Algebra

Pandemic Learning Loss in U.S. High Schools: A National Examination of Student Experiences

As a result of the COVID-19 pandemic, schools across much of the U.S. have been closed since mid-March of 2020 and many students have been attempting to continue their education away from schools. Student experiences across the country are likely to be highly variable depending on a variety of factors at the individual, home, school, district, and state levels. This project will use two, nationally representative, existing databases of high school students to study their experiences in STEM education during the COVID-19 pandemic.

Lead Organization(s): 
Award Number: 
2030436
Funding Period: 
Fri, 05/15/2020 to Fri, 04/30/2021
Full Description: 

As a result of the COVID-19 pandemic, schools across much of the U.S. have been closed since mid-March of 2020 and many students have been attempting to continue their education away from schools. Student experiences across the country are likely to be highly variable depending on a variety of factors at the individual, home, school, district, and state levels. This project will use two, nationally representative, existing databases of high school students to study their experiences in STEM education during the COVID-19 pandemic. The study intends to ascertain whether students are taking STEM courses in high school, the nature of the changes made to the courses, and their plans for the fall. The researchers will identify the electronic learning platforms in use, and other modifications made to STEM experiences in formal and informal settings. The study is particularly interested in finding patterns of inequities for students in various demographic groups underserved in STEM and who may be most likely to be affected by a hiatus in formal education.

This study will collect data using the AmeriSpeak Teen Panel of approximately 2,000 students aged 13 to 17 and the Infinite Campus Student Information System with a sample of approximately 2.5 million high school students. The data sets allow for relevant comparisons of student experiences prior to and during the COVID-19 pandemic and offer unique perspectives with nationally representative samples of U.S. high school students. New data collection will focus on formal and informal STEM learning opportunities, engagement, STEM course taking, the nature and frequency of instruction, interactions with teachers, interest in STEM, and career aspirations. Weighted data will be analyzed using descriptive statistics and within and between district analysis will be conducted to assess group differences. Estimates of between group pandemic learning loss will be provided with attention to demographic factors.

This RAPID award is made by the DRK-12 program in the Division of Research on Learning. The Discovery Research PreK-12 program (DRK-12) seeks to significantly enhance the learning and teaching of science, technology, engineering and mathematics by preK-12 students and teachers, through the research and development of new innovations and approaches. 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 the projects.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

 

 

 

 

CAREER: Implementing Mathematical Modeling for Emergent Bilinguals

This project will support teacher capacity for implementing mathematical modeling lessons by engaging teachers in co-planning and co-teaching with researchers skilled in Emergent Bilingual (EB) mathematics instruction. The outcomes of this project will be a framework for teaching mathematical modeling to EB students, teacher professional development materials that can be used widely to support EB mathematics teachers, and a massive open online course (MOOC) for teachers to support their continued learning about teaching mathematics modeling to EB students.

Lead Organization(s): 
Award Number: 
1941668
Funding Period: 
Tue, 09/01/2020 to Sun, 08/31/2025
Full Description: 

This project supports secondary mathematics teachers in teaching mathematical modeling practices to an Emergent Bilingual (EB) population. EB students in linguistically diverse mathematics classrooms are frequently limited to procedural, rote instruction, despite research-based recommendations that suggest that EBs' mathematical and linguistic proficiency can benefit from engaging in complex mathematical tasks based on real-life situations. The project will support teacher capacity for implementing mathematical modeling lessons by engaging teachers in co-planning and co-teaching with researchers skilled in EB mathematics instruction. The project will collect information about the quality of mathematics instruction in modeling lessons, what students learn, and how teachers changed in how they position EB students as knowers and doers of mathematics. The outcomes of this project will be a framework for teaching mathematical modeling to EB students, teacher professional development materials that can be used widely to support EB mathematics teachers, and a massive open online course (MOOC) for teachers to support their continued learning about teaching mathematics modeling to EB students.

The project draws on three important constructs related to teaching mathematics to emergent bilingual (EB) students: research on the mathematics education of EB students; research on mathematical modeling; and positioning theory. Related to mathematics education of EB students, the project supports teachers in enacting high-quality instruction that incldues high cognitive demand tasks, encourages EBs to engage in and explain their problem solving process, and complements that work with linguistic and contextual supports that support EB students' entry into the tasks. Related to mathematical modeling, the project makes use of the conceptualization of modeling as a vehicle for content (as compared to mathematics content of its own), and envisions the use of modeling practices as particularly supportive of EB students' learning of algebra. In particular, the modeling-as-a-vehicle stance invites teachers to engage students in tasks that contain multiple mathematical representations, which has the potential to both build students' conceptual understandings of algebra and to strengthen EBs' language and communication skills in the context of mathematics. With respect to positioning theory, the project seeks to disrupt the finding that secondary mathematics teachers tend underestimate EB students' mathematical abilities due to their English proficiency standards, causing them to choose lower cognitive demand tasks for these students against established research-based recommendations. The project team will engage EB algebra and pre-algebra teachers in Des Moines Public schools in co-planning and co-teaching lessons using mathematical modeling practice. This co-planning and co-teaching activity constitutes in-situ professional development for teachers. Co-planning sessions, co-taught lessons, and regular teacher interviews will be recorded and analyzed for quality of instruction and changes in teacher positioning of EB students. The research team and teachers will co-analyze student learning data from observations and district-administered standardized assessments to better understand the impact of the modeling lessons on students' algebra learning and achievement. Eight teachers will participate in the work over the life of the project, each supporting EB classes of approximately 20 students per teacher. The outcomes of these analyses will guide the development fo a mathematical modeling framework for teaching EBs, teacher professional development materials made available for similar work in other schools and districts, and a massive open online course designed for teachers to develop their skills for teaching secondary mathematics to EB students.

CAREER: Exploring Teacher Noticing of Students' Multimodal Algebraic Thinking

This project investigates and expands teachers' learning to notice in two important ways. First, the research expands beyond teachers' noticing of written and verbal thinking to attend to gesture and other aspects of embodied and multimodal thinking. Second, the project focuses on algebraic thinking and seeks specifically to understand how teacher noticing relates to the content of algebra. Bringing together multimodal thinking and the mathematical ideas in algebra has the potential to support teachers in providing broader access to algebraic thinking for more students.

Award Number: 
1942580
Funding Period: 
Mon, 06/01/2020 to Sat, 05/31/2025
Full Description: 

Effective teachers of mathematics attend to and respond to the substance of students' thinking in supporting classroom learning. Teacher professional development programs have supported teachers in learning to notice students' mathematical thinking and using that noticing to make instructional decisions in the classroom. This project investigates and expands teachers' learning to notice in two important ways. First, the research expands beyond teachers' noticing of written and verbal thinking to attend to gesture and other aspects of embodied and multimodal thinking. Second, the project focuses on algebraic thinking and seeks specifically to understand how teacher noticing relates to the content of algebra. Bringing together multimodal thinking and the mathematical ideas in algebra has the potential to support teachers in providing broader access to algebraic thinking for more students.

To study teacher noticing of multimodal algebraic thinking, this project will facilitate video club sessions in which teachers examine and annotate classroom video. The video will allow text-based and visual annotation of the videos to obtain rich portraits of the thinking that teachers notice as they examine algebra-related middle school practice. The research team will create a video library focused on three main algebraic thinking areas: equality, functional thinking, and proportional reasoning. Clips will be chosen that feature multimodal student thinking about these content areas, and provide moments that would be fruitful for advancing student thinking. Two cohorts of preservice teachers will engage in year-long video clubs using this video library, annotate videos using an advanced technological tool, and engage in reflective interviews about their noticing practices. Follow-up classroom observations will be conducted to see how teachers then notice multimodal algebraic thinking in their classrooms. Materials to conduct the video clubs in other contexts and the curated video library will be made available, along with analyses of the teacher learning that resulted from their implementation.

CAREER: Promoting Equitable and Inclusive STEM Contexts in High School

This project focuses on fostering equitable and inclusive STEM contexts with attention to documenting and reducing adolescents' experiences of harassment, bias, prejudice and stereotyping. This research will contribute to understanding of the current STEM educational climates in high schools and will help to identify factors that promote resilience in the STEM contexts, documenting how K-12 educators can structure their classrooms and schools to foster success of all students in STEM classes.

Award Number: 
1941992
Funding Period: 
Sat, 02/01/2020 to Fri, 01/31/2025
Full Description: 

This project focuses on fostering equitable and inclusive STEM contexts with attention to documenting and reducing adolescents' experiences of harassment, bias, prejudice and stereotyping. An important barrier to persistence in STEM fields for marginalized groups, including women and ethnic minorities, relates to a culture in many STEM organizations, such as academic institutions, that fosters discrimination, harassment and prejudicial treatment of those from underrepresented groups. This research will contribute to understanding of the current STEM educational climates in high schools and will help to identify factors that promote resilience in the STEM contexts, documenting how K-12 educators can structure their classrooms and schools to foster success of all students in STEM classes. Further, this work will explore how to create schools where students stand-up for each other and support each other so that any student who is interested will feel welcome in STEM classes and programs.

This research aims to examine cultures of discrimination and harassment in STEM contexts with attention to: 1) assessing STEM climates in high schools in order to identify the character of discrimination and harassment, 2) understanding how youth think about these instances of bias and discrimination; 3) identifying pathways to resilience for underrepresented youth pursuing STEM interests, and 4) testing an intervention to promote bystander intervention from those who witness discrimination and harassment in STEM contexts. This research will take an intersectional approach recognizing that those who are marginalized by multiple dimensions of their identity may experience STEM contexts differently than those who are marginalized by one dimension of their identity. Because adolescence is a critical developmental period during which youth are forming their attitudes, orientations and lifelong behaviors, this research will attend to issues of bias and discrimination well before individuals enter college STEM classrooms or the STEM workforce: namely, during high school. Further, this work will examine the creation of equitable STEM climates in both college-preparation classes as well as workforce development STEM programs offered though or in partnership with high schools. This research will provide clear evidence to document the current culture of STEM contexts in high schools, using mixed methods, including surveys, qualitative interviews and longitudinal measurement. Further, the project will involve development and implementation of an intervention, which will provide the first test of whether bystander intervention can be fostered in STEM students and will involve training STEM students in key 21st century skills, such as social-cognitive capacities and interpersonal skills, enabling them to speak up and support peers from marginalized backgrounds when they observe discrimination and harassment.

CAREER: Understanding Latinx Students' Stories of Doing and Learning Mathematics

This project characterizes and analyses the developing mathematical identities of Latinx students transitioning from elementary to middle grades mathematics. The central hypothesis of this project is that elementary Latino students' stories can identify how race and language are influential to their mathematical identities and how school and classroom practices may perpetuate inequities.

Lead Organization(s): 
Award Number: 
1941952
Funding Period: 
Mon, 06/01/2020 to Sat, 05/31/2025
Full Description: 

Although the Latino population throughout the United States continues to increase, various researchers have shown that Latino students are often not afforded high quality learning experiences in their mathematics classrooms. As a result, Latino students are underrepresented in higher level mathematics courses and careers involving mathematics. Having a better understanding of Latino students' perspectives and experiences is imperative to improving their opportunities to learn mathematics. Yet, little research has made central Latinos students' perspectives of learning and doing mathematics, especially over a critical period of time like the transition from elementary to middle school. The goal of this study will be to improve mathematics teaching and learning for Latino youth as they move from upper elementary to early middle school mathematics classrooms. The project involves three major parts: investigating the policy, media, and oral histories of Latino families/communities to understand the context for participating Latino students' mathematics education; exploring Latino students' stories about their experiences learning and doing mathematics to understand these students' perspectives; and creating documentary video portraitures (or composite cases) of participants' stories about learning and doing mathematics that can be used in teacher preparation and professional development. Finally, the project will look across the experiences over the duration of the project to develop a framework that can be used to improve Latino students' mathematics education experiences. This project will provide a window into how Latino students may experience inequities and can broaden mathematics educators' views on opportunities to engage Latino students in rigorous mathematics. The project will also broaden the field's understanding of how Latino students racial/ethnic and linguistic identities influence their experiences learning mathematics. It will also identify key factors that impact Latino students' experiences in learning mathematics to pinpoint specific areas where interventions and programs need to be designed and implemented. An underlying assumption of the project is that carefully capturing and understanding Latino students' stories can illuminate the strengths and resilience these students bring to their learning and doing of mathematics.

This research project characterizes and analyses the developing mathematical identities of Latinx students transitioning from elementary to middle grades mathematics. The overarching research question for this study is: What are the developing stories of learning and doing mathematics of Latino students as they transition from elementary to middle school mathematics? To answer this question, this study is divided into three phases: 1) understanding and documenting the historical context by examining policy documents, local newspaper articles, and doing focus group interviews with community members; 2) using ethnographic methods over two years to explore students' stories of learning and doing mathematics and clinical interviews to understand how they think about and construct arguments about mathematics (i.e., measurement, division, and algebraic patterning); and 3) creating video-cases that can be used in teacher education. Traditional ways of teaching mathematics perpetuate images of who can and cannot do mathematics by not acknowledging contributions of other cultures to the mathematical sciences (Gutiérrez, 2017) and the way mathematics has become a gatekeeper for social mobility (Martin, Gholson, & Leonard, 2010; Stinson, 2004). Focusing on Latino students' stories can illuminate teachers' construction of equitable learning spaces and how they define success for their Latino students. The central hypothesis of this project is that elementary Latino students' stories can identify how race and language are influential to their mathematical identities and how school and classroom practices may perpetuate inequities. Finally, the data and video-cases will then be used to develop a conceptual framework for understanding the development of the participating students' developing mathematical identities. This framework will provide an in-depth understanding of the developing racial/ethnic, linguistic, and mathematical identities of the participating Latino students. The educational material developed (e.g. video documentaries, discussion material) from this project will be made available to all interested parties freely through the project website. The distribution of these materials, along with further understanding of Latino students' experiences learning mathematics, will help in developing programs and interventions at the elementary and middle grade level to increase the representation of Latino students in STEM careers. Additionally, identifying the key factors impacting Latino students' experiences in learning mathematics can pinpoint specific areas where interventions and programs still need to be designed and implemented. Future projects could include the assessment of these programs. This project will also inform the development of professional learning experiences for prospective and practicing teachers working with Latino or other marginalized students.

Validation of the Equity and Access Rubrics for Mathematics Instruction (VEAR-MI)

The main goal of this project is to validate a set of rubrics that attend to the existence and the quality of instructional practices that support equity and access in mathematics classes. The project team will clarify the relationships between the practices outlined in the rubrics and aspects of teachers' perspectives and knowledge as well as student learning outcomes.

Award Number: 
1908481
Funding Period: 
Mon, 07/15/2019 to Fri, 06/30/2023
Full Description: 

High-quality mathematics instruction remains uncommon and opportunities for students to develop the mathematical understanding are not distributed equally. This is particularly true for students of color and students for whom English is not their first language. While educational research has made progress in identifying practices that are considered high-quality, little attention has been given to specific instructional practices that support historically marginalized groups of students particularly as they participate in more rigorous mathematics. The main goal is to validate a set of rubrics that attend to the existence and the quality of instructional practices that support equity and access in mathematics classes. In addition, the project team will clarify the relationships between the practices outlined in the rubrics and aspects of teachers' perspectives and knowledge as well as student learning outcomes.

This project will make use of two existing large-scale datasets focusing on mathematics teachers to develop rubrics on mathematics instructional quality. The datasets include nearly 3,000 video-recorded mathematics lessons and student achievement records from students in Grades 3 through 8. The four phases of this research and development project include training material development, an observation and rubric generalizability study, a coder reliability study, and structural analysis. Data analysis plans involve case studies, exploratory and confirmatory factor analyses, and cognitive interviews. 

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.

Reasoning Language for Teaching Secondary Algebra

This project proposes to study the teaching and learning of algebra in grades 7-9, with a specific focus on the ways in which classroom language explicitly describes properties of and relationships among algebraic objects. The project seeks to investigate the bi-directional relationship between reasoning-rich algebraic discourse and the mathematical meanings students hold for core algebraic concepts such as equations, the equation-solving process, and functions.

Lead Organization(s): 
Award Number: 
2001116
Funding Period: 
Sun, 09/01/2019 to Wed, 08/31/2022
Full Description: 

Decades of research have demonstrated that stronger mathematics classroom discourse, along with the use and connection of multiple mathematical representations, correlates positively with gains in student learning. This relationship is particularly salient in algebra, where diversifying the representations available to students can provide important supports for the development of conceptual understanding. The Reasoning Language for Teaching Secondary Algebra (ReLaTe-SA) project proposes to study the teaching and learning of algebra in grades 7-9, with a specific focus on the ways in which classroom language explicitly describes properties of and relationships among algebraic objects. The project seeks to investigate the bi-directional relationship between reasoning-rich algebraic discourse and the mathematical meanings students hold for core algebraic concepts such as equations, the equation-solving process, and functions. With a focus on the teacher, ReLaTe-SA will analyze classroom narratives about algebraic concepts and procedures and provide an 80-hour professional development program designed to support teachers in developing stronger explanations of algebraic objects, their properties, and their relationships.

The ReLaTe-SA project will investigate three aspects of teacher discourse practice related to algebra. First, the project will study the discourse and discourse routines that teachers use to explain algebraic objects, their properties, and their relationships. This will be accomplished through the development and deployment of an assessment called the Survey of Algebraic Language and Reasoning to identify teachers' discursive routines and narratives in the context of algebra. The instrument asks teachers to interpret student work and explanations by describing the student's mathematical reasoning and underlying mathematical understandings. Second, the project will support potential growth in teachers' algebraic discourse practices through an 80-hour professional development intervention focused on discourse in algebra. The impact of this intervention will be measured by changes to teachers' response patterns on the Survey of Algebraic Language and Reasoning, analyses of teachers' work within the professional development, and the analysis of classroom observations after the professional development has concluded. Third, the project will seek to understand the ways in which teachers develop lessons that explicitly focus on the development of students' algebraic reasoning and discourse. This goal will be realized through analyses of the tasks, plans, and implementations of mathematics lessons in participating teachers' classrooms. Three cohorts of 12 teachers each will be recruited for the project. Based on the results of this exploratory project, the team intends to follow up with a larger-scale study of the professional development and its impact on the teaching and learning of algebra.

This project was previously funded under award #1908825.

Improving Grades 6-8 Students' Mathematics Achievement in Modeling and Problem Solving through Effective Sequencing of Instructional Practices

This project will provide structured and meaningful scaffolds for teachers in examining two research-based teaching strategies hypothesized to positively impact mathematics achievement in the areas of mathematical modeling and problem solving. The project investigates whether the order in which teachers apply these practices within the teaching of mathematics content has an impact on student learning.

Project Email: 
Lead Organization(s): 
Award Number: 
1907840
Funding Period: 
Mon, 07/01/2019 to Fri, 06/30/2023
Project Evaluator: 
Kurt Steuck
Full Description: 

The Researching Order of Teaching project will provide structured and meaningful scaffolds for teachers in examining two research-based teaching strategies hypothesized to positively impact mathematics achievement in the areas of mathematical modeling and problem solving. The first strategy, Explicit Attention to Concepts (EAC), is a set of practices that draw students' attention specifically to mathematical concepts in ways that extend beyond memorization, procedures, or application of skills. This strategy may include teachers asking students to connect multiple mathematical representations, compare solution strategies, discuss mathematical reasoning underlying procedures, or to identify a main mathematical idea in a lesson and how it fits into the broader mathematical landscape. The second strategy, Student Opportunities to Struggle (SOS), entails providing students with time and space to make sense of graspable content, overcoming confusion points, stimulating personal sense-making, building perseverance, and promoting openness to challenge. This strategy may include teachers assigning problems with multiple solution strategies, asking students to look for patterns and make conjectures, encouraging and promoting discourse around confusing or challenging ideas, and asking students for extended mathematical responses. This project investigates whether the order in which teachers apply these practices within the teaching of mathematics content has an impact on student learning. This study builds on previous work that had identified an interaction between the EAC and SOS instructional strategies, and associated teacher reporting of stronger use of the practices with higher student mathematics achievement.

The project will have four key design features. First, the project will adopt and extend the research-based EAC/SOS conceptual framework, and explicitly responds to the call for further research on the interactions. Second, the project will focus on the mathematical areas of modeling and problem solving, two complex and critical competencies for all students in the middle grades. Third, the project will position teachers as collaborators in the research with needed expertise. Finally, the project will make use of research methods from crossover clinical trials to implementation in classrooms. The project aims to identify the affordances and constraints of the EAC/SOS framework in the design and development of instructional practices, to identify student- and teacher-level factors associated with changes in modeling and problem solving outcomes, to analyze teachers' implementations EAC and SOS in teaching modeling and problem solving and to associate those implementation factors with student achievement changes, and to determine whether the ordering of these two strategies correlates with differences in achievement. The project will collect classroom observation data and make use of existing tools to obtain reliable and valid ratings of the EAC and SOS strategies in action.The design of the study features a randomized 2 x 2 cluster crossover trial with a sample of teachers for 80% power. The project builds on existing state infrastructure and relationships with a wide array of school districts in the context of professional development, and aims to create a formal Teacher-Researcher Alliance for Investigating Learning as a part of the project work.

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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