Case Study

Developing Preservice Elementary Teachers' Ability to Facilitate Goal-Oriented Discussions in Science and Mathematics via the Use of Simulated Classroom Interactions

The project will develop, pilot, and validate eight discussion-oriented performance tasks that will be embedded in an online simulated classroom environment. The resulting research and development products could be used nationwide in teacher preparation and professional development settings to assess and develop teachers' ability to support classroom discussion in science and mathematics.

Lead Organization(s): 
Award Number: 
1621344
Funding Period: 
Mon, 08/01/2016 to Fri, 07/31/2020
Full Description: 

There is widespread recognition in educational literatures that academic discourse is important for supporting students' developing understanding in the disciplines of science and mathematics. College and career-ready standards also call for attention to supporting students' learning of how to think and communicate like disciplinary experts. The teaching practice of orchestrating classroom discussion is intended to support students in obtaining higher levels of academic achievement but also to support students' participation in a democratic society. However, research has found that teachers--particularly novice teachers--struggle to orchestrate discussion effectively for science and mathematics. The investigators of this project hypothesize that opportunities to 1) practice orchestrating discussions in simulated classroom environments; 2) receive constructive feedback on their practice; and 3) reflect on that feedback and their experiences with peers and teacher educators, develops preservice teachers' abilities to lead productive classroom discussion. This may allow them to be more effective at orchestrating discussion when they begin teaching real students in science and mathematics classrooms. The project team, which includes investigators from Educational Testing Service (ETS) and software engineers at Mursion, will develop, pilot, and validate eight discussion-oriented performance tasks that will be embedded in an online simulated classroom environment. The resulting research and development products could be used nationwide in teacher preparation and professional development settings to assess and develop teachers' ability to support classroom discussion in science and mathematics.

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 Early Stage Design and Development project will 1) iteratively develop, pilot, and refine eight science and mathematics discussion-oriented performance tasks (six formative, two summative), scoring rubrics, and rater training materials; 2) deploy the intervention in four university sites, collecting data from 240 prospective teachers in both treatment and business-as-usual courses; and 3) use data analyses and expert review to build a five-part argument for the validity of the assessment and scoring rubrics. Data sources include prospective teachers' background and demographic information, cognitive interviews, surveys, scores on content knowledge for teaching (CKT) instruments, performance and scores on the developed performance tasks, discussion scores on Danielson's Framework for Teaching observation protocol, and case study interviews with prospective teachers. The project team will also conduct interviews with teacher educators and observe classroom debrief sessions with prospective teachers and their teacher educators. The research will examine each teacher's scores on two summative performance tasks administered pre- and post-intervention and will look for evidence of growth across three formative tasks. Linear regression models will be used to understand relationships among teachers' CKT scores, pre-intervention performance task scores, group assignment, and post-intervention performance task scores. A grounded theory approach to coding qualitative data of 24 case study teachers, observations of debrief sessions, and interviews with teacher educators will generate descriptive use cases, illustrating how the tools can support prospective teachers in learning how to facilitate discussions focused on science and mathematics argumentation. Mursion will develop a webpage on its website dedicated to this project that will allow the team to post the new performance-based tasks, scoring rubrics, and examples of performance in the simulated environment for teacher educators, educational researchers, and policy makers and collect feedback from them that can be used as another information source for refining tools and their use. Research findings will also be disseminated by more traditional means, such as papers in peer-reviewed research and practitioner journals and conference presentations.


Project Videos

2021 STEM for All Video Showcase

Title: Project Results: PST Learning from Simulated Discussions

Presenter(s): Heather Howell & Jamie Mikeska

2020 STEM for All Video Showcase

Title: Tales from the Sandbox: Learning through Simulated Teaching

Presenter(s): Heather Howell, Jamie Mikeska, & Carrie Straub

2019 STEM for All Video Showcase

Title: Simulated Classrooms as Practice-Based Learning Spaces

Presenter(s): Jamie Mikeska, Heather Howell, & Carrie Straub

2018 STEM for All Video Showcase

Title: Leading Science/Math Discussions in a Simulated Classroom

Presenter(s): Heather Howell, Jamie Mikeska, & Carrie Straub

 2017 STEM for All Video Showcase
Title: Simulated Classroom Environments for Discussions

Presenter(s): Jamie Mikeska, Heather Howell, & Carrie Straub


Developing Teachers as Computational Thinkers Through Supported Authentic Experiences in Computing Modeling and Simulation

This project addresses the need for a computationally-enabled STEM workforce by equipping teachers with the skills necessary to prepare students for future endeavors as computationally-enabled scientists and citizens, and by investigating the most effective ways to provide this instruction to teachers. The project also addresses the immediate challenge presented by NGSS to prepare middle school science teachers to implement rich computational thinking experiences within science classes.

Partner Organization(s): 
Award Number: 
1639069
Funding Period: 
Fri, 01/01/2016 to Sun, 06/30/2019
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 addresses the need for a computationally-enabled STEM workforce by equipping teachers with the skills necessary to prepare students for future endeavors as computationally-enabled scientists and citizens, and by investigating the most effective ways to provide this instruction to teachers. The project also addresses the immediate challenge presented by the Next Generation Science Standards to prepare middle school science teachers to implement rich computational thinking (CT) experiences, such as the use, creation and analysis of computer models and simulations, within science classes.

The project, a partnership between the Santa Fe Institute and the Santa Fe Public School District, directly addresses middle school teachers' understanding, practice, and teaching of modern scientific practice. Using the Project GUTS program and professional development model as a foundation, this project will design and develop a set of Resources, Models, and Tools (RMTs) that collectively form the basis for a comprehensive professional development (PD) program, then study teachers' experiences with the RMTs and assess how well the RMTs prepared teachers to implement the curriculum. The PD program includes: an online PD network; workshops; webinars and conferences; practicum and facilitator support; and curricular and program guides. The overall approach to the project is design based implementation research (DBIR). Methods used for the implementation research includes: unobtrusive measures such as self-assessment sliders and web analytics; the knowledge and skills survey (KS-CT); interviews (teachers and the facilitators); analysis of teacher modified and created models; and observations of practicum and classroom implementations. Data collection and analysis in the implementation research serve two purposes: a) design refinement and b) case study development. The implementation research employs a mixed-method, nonequivalent group design with embedded case studies.

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.

Playing with the Data: Developing Digital Supports for Middle School Science Teachers using Game-based Formative Assessment

This project will use cycles of design-based research to build new knowledge about how to facilitate teachers' interpretation and use of digital game-based formative assessment data. The research will also inform the revision and expansion of Playfully, an existing, online data-reporting dashboard that can be used with multiple digital games.

Award Number: 
1503255
Funding Period: 
Wed, 07/01/2015 to Sat, 06/30/2018
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 (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 use cycles of design-based research to build new knowledge about how to facilitate teachers' interpretation and use of digital game-based formative assessment data. The research will also inform the revision and expansion of Playfully, an existing, online data-reporting dashboard that can be used with multiple digital games. The project is a collaboration between researchers at Education Development Center Inc.'s Center for Children and Technology (EDC|CCT) and the assessment and game development teams at GlassLab. The research and development teams will engage in a three-year partnership with 60 middle-grade science teachers working in diverse school settings in different parts of the country. The aim of the project is to refine an online formative assessment platform that utilizes data from a video game designed to teach argumentation at the middle school level. It provides rigorous research on the design features of data tools and associated materials available to teachers to inform their ongoing instruction (i.e., formative assessment tools) when using game-based platforms.

Dissemination of the results of this project will include practical, evidence-based suggestions for supporting middle school science teachers' use of digital games for assessment, and for the design and implementation of data dashboards. Key audiences include educational game designers, game-based assessment developers, formative assessment experts, and leaders in middle grade science teaching and learning.

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.

Learning Labs: Using Videos, Exemplary STEM Instruction and Online Teacher Collaboration to Enhance K-2 Mathematics and Science Practice and Classroom Discourse

This project will develop and study two sets of instructional materials for K-2 teacher professional development in mathematics and science that are aligned with the CCSS and NGSS. Teachers will be able to review the materials online, watch video of exemplary teaching practice, and then upload their own examples and students' work to be critiqued by other teachers enrolled in professional learning communities as well as expert coaches.

Lead Organization(s): 
Award Number: 
1417757
Funding Period: 
Wed, 04/15/2015 to Sat, 03/31/2018
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 (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 investigators of this study propose to develop and study two sets of instructional materials for K-2 teacher professional development in mathematics and science that are aligned with the Common Core State Standards in Mathematics (CCSS) and the Next Generation Science Standards (NGSS). They will develop two modules in each subject area and an introductory module that prefaces and integrates the science and mathematics materials. Teachers will be able to review the materials online, watch video of exemplary teaching practice, and then upload their own examples and students' work to be critiqued by other teachers enrolled in professional learning communities as well as expert coaches. New instructional materials aligned with the standards are needed to assist teachers in meeting the challenging instructional practices recommended. To date, scant few resources of this type exist and, given many school districts have limited resources, more cost-effective forms of development such as this must be found. A particular strength of this project is that teachers will be able to engage in the courses online, on an ongoing basis and integrate what they have learned into their daily teaching practice.

The investigators propose a program of design research to develop and improve the modules. The central hypothesis is a test of the Teaching Channel model--that the modules and professional learning communities result in significant changes in the quality of instructional practice. Text analytics will be performed on the online discussion to detect changes in group discourse over time. Changes in instructional quality and vision will be measured by observing the videos posted by teachers. Pre-post tests of student work will be performed. The findings of the research will be disseminated through conference presentations, publications, and the Teaching Channel website.

Developing Teachers' Capacity to Promote Argumentation in Secondary Science

This project will produce insights into the challenges teachers face in modifying their teaching in the substantial and complex ways demanded by the Next Generation Science Standards. This project will develop and study a program of professional development to help middle and high school science teachers support their students to learn to argue scientifically. 

Award Number: 
1503511
Funding Period: 
Wed, 07/01/2015 to Sun, 06/30/2019
Full Description: 

This project will produce insights into the challenges teachers face in modifying their teaching in the substantial and complex ways demanded by the Next Generation Science Standards. This project will develop and study a program of professional development to help middle and high school science teachers support their students to learn to argue scientifically. The program includes strategies for organizing science activities to create contexts where students have something to argue about and teaching practices that promote sustained, productive argumentation among students. Results will document what aspects of these new practices teachers find easier and more difficult to implement, and how challenges are influenced by the urban schooling contexts in which project teachers work. The project will also further our understanding of how site-based professional development can be structured to support teacher learning and improvement.

The project is a longitudinal study of a cohort of 30 secondary science teachers from an urban school district in California. The professional development (PD) program will be organized around intensive summer institutes followed by 2 school-based lesson study cycles each year, facilitated by trained coaches. The PD work will be carried out over three years. All PD sessions will be recorded for interaction analysis to identify variations in coaching and teacher participation and the influences of such variation on teacher learning. Repeated measures of teachers' conceptions of argumentation will be given over 3 years as a measure of teacher learning. An observation protocol will be developed and used to measure teacher talk and its change over time. A sub-sample of teachers' classrooms will be video recorded to produce a longitudinal record for interaction analyses to link teacher talk to patterns of student argumentation. The third year of the project will add measures of student learning and link them to variations in teacher practice. The final year of the project will produce retrospective analyses that link pathways in teacher learning to features of the PD program and teachers' participation. 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.

STEM Practice-Rich Investigations for NGSS Teaching (SPRINT)

This is an exploratory project that will research and develop resources and a model for professional learning needed to meet the demand of implementing the Next Generation Science Standards (NGSS). The Exploratorium Teacher Institute will engage middle school science teachers in a one-year professional learning program to study how familiar routines and classroom tools, specifically hands-on science activities, can serve as starting points for teacher learning.

Lead Organization(s): 
Award Number: 
1503153
Funding Period: 
Mon, 06/01/2015 to Wed, 05/31/2017
Full Description: 

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

STEM Practice-rich Investigations for NGSS Teaching (SPRINT) is an exploratory project that will research and develop resources and a model for professional learning needed to meet the demand of implementing the Next Generation Science Standards (NGSS). The Exploratorium Teacher Institute will engage middle school science teachers in a one-year professional learning program to study how familiar routines and classroom tools, specifically hands-on science activities, can serve as starting points for teacher learning. The Teacher Institute will use existing hands-on activities as the basis for developing "practice-rich investigations" that provide teachers and students with opportunities for deep engagement with science and engineering practices. The results of this project will include: (1) empirical evidence from professional learning experiences that support teacher uptake of practice-rich investigations in workshops and their classrooms; (2) a portfolio of STEM practice-rich investigations developed from existing hands-on activities that are shown to enhance teacher understanding of NGSS; and (3) a design tool that supports teachers in modifying existing activities to align with NGSS.

SPRINT conjectures that to address the immediate challenge of supporting teachers to implement NGSS, professional learning models should engage teachers in the same active learning experiences they are expected to provide for their students and that building on teachers' existing strengths and understanding through an asset-based approach could lead to a more sustainable implementation. SPRINT will use design-based research methods to study (a) how creating NGSS-aligned, practice-rich investigations from teachers' existing resources provides them with experiences for three-dimensional science learning and (b) how engaging in these investigations and reflecting on classroom practice can support teachers in understanding and implementing NGSS learning experiences.


Project Videos

2019 STEM for All Video Showcase

Title: Immersed in Phenomena: Helping Teachers Transition to NGSS

Presenter(s): Julie Yu, Sara Heredia, & Jessica Parker


SmartCAD: Guiding Engineering Design with Science Simulations (Collaborative Research: Magana-de-Leon)

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: 
1503436
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.

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

Book

Journal Articles in English

  1. Ding, M., Li, X., G Hassler, R., & G Barnett, E. (2021). Understanding of the properties of operations: A cross-cultural analysis. International Journal of Mathematical Education in Science and Technology, 52(1), 39-64. doi: 10.1080/0020739X.2019.1657595. PDF
  2. Ding, M., G Hassler, R., & Li., X. (2020). Cognitive instructional principles in elementary mathematics classrooms: A case of teaching inverse relations. International Journal of Mathematical Education in Science and Technology. doi: 10.1080/0020739X.2020.1749319
  3. 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
  4. 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
  5. 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
  6. Ding, M. (2018). Modeling with tape diagrams. Teaching Children Mathematics25, 158-165. doi: 10.5951/teacchilmath.25.3.0158  PDF
  7. 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
  8. 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
  9. 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
  10. 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., G Spiro, B., & G Mochaourab, R. (2021). Promoting changes in elementary mathematics teaching: A case study. Presented at 2021 AERA annual conference (virtual).
  • Alibali, M. W., Ding, M., Yeo, A., Huang, H. & Meng, R. (2020, April) Linking Representations of Equality in First-Grade Mathematics Lessons in China [Roundtable Session]. AERA Annual Meeting San Francisco, CA http://tinyurl.com/sjs4ebe (Conference Canceled)
  • Ding, M. (2020, April). Worked examples in elementary mathematics classrooms: A cross-cultural analysis[Paper Session]. AERA Annual Meeting, San Francisco, CA (Conference Canceled).  Paper presented in AERA Interactive Presentation Gallery on July 31th 2020.
  • 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

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