Mathematics

Exploring the Potential of Tablets as Early Math Resources for Urban Kindergarteners in Schools and Homes

This project will examine the impact on mathematics learning of an initiative to provide kindergartners in an urban school district with personal tablet devices that include free, widely available digital mathematics resources. The research questions examine how teachers use table-based mathematics resources during instruction, how caregivers and children engage with table-based mathematics resources, and how the resources then relate to kindergartners mathematics learning.

Lead Organization(s): 
Award Number: 
1744202
Funding Period: 
Tue, 08/01/2017 to Tue, 07/31/2018
Full Description: 

This project will examine the impact on mathematics learning of an initiative to provide kindergartners in an urban school district with personal tablet devices that include free, widely available digital mathematics resources. An important question for schools as tablet devices become more accessible is how to effectively use them in primary grades, especially kindergarten. In addition, since the devices are portable, how children use the resources such as games for mathematics learning at home is also important to understand. This project is set in a high-needs school district with a large number of low-income children. The project provides an opportunity to learn about the potential role of tables and digital resources in early grades through the analysis of assessment data, user analytic data documenting how the resources were used, and survey data from teachers and families.

Most studies of digital learning resources have been small-scale or focused on engagement. This study offers the opportunity to investigate the relationship between the use of these resources and learning outcomes using a quasi-experimental design. The research questions examine how teachers use table-based mathematics resources during instruction, how caregivers and children engage with table-based mathematics resources and how the resources then relate to kindergartners mathematics learning. Assessments of students' learning will focus on number, geometry and measurement concepts. The learner analytic data from the tablets will document the use of the resources on the tablets. Surveys and demographic data will also be collected to document how the tablets were used. Results of the study should inform implementation of tablet use by schools with particular attention to how they are used across in-class and at-home settings.

The Mathematical Knowledge for Teaching Measures: Refreshing the Item Pool

This project proposes an assessment study that focuses on improving existing measures of teachers' Mathematical Knowledge for Teaching (MKT). The research team will update existing measures, adding new items and aligning the instrument to new standards in school mathematics.

Lead Organization(s): 
Award Number: 
1620914
Funding Period: 
Thu, 12/01/2016 to Sat, 11/30/2019
Full Description: 

This project proposes an assessment study that focuses on improving existing measures of teachers' Mathematical Knowledge for Teaching (MKT). The research team will update existing measures, adding new items and aligning the instrument to new standards in school mathematics. In addition, the team will update the delivery system for the assessment to Qualtrics, a more flexible online system.

The research team will build an updated measure of teachers' Mathematical Knowledge for Teaching (MKT). Project researchers will conduct item writing camps, develop new items, cognitively pilot and revise items, and factor analyze items. The researchers will also determine item constructs and calibrate items (and constructs) through an innovative application of Item Response Theory (IRT) employing a variant of the standard 2-parameter IRT model. Finally, the team will oversee the transition of the Teacher Knowledge Assessment System to the Qualtrics data collection environment to allow for more flexible item specification.

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

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

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

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

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

Examining Relationships Between Flipped Instruction and Students' Learning of Mathematics

This study can provide a basis for design research focused on developing effective materials and programs for flipped instruction in secondary mathematics, which is already occurring at an increasing rate, but it is not yet informed by empirical evidence. This project will result in a framework for flipped instruction robust enough to be useful at a variety of grade levels and contexts. The framework will provide a better understanding of the relationships among various implementations of flipped instruction and student learning.

Lead Organization(s): 
Award Number: 
1721025
Funding Period: 
Tue, 08/01/2017 to Fri, 07/31/2020
Full Description: 

Instead of presenting new material in class and then assigning problems to be completed outside of class, flipped instruction involves students watching videos or reading new material outside of class and then completing their "homework" in class. Teachers' implementation of flipped instruction has increased dramatically in recent years, with more than two-thirds of teachers now reporting flipping a lesson, if not an entire course. Although popular media and philanthropic organizations have given a great deal of attention and financial support to flipped instruction, little is known about how teachers implement it and what benefits and drawbacks flipped instruction has in contrast with non-flipped instruction. This study can provide a basis for design research focused on developing effective materials and programs for flipped instruction in secondary mathematics. This design and development is already occurring at an increasing rate, but it is not yet informed by empirical evidence. This project will result in a framework for flipped instruction robust enough to be useful at a variety of grade levels and contexts. The framework will provide a better understanding of the relationships among various implementations of flipped instruction and student learning. These findings can inform teacher educators in better aligning their instruction to instructional formats that correlate with increased student learning outcomes.

Using mixed-methods techniques, the study will look at the nature of the activities and interactions occurring in mathematics classrooms and assess their quality so that the researchers may distinguish high-quality from low-quality univocal discourse, high-quality from low-quality dialogic discourse, and high cognitive demand from low cognitive demand tasks. Working in 40 algebra classrooms -- 20 implementing some form of flipped instruction and 20 serving as a non-flipped basis for comparison -- the project will address the following research questions using a correlational design and multilevel modeling techniques: RQ1. What are salient factors entailed in flipped instruction in secondary algebra? RQ2. What associations, if any, exist among factors entailed in teachers' implementation of flipped algebra instruction and students' learning of algebra as measured on a state-mandated end-of-course assessment and on a concept-of-variable inventory?

Investigating Productive Use of High-Leverage Student Mathematical Thinking Collaborative Research: Stockero)

This project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. The study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks.

Lead Organization(s): 
Award Number: 
1720566
Funding Period: 
Thu, 06/01/2017 to Mon, 05/31/2021
Full Description: 

The project will examine how secondary mathematics teachers respond to and use students' thinking during whole class discussion. An ongoing challenge for teachers is making the best use of students' emerging mathematical ideas during whole class discussion. Teachers need to draw on the ideas students have developed in order to create opportunities for learning about significant mathematical concepts. This study will create tasks specifically designed to generate opportunities for teachers to build on students' thinking and then use classroom observation and analysis of classroom video to develop tools to support teachers in leading whole class discussion.

The project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. This study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks. The project engages teacher-researchers in exploring the building practice. The teacher-researchers will use the project-designed tasks in their classrooms and then engage in a cycle of analysis of their own teaching with the research team. Data collection and analysis will rely on video analysis of classrooms, teachers' reflections on task enactment, and data collected during research team meetings convened with teacher-researchers to analyze practice.

Investigating Productive Use of High-Leverage Student Mathematical Thinking (Collaborative Research: Peterson)

This project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. The study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks.

Lead Organization(s): 
Award Number: 
1720410
Funding Period: 
Sat, 07/01/2017 to Mon, 05/31/2021
Full Description: 

The project will examine how secondary mathematics teachers respond to and use students' thinking during whole class discussion. An ongoing challenge for teachers is making the best use of students' emerging mathematical ideas during whole class discussion. Teachers need to draw on the ideas students have developed in order to create opportunities for learning about significant mathematical concepts. This study will create tasks specifically designed to generate opportunities for teachers to build on students' thinking and then use classroom observation and analysis of classroom video to develop tools to support teachers in leading whole class discussion.

The project focuses on the teaching practice of building on student thinking, a practice in which teachers engage students in making sense of their peers' mathematical ideas in ways that help the whole class move forward in their mathematical understanding. This study examines how teachers incorporate this practice into mathematics discussions in secondary classrooms by designing tasks that generate opportunities for teachers to build on students' thinking and by studying teachers' orchestration of whole class discussions around student responses to these tasks. The project engages teacher-researchers in exploring the building practice. The teacher-researchers will use the project-designed tasks in their classrooms and then engage in a cycle of analysis of their own teaching with the research team. Data collection and analysis will rely on video analysis of classrooms, teachers' reflections on task enactment, and data collected during research team meetings convened with teacher-researchers to analyze practice.

Mathematics Immersion for Secondary Teachers at Scale (Collaborative Research: Cuoco)

The goal of this project will be to provide the field with a cost-effective model for intense content-based professional development in ways that have not been possible before, except through costly face-to-face models, by creating and testing design principles for blended online courses. Team members will design, implement, and research the effects of a professional development immersion experience in mathematics for practicing secondary teachers (grades 7-12).

Partner Organization(s): 
Award Number: 
1719555
Funding Period: 
Sat, 07/01/2017 to Thu, 12/31/2020
Full Description: 

Current reforms in mathematics place new demands on teachers, changing the focus of the mathematics they teach focusing on what it means to do mathematics, not just learn facts and methods that are the results of the work of others. Teachers need strong professional development to meet these new demands. The goal of this project will be to provide the field with a cost-effective model for intense content-based professional development in ways that have not been possible before, except through costly face-to-face models, by creating and testing design principles for blended online courses. Team members will design, implement, and research the effects of a professional development immersion experience in mathematics for practicing secondary teachers (grades 7-12). The project will provide mathematics immersion experience to over 300 teachers at 56 sites across the country. Over the course of two years, each of 14 instructors will work with four geographically separated groups of 4-7 teachers, engaging them in mathematics as learners and facilitating conversations that connect the experience to their teaching and professional work. The project will provide the field a concrete model for modern practice-based mathematics immersion, conducted at scale. The model has the potential to broaden participation in immersive professional development experiences, offering opportunities to greater numbers of teachers and expanding the diversity of school contexts affected. 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 research questions will investigate fidelity of course implementation and differences in enactment. RQ1. How well can instructors enact the blended course design with fidelity and create immersion experiences in mathematics for participating teachers? RQ2.What variations exist among instructors' enactment of the courses? What explains differences in enactment, and how do they relate to teachers' experiences in the courses? RQ3. What is the impact of the professional development on teachers' (a) mathematical habits of mind, (b) beliefs about the nature of mathematics and mathematics teaching, and (c) engagement in their professional mathematics community? RQ4. What is the impact of the professional development on teachers' instructional practices, particularly on the types of investigative mathematics learning experiences that teachers provide for students? The project will use established measures to research the effects of these experiences on teachers' content knowledge, mathematical habits of mind, beliefs about mathematics, involvement in a professional community, and teaching practices. The first two research questions will be answered through qualitative data analysis of session enactment logs, video-recorded course sessions, and interviews. The second two research questions will be addressed through repeated measures analysis, with all teachers assessed three times over the course of the project. For research question 3, the outcome measures will be total and scale scores of the measures of teachers' knowledge, preparedness to teach mathematics, and beliefs. Additionally, qualitative analysis of interview data will explore trends in the frequency and nature of teachers' engagement over time. For research question 4, the outcome measures will be teaching practices with qualitative analysis of observations and interviews.


Project Videos

2019 STEM for All Video Showcase

Title: Mathematics Immersion for Secondary Teachers (MIST)

Presenter(s): Matt McLeod, Miriam Gates, Daniel Heck, & Pippa Hoover

2018 STEM for All Video Showcase

Title: Building a Virtual Mathematics Immersion Experience

Presenter(s): Matt McLeod, Eden Badertscher, Al Cuoco, Miriam Gates, Daniel Heck, & Bowen Kerins


Mathematics Immersion for Secondary Teachers at Scale (Collaborative Research: Heck)

The goal of this project will be to provide the field with a cost-effective model for intense content-based professional development in ways that have not been possible before, except through costly face-to-face models, by creating and testing design principles for blended online courses. Team members will design, implement, and research the effects of a professional development immersion experience in mathematics for practicing secondary teachers (grades 7-12).

Lead Organization(s): 
Award Number: 
1719554
Funding Period: 
Sat, 07/01/2017 to Thu, 12/31/2020
Full Description: 

Current reforms in mathematics place new demands on teachers, changing the focus of the mathematics they teach focusing on what it means to do mathematics, not just learn facts and methods that are the results of the work of others. Teachers need strong professional development to meet these new demands. The goal of this project will be to provide the field with a cost-effective model for intense content-based professional development in ways that have not been possible before, except through costly face-to-face models, by creating and testing design principles for blended online courses. Team members will design, implement, and research the effects of a professional development immersion experience in mathematics for practicing secondary teachers (grades 7-12). The project will provide mathematics immersion experience to over 300 teachers at 56 sites across the country. Over the course of two years, each of 14 instructors will work with four geographically separated groups of 4-7 teachers, engaging them in mathematics as learners and facilitating conversations that connect the experience to their teaching and professional work. The project will provide the field a concrete model for modern practice-based mathematics immersion, conducted at scale. The model has the potential to broaden participation in immersive professional development experiences, offering opportunities to greater numbers of teachers and expanding the diversity of school contexts affected. 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 research questions will investigate fidelity of course implementation and differences in enactment. RQ1. How well can instructors enact the blended course design with fidelity and create immersion experiences in mathematics for participating teachers? RQ2.What variations exist among instructors' enactment of the courses? What explains differences in enactment, and how do they relate to teachers' experiences in the courses? RQ3. What is the impact of the professional development on teachers' (a) mathematical habits of mind, (b) beliefs about the nature of mathematics and mathematics teaching, and (c) engagement in their professional mathematics community? RQ4. What is the impact of the professional development on teachers' instructional practices, particularly on the types of investigative mathematics learning experiences that teachers provide for students? The project will use established measures to research the effects of these experiences on teachers' content knowledge, mathematical habits of mind, beliefs about mathematics, involvement in a professional community, and teaching practices. The first two research questions will be answered through qualitative data analysis of session enactment logs, video-recorded course sessions, and interviews. The second two research questions will be addressed through repeated measures analysis, with all teachers assessed three times over the course of the project. For research question 3, the outcome measures will be total and scale scores of the measures of teachers' knowledge, preparedness to teach mathematics, and beliefs. Additionally, qualitative analysis of interview data will explore trends in the frequency and nature of teachers' engagement over time. For research question 4, the outcome measures will be teaching practices with qualitative analysis of observations and interviews.


Project Videos

2019 STEM for All Video Showcase

Title: Mathematics Immersion for Secondary Teachers (MIST)

Presenter(s): Matt McLeod, Miriam Gates, Daniel Heck, & Pippa Hoover

2018 STEM for All Video Showcase

Title: Building a Virtual Mathematics Immersion Experience

Presenter(s): Matt McLeod, Eden Badertscher, Al Cuoco, Miriam Gates, Daniel Heck, & Bowen Kerins


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

This project lays the foundation and framework for enabling digital, multimodal tactile graphics on touchscreens for individuals with visual impairments (VI). Given the low-cost, portability, and wide availability of touchscreens, this work promotes the use of vibrations and sounds on these readily available platforms for addressing the graphical access challenge for individuals with VI.

Lead Organization(s): 
Award Number: 
1644538
Funding Period: 
Sun, 01/15/2017 to Tue, 12/31/2019
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.

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

This project lays the foundation and framework for enabling digital, multimodal tactile graphics on touchscreens for individuals with visual impairments (VI). Given the low-cost, portability, and wide availability of touchscreens, this work promotes the use of vibrations and sounds on these readily available platforms for addressing the graphical access challenge for individuals with VI.

Award Number: 
1644491
Funding Period: 
Sun, 01/15/2017 to Tue, 12/31/2019
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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