Narrative

CAREER: Designing and Enacting Mathematically Captivating Learning Experiences for High School Mathematics

This project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). The study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion.

Lead Organization(s): 
Award Number: 
1652513
Funding Period: 
Wed, 02/15/2017 to Mon, 01/31/2022
Full Description: 

This design and development project explores how secondary mathematics teachers can plan and enact learning experiences that spur student curiosity, captivate students with complex mathematical content, and compel students to engage and persevere (referred to as "mathematically captivating learning experiences" or "MCLEs"). This study is important because of persistent disinterest by secondary students in mathematics in the United States. This study will examine how high school teachers can design lessons so that mathematical content itself is the source of student intrigue, pursuit, and passion. To do this, the content within mathematical lessons (both planned and enacted) is framed as mathematical stories and the felt tension between how information is revealed and withheld from students as the mathematical story unfolds is framed as its mathematical plot. The Mathematical Story Framework (Dietiker, 2013, 2015) foregrounds both the coherence (does the story make sense?) and aesthetic (does it stimulate anticipation for what is to come, and if so, how?) dimensions of mathematics lessons. The project will generate principles for lesson design usable by teachers in other settings and exemplar lessons that can be shared.

Specifically, this project draws from prior curriculum research and design to (a) develop a theory of teacher MCLE design and enactment with the Mathematical Story Framework, (b) increase the understanding(s) of the aesthetic nature of mathematics curriculum by both researchers and teachers, and (c) generate detailed MCLE exemplars that demonstrate curricular coherence, cognitive demand, and aesthetic dimensions of mathematical lessons. The project is grounded in a design-based research framework for education research. A team of experienced high school teachers will design and test MCLEs (four per teacher) with researchers through three year-long cycles. Prior to the first cycle, data will be collected (interview, observations) to record initial teacher curricular strategies regarding student dispositions toward mathematics. Then, a professional development experience will introduce the Mathematical Story Framework, along with other curricular frameworks to support the planning and enacting of lessons (i.e., cognitive demand and coherence). During the design cycles, videotaped observations and student aesthetic measures (surveys and interviews) for both MCLEs and a non-MCLEs (randomly selected to be the lesson before or after the MCLE) will be collected to enable comparison. Also, student dispositional measures, collected at the beginning and end of each cycle, will be used to learn whether and how student attitudes in mathematics change over time. Of the MCLEs designed and tested, a sample will be selected (based on aesthetic and mathematical differences) and developed into models, complete with the rationale for and description of aesthetic dimensions.

INFEWS/T4: The INFEWS-ER: a Virtual Resource Center Enabling Graduate Innovations at the Nexus of Food, Energy, and Water Systems

This project will provide a virtual environment for completing the Food, Energy, and Water (FEW) graduate student experience. The proposed work facilitates a transition from interdisciplinary to transdisciplinary training of existing faculty and current graduate students through a virtual resource center to help develop systematic processes for interdisciplinary thinking about large societal problems, especially those at the nexus of food, energy, and water.

Award Number: 
1639340
Funding Period: 
Thu, 09/01/2016 to Mon, 08/31/2020
Full Description: 

This project will provide a virtual environment for completing the Food, Energy, and Water (FEW) graduate student experience, thereby facilitating the generation of human capital who can address grand challenges at the nexus of food, energy, and water. The INFEWS-ER will provide educational resources (ER) targeting innovations at the nexus of FEW by combining the fundamental sciences of food, energy, and water with the skills and knowledge of interdisciplinary problem solving and the latest computational modeling and analysis tools and data. These individuals will be capable of analyzing scenarios at the scale of nations, continents, and the globe. The INFEWS-ER will offer certificate programs where FEW Graduate Scholars can demonstrate their capabilities in interdisciplinary thinking, Big Data, and computational modeling and analysis, thereby receiving a credential demonstrating their level of achievement. Further, The INFEWS-ER will offer a faculty fellowship program to incentivize a network of academics that will provide a scaffolded learning environment for graduates, effectively creating a hub for INFEWS research, education, and training.

The proposed work facilitates a transition from interdisciplinary to transdisciplinary training of existing faculty and current graduate students (who will become future faculty, practitioners, and policy makers) through a virtual resource center that will be accessible beyond the project team and project timeframe. Students will develop systematic processes for interdisciplinary thinking. They will be in the best possible position to target large societal problems, especially those at the nexus of food, energy, and water. New, interdisciplinary solutions will emerge, solutions that are sensitive to a wider array of constraints and ideals. Those solutions will reflect the best possible integration of technological, socio-economic, and socio-political constructs. Project impacts include educational and workforce development of the next generation of academics, multi-institution collaboration, and enhanced infrastructure for transdisciplinary research and education. The INFEWS-ER also has the potential to influence the way interdisciplinary research and education is implemented in the future through the archival dissemination of not only learning modules, but also the evaluations and lessons learned from the implementation of the center.

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

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


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.

Multiple Instrumental Case Studies of Inclusive STEM-Focused High Schools: Opportunity Structures for Preparation and Inspiration (OSPrl)

The aim of this project is to examine opportunity structures provided to students by inclusive STEM-focused high schools, with an emphasis on studying schools that serve students from underrepresented groups. The project is studying inclusive STEM-focused high schools across the United States to determine what defines them. The research team initially identified ten candidate critical components that define STEM-focused high schools and is refining and further clarifying the critical components through the research study.

Lead Organization(s): 
Award Number: 
1118851
Funding Period: 
Thu, 09/01/2011 to Mon, 08/31/2015
Full Description: 

The aim of this project is to examine opportunity structures provided to students by inclusive STEM-focused high schools, with an emphasis on studying schools that serve students from underrepresented groups. In contrast to highly selective STEM-focused schools that target students who are already identified as gifted and talented in STEM, inclusive STEM-focused high schools aim to develop new sources of STEM talent, particularly among underrepresented minority students, to improve workforce development and prepare STEM professionals. A new NRC report, Successful K-12 STEM Education (2011), identifies areas in which research on STEM-focused schools is most needed. The NRC report points out the importance of providing opportunities for groups that are underrepresented in the sciences, especially Blacks, Hispanics, and low-income students who disproportionately fall out of the high-achieving group in K-12 education. This project responds specifically to the call for research in the NRC report and provides systematic data to define and clarify the nature of such schools. 

The project is studying inclusive STEM-focused high schools across the United States to determine what defines them. The research team initially identified ten candidate critical components that define STEM-focused high schools and is refining and further clarifying the critical components through the research study. The first phase of the study is focusing on 12 well-established and carefully planned schools with good reputations and strong community and business support, in order to capture the critical components as intended and implemented. Case studies of these high-functioning schools and a cross-case analysis using a set of instruments for gauging STEM design and implementation are contributing toward building a theory of action for such schools that can be applied more generally to STEM education. The second phase of the study involves selecting four school models for further study, focusing on student-level experiences and comparing student outcomes against comprehensive schools in the same district. Research questions being studied include: 1) Is there a core set of likely critical components shared by well-established, promising inclusive STEM-focused high schools? Do other components emerge from the study? 2) How are the critical components implemented in each school? 3) What are the contextual affordances and constraints that influence schools' designs, their implementation, and student outcomes? 4) How do student STEM outcomes in these schools compare with school district and state averages? 5) How do four promising such schools compare with matched comprehensive high schools within their respective school districts, and how are the critical components displayed? 6) From the points of view of students underrepresented in STEM fields, how do education experiences at the schools and their matched counterparts compare? And 7) How do student outcomes compare?

The research uses a multiple instrumental case study design in order to describe and compare similar phenomena. Schools as critical cases are being selected through a nomination process by experts, followed by screening and categorization according to key design dimensions. Data sources include school documents and public database information; a survey, followed by telephone interviews that probe for elaborated information, to provide a systematic overview of the candidate components; on-site visitations to each school provide data on classroom observations at the schools; interviews with students, teachers and administrators in focus groups; and discussions with critical members of the school community that provide unique opportunities to learn such as mentors, business leaders, and members of higher education community that provide outside of school learning experiences. The project is also gathering data on a variety of school-level student outcome indicators, and is tracking the likely STEM course trajectories for students, graduation rates, and college admission rates for students in the inclusive STEM-focused schools, as compared to other schools in the same jurisdiction. Analysis of the first phase of the study aims to develop rich descriptions that showcase characteristics of the schools, using axial and open coding, to determine a theory of action that illustrates interconnections among context, design, implementation, and outcome elements. Analysis of the second phase of the study involves similar processes on four levels: school, student, databases, and a synthesis of the three. Evaluation of the project consists of an internal advisory board and an external advisory board, both of which provide primarily formative feedback on research procedures.

Research findings, as well as case studies, records of instrument and rubric development and use, annual reports, and conference proposals and papers are being provided on a website, in order to provide an immediate and ongoing resource for education leaders, researchers and policymakers to learn about research on these schools and particular models. An effort is also being made to give voice to the experiences of high school students from the four pairs of high schools studied in the second phase of the study. Findings are also being disseminated by more traditional means, such as papers in peer-reviewed journals and conference presentations.

Professional Development for Culturally Relevant Teaching and Learning in Pre-K Mathematics

This project is creating and studying a professional development model to support preK teachers in developing culturally and developmentally appropriate practices in counting and early number. The proposed model is targeted at teachers of children in four-year-old kindergarten, and focuses on culturally relevant teaching and learning. The model stresses counting and basic number operations with the intention of exploring the domain as it connects to children's experiences in their homes and communities.

Award Number: 
1019431
Funding Period: 
Wed, 09/01/2010 to Fri, 08/31/2018
Project Evaluator: 
Victoria Jacobs
Full Description: 

Developers and researchers at the University of Wisconsin are creating and studying a professional development model that connects research in counting and early number (CGI), early childhood, and funds of knowledge. The proposed model is targeted at teachers of children in four-year-old kindergarten, and focuses on culturally relevant teaching and learning. The model stresses a specific, circumscribed content domain - counting and basic number operations - with the intention of exploring the domain in depth particularly as it connects to children's experiences in their homes and communities and how it is learned and taught through play.

The project designs, develops, and tests innovative resources and models for teachers to support ongoing professional learning communities. These learning communities are designed to identify and build on the rich mathematical understandings of all pre-K children. The project's specific goals are to instantiate a reciprocal "funds of knowledge" framework for (a) accessing children's out-of-school experiences in order to provide instruction that is equitable and culturally relevant and (b) developing culturally effective ways to support families in understanding how to mathematize their children's out-of-school activities. Teachers are observed weekly during the development and evaluation process and student assessments are used to measure students' progress toward meeting project benchmarks and the program's effectiveness in reducing or eliminating the achievement gap.

The outcome is a complete professional development model that includes written and digital materials. The product includes case studies, classroom video, examples of student work, and strategies for responding to students' understandings.

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