Learning Progression

Developing and Investigating Unscripted Mathematics Videos

This project will use an alternative model for online videos to develop video units that feature the unscripted dialogue of pairs of students. The project team will create a repository of 6 dialogic mathematics video units that target important Algebra 1 and 2 topics for high school and upper middle school students, though the approach can be applied to any STEM topic, for any age level.

Lead Organization(s): 
Award Number: 
1907782
Funding Period: 
Sun, 09/01/2019 to Thu, 08/31/2023
Full Description: 

This project responds to the recent internet phenomenon of widespread accessibility to online instructional videos, which offer many benefits, such as student control of the pace of learning. However, these videos primarily focus on a single speaker working through procedural problems and providing an explanation. While the immense reach of free online instructional videos is potentially transformative, this potential can only be attained if access transcends physical availability to also include entry into important disciplinary understandings and practices, and only if the instructional method pushes past what would be considered outdated pedagogy in any other setting than a digital one. This project will use an alternative model for online videos, originally developed for a previous exploratory project, to develop 6 video units that feature the unscripted dialogue of pairs of students. The project team will use the filming and post-production processes established during the previous grant to create a repository of 6 dialogic mathematics video units that target important Algebra 1 and 2 topics for high school and upper middle school students, though the approach can be applied to any STEM topic, for any age level. They will also conduct 8 research studies to investigate the promise of these unscripted dialogic videos with a diverse population to better understand the vicarious learning process, which refers to learning from video- or audio-taped presentations of other people learning. Additionally, the project team will provide broader access to the project videos and support a variety of users, by: (a) subtitling the videos and checking math task statements for linguistic accessibility; (b) representing diversity of race, ethnicity, and language in both the pool of students who appear in the videos and the research study participants; (c) providing teachers with an array of resources including focus questions to pose in class with each video, printable task worksheets, specific ways to support dialogue about the videos, and alignment of the video content with Common Core mathematics standards and practices; and (d) modernizing the project website and making it functional across a variety of platforms.

The videos created for this project will feature pairs of students (called the talent), highlighting their unscripted dialogue, authentic confusion, and conceptual resources. Each video unit will consist of 7 video lessons (each split into 4-5 short video episodes) meant to be viewed in succession to support conceptual development over time. The project will build upon emerging evidence from the exploratory grant that as students engage with videos that feature peers grappling with complex mathematics, they can enter a quasi-collaborative relationship with the on-screen talent to learn complex conceptual content and engage in authentic mathematical practices. The research focuses on the questions: 1. What can diverse populations of vicarious learners learn mathematically from dialogic videos, and how do the vicarious learners orient to the talent in the videos? 2. What is the nature of vicarious learners' evolving ways of reasoning as they engage with multiple dialogic video lessons over time and what processes are involved in vicarious learning? and, 3. What instructional practices encourage a classroom community to adopt productive ways of reasoning from dialogic videos? To address the first question, the project team will conduct two Learning Outcomes and Orientation Studies, in which they analyze students' learning outcomes and survey responses after they have learned from one of the video units in a classroom setting. Before administering an assessment to a classroom of students, they will first conduct an exploratory Interpretation Study for each unit, in which they link the mathematical interpretations that VLs generate from viewing the project videos with their performance on an assessment instrument. Both types of studies will be conducted twice, once for each of two video units - Exponential Functions and Meaning and Use of Algebraic Symbols. For the second research question, the project team will identify a learning trajectory associated with each of four video units. These two learning trajectories will inform the instructional planning for the classroom studies by identifying what meaningful appropriation can occur, as well as conceptual challenges for VLs. By delivering learning trajectories for two additional units, the project can contribute to vicarious learning theory by identifying commonalities in learning processes evident across the four studies. For the final research question, the project team will investigate how instructors can support students with the instrumental genesis process, which occurs through a process called instrumental orchestration, as they teach the two videos on exponential functions and algebraic symbols.

Learning Trajectories as a Complete Early Mathematics Intervention: Achieving Efficacies of Economies at Scale

The purpose of this project is to test the efficacy of the Learning and Teaching with Learning Trajectories (LT2) program with the goal of improving mathematics teaching and thereby increasing young students' math learning. LT2 is a professional development tool and a curriculum resource intended for teachers to be used to support early math instruction and includes the mathematical learning goal, the developmental progression, and relevant instructional activities.

Lead Organization(s): 
Award Number: 
1908889
Funding Period: 
Mon, 07/01/2019 to Sun, 06/30/2024
Full Description: 

U.S. proficiency in mathematics continues to be low and early math performance is a powerful predictor of long-term academic success and employability. However, relatively few early childhood degree programs have any curriculum requirements focused on key mathematics topics. Thus, teacher professional development programs offer a viable and promising method for supporting and improving teachers' instructional approaches to mathematics and thus, improving student math outcomes. The purpose of this project is to test the efficacy of the Learning and Teaching with Learning Trajectories (LT2) program with the goal of improving mathematics teaching and thereby increasing young students' math learning. LT2 is a professional development tool and a curriculum resource intended for teachers to be used to support early math instruction. The LT2 program modules uniquely include the mathematical learning goal, the developmental progression, and relevant instructional activities. All three aspects are critical for high-quality and coherent mathematics instruction in the early grades.

This project will address the following research questions: 1) What are the medium-range effects of LT2 on student achievement and the achievement gap? 2) What are the short- and long-term effects of LT2 on teacher instructional approach, beliefs, and quality? and 3) How cost effective is the LT2 intervention relative to the original Building Blocks intervention? To address the research questions, this project will conduct a multisite cluster randomized experimental design, with 90 schools randomly assigned within school districts to either experimental or control groups. Outcome measures for the approximately 250 kindergarten classrooms across these districts will include the Research-based Elementary Math Assessment, observations of instructional quality, a questionnaire focused on teacher beliefs and practices, in addition to school level administrative data. Data will be analyzed using multi-level regression models to determine the effect of the Learning Trajectories intervention on student learning.

Case Studies of a Suite of Next Generation Science Instructional, Assessment, and Professional Development Materials in Diverse Middle School Settings

This project addresses a gap between vision and implementation of state science standards by designing a coordinated suite of instructional, assessment and teacher professional learning materials that attempt to enact the vision behind the Next Generation Science Standards. The study focuses on using state-of-the-art technology to create an 8-week long, immersive, life science field experience organized around three investigations.

Lead Organization(s): 
Award Number: 
1907944
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

New state science standards are ambitious and require important changes to instructional practices, accompanied by a coordinated system of curriculum, assessment, and professional development materials. This project addresses a gap between vision and implementation of such standards by designing a coordinated suite of instructional, assessment and teacher professional learning materials that attempt to enact the vision behind the Next Generation Science Standards. The study focuses on the design of such materials using state-of-the-art technology to create an 8-week long, immersive, life science field experience organized around three investigations. Classes of urban students in two states will collect data on local insect species with the goal of understanding, sharing, and critiquing environmental management solutions. An integrated learning technology system, the Learning Navigator, draws on big data to organize student-gathered data, dialogue, lessons, an assessment information. The Learning Navigator will also amplify the teacher's role in guiding and fostering next generation science learning. This project advances the field through an in-depth exploration of the goals for the standards documents. The study begins to address questions about what works when, where, and for whom in the context of the Next Generation Science Standards.

The project uses a series of case studies to create, test, evaluate and refine the system of instructional, assessment and professional development materials as they are enacted in two distinct urban school settings. It is designed with 330 students and 22 teachers in culturally, racially and linguistically diverse, under-resourced schools in Pennsylvania and California. These schools are located in neighborhoods that are economically challenged and have students who demonstrate patterns of underperformance on state standardized tests. It will document the process of team co-construction of Next Generation Science-fostering instructional materials; develop assessment tasks for an instructional unit that are valid and reliable; and, track the patterns of use of the instructional and assessment materials by teachers. The study will also record if new misconceptions are revealed as students develop Next Generation Science knowledge,  comparing findings across two diverse school locations in two states. Data collection will include: (a) multiple types of data to establish validity and reliability of educational assessments, (b) the design, evaluation and use of a classroom observation protocol to gather information on both frequency and categorical degree of classroom practices that support the vision, and (c) consecutive years of ten individual classroom enactments through case studies analyzed through cross-case analyses. This should lead to stronger and better developed understandings about what constitutes strong Next Generation Science learning and the classroom conditions, instructional materials, assessments and teacher development that foster it.

Aligning the Science Teacher Education Pathway: A Networked Improvement Community

This project will study the activities of a Networked Improvement Community (NIC) as a vehicle to bridge gaps across four identified steps along the science teacher training and development pathways within local contexts of 8 participating universities. The overarching goal of the project is to strengthen the capacity of universities and school districts to reliably produce teachers of science who are knowledgeable about and can effectively enact the Next Generation Science Standards (NGSS), although prepared in varied organizational contexts.

Award Number: 
1908900
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Full Description: 

California State University will study the activities of a Networked Improvement Community (NIC) as a vehicle to bridge gaps across four identified steps along the science teacher training and development pathways within local contexts of 8 participating universities (NIC sites). Networked Improvement Community (NIC) will co-create a shared vision and co-defined research agenda between university researchers, science educators and school district practitioners working together to reform teacher education across a variety of local contexts. By studying outcomes of shared supports and teacher tools for use in multiple steps along the science teacher education pathway, researchers will map variation existing in the system and align efforts across the science teacher education pathway. This process will integrate an iterative nature of educational change in local contexts impacting enactment of the NGSS in both university teacher preparation programs and in school district professional training activities and classrooms.

The overarching goal of the project is to strengthen the capacity of universities and school districts to reliably produce teachers of science who are knowledgeable about and can effectively enact the Next Generation Science Standards (NGSS), although prepared in varied organizational contexts. The project will accomplish this goal 1) leveraging the use of an established Networked Improvement Community, composed of science education faculty from eight university campuses and by 2) improving and studying coherence in the steps along the science teacher education pathway within and across these universities and school districts. The project will use a mixed methods approach to data collection and analysis. Consistent with Improvement Science Theory, research questions will be co-defined by all stakeholders.

CAREER: Black Youth Development and Curricular Supports for Robust Identities in Mathematics

This study seeks to describe trajectories that describe the ways in which Black learners develop as particular kinds of mathematical learners. The study takes place in the context of an established, multi-year college bridge program that has as its goals to increase the representation of historically marginalized groups in the university community.

Lead Organization(s): 
Award Number: 
1845841
Funding Period: 
Wed, 05/01/2019 to Tue, 04/30/2024
Full Description: 

Student success in mathematics correlates with positive identities, dispositions, and relationships towards the subject. As mathematics education research strives to understand historic inequities in mathematics for Black learners, small-scale research has described the relationships between identity, subjectivity, and positionality in Black learners as it relates to their achievement and interest in mathematics. This study builds on that descriptive work by seeking to describe trajectories that describe the ways in which Black learners develop as particular kinds of mathematical learners. The study takes place in the context of an established, multi-year college bridge program that has as its goals to increase the representation of historically marginalized groups in the university community. Students in the bridge program from three communities in the greater Detroit area with strong academic achievement in mathematics will be recruited. Their experiences in the bridge program will be traced to identify trajectories that describe the development of Black learners relative to mathematics, and document the design features of classroom activities that support learners in moving through those trajectories.

At the center of the project is the study of cohorts of students in grades 8-11 as they move through the summer bridge program. The bridge project's current curriculum features a series of lessons focused on identity development related to mathematics. These lessons will be implemented, studied, revised, and redeployed across the duration of the project across the summer sessions. Teacher focus groups and surveys will assess the implementation of the activities and aggregate feedback on the design. Three cohorts of students will be recruited to participate in the broader project activities from three metro areas with distinctly different demographic profiles. Student mathematical efficacy will be assessed for all participating students. Within each of the three metro areas, students will be recruited that represent differing levels of mathematics efficacy to ensure that focus students are likely to experience different trajectories through their engagement with the study. The students will be interviewed three times in each academic year to describe their trajectories. Student achievement data will also be collected for all participating students along with narrative descriptions and autobiographies about the messages students receive about mathematics. These messages include their own internal thinking about how they see themselves as mathematics learners, and messages that are sent to them by other students, teachers, and the community. Products of the study will be case studies that describe trajectories of identity development in Black mathematics learners, and a disseminated curriculum for a mathematics identity-focused bridge program supporting Black learners.

Engaging High School Students in Computer Science with Co-Creative Learning Companions (Collaborative Research: Magerko)

This research investigates how state-of-the-art creative and pedagogical agents can improve students' learning, attitudes, and engagement with computer science. The project will be conducted in high school classrooms using EarSketch, an online computer science learning environments that engages learners in making music with JavaScript or Python code.

Award Number: 
1814083
Funding Period: 
Sat, 09/15/2018 to Wed, 08/31/2022
Full Description: 
This research investigates how state-of-the-art creative and pedagogical agents can improve students' learning, attitudes, and engagement with computer science. The project will be conducted in high school classrooms using EarSketch, an online computer science learning environments that engages over 160,000 learners worldwide in making music with JavaScript or Python code. The researchers will build the first co-creative learning companion, Cai, that will scaffold students with pedagogical strategies that include making use of learner code to illustrate abstraction and modularity, suggesting new code to scaffold new concepts, providing help and hints, and explaining its decisions. This work will directly address the national need to develop computing literacy as a core STEM skill.
 
The proposed work brings together an experienced interdisciplinary team to investigate the hypothesis that adding a co-creative learning companion to an expressive computer science learning environment will improve students' computer science learning (as measured by code sophistication and concept knowledge), positive attitudes towards computing (self-efficacy and motivation), and engagement (focused attention and involvement during learning). The iterative design and development of the co-creative learning companion will be based on studies of human collaboration in EarSketch classrooms, the findings in the co-creative literature and virtual agents research, and the researchers' observations of EarSketch use in classrooms. This work will address the following research questions: 1) What are the foundational pedagogical moves that a co-creative learning companion for expressive programming should perform?; 2) What educational strategies for a co-creative learning companion most effectively scaffold learning, favorable attitudes toward computing, and engagement?; and 3) In what ways does a co-creative learning companion in EarSketch increase computer science learning, engagement, and positive attitudes toward computer science when deployed within the sociocultural context of a high school classroom? The proposed research has the potential to transform our understanding of how to support student learning in and broaden participation through expressive computing environments.

Promoting Engineering Problem Framing Skill-Development in High School Science and Engineering Courses

This project will develop curricular activities and assessment guidance for K-12 science and engineering educators who seek to incorporate engineering design content into their biology, chemistry, and physics classes.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1812823
Funding Period: 
Wed, 08/01/2018 to Sat, 07/31/2021
Full Description: 

This collaborative project involving Ohio Northern University, Ohio State University, and Olathe Northwest High School will develop curricular activities and assessment guidance for K-12 science and engineering educators who seek to incorporate engineering design content into their biology, chemistry, and physics classes. This work is important because students' limited exposure to engineering activities can negatively impact their decisions to enroll in STEM courses and to pursue engineering careers. Further, many states are adopting or considering adopting the Next Generation Science Standards (NGSS), a set of classroom standards which integrate engineering content into traditional science disciplines. While high school teachers under these standards are expected to incorporate the cross-cutting engineering content into their courses, they generally receive little high-quality support for doing so. If successful, the project could provide a powerful model of how to support busy and resource-constrained STEM teachers, and create broader student interest in STEM careers.

Drawing from best practices on instructional design, the project's main objectives are to: (1) design, field-test, and evaluate the impact of 12 NGSS-aligned, engineering problem-framing design activities on students enrolled in grades 9-12 science courses and (2) design and conduct high-quality, sustained professional development that fosters participating high school science teachers' ability to deploy the NGSS concepts-linked activities. Data sources include student design artifacts, video of classroom instruction, and surveys assessing student and teacher attitudes toward engineering, student design self-efficacy and teacher self-efficacy for teaching engineering content. These data will be analyzed to determine what teachers learned from the professional development activities, how those activities informed their teaching and in turn, how students' engagement with the engineering activities relates to their engineering design skills and attitudes. In terms of intellectual merit, the project aims to develop a learning progression of students' engineering design problem-framing skills by characterizing any observed change in students' design work and attitudes over time.

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

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

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

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

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

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

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

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

Numeric relational reasoning and spatial reasoning are critical to success in later mathematics coursework, including Algebra 1, a gatekeeper to success at the post-secondary level, and success in additional STEM domains, such as chemistry, geology, biology, and engineering. Given the importance of these skills for later success, it is imperative that there are high-quality screening tools available to identify students at-risk for difficulty in these areas. The primary aim of this study is to develop mathematics screening assessment tools for Grades K-2 over the course of four years that measure students' abilities in numeric relational reasoning and spatial reasoning. The team of researchers will develop Measures of Mathematical Reasoning Skills system, which will contain Tests of Numeric Relational Reasoning (T-NRR) and Tests of Spatial Reasoning (T-SR). The measures will be intended for use by teachers and school systems to screen students to determine who is at-risk for difficulty in early mathematics, including students with disabilities. The measures will help provide important information about the intensity of support that may be needed for a given student. Three forms per grade level will be developed for both the T-NRR and T-SR with accompanying validity and reliability evidence collected. The Discovery Research K-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics (STEM) by preK-12 students and teachers, through research and development of innovative resources, models and tools (RMTs). Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

The development of the T-NRR and T-SR measures will follow an iterative process across five phases. The phases include (1) refining the construct; (2) developing test specifications and item models; (3) developing items; (4) field testing the items; and (5) conducting validity studies. The evidence collected and evaluated during each phase will contribute to the overall evaluation of the reliability of the measures and the validity of the interpretations made using the measures. Item models, test specifications, and item development will be continuously evaluated and refined based on data from cognitive interviews, field tests, and reviews by mathematics educators, teachers of struggling students, teachers of culturally and linguistically diverse populations, and a Technical Advisory Board. In the final phase of development of the T-NRR and T-SR, reliability of the results will be estimated and multiple sources of validity evidence will be collected to examine the concurrent and predictive relation with other criterion measures, classification accuracy, and sensitivity to growth. Approximately 4,500 students in Grades K-2 will be involved in all phases of the research including field tests and cognitive interviews. Data will be analyzed using a two-parameter IRT model to ensure item and test form comparability.

Identifying Effective Instructional Practices that Foster the Development of Algebraic Thinking in Elementary School

This project seeks to identify teaching practices that can be linked to students' early algebra learning in grades three, four and five. The goal of the project is to use assessment data and videos of classroom teaching in order to create a tool that can be used to document effective instructional practices. This observation tool can then be used to support teacher professional development in early algebra and research about how teachers' actions can be linked to students' learning.

Lead Organization(s): 
Award Number: 
1721192
Funding Period: 
Thu, 06/01/2017 to Mon, 05/31/2021
Full Description: 

There is a critical need to better prepare all students for learning algebra. Part of this preparation involves developing a strong foundation for algebra in the elementary grades by building on students' informal intuitions about patterns, relationships and structure into more formalized ways of mathematical thinking. This project seeks to identify teaching practices that can be linked to students' early algebra learning in grades three, four and five. The goal of the project is to use assessment data and videos of classroom teaching in order to create a tool that can be used to document effective instructional practices. This observation tool can then be used to support teacher professional development in early algebra and research about how teachers' actions can be linked to students' learning. The project is unique in its work to link an early algebra curriculum with understanding of teachers' practices in implementing that curriculum and students' learning of mathematics.

The project aims to address two research questions. First, what profiles of instructional practice are associated with greater student performance in early algebra? Second, to what extent do these profiles of effective instructional practices vary by grade level? The primary product of the work is an early algebra observation protocol that will capture non-domain and non-grade level specific practices of effective teaching in combination with practices specific to early algebra. Videos of early algebra classrooms will be used to design the observation protocol, which in turn, will then be used along with student assessment data to identify profiles of instructional practices associated with students' learning. Multiple phases of testing and revision will be used to create the observation protocol. The observation protocol will also generate profiles of teacher practices that can be used to describe different models for effectively teaching early algebra. The project will also examine implications of their work for teacher preparation and professional development.

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