
Full Description: 

Successful development of numeracy and geometry skills during preschool provides a strong foundation for later academic and career success. Recent evidence shows that learning math language (e.g., concepts such as more, few, less, near, before) during preschool supports this development. The purpose of this Faculty Early Career Development (CAREER) project is to examine the process by which math language instruction improves learning of mathematics skills in order to design and translate the most effective interventions into practical classroom instruction. The first objective of this project is to examine if quantitative and spatial math language effect the development of different aspects of mathematics performance (e.g., numeracy, geometry). The second objective is to examine how quantitative math language versus numeracy instruction, either alone or in combination, effect numeracy development. The findings from this study will not only be used to improve theoretical understanding of how math language and mathematics skills develop, but the instructional materials developed for this study will also result in practical tools for enhancing young children's math language and mathematics skills.

This project is focused on evaluating the role of early math language skills in the acquisition of early mathematics skills. Two randomized control trials (RCTs) will be conducted. The first RCT will be used to evaluate the effects of different types of math language instruction (quantitative, spatial) on distinct aspects of mathematics (numeracy, geometry). It is expected that quantitative language instruction will improve numeracy skills and spatial language instruction will improve geometry skills. The second RCT will be used to examine the unique and joint effects of quantitative language instruction and numeracy instruction on children's numeracy skills. It is expected that both types of instruction alone will be sufficient to generate improvement on numeracy outcomes compared to an active control group, but that the combination of the two will result in enhanced numeracy performance compared to either alone. Educational goals will be integrated with and supported through engaging diverse groups of undergraduate and graduate students in hands-on research experiences, training pre- and in-service teachers on mathematical language instruction, and building collaborative relationships with early career researchers. Intervention materials including storybooks developed for the project and pre- and in-service teacher training/lesson plan materials will be made available at the completion of the project.

Measuring Early Mathematical Reasoning Skills: Developing Tests of Numeric Relational Reasoning and Spatial Reasoning

The primary aim of this study is to develop mathematics screening assessment tools for Grades K-2 over the course of four years that measure students' abilities in numeric relational reasoning and spatial reasoning. The team of researchers will develop Measures of Mathematical Reasoning Skills system, which will contain Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR).

Award Number: 
1721100
Funding Period: 
Fri, 09/15/2017 to Tue, 08/31/2021
Full Description: 

Numeric relational reasoning and spatial reasoning are critical to success in later mathematics coursework, including Algebra 1, a gatekeeper to success at the post-secondary level, and success in additional STEM domains, such as chemistry, geology, biology, and engineering. Given the importance of these skills for later success, it is imperative that there are high-quality screening tools available to identify students at-risk for difficulty in these areas. The primary aim of this study is to develop mathematics screening assessment tools for Grades K-2 over the course of four years that measure students' abilities in numeric relational reasoning and spatial reasoning. The team of researchers will develop Measures of Mathematical Reasoning Skills system, which will contain Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR). The measures will be intended for use by teachers and school systems to screen students to determine who is at-risk for difficulty in early mathematics, including students with disabilities. The measures will help provide important information about the intensity of support that may be needed for a given student. Three forms per grade level will be developed for both the T-NRR and T-SR with accompanying validity and reliability evidence collected. 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 development of the T-NRR and T-SR measures will follow an iterative process across five phases. The phases include (1) refining the construct; (2) developing test specifications and item models; (3) developing items; (4) field testing the items; and (5) conducting validity studies. The evidence collected and evaluated during each phase will contribute to the overall evaluation of the reliability of the measures and the validity of the interpretations made using the measures. Item models, test specifications, and item development will be continuously evaluated and refined based on data from cognitive interviews, field tests, and reviews by mathematics educators, teachers of struggling students, teachers of culturally and linguistically diverse populations, and a Technical Advisory Board. In the final phase of development of the T-NRR and T-SR, reliability of the results will be estimated and multiple sources of validity evidence will be collected to examine the concurrent and predictive relation with other criterion measures, classification accuracy, and sensitivity to growth. Approximately 4,500 students in Grades K-2 will be involved in all phases of the research including field tests and cognitive interviews. Data will be analyzed using a two-parameter IRT model to ensure item and test form comparability.

Developing and Evaluating Assessments of Problem Solving (Collaborative Research: Sondergeld)

This project builds upon the prior work by creating problem-solving measures for grades 3-5. The elementary assessments will be connected to the middle-grades assessments and will be available for use by school districts, researchers, and other education professionals seeking to effectively measure children's problem solving.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1720661
Funding Period: 
Fri, 09/01/2017 to Tue, 08/31/2021
Full Description: 

Current state standards in mathematics are strategically focused on problem-solving skills in both content standards and practice standards. Content standards describe what math students are expected to learn at each grade level while practice standards characterize math behaviors that all students should experience (e.g., perseverance while problem solving and reasoning effectively about real-world situations). Problem solving is found at every grade level. If math teachers are expected to engage students in problem solving during everyday instruction, then students' problem-solving performance must be assessed in a manner that produces meaningful, valid, and reliable scores, without unduly burdening teachers or students. Unfortunately, most problem-solving assessments are generally framed by a set of mathematics expectations that differ from state standards. Thus, results from those assessments are disconnected from the mathematics content that students learn in the classroom. Previously, this research team has built problem-solving measures for grades 6-8, which address this gap in framing and generates meaningful, valid, and reliable scores, and do not have unintended negative consequences on students. The current project, titled Developing and Evaluating Assessments of Problem Solving (DEAP), builds upon the team's prior work by creating problem-solving measures for grades 3-5. The elementary assessments will be connected to the middle-grades assessments and will be available for use by school districts, researchers, and other education professionals seeking to effectively measure children's problem solving. 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.

Broadly speaking, the aims of DEAP are to (a) create three new mathematical problem-solving assessments and gather validity evidence for their use, (b) link the problem-solving measures (PSMs) with prior problem-solving measures (i.e., PSM6, PSM7, and PSM8), and (c) develop a meaningful reporting system for the PSMs. The research questions are: (a) What are the psychometric properties of the PSM3, PSM4, and PSM5 as they relate to students' problem-solving performance? (b) How does the evidence support vertical equating (linking) of the PSM3, PSM4, PSM5, PSM6, PSM7, and PSM8? (c) How do the PSM3, PSM4, and PSM5, and their related reporting systems impact teachers' instructional decision making when used formatively? Year 1 focuses on item and test development. The study will conduct cognitive interviews and administer tests with a small group of students to explore how items and tests function. Rasch (1-PL) measurement will be employed, similar to prior PSM development. Year 2 includes further pilot testing and gathering validity evidence through cognitive interviews and test administration. Year 3 has a final round of pilot testing and selection of linking items for vertical equating. Year 4 involves pilot testing the PSM series with linking items and developing a reporting system. DEAP's potential contributions to the field are three-fold. (1) Assessments will be available for use by the public. (2) A set of vertically equated problem-solving measures will allow users the opportunity to explore students' problem-solving performance as they matriculate across grade levels, which is currently not possible at the state or national level. (3) This project fills a need in the field as no set of measures uses vertical equating to assess elementary students' problem-solving performance in a rigorous fashion within the context of state testing.

Developing and Evaluating Assessments of Problem Solving (Collaborative Research: Bostic)

This project builds upon the prior work by creating problem-solving measures for grades 3-5. The elementary assessments will be connected to the middle-grades assessments and will be available for use by school districts, researchers, and other education professionals seeking to effectively measure children's problem solving.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1720646
Funding Period: 
Fri, 09/01/2017 to Tue, 08/31/2021
Full Description: 

Current state standards in mathematics are strategically focused on problem-solving skills in both content standards and practice standards. Content standards describe what math students are expected to learn at each grade level while practice standards characterize math behaviors that all students should experience (e.g., perseverance while problem solving and reasoning effectively about real-world situations). Problem solving is found at every grade level. If math teachers are expected to engage students in problem solving during everyday instruction, then students' problem-solving performance must be assessed in a manner that produces meaningful, valid, and reliable scores, without unduly burdening teachers or students. Unfortunately, most problem-solving assessments are generally framed by a set of mathematics expectations that differ from state standards. Thus, results from those assessments are disconnected from the mathematics content that students learn in the classroom. Previously, this research team has built problem-solving measures for grades 6-8, which address this gap in framing and generates meaningful, valid, and reliable scores, and do not have unintended negative consequences on students. The current project, titled Developing and Evaluating Assessments of Problem Solving (DEAP), builds upon the team's prior work by creating problem-solving measures for grades 3-5. The elementary assessments will be connected to the middle-grades assessments and will be available for use by school districts, researchers, and other education professionals seeking to effectively measure children's problem solving.

Broadly speaking, the aims of DEAP are to (a) create three new mathematical problem-solving assessments and gather validity evidence for their use, (b) link the problem-solving measures (PSMs) with prior problem-solving measures (i.e., PSM6, PSM7, and PSM8), and (c) develop a meaningful reporting system for the PSMs. The research questions are: (a) What are the psychometric properties of the PSM3, PSM4, and PSM5 as they relate to students' problem-solving performance? (b) How does the evidence support vertical equating (linking) of the PSM3, PSM4, PSM5, PSM6, PSM7, and PSM8? (c) How do the PSM3, PSM4, and PSM5, and their related reporting systems impact teachers' instructional decision making when used formatively? Year 1 focuses on item and test development. The study will conduct cognitive interviews and administer tests with a small group of students to explore how items and tests function. Rasch (1-PL) measurement will be employed, similar to prior PSM development. Year 2 includes further pilot testing and gathering validity evidence through cognitive interviews and test administration. Year 3 has a final round of pilot testing and selection of linking items for vertical equating. Year 4 involves pilot testing the PSM series with linking items and developing a reporting system. DEAP's potential contributions to the field are three-fold. (1) Assessments will be available for use by the public. (2) A set of vertically equated problem-solving measures will allow users the opportunity to explore students' problem-solving performance as they matriculate across grade levels, which is currently not possible at the state or national level. (3) This project fills a need in the field as no set of measures uses vertical equating to assess elementary students' problem-solving performance in a rigorous fashion within the context of state testing.

Pages

Subscribe to Mathematics