Algebra

Perceptual and Implementation Strategies for Knowledge Acquisition of Digital Tactile Graphics for Blind and Visually Impaired Students (Collaborative Research: Gorlewicz)

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and blind and visually impaired students.

Project Email: 
Lead Organization(s): 
Award Number: 
1644538
Funding Period: 
Sun, 01/15/2017 to Tue, 12/31/2019
Project Evaluator: 
Full Description: 

Students with disabilities often have fewer opportunities for experiential learning, an important component of quality STEM education. With continued shifts toward the use of digital media to supplement instruction in STEM classrooms, much of the content remains inaccessible, particular for students with visual impairments. The promise of technology and use of tactile graphics is an effective, emerging innovation for providing more complete access to important information and materials. Tactile graphics are images that use raised surfaces to convey non-textual information such as maps, paintings, graphs and diagrams. Touchscreen-based smart devices allow visual information to be digitally and dynamically represented via tactile, auditory, visual, and kinesthetic feedback. Tactile graphic technology embedded in touchscreen devices can be leveraged to make STEM content more accessible to blind and visually impaired students.

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and BVI students. The investigators will work with approximately 150 students with visual impairments to understand the kind of feedback that is most appropriate for specific content in algebra (coordinate plane), cell biology, and geography. Qualitative research methods will be used to analyze the video-based data set.

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Perceptual and Implementation Strategies for Knowledge Acquisition of Digital Tactile Graphics for Blind and Visually Impaired Students (Collaborative Research: Stefik)

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and blind and visually impaired students.

Project Email: 
Award Number: 
1644491
Funding Period: 
Sun, 01/15/2017 to Tue, 12/31/2019
Project Evaluator: 
Full Description: 

Students with disabilities often have fewer opportunities for experiential learning, an important component of quality STEM education. With continued shifts toward the use of digital media to supplement instruction in STEM classrooms, much of the content remains inaccessible, particular for students with visual impairments. The promise of technology and use of tactile graphics is an effective, emerging innovation for providing more complete access to important information and materials. Tactile graphics are images that use raised surfaces to convey non-textual information such as maps, paintings, graphs and diagrams. Touchscreen-based smart devices allow visual information to be digitally and dynamically represented via tactile, auditory, visual, and kinesthetic feedback. Tactile graphic technology embedded in touchscreen devices can be leveraged to make STEM content more accessible to blind and visually impaired students.

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and BVI students. The investigators will work with approximately 150 students with visual impairments to understand the kind of feedback that is most appropriate for specific content in algebra (coordinate plane), cell biology, and geography. Qualitative research methods will be used to analyze the video-based data set.

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Perceptual and Implementation Strategies for Knowledge Acquisition of Digital Tactile Graphics for Blind and Visually Impaired Students (Collaborative Research: Smith)

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and blind and visually impaired students.

Project Email: 
Award Number: 
1644476
Funding Period: 
Sun, 01/15/2017 to Tue, 12/31/2019
Project Evaluator: 
Full Description: 

Students with disabilities often have fewer opportunities for experiential learning, an important component of quality STEM education. With continued shifts toward the use of digital media to supplement instruction in STEM classrooms, much of the content remains inaccessible, particular for students with visual impairments. The promise of technology and use of tactile graphics is an effective, emerging innovation for providing more complete access to important information and materials. Tactile graphics are images that use raised surfaces to convey non-textual information such as maps, paintings, graphs and diagrams. Touchscreen-based smart devices allow visual information to be digitally and dynamically represented via tactile, auditory, visual, and kinesthetic feedback. Tactile graphic technology embedded in touchscreen devices can be leveraged to make STEM content more accessible to blind and visually impaired students.

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and BVI students. The investigators will work with approximately 150 students with visual impairments to understand the kind of feedback that is most appropriate for specific content in algebra (coordinate plane), cell biology, and geography. Qualitative research methods will be used to analyze the video-based data set.

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Perceptual and Implementation Strategies for Knowledge Acquisition of Digital Tactile Graphics for Blind and Visually Impaired Students (Collaborative Research: Giudice)

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and blind and visually impaired students.

Project Email: 
Lead Organization(s): 
Award Number: 
1644471
Funding Period: 
Sun, 01/15/2017 to Tue, 12/31/2019
Project Evaluator: 
Full Description: 

Students with disabilities often have fewer opportunities for experiential learning, an important component of quality STEM education. With continued shifts toward the use of digital media to supplement instruction in STEM classrooms, much of the content remains inaccessible, particular for students with visual impairments. The promise of technology and use of tactile graphics is an effective, emerging innovation for providing more complete access to important information and materials. Tactile graphics are images that use raised surfaces to convey non-textual information such as maps, paintings, graphs and diagrams. Touchscreen-based smart devices allow visual information to be digitally and dynamically represented via tactile, auditory, visual, and kinesthetic feedback. Tactile graphic technology embedded in touchscreen devices can be leveraged to make STEM content more accessible to blind and visually impaired students.

This project will develop a learner-centered, perceptually-motivated framework addressing the requirements for students with blindness and visual impairments to access graphical content in STEM. Using TouchSense technology, the investigators will create instructional materials using tactile graphics and test them in a pilot classroom of both sighted and BVI students. The investigators will work with approximately 150 students with visual impairments to understand the kind of feedback that is most appropriate for specific content in algebra (coordinate plane), cell biology, and geography. Qualitative research methods will be used to analyze the video-based data set.

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CAREER: Investigating Changes in Students' Prior Mathematical Reasoning: An Exploration of Backward Transfer Effects in School Algebra

This project explores "backward transfer", or the ways in which new learning impacts previously-established ways of reasoning. The PI will observe and evaluate algebra I students as they learn quadratic functions and examine how different kinds of instruction about the new concept of quadratic functions helps or hinders students' prior mathematical knowledge of the previous concept of linear functions.

Project Email: 
Lead Organization(s): 
Award Number: 
1651571
Funding Period: 
Sat, 07/01/2017 to Thu, 06/30/2022
Project Evaluator: 
Full Description: 

As students learn new mathematical concepts, teachers need to ensure that prior knowledge and prior ways understanding are not negatively affected. This award explores "backward transfer", or the ways in which new learning impacts previously-established ways of reasoning. The PI will observe and evaluate students in four Algebra I classrooms as they learn quadratic functions. The PI will examine how different kinds of instruction about the new concept of quadratic functions helps or hinders students' prior mathematical knowledge of the previous concept of linear functions. More generally, this award will contribute to the field of mathematics education by expanding the application of knowledge transfer, moving it from only a forward focused direction to include, also, a backward focused direction. An advisory board of scholars with expertise in mathematics education, assessment, social interactions, quantitative reasoning and measurement will support the project. The research will occur in diverse classrooms and result in presentations at the annual conferences of national organizations, peer-reviewed publications, as well as a website for teachers which will explain both the theoretical model and the findings from the project. An undergraduate university course and professional development workshops using video data from the project are also being developed for pre-service and in-service teachers. Ultimately, the research findings will generate new knowledge and offer guidance to elementary school teachers as they prepare their students for algebra.

The research involves three phases. The first phase includes observations and recordings of four Algebra I classrooms and will test students' understanding of linear functions before and after the lessons on quadratic functions. This phase will also include interviews with students to better understand their reasoning about linear function problems. The class sessions will be coded for the kind of reasoning that they promote. The second phase of the project will involve four cycles of design research to create quadratic and linear function activities that can be used as instructional interventions. In conjunction with this phase, pre-service teachers will observe teaching sessions through a course that will be offered concurrently with the design research. The final phase of the project will involve pilot-applied research which will test the effects of the instructional activities on students' linear function reasoning in classroom settings. This phase will include treatment and control groups and further test the hypotheses and instructional products developed in the first two phases.

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

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

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

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

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

Development and Empirical Recovery for a Learning Progression-Based Assessment of the Function Concept

The project will design an assessment based on learning progressions for the concept of function - a critical concept for algebra learning and understanding. The goal of the assessment and learning progression design is to specifically incorporate findings about the learning of students traditionally under-served and under-performing in algebra courses.

Lead Organization(s): 
Award Number: 
1621117
Funding Period: 
Thu, 09/15/2016 to Mon, 08/31/2020
Full Description: 

The project will design an assessment based on learning progressions for the concept of function. A learning progression describes how students develop understanding of a topic over time. Function is a critical concept for algebra learning and understanding. The goal of the assessment and learning progression design in this project is to specifically incorporate findings about the learning of students traditionally under-served and under-performing in algebra courses. The project will include accounting for the social and cultural experiences of the middle and high school students when creating assessment tasks. The resources developed should impact mathematics instruction (especially for algebra courses) by creating a learning progression which captures the range of student performance and appropriately places them at distinct levels of performance. The important contribution of the work is the development of a learning progression and related assessment tasks that account for the experiences of students often under-served in mathematics. 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 learning progression development will begin by comparing and integrating existing learning progressions and current research on function learning. This project will develop an assessment of student knowledge of function based on learning progressions via empirical recovery (looking for the reconstruction of theoretical levels of the learning theory). Empirical recovery is the process through which data will be collected that reconstruct the various levels, stages, or sequences of said learning progression. The development of tasks and task models will include testing computer-delivered, interactive tasks and rubrics that can be used for human and automated scoring (depending on the task). Item response theory methods will be used to evaluate the assessment tasks' incorporation of the learning progression.

Supporting Success in Algebra: A Study of the Implementation of Transition to Algebra

The project will research the implementation of Transition to Algebra, a year-long mathematics course for underprepared ninth grade students taken concurrently with Algebra 1 to provide additional support, and its impact on students' attitudes and achievement in mathematics in combination with teachers' instruction and the types of supports teachers need to successfully implement the intervention.

Partner Organization(s): 
Award Number: 
1621011
Funding Period: 
Sat, 10/01/2016 to Wed, 09/30/2020
Full Description: 

The project will research the impact and implementation of Transition to Algebra, a year-long mathematics course for underprepared ninth grade students taken concurrently with Algebra 1 to provide additional support. Nationally, there is a need for programs that support students' learning of algebra and that provide research-based resources and models particularly for students in need of additional support. The design of the Transition to Algebra curriculum reflects the idea that students underprepared for Algebra 1 can benefit from very specific help in building the logic of algebra by connecting arithmetic pattern and algebraic structure. The materials feature the use of mental mathematics, puzzles, explorations, and student dialogues to connect arithmetic pattern to algebraic structure. These features should encourage students to expect mathematics ideas to make sense, and to build algebraic habits of mind and problem solving stamina. The research will investigate the effects of the curriculum on students' algebra achievement and their attitudes towards mathematics. The Discovery Research PreK-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. 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 research questions examine the impact of the Transition to Algebra course on students' attitudes and achievement in mathematics in combination with teachers' instruction and the types of supports teachers need to successfully implement the intervention. The project will use a pre-post quasi-experimental design, along with propensity score methods to reduce selection bias threats, to examine the implementation in approximately 35 treatment schools and 35 comparison schools. Qualitative and quantitative data will be collected and analyzed to address research questions. The study will also investigate how teachers use and adapt Transition to Algebra materials, and the supports critical to successful implementation. For example, the study will examine whether and how school and district activities such as common planning time, coaching, and other professional development experiences influence the implementation fidelity of the curriculum. Qualitative data will be collected through interviews and classroom observations. Quantitative data will be collected using student and teacher surveys, an algebra readiness assessment, a standardized end-of-course assessment, and students' scores on state tests.

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

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

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

The primary goal of this project is to help middle school students deepen and communicate their understanding of mathematics. The project will develop and test a digital platform for middle school mathematics classrooms. The digital platform will allow students to collaboratively create representations of their mathematics thinking, incorporate ideas from other students, and share their work with the class. The digital learning environment makes use of a problem-centered mathematics curriculum that evolved from extensive development, field-testing and evaluation, and is widely used in middle schools. The research will also contribute to understanding about the design and innovative use of digital resources and collaboration in classrooms as an increasing number of schools are drawing on these kinds of tools. Projects in the DRK-12 program build on fundamental research in STEM education and prior research and development efforts that provide theoretical and empirical justification for proposed projects.

The project will support students to collaboratively construct, manipulate, and interpret shared representations of mathematics using digital inscriptional resources. The research activities will significantly enhance our understanding of student learning in mathematics in three important ways. The project will report on how (1) evidence of student thinking is made visible through the use of digital inscriptional resources, (2) student inscriptions are documented, discussed, and manipulated in collaborative settings, and (3) students' conceptual growth of big mathematical ideas grows over time. An iterative design research process will incorporate four phases of development, testing and revision, and will be conducted to study student use of the digital learning space and related inscriptional resources. Data sources will include: classroom observations and artifacts, student and teacher interviews and surveys, student assessment data, and analytics from the digital platform. The process will include close collaboration with teachers to understand the implementation and create revisions to the resources.

CAREER: Designing Learning Environments to Foster Productive and Powerful Discussions Among Linguistically Diverse Students in Secondary Mathematics

Award Number: 
1553708
Funding Period: 
Mon, 02/01/2016 to Sun, 01/31/2021
Full Description: 

The project will design and investigate learning environments in secondary mathematics classrooms focused on meeting the needs of English language learners. An ongoing challenge for mathematics teachers is promoting deep mathematics learning among linguistically diverse groups of students while taking into consideration how students' language background influences their classroom experiences and the mathematical understandings they develop. In response to this challenge, this project will design and develop specialized instructional materials and guidelines for teaching fundamental topics in secondary algebra in linguistically diverse classrooms. The materials will incorporate insights from current research on student learning in mathematics as well as insights from research on the role of language in students' mathematical thinking and learning. A significant contribution of the work will be connecting research on mathematics learning generally with research on the mathematics learning of English language learners. In addition to advancing theoretical understandings, the research will also contribute practical resources and guidance for mathematics teachers who teach English language learners. The Faculty Early Career Development (CAREER) program is a National Science Foundation (NSF)-wide activity that offers awards in support of junior faculty who exemplify the role of teacher-scholars through outstanding research, excellent education, and the integration of education and research within the context of the mission of their organizations.

The project is focused on the design of specialized hypothetical learning trajectories that incorporate considerations for linguistically diverse students. One goal for the specialized trajectories is to foster productive and powerful mathematics discussions about linear and exponential rates in linguistically diverse classrooms. The specialized learning trajectories will include both mathematical and language development learning goals. While this project focuses on concepts related to reasoning with linear and exponential functions, the resulting framework should inform the design of specialized hypothetical learning trajectories in other topic areas. Additionally, the project will add to the field's understanding of how linguistically diverse students develop mathematical understandings of a key conceptual domain. The project uses a design-based research framework gathering classroom-based data, assessment data, and interviews with teachers and students to design and refine the learning trajectories. Consistent with a design-based approach, the project results will include development of theory about linguistically diverse students' mathematics learning and development of guidance and resources for secondary mathematics teachers. This research involves sustained collaboration with secondary mathematics teachers and the impacts will include developing capacity of teachers locally, and propagating the results of this work in professional development activities.

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