Quantitative

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 Fri, 07/31/2020
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.


Project Videos

2019 STEM for All Video Showcase

Title: Designing PD for Math Educators of Students Who are ELs

Presenter(s): Peter Tierney-Fife, Pamela Buffington, Josephine Louie, Jill Neumayer Depiper, & Johannah Nikula

2016 STEM for All Video Showcase

Title: Visual Access to Mathematics: Supporting Teachers of ELs

Presenter(s): Johannah Nikula, Pam Buffington, Mark Driscoll & Peter Tierney-Fife


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.

Development of Language-Focused Three-Dimensional Science Instructional Materials to Support English Language Learners in Fifth Grade (Collaborative Research: Lee)

The main purpose of this project is to develop instructional materials for a year-long, fifth grade curriculum for all students, including ELLs. The planned curriculum will promote language-focused and three-dimensional science learning (through blending of science and engineering practices, crosscutting concepts, and disciplinary core ideas), aligned with the Framework for K-12 Science Education, the Next Generation Science Standards, and the Conceptual Framework for Language use in the Science Classroom.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1503330
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 is responsive to the societal challenges emerging from the nation's diverse and rapidly changing student demographics, including the rise of English language learners (ELLs), the fastest growing student population (see, for example, "U.S. school enrollment hits majority-minority milestone", Education Week, February 1, 2015). ELLs have grown exponentially: 1 in 5 students (21%) in the nation spoke a language other than English at home in 2011. The project's main purpose is to develop instructional materials for a year-long, fifth grade curriculum for all students, including ELLs. The planned curriculum will promote language-focused and three-dimensional science learning (through blending of science and engineering practices, crosscutting concepts, and disciplinary core ideas), aligned with the Framework for K-12 Science Education (National Research Council, 2012), the Next Generation Science Standards (Achieve, 2013), and the Conceptual Framework for Language use in the Science Classroom (Lee, Quinn & Valdés, 2013). The grade-level science content will target topics, such as structure and properties of matter, matter and energy in organisms and ecosystems, and Earth's and space systems, with engineering design embedded in each topic. The language approach will emphasize analytical science tasks aimed at making sense of and constructing scientific knowledge; and receptive (listening and reading) and productive (speaking and writing) language functions. Products and research results from this project will help to reduce the science achievement gaps between ELLs and non-ELLs, and enable all students to attain higher levels of proficiency in subsequent grade levels.

After the curriculum has been developed and field-tested during Years 1-3, a pilot study will be conducted in Year 4 to investigate promise of effectiveness. Using a randomized controlled trial design, the pilot study will address three research questions: (1) What is the impact of the intervention on science learning and language development for all students, including ELLs and former ELLs?; (2) What is the impact of the intervention on teachers' instructional practices?; and (3) To what extent are teachers able to implement the instructional materials with fidelity? To address research question 1, a sequence of multi-level models (MLMs) in which the posttest score for each student measure (the state/district science test score, and the science score and the language score on the researcher-developed assessment) will be regressed on a dummy variable representing condition (treatment or control) and pretest covariates. To examine whether the intervention is beneficial for students of varying levels of English proficiency, subgroup analyses will be conducted comparing ELLs in the treatment group against ELLs in the control group; former ELLs in the treatment group against former ELLs in the control group; and non-ELLs in the treatment group against non-ELLs in the control group, using the same MLMs. Exploratory analyses will be employed to examine the extent to which the level of English proficiency moderates the impact of the intervention on ELLs. To address research question 2, a 2-level model (teachers as level-1, and schools as level-2) in which the post-questionnaire scale score will be regressed on a dummy variable representing condition (treatment or control) will be conducted. To address research question 3, plans are to analyze ratings on coverage, adherence, and quality of instruction from classroom observations, along with ratings on program differentiation and participant responsiveness from the implementation and feedback form.

CAREER: Exploring Beginning Mathematics Teachers' Career Patterns

Research increasingly provides insights into the magnitude of mathematics teacher turnover, but has identified only a limited number of factors that influence teachers' career decisions and often fails to capture the complexity of the teacher labor market. This project will address these issues, building evidence-based theories of ways to improve the quality and equity of the distribution of the mathematics teaching workforce. 

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1506494
Funding Period: 
Fri, 08/15/2014 to Fri, 07/31/2020
Full Description: 

Recruiting and retaining effective mathematics teachers has been emphasized in national reports as a top priority in educational policy initiatives. Research indicates that the average turnover rate is nearly 23% for beginning teachers (compared to 15% for veteran instructors); turnover rates for beginning mathematics teachers are even higher. Many mathematics teachers with three or fewer years' experience begin their careers in high-needs schools and often transfer to low-need schools at their first opportunity. This reshuffling, as effective teachers move from high- to low-need schools, exacerbates the unequal distribution of teacher quality, with important implications for disparities in student achievement. Research increasingly provides insights into the magnitude of mathematics teacher turnover, but has identified only a limited number of factors that influence teachers' career decisions and often fails to capture the complexity of the teacher labor market. Thus, it is essential to understand the features, practices, and local contexts that are relevant to beginning teachers' career decisions in order to identify relevant strategies for retention. This project will address these issues, building evidence-based theories of ways to improve the quality and equity of the distribution of the mathematics teaching workforce. This support for an early CAREER scholar in mathematics policy will enhance capacity to address issues in the future.

This work will be guided by three research objectives, to: (1) explore patterns in mathematics teachers' career movements, comparing patterns between elementary and middle school teachers, and between high- and low-need schools; (2) compare qualifications and effectiveness of teachers on different career paths (e.g., movement in/out of school, district, field); and (3) test a conceptual model of how policy-malleable factors influence beginning math teachers' performance improvement and career movements. The PI will use large-scale federal and state longitudinal data on a cohort of teachers who were first-year teachers in 2007-08 and taught mathematics in grades 3-8. Three samples will be analyzed separately and then collectively: a nationally representative sample from the Beginning Teacher Longitudinal Study (about 870 teachers who represent a national population of nearly 85,970); about 4,220 Florida teachers; and about 2,410 North Carolina teachers. In addition, the PI will collaborate with Education Policy Initiative at Carolina (EPIC) at UNC-Chapel Hill to collect new data from the 2015-16 cohort of first-year teachers in NC (about 800 teachers) and follow them for 2 years. The new data collection will provide detailed and reliable measures on the quality of both pre- and in-service teacher supports in order to understand how they may be linked to teachers' career movements and performance.

The original award # of this project was 1350158.

CAREER: Algebraic Knowledge for Teaching: A Cross-Cultural Perspective

The goal of this CAREER program of research is to identify, from a cross-cultural perspective, essential Algebraic Knowledge for Teaching (AKT) that will enable elementary teachers to better develop students' algebraic thinking. This study explores AKT based on integrated insights of the U.S. and Chinese expert teachers' classroom performance.

Lead Organization(s): 
Award Number: 
1350068
Funding Period: 
Fri, 08/15/2014 to Fri, 07/31/2020
Full Description: 

What content knowledge is needed for the teaching of mathematics? What practices are more effective for realizing student success? These questions have received considerable attention in the mathematics education community. The goal of this CAREER program of research is to identify, from a cross-cultural perspective, essential Algebraic Knowledge for Teaching (AKT) that will enable elementary teachers to better develop students' algebraic thinking. Focusing on two fundamental mathematical ideas recently emphasized by the Common Core State Standards - inverse relations and properties of operations - this study explores AKT based on integrated insights of the U.S. and Chinese expert teachers' classroom performance. It will be focused on three objectives: (1) identify AKT that facilitates algebraic thinking and develop preliminary findings into teaching materials; (2) refine research-based teaching materials based on the evaluative data; and (3) integrate research with education through course development at Temple University and teacher outreach in Philadelphia.

The model underlying this research program is that improved pedagogy will improve student learning, both directly and indirectly. A design-based research method will be used to accomplish objectives #1 and #2. Cross-cultural videotaped lessons will be first analyzed to identify AKT, focusing on teachers' use of worked examples, representations, and deep questions. This initial set of findings will then be developed into teaching materials. The U.S. and Chinese expert teachers will re-teach the lessons as part of the refinement process. Data sources will include: baseline and updated survey data (control, context, and process variables), observation, documents, videos, and interviews. The statistical techniques will include descriptive and inferential statistics and HLM will to address the hierarchical nature of the data.

This project involves students and teachers at various levels (elementary, undergraduate, and graduate) at Temple University and the School District of Philadelphia (SDP) in the U.S. and Nanjing Normal University and Nantong School District in China. A total of 600 current and future elementary teachers and many of their students will benefit directly or indirectly from this project. Project findings will be disseminated through various venues. Activities of the project will promote school district-university collaboration, a novice-expert teacher network, and cross-disciplinary and international collaboration. It is anticipated that the videos of expert teaching will also be useful future research by cognitive researchers studying ways to improve mathematics learning.

Publications
G indicates graduate student author; U indicates undergraduate student author

Journal Articles in English

  1. Ding, M., G Chen, W., & G Hassler, R. (2019). Linear quantity models in the US and Chinese elementary mathematics classrooms. Mathematical Thinking and Learning, 21, 105-130 doi: 10.1080/10986065.2019.1570834 . PDF
  2. Barnett, E., & Ding, M. (2019). Teaching of the associative property: A natural classroom investigation. Investigations of Mathematics Learning, 11, 148-166. doi: 10.1080/19477503.2018.1425592  PDF
  3. Ding, M., & G Heffernan, K. (2018). Transferring specialized content knowledge to elementary classrooms: Preservice teachers’ learning to teach the associative property. International Journal of Mathematics Educational in Science and Technology, 49, 899-921.doi: 10.1080/0020739X.2018.1426793 PDF
  4. Ding, M. (2018). Modeling with tape diagrams. Teaching Children Mathematics25, 158-165. doi: 10.5951/teacchilmath.25.3.0158  PDF
  5. G Chen, W., & Ding, M.* (2018). Transitioning from mathematics textbook to classroom instruction: The case of a Chinese expert teacher. Frontiers of Education in China, 13, 601-632. doi: 10.1007/s11516-018-0031-z (*Both authors contributed equally). PDF
  6. Ding, M., & G Auxter, A. (2017). Children’s strategies to solving additive inverse problems: A preliminary analysis. Mathematics Education Research Journal, 29, 73-92. doi:10.1007/s13394-017-0188-4  PDF
  7. Ding, M. (2016).  Developing preservice elementary teachers’ specialized content knowledge for teaching fundamental mathematical ideas: The case of associative property. International Journal of STEM Education, 3(9), 1-19doi: 10.1186/s40594-016-0041-4  PDF
  8. Ding, M. (2016). Opportunities to learn: Inverse operations in U.S. and Chinese elementary mathematics textbooks. Mathematical Thinking and Learning, 18, 45-68. doi: 10.1080/10986065.2016.1107819  PDF

Journal Articles in Chinese
Note: The Chinese journals Educational Research and Evaluation (Elementary Education and Instruction教育研究与评论 (小学教育教学) and Curriculum and Instructional Methods (课程教材教法) are both official, core journals in mathematics education field in China.

  1. Chen, W. (2018). Strategies to deal with mathematical representations – an analysis of expert’s classroom instruction. Curriculum and Instructional Methods. 数学教学的表征处理策略——基于专家教师的课堂教学分析. 课程教材教法. PDF
  2. Ma, F. ( 2018) – Necessary algebraic knowledge for elementary teachers- an ongoing cross-cultural study. Educational Research and Evaluation (Elementary Education and Instruction), 2, 5-7.  小学教师必备的代数学科知识-跨文化研究进行时。教育研究与评论 (小学教育教学), 2, 5-7. PDF
  3. Chen, J. (2018) Infusion and development of children’s early algebraic thinking – a comparative study of the US and Chinese elementary mathematics teaching. Educational Research and Evaluation (Elementary Education and Instruction), 2, 8-13.  儿童早期代数思维的渗透与培养-中美小学数学教学比较研究。教育研究与评论(小学教育教学),28-13.  PDF
  4. Zong, L. (2018). A comparative study on the infusion of inverse relations in the US and Chinese classroom teaching. Educational Research and Evaluation (Elementary Education and Instruction), 2, 14-19.  中美逆运算渗透教学对比研究。教育研究与评论(小学教育教学,2,14-19.  PDF
  5. Wu, X. (2018). Mathematical representations and development of children’s mathematical thinking: A perspective of US-Chinese comparison. Educational Research and Evaluation (Elementary Education and Instruction), 2, 20-24.  数学表征与儿童数学思维发展-基于中美比较视角。教育研究与评论(小学教育教学,2, 20-24.  PDF

Dissertations

  1. Hassler, R. (2016). Mathematical comprehension facilitated by situation models: Learning opportunities for inverse relations in elementary school.Published dissertation, Temple University, Philadelphia, PA. (Chair: Dr. Meixia Ding)  PDF
  2. Chen, W. (2018). Elementary mathematics teachers’ professional growth: A perspectives of TPACK (TPACK 视角下小学数学教师专业发展的研究). Dissertation, Nanjing Normal University. Nanjing, China. PDF

National Presentations
G indicates graduate student author; U indicates undergraduate student author

  • Ding, M (symposium organizer, 2019, April). Enhancing elementary mathematics instruction: A U.S.-China collaboration. Papers presented at NCTM research conference (Discussant: Jinfa Cai). (The following three action research papers were written by my NSF project teachers under my guidance).
      • Milewski Moskal, M., & Varano, A. (2019). The teaching of worked examples: Chinese approaches in U.S. classrooms. Paper 
      • Larese, T., Milewski Moskal, M., Ottinger, M., & Varano, A., (2019). Introducing Investigations math games in China: Successes and surprises. Paper
      • Murray, D., Seidman, J., Blackmon, E., Maimon, G., & Domsky, A. (2019). Mathematic instruction across two cultures: A teacher perspective. Paper
    • Ding, M., & Ying Y. (2018, June). CAREER: Algebraic knowledge for teaching: A cross-cultural perspective. Poster presentation at the National Science Foundation (NSF) PI meeting, Washington, DC.  Poster
    • Ding, M., Brynes, J., G Barnett, E., & Hassler, R. (2018, April). When classroom instruction predicts students’ learning of early algebra: A cross-cultural opportunity-propensity analysis. Paper presented at 2018 AERA conference. New York, NY.  Paper
    • Ding, M., Li, X., Manfredonia, M., & Luo, W. (2018, April). Video as a tool to support teacher learning: A Cross-cultural analysis. Paper presented at 2018 NCTM conference. Washington, DC.  PPT
    • GBarnett, E., & Ding, M. (2018, April). Teaching the basic properties of arithmetic: A natural classroom investigation of associativity. Poster presentation at 2018AERA conference, New York, NY.  Poster
    • Hassler, R., & Ding, M. (2018, April). The role of deep questions in promoting elementary students’ mathematical comprehension. Poster presentation at 2018AERA conference, New York, NY.
    • Ding, M., G Chen, W., G Hassler, R., Li, X., & G Barnett, E. (April, 2017). Comparisons in the US and Chinese elementary mathematics classrooms. Poster presentation at AERA 2017 conference (In the session of “Advancing Mathematics Education Through NSF’s DRK-12 Program”). San Antonio, TX. Poster
    • Ding, M., Li, X., G Hassler, R., & G Barnett, E. (April, 2017). Understanding the basic properties of operations in US and Chinese elementary School. Paper presented at AERA 2017 conference. San Antonio, TX.  Paper
    • Ding, M., G Chen, W., & G Hassler, R. (April, 2017). Tape diagrams in the US and Chinese elementary mathematics classrooms. Paper presented at NCTM 2017 conference. San Antonio, TX.  Paper
    • Ding, M., & G Hassler, R. (2016, June). CAREER: Algebraic knowledge for teaching in elementary school: A cross-cultural perspective. Poster presentation at the NSF PI meeting, Washington, DC. Poster
    • Ding, M. (symposium organizer, 2016, April). Early algebraic in elementary school: A cross-cultural perspective. Proposals presented at 2016 AERA conference, Washington, DC.
        • Ding, M. (2016, April). A comparative analysis of inverse operations in U.S. and Chinese elementary mathematics textbooks. Paper 
        • G Hassler, R. (2016, April). Elementary Textbooks to Classroom Teaching: A Situation Model Perspective. Paper
        • G Chen, W., & Ding, M. (2016, April). Transitioning textbooks into classroom teaching: An action research on Chinese elementary mathematics lessons. Paper
        • Li, X., G Hassler, R., & Ding, M. (2016, April). Elementary students’ understanding of inverse relations in the U.S. and China.  Paper
        • Stull, J., Ding, M., G Hassler, R., Li, X., & U George, C. (2016, April). The impact of algebraic knowledge for teaching on student learning: A Preliminary analysis. Paper
      • Ding, M., G Hassler, R., Li., X., & G Chen, W. (2016, April). Algebraic knowledge for teaching: An analysis of US experts' lessons on inverse relations. Paper presented at 2016 NCTM conference, San Francisco, CA. Paper
      • G Hassler. R., & Ding, M. (2016, April). Situation model perspective on mathematics classroom teaching: A case study on inverse relations. Paper presented at 2016 NCTM conference, San Francisco, CA.  Paper
      • Ding, M., & G Copeland, K. (2015, April). Transforming specialized content knowledge: Preservice elementary teachers’ learning to teach the associative property of multiplication. Paper presented at AERA 2015 conference, Chicago, IL. Paper PPT
      • Ding, M., & G Auxter, A. (2015, April). Children’s strategies to solving additive inverse problems: A preliminary analysis. Paper presented at AERA 2015 conference, Chicago, IL.  Paper

      Learning about Ecosystems Science and Complex Causality through Experimentation in a Virtual World

      This project will develop a modified virtual world and accompanying curriculum for middle school students to help them learn to more deeply understand ecosystems patterns and the strengths and limitations of experimentation in ecosystems science. The project will build upon a computer world called EcoMUVE, a Multi-User Virtual Environment or MUVE, and will develop ways for students to conduct experiments within the virtual world and to see the results of those experiments.

      Project Email: 
      Lead Organization(s): 
      Award Number: 
      1416781
      Funding Period: 
      Mon, 09/01/2014 to Thu, 08/31/2017
      Full Description: 

      EcoXPT from videohall.com on Vimeo.

      Comprehending how ecosystems function is important knowledge for citizens in making decisions and for students who aspire to become scientists. This understanding requires deep thinking about complex causality, unintended side-effects, and the strengths and limitations of experimental science. These are difficult concepts to learn due to the many interacting components and non-linear interrelationships involved. Ecosystems dynamics is particularly difficult to teach in classrooms because ecosystems involve complexities such as phenomena distributed widely across space that change over long time frames. Learning when and how experimental science can provide useful information in understanding ecosystems dynamics requires moving beyond the limited affordances of classrooms. The project will: 1) advance understanding of experimentation in ecosystems as it can be applied to education; 2) show how student learning is affected by having opportunities to experiment in the virtual world that simulate what scientists do in the real world and with models; and 3) produce results comparing this form of teaching to earlier instructional approaches. This project will result in a learning environment that will support learning about the complexities of the earth's ecosystem.

      The project will build upon a computer world called EcoMUVE, a Multi-User Virtual Environment or MUVE, developed as part of an earlier NSF-funded project. A MUVE is a simulated world in which students can virtually walk around, make observations, talk to others, and collect data. EcoMUVE simulates a pond and a forest ecosystem. It offers an immersive context that makes it possible to teach about ecosystems in the classroom, allowing exploration of the complexities of large scale problems, extended time frames and and multiple causality. To more fully understand how ecosystems work, students need the opportunity to experiment and to observe what happens. This project will advance this earlier work by developing ways for students to conduct experiments within the virtual world and to see the results of those experiments. The project will work with ecosystem scientists to study the types of experiments that they conduct, informing knowledge in education about how ecosystem scientists think, and will build opportunities for students that mirror what scientists do. The project will develop a modified virtual world and accompanying curriculum for middle school students to help them learn to more deeply understand ecosystems patterns and the strengths and limitations of experimentation in ecosystems science. The resulting program will be tested against existing practice, the EcoMUVE program alone, and other programs that teach aspects of ecosystems dynamics to help teachers know how to best use these curricula in the classroom.

      Understanding the Role of Contextual Effects in STEM Pursuit and Persistence: A Synthesis Approach

      This synthesis project will inform educators and policymakers about the cumulative evidence that exists on the impacts of a variety of contextual factors on a multitude of STEM outcomes (e.g., math and science achievement, self-efficacy, future goals). This project will provide new evidence regarding the significance of youth contexts on STEM outcomes that will assist policy makers and educators in evaluating productive educational environments.

      Award Number: 
      1417601
      Funding Period: 
      Mon, 09/01/2014 to Wed, 08/31/2016
      Full Description: 

      The percentage of U.S. high school graduates pursuing STEM majors has declined over the last three decades with the largest decline among the highest achieving students. American youth are ill-prepared relative to their international counterparts - U.S. 15 year olds rank 16 out of 26 developed countries in science literacy and 19 out of 26 developed counties in mathematical literacy. There is much research in the areas of how students learn STEM in formal settings, but there is little knowledge of the impact of youth contexts on STEM. Youth contexts are social groups in the lives of young people such as neighborhoods, communities, schools, classrooms or friends. Understanding the role of youth contexts is crucial to ensuring that all students have the opportunity to learn STEM content. This project will synthesize the research literature on youth context and assess whether and how a range of these contexts shape K-12 STEM outcomes and engagement - predictors critical for later educational and occupational attainment. The researchers will conduct two large-scale meta-analyses - one based on the quantitative research body and one based on the qualitative research body - in order to draw conclusions about which contextual factors relate to which STEM outcomes across the span of extant research. In doing so, this synthesis project will inform educators and policymakers about the cumulative evidence that exists on the impacts of a variety of contextual factors on a multitude of STEM outcomes (e.g., math and science achievement, self-efficacy, future goals). This project will provide new evidence regarding the significance of youth contexts on STEM outcomes that will assist policy makers and educators in evaluating productive educational environments.

      Syntheses of the research in youth contexts and their impact in STEM will address the following four research questions: (1) How do contextual factors impact STEM learning?; (2) How do these factors vary by the specific type of context?; (3) How do these factors vary by gender and race within each context?; and, (4) Are these factors influenced by the methodological features of the research? The review will include electronic searches of educational, economics, sociology, psychology, and general science databases covering the years 1980-2014. Results will be narrowed by youth context area, and separate analysis will be conducted on gender and race/ethnicity differences in STEM outcomes. The data for the full review will be evaluated by a common set of guidelines to be published along with the findings, enabling the conclusions of the review to be transparent and allowing for detailed information to be easily accessible. The review will discuss each study that meets the inclusion requirements for a valid research design. With this methodology, this study will be the first to provide a clearinghouse of rigorous research related to contextual factors of STEM outcomes.

      Teaching Environmental Sustainability - Model My Watershed (Collaborative Research: Kerlin)

      This project will develop curricula for environmental/geoscience disciplines for high-school classrooms. The Model My Watershed (MMW) v2 app will bring new environmental datasets and geospatial capabilities into the classroom, to provide a cloud-based learning and analysis platform accessible from a web browser on any computer or mobile device, thus overcoming the cost and technical obstacles to integrating Geographic Information System technology in secondary education.

      Lead Organization(s): 
      Award Number: 
      1418133
      Funding Period: 
      Mon, 09/01/2014 to Fri, 08/31/2018
      Project Evaluator: 
      Education Design
      Full Description: 

      This project will develop curricula for environmental/geoscience disciplines for high-school classrooms. It will teach a systems approach to problem solving through hands-on activities based on local data and issues. This will provide an opportunity for students to act in their communities while engaging in solving problems they find interesting, and require synthesis of prior learning. The Model My Watershed (MMW) v2 app will bring new environmental datasets and geospatial capabilities into the classroom, to provide a cloud-based learning and analysis platform accessible from a web browser on any computer or mobile device, thus overcoming the cost and technical obstacles to integrating Geographic Information System technology in secondary education. It will also integrate new low-cost environmental sensors that allow students to collect and upload their own data and compare them to data visualized on the new MMW v2. This project will transform the ability of teachers throughout the nation to introduce hands-on geospatial analysis activities in the classroom, to explore a wide range of geographic, social, political and environmental concepts and problems beyond the project's specific curricular focus.

      The Next Generation Science Standards state that authentic research experiences are necessary to enhance STEM learning. A combination of computational modeling and data collection and analysis will be integrated into this project to address this need. Placing STEM content within a place- and problem-based framework enhances STEM learning. Students, working in groups, will not only design solutions, they will be required to defend them within the application portal through the creation of multimedia products such as videos, articles and web 2.0 presentations. The research plan tests the overall hypothesis that students are much more likely to develop an interest in careers that require systems thinking and/or spatial thinking, such as environmental sciences, if they are provided with problem-based, place-based, hands-on learning experiences using real data, authentic geospatial analysis tools and models, and opportunities to collect their own supporting data. The MMW v2 web app will include a data visualization tool that streams data related to the modeling application. This database will be modified to integrate student data so teachers and students can easily compare their data to data collected by other students and the government and research data. All data will be easily downloadable so that students can increase the use of real data to support the educational exercises. As a complement to the model-based activities, the project partners will design, manufacture, and distribute a low-cost environmental monitoring device, called the Watershed Tracker. This device will allow students to collect real-world data to enhance their understanding of watershed dynamics. Featuring temperature, light, humidity, and soil moisture sensors, the Watershed Tracker will be designed to connect to tablets and smartphones through the audio jack common to all of these devices.

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