Mathematics

Co-developing a Curriculum Coherence Toolkit with Teachers (Collaborative Research: Drake)

This project will investigate the factors that influence curriculum coherence and how teachers in Grades 3-5 respond to these factors as they make decisions about their mathematics curriculum.

Lead Organization(s): 
Award Number: 
1908165
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

One important aspect of any mathematics curriculum is its coherence, or the mathematical connections across lessons. This coherence links lessons and activities so that mathematical ideas, representations, practices, skills, and ways of thinking build upon each other to help students construct mathematical meaning and enhance their learning. When teachers relied predominantly on published curriculum materials, curricular coherence was largely provided by the curriculum authors. However, many of today's teachers are no longer given a foundational textbook or single set of resources. Further, teachers have unprecedented access via the internet and social media to lessons and activities produced by many different curriculum developers (including other teachers). As a result, the important task of building curricular coherence becomes the responsibility of the classroom teacher. And yet, very little is known about how teachers think about curricular coherence or how their decisions about lessons and activities reflect the coherent mathematical story they hope to students will learn in their classrooms. This project will investigate the factors that influence curriculum coherence and how teachers in Grades 3-5 respond to these factors as they make decisions about their mathematics curriculum. A national survey of 300 Grades 3-5 teachers will be conducted in in the first phase of the project and the work will continue with small groups of four case study teachers in each of four different districts across four states. Case study participants will work with project researchers to co-develop a set of tools for supporting curriculum coherence. The structure of the project and the selection of case study participants will facilitate the collaborative co-development of tools across institutions and across geographic and curricular contexts, supporting the use of the tools across a wide range of contexts. The outcomes of this study will contribute to broader impacts by developing understandings of curriculum coherence that are robust across a range of curricular, policy, and district/school contexts, with implications that support the participation of students in diverse mathematics classrooms. The survey findings and the coherence toolkit co-developed with teachers will be disseminated widely through conference presentations, including teacher-oriented conferences, through journal publications, and through making survey data available to other researchers.

The research objectives of this study are to explore 1) patterns of Grade 3-5 teacher curricular resource use across a range of curriculum contexts, 2) teacher decisions about curriculum coherence, and 3) how curriculum toolkits co-developed with teachers might support teachers in making decisions related to curriculum coherence. Given the potential variation among and within states and districts in terms of contextual factors impacting curriculum use, teachers will be surveyed about their contexts, available resources, and curricular decision-making. Survey data will be analyzed using primarily descriptive analyses. Following the survey, in-depth case studies of teacher curricular resource use in contexts that vary along two dimensions (autonomy to select curricular resources and the complexity of curricular influences, including the number of resources available) will be developed. Case study data, including interviews, video-recorded co-design groups, and curriculum use artifacts, will be analyzed using methods of discourse analysis, thematic analysis, and document analysis and synthesized within and across cases. By selecting cases along these dimensions, a set of tools will be co-developed to support teachers as they navigate diverse curricular contexts to enact a coherent curriculum for students.

Co-developing a Curriculum Coherence Toolkit with Teachers (Collaborative Research: Wood)

This project will investigate the factors that influence curriculum coherence and how teachers in Grades 3-5 respond to these factors as they make decisions about their mathematics curriculum.

Lead Organization(s): 
Award Number: 
1907831
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

One important aspect of any mathematics curriculum is its coherence, or the mathematical connections across lessons. This coherence links lessons and activities so that mathematical ideas, representations, practices, skills, and ways of thinking build upon each other to help students construct mathematical meaning and enhance their learning. When teachers relied predominantly on published curriculum materials, curricular coherence was largely provided by the curriculum authors. However, many of today's teachers are no longer given a foundational textbook or single set of resources. Further, teachers have unprecedented access via the internet and social media to lessons and activities produced by many different curriculum developers (including other teachers). As a result, the important task of building curricular coherence becomes the responsibility of the classroom teacher. And yet, very little is known about how teachers think about curricular coherence or how their decisions about lessons and activities reflect the coherent mathematical story they hope to students will learn in their classrooms. This project will investigate the factors that influence curriculum coherence and how teachers in Grades 3-5 respond to these factors as they make decisions about their mathematics curriculum. A national survey of 300 Grades 3-5 teachers will be conducted in in the first phase of the project and the work will continue with small groups of four case study teachers in each of four different districts across four states. Case study participants will work with project researchers to co-develop a set of tools for supporting curriculum coherence. The structure of the project and the selection of case study participants will facilitate the collaborative co-development of tools across institutions and across geographic and curricular contexts, supporting the use of the tools across a wide range of contexts. The outcomes of this study will contribute to broader impacts by developing understandings of curriculum coherence that are robust across a range of curricular, policy, and district/school contexts, with implications that support the participation of students in diverse mathematics classrooms. The survey findings and the coherence toolkit co-developed with teachers will be disseminated widely through conference presentations, including teacher-oriented conferences, through journal publications, and through making survey data available to other researchers.

The research objectives of this study are to explore 1) patterns of Grade 3-5 teacher curricular resource use across a range of curriculum contexts, 2) teacher decisions about curriculum coherence, and 3) how curriculum toolkits co-developed with teachers might support teachers in making decisions related to curriculum coherence. Given the potential variation among and within states and districts in terms of contextual factors impacting curriculum use, teachers will be surveyed about their contexts, available resources, and curricular decision-making. Survey data will be analyzed using primarily descriptive analyses. Following the survey, in-depth case studies of teacher curricular resource use in contexts that vary along two dimensions (autonomy to select curricular resources and the complexity of curricular influences, including the number of resources available) will be developed. Case study data, including interviews, video-recorded co-design groups, and curriculum use artifacts, will be analyzed using methods of discourse analysis, thematic analysis, and document analysis and synthesized within and across cases. By selecting cases along these dimensions, a set of tools will be co-developed to support teachers as they navigate diverse curricular contexts to enact a coherent curriculum for students.

Co-developing a Curriculum Coherence Toolkit with Teachers (Collaborative Research: Newton)

This project will investigate the factors that influence curriculum coherence and how teachers in Grades 3-5 respond to these factors as they make decisions about their mathematics curriculum.

Project Email: 
Lead Organization(s): 
Award Number: 
1907808
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Project Evaluator: 
Full Description: 

One important aspect of any mathematics curriculum is its coherence, or the mathematical connections across lessons. This coherence links lessons and activities so that mathematical ideas, representations, practices, skills, and ways of thinking build upon each other to help students construct mathematical meaning and enhance their learning. When teachers relied predominantly on published curriculum materials, curricular coherence was largely provided by the curriculum authors. However, many of today's teachers are no longer given a foundational textbook or single set of resources. Further, teachers have unprecedented access via the internet and social media to lessons and activities produced by many different curriculum developers (including other teachers). As a result, the important task of building curricular coherence becomes the responsibility of the classroom teacher. And yet, very little is known about how teachers think about curricular coherence or how their decisions about lessons and activities reflect the coherent mathematical story they hope to students will learn in their classrooms. This project will investigate the factors that influence curriculum coherence and how teachers in Grades 3-5 respond to these factors as they make decisions about their mathematics curriculum. A national survey of 300 Grades 3-5 teachers will be conducted in in the first phase of the project and the work will continue with small groups of four case study teachers in each of four different districts across four states. Case study participants will work with project researchers to co-develop a set of tools for supporting curriculum coherence. The structure of the project and the selection of case study participants will facilitate the collaborative co-development of tools across institutions and across geographic and curricular contexts, supporting the use of the tools across a wide range of contexts. The outcomes of this study will contribute to broader impacts by developing understandings of curriculum coherence that are robust across a range of curricular, policy, and district/school contexts, with implications that support the participation of students in diverse mathematics classrooms. The survey findings and the coherence toolkit co-developed with teachers will be disseminated widely through conference presentations, including teacher-oriented conferences, through journal publications, and through making survey data available to other researchers.

The research objectives of this study are to explore 1) patterns of Grade 3-5 teacher curricular resource use across a range of curriculum contexts, 2) teacher decisions about curriculum coherence, and 3) how curriculum toolkits co-developed with teachers might support teachers in making decisions related to curriculum coherence. Given the potential variation among and within states and districts in terms of contextual factors impacting curriculum use, teachers will be surveyed about their contexts, available resources, and curricular decision-making. Survey data will be analyzed using primarily descriptive analyses. Following the survey, in-depth case studies of teacher curricular resource use in contexts that vary along two dimensions (autonomy to select curricular resources and the complexity of curricular influences, including the number of resources available) will be developed. Case study data, including interviews, video-recorded co-design groups, and curriculum use artifacts, will be analyzed using methods of discourse analysis, thematic analysis, and document analysis and synthesized within and across cases. By selecting cases along these dimensions, a set of tools will be co-developed to support teachers as they navigate diverse curricular contexts to enact a coherent curriculum for students.

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Using Animated Contrasting Cases to Improve Procedural and Conceptual Knowledge in Geometry

This project aims to support stronger student outcomes in the teaching and learning of geometry in the middle grades through engaging students in animated contrasting cases of worked examples. The project will design a series of animated geometry curricular materials on a digital platform that ask students to compare different approaches to solving the same geometry problem. The study will measure changes in students' procedural and conceptual knowledge of geometry after engaging with the materials and will explore the ways in which teachers implement the materials in their classrooms.

Award Number: 
1907745
Funding Period: 
Thu, 08/01/2019 to Sun, 07/31/2022
Full Description: 

This project aims to support stronger student outcomes in the teaching and learning of geometry in the middle grades through engaging students in animated contrasting cases of worked examples. Animated contrasting cases are a set of two worked examples for the same geometry problem, approached in different ways. The animations show the visual moves and annotations students would make in solving the problems. Students are asked to compare and discuss the approaches. This theoretically-grounded approach extends the work of cognitive scientists and mathematics educators who have shown this approach supports strong student learning in algebra. The project will design a series of animated geometry curricular materials on a digital platform that ask students to compare different approaches to solving the same geometry problem. The study will measure changes in students' procedural and conceptual knowledge of geometry after engaging with the materials and will explore the ways in which teachers implement the materials in their classrooms. This work is particularly important as geometry is an understudied area in mathematics education, and national and international assessments at the middle school level consistently identify geometry as a mathematics content area in which students score the lowest.

This project draws on prior work that documents the impact of comparison on students' learning in algebra. Providing students with opportunities to compare multiple strategies is recommended by a range of mathematics policy documents, as research has shown this approach promotes flexibility and enhances conceptual knowledge and procedural fluency. More specifically, the approach allows students to compare the effectiveness and efficiency of mathematical arguments in the context of problem solving. An initial pilot study on non-animated contrasting cases in geometry shows promise for the general approach and suggests that animating the cases has the potential for stronger student learning gains. This study will examine the extent to which the animated cases improve students' conceptual and procedural knowledge of geometry and identify factors that relate to changes in knowledge. The project team will develop 24 worked example contrasting cases based on design principles from the prior work in algebra. The materials will be implemented in four treatment classrooms in the first cycle, revised, and then implemented in eight treatment classrooms. Students' written work will be collected along with data on the nature of the classroom discussions and small-group interviews with students. Teachers' perspectives on lessons will also be collected to support revision and strengthening of the materials. Assessments of students' geometry knowledge will be developed using measures with demonstrated validity and reliability to measure changes in student learning.

Developing Organizational Capacity to Improve K-8 Mathematics Teaching and Learning

This project will develop and test a leadership model to improve K-8 mathematics teaching and learning by involving stakeholders across the K-8 spectrum. The project will support teachers, teacher leaders, and administrators in collectively identifying and addressing problems of practice in the teaching and learning of mathematics, and in turn develop plans to improve school and district organizational capacities to support stronger mathematics teaching.

Award Number: 
1907681
Funding Period: 
Mon, 07/01/2019 to Sun, 06/30/2024
Full Description: 

The Developing Organizational Capacity to Improve K-8 Mathematics Teaching and Learning is a 4-year implementation and improvement project. The project will develop and test a leadership model to improve K-8 mathematics teaching and learning by involving stakeholders across the K-8 spectrum. The project will support teachers, teacher leaders, and administrators in collectively identifying and addressing problems of practice in the teaching and learning of mathematics, and in turn develop plans to improve school and district organizational capacities to support stronger mathematics teaching. At the heart of the project is the Elementary Mathematics Leadership (EML) model, which is designed to improve stakeholder understandings of effective math teaching practices. The EML model involves collaboratively identifying classroom-based problems of practice with school and district personnel, designing and implementing professional development aligned with the problems of practice, and iterating those cycles of development, implementation, and revision to assess the model's effectiveness.

The EML model operates at the teacher, school, and district level using a design-based implementation research approach. At the district level, leadership teams in conjunction with researchers will identify problems of practice for which work on those problems will lead to a more coherent mathematics instruction in the district. Following this, professional development and coaching at the teacher level will be designed and implemented to target the problem of practice, with a focus on big ideas within the Common Core State Standards for Mathematics. This phase of the model also includes professional development aimed at school leaders and district administrators to strengthen organizational capacity to support and lead change related to the problem of practice. The final phase of the model calls on researchers, district, and school personnel to engage in an annual redesign of the intervention, making use of data gathered during the school year and evidence about what is happening in classrooms. This design acknowledges the broader policy context in which schools and districts operate as they work towards instructional change. To evaluate the effectiveness of the overall EML model, the project will collect a wide variety of data, including student achievement outcomes using standardized tests; assessments of teachers' mathematical knowledge, instructional practices, and efficacy measures; and measures of leader, administrator, and organizational capacities to support high-quality mathematics instruction. Four districts will be recruited to participate, enacting the model in pairs with a staggered start for one pair of districts to be able to measure treatment effects, using a variation of a switching replications design. Classroom practice and teacher outcomes will be assessed using a variety of MKT assessments, the Mathematical Quality of Instruction (MQI), and the Instructional Quality Assessment (IQA). School level outcomes will be collected via a leadership assessment and interview data, and district level outcomes will be assessed through the use of interview and documentary data. Analysis will include a statistical analysis of the EML model using hierarchical linear modeling, MANOVA/ANOVA, and regression as appropriate at the level of students and teachers, and qualitative analysis and descriptive statistics will be used at the school and district level due to small sample size.

Co-developing a Curriculum Coherence Toolkit with Teachers (Collaborative Research: Olson)

This project will investigate the factors that influence curriculum coherence and how teachers in Grades 3-5 respond to these factors as they make decisions about their mathematics curriculum.

Lead Organization(s): 
Award Number: 
1907650
Funding Period: 
Mon, 07/01/2019 to Wed, 06/30/2021
Full Description: 

One important aspect of any mathematics curriculum is its coherence, or the mathematical connections across lessons. This coherence links lessons and activities so that mathematical ideas, representations, practices, skills, and ways of thinking build upon each other to help students construct mathematical meaning and enhance their learning. When teachers relied predominantly on published curriculum materials, curricular coherence was largely provided by the curriculum authors. However, many of today's teachers are no longer given a foundational textbook or single set of resources. Further, teachers have unprecedented access via the internet and social media to lessons and activities produced by many different curriculum developers (including other teachers). As a result, the important task of building curricular coherence becomes the responsibility of the classroom teacher. And yet, very little is known about how teachers think about curricular coherence or how their decisions about lessons and activities reflect the coherent mathematical story they hope to students will learn in their classrooms. This project will investigate the factors that influence curriculum coherence and how teachers in Grades 3-5 respond to these factors as they make decisions about their mathematics curriculum. A national survey of 300 Grades 3-5 teachers will be conducted in in the first phase of the project and the work will continue with small groups of four case study teachers in each of four different districts across four states. Case study participants will work with project researchers to co-develop a set of tools for supporting curriculum coherence. The structure of the project and the selection of case study participants will facilitate the collaborative co-development of tools across institutions and across geographic and curricular contexts, supporting the use of the tools across a wide range of contexts. The outcomes of this study will contribute to broader impacts by developing understandings of curriculum coherence that are robust across a range of curricular, policy, and district/school contexts, with implications that support the participation of students in diverse mathematics classrooms. The survey findings and the coherence toolkit co-developed with teachers will be disseminated widely through conference presentations, including teacher-oriented conferences, through journal publications, and through making survey data available to other researchers.

The research objectives of this study are to explore 1) patterns of Grade 3-5 teacher curricular resource use across a range of curriculum contexts, 2) teacher decisions about curriculum coherence, and 3) how curriculum toolkits co-developed with teachers might support teachers in making decisions related to curriculum coherence. Given the potential variation among and within states and districts in terms of contextual factors impacting curriculum use, teachers will be surveyed about their contexts, available resources, and curricular decision-making. Survey data will be analyzed using primarily descriptive analyses. Following the survey, in-depth case studies of teacher curricular resource use in contexts that vary along two dimensions (autonomy to select curricular resources and the complexity of curricular influences, including the number of resources available) will be developed. Case study data, including interviews, video-recorded co-design groups, and curriculum use artifacts, will be analyzed using methods of discourse analysis, thematic analysis, and document analysis and synthesized within and across cases. By selecting cases along these dimensions, a set of tools will be co-developed to support teachers as they navigate diverse curricular contexts to enact a coherent curriculum for students.

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.

CAREER: Bridging the Digital Accessibility Gap in STEM Using Multisensory Haptic Platforms

This project investigates how to use new touch technologies, like touchscreens, to create graphics and simulations that can be felt, heard, and seen. Using readily available, low-cost systems, the principal investigator will investigate how to map visual information to touch and sound for students with visual impairments.

Lead Organization(s): 
Award Number: 
1845490
Funding Period: 
Thu, 08/01/2019 to Wed, 07/31/2024
Full Description: 

Consider learning visual subjects such as math, engineering, or science without being able to see. Suddenly, the graphs, charts, and diagrams that provide a quick way to gather information are no longer effective. This is a challenge that students with visual impairments face in classrooms today as educational materials are most often presented electronically. The current way that individuals with visual impairments "read" graphics is through touch, feeling raised dots and patterns on paper that represent images. Creating these touch-based graphics requires extensive time and resources, and the output provides a static, hard-copy image. Lack of access to graphics in STEM subjects is one of the most pressing challenges currently facing individuals with visual impairments. This is a concern given the low representation of students with these disabilities in STEM fields and professions.

This project investigates how to use new touch technologies, like touchscreens, to create graphics and simulations that can be felt, heard, and seen. Using readily available, low-cost systems, the principal investigator will investigate how to map visual information to touch and sound. This research builds on prior research focused on representing the building blocks of graphics (points, lines, and shapes) nonvisually. In this project, the investigator will determine how to represent more challenging graphics such as charts, plots, and diagrams, nonvisually. The project will then explore the role of touch feedback in interactive simulations, which have moving elements that change with user input, making nonvisual access challenging. Finally, the projects extends the research to students with other disabilities, toward understanding the benefits and changes necessary for touch technologies to have broad impact. The project involves group and single-subject designs with approximately 65 students with visual impairments and focuses on the following outcomes of interest: students' graph literacy, percent correct on task assessments, time of exploration, response time, number of revisits to particular areas of the graphic, and number of switches between layers. Working closely with individuals with disabilities and their teachers, this work seeks to bridge the current graphical accessibility gap in STEM and raise awareness of universal design in technology use and development.

CAREER: Cultivating Teachers' Epistemic Empathy to Promote Responsive Teaching

This CAREER award aims to study the construct of "epistemic empathy" and examine how it can be cultivated in science and mathematics teacher education, how it functions to promote responsive teaching, and how it shapes learners' engagement in the classroom. In the context of this project, epistemic empathy is defined as the act of understanding and appreciating another's cognitive and emotional experience within an epistemic activity aimed at the construction, communication, and critique of knowledge.

Lead Organization(s): 
Award Number: 
1844453
Funding Period: 
Mon, 07/01/2019 to Sun, 06/30/2024
Full Description: 

When students perceive that their sense-making resources, including their cultural, linguistic, and everyday experiences, are not relevant to their science and mathematics classrooms, they may view these fields as inaccessible to them. This in turn creates an obstacle to their engagement and active participation which becomes particularly consequential for students from traditionally underrepresented populations. This issue points at the pressing need to prepare science and mathematics teachers to open up their instruction to students’ diverse ideas and meaning-making repertoires. This CAREER award aims to address this need by studying the construct of teachers’ "epistemic empathy” which is defined as the act of understanding and appreciating another's cognitive and emotional experience within an epistemic activity—an activity aimed at the construction, communication, and critique of knowledge. Through epistemic empathy, teachers take learners' perspectives and identify with their sense-making experiences in service of fostering their inquiries. The project’s goals are to examine how epistemic empathy can be cultivated in science and mathematics teacher education, how it functions to promote responsive teaching, and how it shapes learners' engagement in the classroom.

The five research questions will be: (1) Do the ways in which pre-service teachers display epistemic empathy change throughout a course aimed at promoting attention to and knowledge about learners’ varied ways of knowing in science and mathematics?; (2) How do the teaching domain and teaching context influence how teachers express epistemic empathy, and the concerns and tensions they report around empathizing with learners’ thinking and emotions?; (3) How does epistemic empathy shape the ways in which teachers understand and reflect on their roles, goals, and priorities as science or mathematics teachers?; (4) How does epistemic empathy shape teachers’ responsiveness to student thinking and emotions during instruction?; and (5) How does teachers’ epistemic empathy influence how students orient and respond to each other’s thinking in science and mathematics classrooms?

To address these questions, the project will conduct a series of design-based research studies working with science and mathematics pre-service and in-service K-12 teachers (n=140) to design, implement, and analyze ways to elicit and cultivate their epistemic empathy. Further, the project will explore how epistemic empathy shapes teachers’ views of their roles, goals, and priorities as science or mathematics teachers and how it influences their enactment of responsive teaching practices. The project will also examine the influence of teachers’ epistemic empathy on student engagement, in particular in the ways students attend and respond to each other’s epistemic experiences in the classroom. Data collection will include video and audio recording of teacher education and professional development sessions; collection of teachers’ work within those sessions such as their responses to a pre- and post- video assessment task and their written analyses of different videos of student inquiry; interviews with the teachers; and videos from the teachers’ own instruction as well as teachers’ reflections on these videos in stimulated recall interviews. These data will be analyzed using both qualitative methods (i.e., discourse analysis, interaction analysis) and quantitative methods (i.e., blind coding, descriptive statistics). The project’s outcomes will be: (1) an instructional model that targets epistemic empathy as a pedagogical resource for teachers, with exemplars of activities and tasks aimed at developing teachers' attunement to and ways of leveraging learners' meaning-making repertoires (2) local theory of teachers' learning to epistemically empathize with learners in science and mathematics; and (3) empirical descriptions of how epistemic empathy functions to guide and shape teachers' responsiveness and students' engagement. An advisory board will provide feedback on the project’s progress, as well as formative and summative evaluation.

Algebraic Learning and Cognition in Learning Disabled Students

The project is a longitudinal assessment of the prerequisite (e.g. fractions), cognitive (e.g. working memory), and non-cognitive (e.g. math anxiety) factors that dynamically influence 7-9th grade students' algebraic learning and cognition, with a focus on students with learning disabilities in mathematics.

Lead Organization(s): 
Award Number: 
1659133
Funding Period: 
Tue, 08/15/2017 to Sat, 07/31/2021
Full Description: 

High school algebra is the gateway to a career in science, technology, engineering, and mathematics (STEM), and can influence employability and wages in many non-STEM occupations. Students who struggle with or fail high school algebra have compromised occupational prospects, and nations that do not produce mathematically competent citizens may compromise their economic growth. Much is known about the factors that contribute to students' difficulties with arithmetic learning and interventions are being developed to address these difficulties. Little is known, however, about why some students struggle with algebra. Accordingly, the project will follow at risk students (including for example, those with dyslexia) from 7th grade through high school algebra and assess their prerequisite knowledge (e.g. fractions skills), cognitive systems (e.g., memory), attitudes and reactions to mathematics (e.g. math anxiety) and their attentiveness in math classrooms. The comprehensive evaluation of these students will allow us to identify the factors that influence difficulties in learning different aspects of algebra and risk of failing algebra more generally. The results will provide unique scientific insights into the cognitive and motivational influences on students' understanding and learning of algebra and identify areas for intervention with at-risk students. The results will also be used to develop a screening measure for the early identification of at-risk students and to identify specific areas for targeted intervention. The measure will be made freely available to interested school districts throughout the United States.

The project is a 7th to 9th grade longitudinal assessment of the prerequisite (e.g. fractions), cognitive (e.g. working memory), and non-cognitive (e.g. math anxiety) factors that dynamically influence students' algebraic learning and cognition, with a focus on students with learning disabilities in mathematics. The study will provide the most comprehensive assessment of the development of algebra competence ever conducted and is organized by an integrative model of cognitive and non-cognitive influences on students' engagement in math classrooms and on the learning of procedural and spatial-related aspects of algebra. The focus on students at risk for failing high school algebra is informed by research on the number and arithmetic deficits of these students, providing continuity with previous work, and a strong a priori framework for assessing their most likely difficulties in learning algebra; specifically, we developed novel measures that assess different aspects of procedural algebra (e.g. memory for the structure of algebra equations) and spatial-related algebra (e.g. recognizing how common functions map to coordinate space) that will allow for the study of different types of learning deficits and a determination of how more basic cognitive abilities, such as visuospatial working memory, may underlie these deficits. Prior cognitive studies of at-risk students have largely ignored the contributions of non-cognitive factors, such as math anxiety, on their learning or how their learning difficulties change attitudes about and reactions to mathematics (e.g. increasing math anxiety). The proposed research will address this important oversight and integrate these non-cognitive factors with assessments of teacher-rated student engagement in pre-algebra and algebra classrooms (and language arts classrooms as a contrast) and how engagement in the classroom influences the learning of procedural and spatial-related algebra. The research will also provide a thorough analysis of cognitive and non-cognitive influences on algebraic learning and cognition more generally, and thus inform general educational practices. In all, the proposed research will provide a comprehensive model for the study algebraic learning and cognition generally, and will provide a comprehensive assessment of associated deficits of learning disabled students and students at risk for failing high school algebra. The research will also make available revised or newly developed cognitive measures of procedural and spatial-related algebra skills that should facilitate future cognitive science and educational studies of algebra learning.

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