Quantitative

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.

Readiness through Integrative Science and Engineering: Refining and Testing a Co-constructed Curriculum Approach with Head Start Partners

Building upon prior research on Head Start curriculum, this phase of Readiness through Integrative Science and Engineering (RISE) will be expanded to include classroom coaches and community experts to enable implementation and assessment of RISE in a larger sample of classrooms. The goal is to improve school readiness for culturally and linguistically diverse, urban-residing children from low-income families, and the focus on science, technology, and engineering will address a gap in early STEM education.

Lead Organization(s): 
Award Number: 
1621161
Funding Period: 
Sat, 10/01/2016 to Wed, 09/30/2020
Full Description: 

Readiness through Integrative Science and Engineering (RISE) is a late stage design and development project that will build upon the results of an earlier NSF-funded design and development study in which a co-construction process for curriculum development was designed by a team of education researchers with a small group of Head Start educators and parent leaders. In this phase, the design team will be expanded to include Classroom Coaches and Community Experts to enable implementation and assessment of the RISE model in a larger sample of Head Start classrooms. In this current phase, an iterative design process will further develop the science, technology, and engineering curricular materials as well continue to refine supports for teachers to access families' funds of knowledge related to science, technology, and engineering in order to build on children's prior knowledge as home-school connections. The ultimate goal of the project is to improve school readiness for culturally and linguistically diverse, urban-residing children from low-income families who tend to be underrepresented in curriculum development studies even though they are most at-risk for later school adjustment difficulties. The focus on science, technology, and engineering will address a gap in early STEM education.

The proposed group-randomized design, consisting of 90 teachers/classrooms (45 RISE/45 Control), will allow for assessment of the impact of a 2-year RISE intervention compared with a no-intervention control group. Year 1 will consist of recruitment, induction, and training of Classroom Coaches and Community Experts in the full RISE model, as well as preparation of integrative curricular materials and resources. In Year 2, participating teachers will implement the RISE curriculum approach supported by Classroom Coaches and Community Experts; data on teacher practice, classroom quality, and implementation fidelity will be collected, and these formative assessments will inform redesign and any refinements for Year 3. During Year 2, project-specific measures of learning for science, technology, and engineering concepts and skills will also be tested and refined. In Year 3, pre-post data on teachers (as in Year 2) as well as on 10 randomly selected children in each classroom (N = 900) will be collected. When child outcomes are assessed, multilevel modeling will be used to account for nesting of children in classrooms. In addition, several moderators will be examined in final summative analyses (e.g., teacher education, part or full-day classroom, parent demographics, implementation fidelity). At the end of this project, all materials will be finalized and the RISE co-construction approach will be ready for scale-up and replication studies in other communities.

Development of the Electronic Test of Early Numeracy

The project will develop and refine an electronic Test of Early Numeracy (e-TEN) in English and Spanish that will assess informal and formal knowledge of number and operations in domains including verbal counting, numbering, numerical relationships, and mental addition/subtraction. The overarching goal of the assessment design is to create a measure that is more accurate, more accessible to a wider range of children, and easier to administer than existing measures.

Partner Organization(s): 
Award Number: 
1621470
Funding Period: 
Thu, 09/15/2016 to Tue, 08/31/2021
Full Description: 

The project will develop and refine an electronic Test of Early Numeracy (e-TEN) in English and Spanish, focused on number and operations. The assessment will incorporate a learning trajectory that describes students' development of the understanding of number. The electronic assessment will allow for the test to adapt to students' responses and incorporate games to increase children's engagement with the tasks. These features take advantage of the electronic format. The achievement test will be designed to be efficient, user-friendly, affordable, and accessible for a variety of learning environments and a broad age range (3 to 8 years old). The overarching goal of the assessment design is to create a measure that is more accurate, more accessible to a wider range of children, and easier to administer than existing measures. This project is funded by the Discovery Research Pre-K-12 Program, which funds research and development of STEM innovations and approaches in assessment, teaching and learning.

The e-TEN will assess informal and formal knowledge of number and operations in domains including verbal counting, numbering, numerical relationships, and mental addition/subtraction. The items will be designed using domain-based learning trajectories that describe students' development of understanding of the topics. The test will be designed with some key characteristics. First, it will be semi-adaptive over six-month age spans. Second, it will have an electronic format that allows for uniform implementation and an efficient, user-friendly administration. The test will also be accessible to Spanish speakers using an inclusive assessment model. Finally, the game-based aspect should increase children's engagement and present more meaningful questions. The user-friendly aspect includes simplifying the assessment process compared to other tests of numeracy in early-childhood. The first phase of the development will test a preliminary version of the e-TEN to test its functionality and feasibility. The second phase will focus on norming of the items, reliability and validity. Reliability will be assessed using Item Response Theory methods and test-retest reliability measures. Validity will be examined using criterion-prediction validity and construct validity. The final phase of the work will include creating a Spanish version of the test including collecting data from bilingual children using both versions of the e-TEN.

Longitudinal Learning of Viable Argument in Mathematics for Adolescents

This project builds on a prior study that demonstrated increases in students' knowledge of argumentation and their performance on mathematics assessments. The project will extend the use of the argumentation intervention into all eighth grade content areas, with a specific focus on students' learning of reasoning and proof, and contribute to understanding how students' learning about mathematical practices that can help them learn mathematics better.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1621438
Funding Period: 
Thu, 09/01/2016 to Wed, 08/31/2022
Full Description: 

The project will examine learning in eighth grade mathematics with a specific focus on students' learning of reasoning and proof. The intervention builds on a prior study in algebra that demonstrated increases in students' knowledge of argumentation and their performance on mathematics assessments. This project will extend the use of the argumentation intervention into all eighth grade content areas. The investigators will also address support for teachers in the form of teacher materials that link the argumentation content with mathematics standards and state-wide assessments, and a learning progression to engage students in proving tasks. The project will use assessments of mathematics learning and additional data from teachers and students to understand the impact of the argumentation intervention on teachers and students. The project contributes to understanding how students can learn about mathematical practices, such as proving, that can help them learn mathematics better. A significant contribution will be the definition of aspects of proving and descriptions of student outcomes that can be used to measure how well students have achieved these components of proving.

The project suggests twelve conceptual pillars that are combined with classroom processes and assessable outcomes to examine the use of argumentation practices in the teaching of eighth grade mathematics content. The investigation of classroom support for argumentation includes research questions that focus on improvement on state-level assessments, students' ability to construct mathematical arguments, and the conceptual progression that supports students' understanding of argumentation and proof. In addition, the study will examine teachers' role in argumentation in the classroom and their perception of potential challenges for classroom implementation. The study will use an experimental design to examine an intervention for mathematical reasoning and proof in eighth grade. The project includes a treatment group of teachers that will participate in professional development including a summer institute followed by instructional coaching over a two year period.

Algebra Project Mathematics Content and Pedagogy Initiative

This project will scale up, implement, and assess the efficacy of interventions in K-12 mathematics education based on the well-established Algebra Project (AP) pedagogical framework, which seeks to improve performance and participation in mathematics of students in distressed school districts, particularly low-income students from underserved populations.

Award Number: 
1749483
Funding Period: 
Thu, 09/15/2016 to Mon, 08/31/2020
Full Description: 

Algebra continues to serve as a gatekeeper and potential barrier for high school students. The Algebra Project Mathematics Content and Pedagogy Initiative (APMCPI) will scale up, implement and assess the efficacy of interventions in K-12 mathematics education based on the well-established Algebra Project (AP) pedagogical framework. The APMCPI project team is comprised of four HBCUs (Virginia State University, Dillard University, Xavier University, Lincoln University), the Southern Initiative Algebra Project (SIAP), and four school districts that are closely aligned with partner universities. The purpose of the Algebra Project is to improve performance and participation in mathematics by members of students in distressed school districts, particularly those with a large population of low-income students from underserved populations including African American and Hispanics. The project will provide professional development and implement the Algebra Project in four districts and study the impact on student learning. The research results will inform the nation's learning how to improve mathematics achievement for all children, particularly those in distressed inner-city school districts.

The study builds on a prior pilot project with a 74% increase in students who passed the state exam. In the early stages of this project, teachers in four districts closely associated with the four universities will receive Algebra Project professional development in Summer Teacher Institutes with ongoing support during the academic year, including a community development plan. The professional development is designed to help teachers combine mathematical problem solving with context-rich lessons, which both strengthen and integrate teachers' understanding of key concepts in mathematics so that they better engage their students. The project also will focus on helping teachers establish a framework for mathematically substantive, conceptually-rich and experientially-grounded conversations with students. The first year of the study will begin a longitudinal quasi-experimental, explanatory, mixed-method design. Over the course of the project, researchers will follow cohorts who are in grade-levels 5 through 12 in Year 1 to allow analyses across crucial transition periods - grades 5 to 6; grades 8 to 9; and grades 12 to college/workforce. Student and teacher data will be collected in September of Project Year 1, and in May of each project year, providing five data points for each student and teacher participant. Student data will include student attitude, belief, anxiety, and relationship to mathematics and science, in addition to student learning outcome measures. Teacher data will include content knowledge, attitudes and beliefs, and practices. Qualitative data will provide information on the implementation in both the experimental and control conditions. Analysis will include hierarchical linear modeling and multivariate analysis of covariance.

This project was previously funded under award #1621416.

Building a Next Generation Diagnostic Assessment and Reporting System within a Learning Trajectory-Based Mathematics Learning Map for Grades 6-8

This project will build on prior funding to design a next generation diagnostic assessment using learning progressions and other learning sciences research to support middle grades mathematics teaching and learning. The project will contribute to the nationally supported move to create, use, and apply research based open educational resources at scale.

Award Number: 
1621254
Funding Period: 
Thu, 09/15/2016 to Sat, 08/31/2019
Full Description: 

This project seeks to design a next generation diagnostic assessment using learning progressions and other research (in the learning sciences) to support middle grades mathematics teaching and learning. It will focus on nine large content ideas, and associated Common Core State Standards for Mathematics. The PIs will track students over time, and work within school districts to ensure feasibility and use of the assessment system.

The research will build on prior funding by multiple funding agencies and address four major goals. The partnership seeks to address these goals: 1) revising and strengthening the diagnostic assessments in mathematics by adding new item types and dynamic tools for data gathering 2) studying alternative ways to use measurement models to assess student mathematical progress over time using the concept of learning trajectories, 3) investigating how to assist students and teachers to effectively interpret reports on math progress, both at the individual and the class level, and 4) engineering and studying instructional strategies based on student results and interpretations, as they are implemented within competency-based and personalized learning classrooms. The learning map, assessment system, and analytics are open source and can be used by other research and implementation teams. The project will exhibit broad impact due to the number of states, school districts and varied kinds of schools seeking this kind of resource as a means to improve instruction. Finally, the research project contributes to the nationally supported move to create, use, and apply research based open educational resources at scale.

Learning Evolution through Human and Non-Human Case Studies

This project will develop and test two curriculum units on the topic of evolution for high school general biology courses, with one unit focusing primarily on human case studies to teach evolution and one unit focusing primarily on case studies of evolution in other species. The two units will be compared to examine how different approaches to teaching evolution affect students and teachers.

Lead Organization(s): 
Award Number: 
1621194
Funding Period: 
Thu, 09/15/2016 to Tue, 08/31/2021
Full Description: 

This project aligns with Alabama's College & Career-Ready Standards (CCRS) for biology in grades 9-12 relating to Unity and Diversity. These standards are based on the Next Generation Science Standards (NGSS) and go into effect during the 2016-2017 school year. Building on prior work (DRL-119468), this project will develop and test two curriculum units on the topic of evolution for high school general biology courses, with one unit focusing primarily on human case studies to teach evolution and one unit focusing primarily on case studies of evolution in other species. The two units will be compared to examine how different approaches to teaching evolution affect students and teachers. The project will also develop and field test a Cultural and Religious Sensitivity (CRS) Resource to provide teachers with strategies for creating supportive learning environments where understanding of the scientific account of evolution is aided while also acknowledging the cultural controversy associated with learning about evolution. The impacts on student and teacher outcomes of using the curriculum units and the CRS Resource will be tested in classrooms by comparing the outcomes of the human versus non-human units, and by using or not using classroom strategies from the CRS Resource.

The project will examine student and teacher outcomes of four treatment groups: 1) Curriculum Unit 1, 2) Curriculum Unit 1 with the CRS Resource, 3) Curriculum Unit 2, and 4) Curriculum Unit 2 with the CRS Resource. The research questions are: 1) In what ways does using examples of human versus non-human evolution to teach core evolutionary concepts affect understanding of, acceptance of, and motivation to learn about evolution among high school introductory biology students? 2) In what ways do using teaching strategies that focus on acknowledging the cultural controversy about evolution using a procedural neutrality approach affect high school introductory biology teachers' comfort and confidence with teaching evolution? 3) In what ways does using examples of human versus non-human evolution to teach fundamental evolutionary concepts in conjunction with teaching strategies that focus on acknowledging the cultural controversy about evolution using a procedural neutrality approach affect understanding of, acceptance of, and motivation to learn about evolution among high school introductory biology students? And 4) In what ways does using examples of human versus non-human evolution to teach fundamental evolutionary concepts in conjunction with teaching strategies that focus on acknowledging the cultural controversy about evolution using a procedural neutrality approach affect high school introductory biology teachers' comfort and confidence with teaching evolution? The project will use a 2 X 2 X 2 mixed factorial quasi-experimental research design to answer these questions, and will include a total of 32 teachers, 8 in each treatment group, along with approximately 800 students. Each assessment will be administered as a pretest two weeks prior to starting the curriculum unit and as a posttest immediately after completing the unit. Test scores will be the within-subjects factors, and Curriculum Unit and CRS Resource will be the between-subjects factors.

Geological Models for Explorations of Dynamic Earth (GEODE): Integrating the Power of Geodynamic Models in Middle School Earth Science Curriculum

This project will develop and research the transformational potential of geodynamic models embedded in learning progression-informed online curricula modules for middle school teaching and learning of Earth science. The primary goal of the project is to conduct design-based research to study the development of model-based curriculum modules, assessment instruments, and professional development materials for supporting student learning of (1) plate tectonics and related Earth processes, (2) modeling practices, and (3) uncertainty-infused argumentation practices.

Lead Organization(s): 
Award Number: 
1621176
Funding Period: 
Mon, 08/15/2016 to Fri, 07/31/2020
Full Description: 

This project will contribute to the Earth science education community's understanding of how engaging students with dynamic computer-based systems models supports their learning of complex Earth science concepts regarding Earth's surface phenomena and sub-surface processes. It will also extend the field's understandings of how students develop modeling practices and how models are used to support scientific endeavors. This research will shed light on the role uncertainty plays when students use models to develop scientific arguments with model-based evidence. The GEODE project will directly involve over 4,000 students and 22 teachers from diverse school systems serving students from families with a variety of socioeconomic, cultural, and racial backgrounds. These students will engage with important geoscience concepts that underlie some of the most critical socio-scientific challenges facing humanity at this time. The GEODE project research will also seek to understand how teachers' practices need to change in order to take advantage of these sophisticated geodynamic modeling tools. The materials generated through design and development will be made available for free to all future learners, teachers, and researchers beyond the participants outlined in the project.

The GEODE project will develop and research the transformational potential of geodynamic models embedded in learning progression-informed online curricula modules for middle school teaching and learning of Earth science. The primary goal of the project is to conduct design-based research to study the development of model-based curriculum modules, assessment instruments, and professional development materials for supporting student learning of (1) plate tectonics and related Earth processes, (2) modeling practices, and (3) uncertainty-infused argumentation practices. The GEODE software will permit students to "program" a series of geologic events into the model, gather evidence from the emergent phenomena that result from the model, revise the model, and use their models to explain the dynamic mechanisms related to plate motion and associated geologic phenomena such as sedimentation, volcanic eruptions, earthquakes, and deformation of strata. The project will also study the types of teacher practices necessary for supporting the use of dynamic computer models of complex phenomena and the use of curriculum that include an explicit focus on uncertainty-infused argumentation.

Modest Supports for Sustaining Professional Development Outcomes over the Long-Term

This study will investigate factors influencing the persistence of teacher change after professional development (PD) experiences, and will examine the extent to which modest supports for science teaching in grades K-5 sustain PD outcomes over the long term.

Lead Organization(s): 
Award Number: 
1620979
Funding Period: 
Thu, 09/15/2016 to Mon, 08/31/2020
Full Description: 

This study will investigate factors influencing the persistence of teacher change after professional development (PD) experiences, and will examine the extent to which modest supports for science teaching in grades K-5 sustain PD outcomes over the long term. Fifty K-12 teachers who completed one of four PD programs situated in small, rural school districts will be recruited for the study, and they will participate in summer refresher sessions for two days, cluster meetings at local schools twice during the academic year, and optional Webinar sessions two times per year. Electronic supports for participants will include a dedicated email address, a project Facebook page, a biweekly newsletter, and access to archived Webinars on a range of topics related to teaching elementary school science. Modest support for replacement of consumable supplies needed for hands-on classroom activities will also be provided. The project will examine the extent to which these modest supports individually and collectively foster the sustainability of PD outcomes in terms of the instructional time devoted to science, teacher self-efficacy in science, and teacher use of inquiry-based instructional strategies. The effects of contextual factors on sustainability of PD outcomes will also be examined.

This longitudinal study will seek answers to three research questions: 1) To what extent do modest supports foster the sustainability of professional development outcomes in: a) instructional time in science; b) teachers' self-efficacy in science; and c) teachers' use of inquiry-based instructional strategies? 2) Which supports are: a) the most critical for sustainability of outcomes; and b) the most cost-effective; and 3) What contextual factors support or impede the sustainability of professional development outcomes? The project will employ a mixed-methods research design to examine the effects of PD in science among elementary schoolteachers over a 10 to 12 year period that includes a 3-year PD program, a 4-6 year span after the initial PD program, and a 3-year intervention of modest supports. Quantitative and qualitative data will be collected from multiple sources, including: a general survey of participating teachers regarding their beliefs about science, their instructional practices, and their instructional time in science; a teacher self-efficacy measure; intervention feedback surveys; electronic data sources associated with Webinars; teacher interviews; school administrator interviews; and receipts for purchases of classroom supplies. Quantitative data from the teacher survey and self-efficacy measure will be analyzed using hierarchical modeling to examine growth rates after the original PD and the change in growth after the provision of modest supports. Data gathered from other sources will be tracked, coded, and analyzed for each teacher, and linked to the survey and self-efficacy data for analysis by individual teacher, by grade level, by school, by district, and by original PD experience. Together, these data will enable the project team to address the project's research questions, with particular emphasis on determining the extent to which teachers make use of the various supports offered, and identifying the most cost-effective and critical supports.

Enhancing Middle Grades Students' Capacity to Develop and Communicate Their Mathematical Understanding of Big Ideas Using Digital Inscriptional Resources (Collaborative Research: Phillips)

This project will develop and test a digital platform for middle school mathematics classrooms to help students deepen and communicate their understanding of mathematics. The digital platform will allow students to collaboratively create representations of their mathematics thinking, incorporate ideas from other students, and share their work with the class.

Lead Organization(s): 
Award Number: 
1620934
Funding Period: 
Thu, 09/01/2016 to Mon, 08/31/2020
Full Description: 

The primary goal of this project is to help middle school students deepen and communicate their understanding of mathematics. The project will develop and test a digital platform for middle school mathematics classrooms. The digital platform will allow students to collaboratively create representations of their mathematics thinking, incorporate ideas from other students, and share their work with the class. The digital learning environment makes use of a problem-centered mathematics curriculum that evolved from extensive development, field-testing and evaluation, and is widely used in middle schools. The research will also contribute to understanding about the design and innovative use of digital resources and collaboration in classrooms as an increasing number of schools are drawing on these kinds of 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 will support students to collaboratively construct, manipulate, and interpret shared representations of mathematics using digital inscriptional resources. The research activities will significantly enhance our understanding of student learning in mathematics in three important ways. The project will report on how (1) evidence of student thinking is made visible through the use of digital inscriptional resources, (2) student inscriptions are documented, discussed, and manipulated in collaborative settings, and (3) students' conceptual growth of big mathematical ideas grows over time. An iterative design research process will incorporate four phases of development, testing and revision, and will be conducted to study student use of the digital learning space and related inscriptional resources. Data sources will include: classroom observations and artifacts, student and teacher interviews and surveys, student assessment data, and analytics from the digital platform. The process will include close collaboration with teachers to understand the implementation and create revisions to the resources.


Project Videos

2019 STEM for All Video Showcase

Title: Math Understanding in a Digital Collaborative Environment

Presenter(s): Alden Edson, Kristen Bieda, Chad Dorsey, Nathan Kimball, & Elizabeth Phillips


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