Algebra

Developing Rich Media-Based Materials for Practice-Based Teacher Education

This research and development project is premised on the notion that recent technological developments have made it feasible to represent classroom work in new ways. In addition to watching recorded videos of classroom interactions or reading written cases, teacher educators and teachers can now watch animations and image sequences, realized with cartoon characters, and made to depict activities that happened, or could have happened, in a mathematics classroom.

Award Number: 
1316241
Funding Period: 
Thu, 08/15/2013 to Tue, 07/31/2018
Full Description: 

The 4-year research and development project, Developing Rich Media-based Materials for Practice-based Teacher Education, is premised on the notion that recent technological developments have made it feasible to represent classroom work in new ways. In addition to watching recorded videos of classroom interactions or reading written cases, teacher educators and teachers can now watch animations and image sequences, realized with cartoon characters, and made to depict activities that happened, or could have happened, in a mathematics classroom. Furthermore, teacher educators and teachers can react to such animations or image sequences by making their own depictions of alternative moves by students or teachers in classroom interaction. And all of that can take place in an on-line, cloud-based environment that also supports discussion fora, questionnaires, and the kinds of capabilities associated with learning management systems. Such technologies offer important affordances to teacher educators seeking to provide candidates with course-based experiences that emphasize the development of practice-based skills. The focus of the project is on mathematics teacher education. This joint project of the University of Maryland Center for Mathematics Education and the University of Michigan will produce 6 to 8 field-tested modules for use in different courses that are a part of mathematics teacher preparation programs. The following two-pronged research question will be resolved: What are the affordances and constraints of the modules and the environment as supports for: (1) practice based teacher education and (2) a shift toward blended teacher education?

The project involves the following activities: (1) a teacher education materials development component; (2) a related evaluation component; and (3) two research components. The development phase seeks to develop both the LessonSketch.org platform and six to eight mathematics teacher education modules for use in preservice teacher education programs from around the country. The modules will be written with practice-based teacher education goals in mind and will use the capacities of the LessonSketch.org platform as a vehicle for using rich-media artifacts of teaching with preservice teacher candidates. LessonSketch Teacher Education Research and Development Fellows will be chosen through a competitive application process. They will develop their respective modules along with teams of colleagues that will be recruited to form their inquiry group and pilot the module activities. The evaluation activity will focus on the materials development aspect of the project. Data will be collected by the LessonSketch platform, which includes interviews with Fellows and their teams, perspectives of module writers, descriptive statistics of module use, and feedback from both teacher educator and preservice teacher end-users about the quality of their experiences. The first research activity of the project is design research on the kinds of technological infrastructure that are useful for practice-based teacher education. The PIs will identify tools that teacher educators need and want beyond the current capabilities for web-based support for use of rich media and will produce prototype tools inside the LessonSketch environment to meet these needs. The second research activity of the project will supplement the evaluation activity by examining the implementation of two of the modules in detail. This aspect of the research will examine the goals of the intended curriculum, the proposed modes of media use, the fidelity of the implemented curriculum, and learnings produced by preservice teachers. This research activity will help the field understand the degree to which practice-based teacher education that is mediated by an online access to rich media would be a kind of practice that could be easily incorporated into existing teacher education structures.

The project will produce 6 to 8 LessonSketch modules for use in teacher education classes. Each module will be implemented in at least eight teacher education classes across the country, which means that between 720 and 960 preservice teacher candidates will study the materials. The project aims to shift the field toward practice-based teacher education by supporting university programs to implement classroom-driven activities that will produce mathematics teachers with strong capabilities to teach mathematics effectively and meaningfully.

CAREER: Investigating Differentiated Instruction and Relationships Between Rational Number Knowledge and Algebraic Reasoning in Middle School

The proposed project initiates new research and an integrated education plan to address specific problems in middle school mathematics classrooms by investigating (1) how to effectively differentiate instruction for middle school students at different reasoning levels; and (2) how to foster middle school students' algebraic reasoning and rational number knowledge in mutually supportive ways.

Lead Organization(s): 
Award Number: 
1252575
Funding Period: 
Thu, 08/01/2013 to Fri, 07/31/2020
Full Description: 

Middle school mathematics classrooms are marked by increasing cognitive diversity and students' persistent difficulties in learning algebra. Currently middle school mathematics instruction in a single classroom is often not differentiated for different thinkers, which can bore some students or overly challenge others. One way schools often deal with different thinkers at the same grade level is by tracking, which has also been shown to have deleterious effects on students, both cognitively and affectively. In addition, students continue to struggle to learn algebra, and increasing numbers of middle school students are receiving algebra instruction. The proposed project initiates new research and an integrated education plan to address these problems by investigating (1) how to effectively differentiate instruction for middle school students at different reasoning levels; and (2) how to foster middle school students' algebraic reasoning and rational number knowledge in mutually supportive ways. Educational goals of the project are to enhance the abilities of prospective and practicing teachers to teach cognitively diverse students, to improve doctoral students' understanding of relationships between students' learning and teachers' practice, and to form a community of mathematics teachers committed to on-going professional learning about how to differentiate instruction.

Three research-based products are being developed: two learning trajectories, materials for differentiating instruction developed collaboratively with teachers, and a written assessment to evaluate students' levels of reasoning. The first trajectory, elaborated for students at each of three levels of reasoning, focuses on developing algebraic expressions and solving basic equations that involve rational numbers; the second learning trajectory, also elaborated for students at each of three levels of reasoning, focuses on co-variational reasoning in linear contexts. In addition, the project investigates how students' classroom experience is influenced by differentiated instruction, which will allow for comparisons with research findings on student experiences in tracked classrooms. Above all, the project enhances middle school mathematics teachers' abilities to serve cognitively diverse students. This aspect of the project has the potential to decrease opportunity gaps. Finally, the project generates an understanding of the kinds of support needed to help prospective and practicing teachers learn to differentiate instruction.

The project advances discovery and understanding while promoting teaching, training, and learning by (a) integrating research into the teaching of middle school mathematics, (b) fostering the learning of all students by tailoring instruction to their cognitive needs, (c) partnering with practicing teachers to learn how to implement this kind of instruction, (d) improving the training of prospective mathematics teachers and graduate students in mathematics education, and (e) generating a community of mathematics teachers who engage in on-going learning to differentiate instruction. The project broadens participation by including students from underrepresented groups, particularly those with learning disabilities. Results from the project will be broadly disseminated via conference presentations; articles in diverse media outlets; and a project website that will make project products available, be a location for information about the project for the press and the public, and be a tool to foster teacher-to-teacher communication.


Project Videos

2019 STEM for All Video Showcase

Title: Differentiating Mathematics Instruction for Middle School

Presenter(s): Amy Hackenberg, Rebecca Borowski, Mihyun Jeon, Robin Jones, & Rob Matyska


The Impact of Early Algebra on Students' Algebra-Readiness (Collaborative Research: Knuth)

In this project researchers are implementing and studying a research-based curriculum that was designed to help children in grades 3-5 prepare for learning algebra at the middle school level. Researchers are investigating the impact of a long-term, comprehensive early algebra experience on students as they proceed from third grade to sixth grade. Researchers are working to build a learning progression that describes how algebraic concepts develop and mature from early grades through high school.

Award Number: 
1219606
Funding Period: 
Mon, 10/01/2012 to Wed, 09/30/2015
Full Description: 

The Impact of Early Algebra on Students' Algebra-Readiness is a collaborative project at the University of Wisconsin and TERC, Inc. They are implementing and studying a research-based curriculum that was designed to help children in grades 3-5 prepare for learning algebra at the middle school level. Researchers are investigating the impact of a long-term, comprehensive early algebra experience on students as they proceed from third grade to sixth grade. Researchers are working to build a learning progression that describes how algebraic concepts develop and mature from early grades through high school. This study helps to build our knowledge about the piece of the progression that is just prior to entering middle school where many students begin formal instruction in algebra.

Building on previous research about early algebra learning, researchers will teach a curriculum that was carefully designed to reflect what we know about learning algebraic concepts. Previous research has shown that young children from very diverse backgrounds have the ability to construct algebraic ideas such as equality, representation, generalization, and functions. Researchers are collecting data about students' algebraic knowledge as well as arithmetical knowledge.

We know that the majority of students in the United States struggle with learning formal algebra. By studying the implementation of the research-based curriculum for an extended period of time, researcher's are learning about how algebraic ideas are connected and whether or not early instruction on algebraic ideas will help students learn more formal ideas in middle school.

The Impact of Early Algebra on Students' Algebra-Readiness (Collaborative Research: Blanton)

In this project researchers are implementing and studying a research-based curriculum that was designed to help children in grades 3-5 prepare for learning algebra at the middle school level. Researchers are investigating the impact of a long-term, comprehensive early algebra experience on students as they proceed from third grade to sixth grade. Researchers are working to build a learning progression that describes how algebraic concepts develop and mature from early grades through high school.

Award Number: 
1219605
Funding Period: 
Mon, 10/01/2012 to Wed, 09/30/2015
Full Description: 

The Impact of Early Algebra on Students' Algebra-Readiness is a collaborative project at the University of Wisconsin and TERC, Inc. They are implementing and studying a research-based curriculum that was designed to help children in grades 3-5 prepare for learning algebra at the middle school level. Researchers are investigating the impact of a long-term, comprehensive early algebra experience on students as they proceed from third grade to sixth grade. Researchers are working to build a learning progression that describes how algebraic concepts develop and mature from early grades through high school. This study helps to build our knowledge about the piece of the progression that is just prior to entering middle school where many students begin formal instruction in algebra.

Building on previous research about early algebra learning, researchers will teach a curriculum that was carefully designed to reflect what we know about learning algebraic concepts. Previous research has shown that young children from very diverse backgrounds have the ability to construct algebraic ideas such as equality, representation, generalization, and functions. Researchers are collecting data about students' algebraic knowledge as well as arithmetical knowledge.

We know that the majority of students in the United States struggle with learning formal algebra. By studying the implementation of the research-based curriculum for an extended period of time, researcher's are learning about how algebraic ideas are connected and whether or not early instruction on algebraic ideas will help students learn more formal ideas in middle school.

Learning Trajectories to Support the Growth of Measurement Knowledge: Pre-K Through Middle School

This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This research project tests, revises and extends learning trajectories for children's knowledge of geometric measurement across a ten-year span of human development. The goal will be to validate all components of each learning trajectory, goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1222944
Funding Period: 
Wed, 08/01/2012 to Tue, 07/31/2018
Full Description: 

This project is studying measurement practices from pre-K to Grade 8, as a coordination of the STEM disciplines of mathematics and science. This four-year, mixed methods research project tests, revises and extends learning trajectories (LTs) for children's knowledge of geometric measurement across a ten-year span of human development. Specifically, research teams from Illinois State University and the University at Denver are working with children in urban and suburban schools to (1) validate and extend prior findings from previous NSF-funded research developing measurement learning trajectories with children in pre-K to Grade 5, and (2) generate and extend portions of trajectories for geometric measurement for Grades 6-8.

The project employs a form of microgenetic studies with 24-50 children per grade from pre-K through Grade 5 representing a stratified random sample from a specific set of suburban schools. These studies will test the validity, replicability and generalizability of the LTs for length, area, and volume. The goal will be to validate all components of each learning trajectory, goal, developmental progression, and instruction tasks, as well as revising each LT to reflect the outcomes of the experiments. Analysis of variance measures with pre/post assessments in an experimental/control design will complement the repeated sessions method of microgenetic analysis.

To explore and extend LTs for children in Grade 6-8, the project employs teaching experiments. This design is used to generate and extend portions of trajectories for geometric measurement, and to explore critical aspects of measurement in clinical and classroom contexts. This work is coordinated with the teaching and learning standards issued by the Council of Chief State School Officials/National Governors Association, the National Council of Teachers of Mathematics, the National Science Teachers Association, the American Association of the Advancement of Science, and the National Research Council with cognitive and mathematics/science education literature. Emerging constructs for the hypothetical LT levels in relation to relevant frameworks generated by other researchers and those implied by standards documents to establish ongoing sequences of the experimental interventions for grades 6-8 are being compared, critiqued and evaluated.

This project provides a longitudinal account of pre-K to Grade 8 children's ways of thinking and understanding mathematical and scientific concepts of measurement based upon empirical analysis. The resulting learning trajectory will represent state of the art integrated, interdisciplinary, theoretically- and empirically-based descriptions of increasingly sophisticated and complex levels of thinking in the domain of measurement (albeit, more tentative for Grades 6-8). This account will be used to verify and/or modify existing accounts of children's development of reasoning from short-term analyses of learning or cross-sectional studies. There are not yet integrative longitudinal studies describing this cognitive domain for area or volume measurement. This trajectory-based analysis of development and instruction supports the design and testing of integrative, formative assessment of individuals and groups of children. Such learning trajectories will be useful in implementing the standard-focused curriculum described in the Common Core State Standards Mathematics and in supporting the multiple large assessment projects currently underway

Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Sword)

This collaborative project is developing instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement.

Award Number: 
1222426
Funding Period: 
Wed, 08/15/2012 to Sun, 07/31/2016
Full Description: 

Boston University, Education Development Center, Inc., and St. Olaf College are collaborating on Assessing Secondary Teachers' Algebraic Habits of Mind (ASTAHM) to develop instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. MHoM is a critical component of mathematical knowledge for teaching at the secondary level. Recognizing the need for a scientific approach to investigate the ways in which MHoM is an indicator of teacher effectiveness, the partnership is researching the following questions:

1. How do teachers who engage MHoM when doing mathematics for themselves also bring MHoM to their teaching practice?

2. How are teachers' engagement with MHoM and their use of these habits in teaching related to student understanding and achievement?

To investigate these questions, ASTAHM is developing two instruments: a paper and pencil (P&P) assessment and an observation protocol that measure teachers' knowledge and classroom use, respectively, of MHoM.

The work is being conducted in two phases: (1) an instrument-refinement and learning phase, and (2) an instrument-testing and research phase. Objectives of Phase 1 are to gather data to refine the project's existing instruments and to learn about the bridge factors that impact the relationship between teachers' knowledge and classroom use of MHoM. Specific research activities include: administering the pilot P&P assessment to 40 teachers, videotaping Algebra instructions of 8 teachers, performing initial testing and refinement of the instruments, and using the data to analyze the bridge factors. Phase 2 is a large-scale study involving field-testing the P&P assessment with 200 teachers, videotaping 20 teachers and studying them using the observation protocol, collecting achievement data from 3000 students, and checking P&P content validity with 200 mathematicians. With these validated instruments in hand, the project will then conduct an investigation into the above research questions. Lesley University's Program Evaluation and Research Group (PERG) is the external evaluator. PERG is assessing ASTAHM's overall success in developing valid and reliable instruments to investigate the extent to which a relationship exists between teachers' MHoM and their classroom practice, as well as student achievement. Evaluators are also investigating whether users' coding guides for both instruments enable field-testers to effectively use and adequately score them.

This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement. The MHoM construct is closely aligned with the Common Core State Standards-Mathematics (CCSS-M); especially its Standards for Mathematical Practice. For example, both place importance on seeking and using mathematical structure. Thus the instruments this project produces can act as pre- and post-measures of the effectiveness of professional development programs in preparing teachers to implement the CCSS-M. Mathematics teacher knowledge at the secondary level is an understudied field. Through analyses of the practices and habits of mind that teachers bring to their work, ASTAHM is developing instruments that can be used to shed light on effective secondary teaching.


Project Videos

2019 STEM for All Video Showcase

Title: Studying Teachers' Mathematical Habits of Mind

Presenter(s): Sarah Sword, Eden Badertscher, Al Cuoco, Miriam Gates, Ryota Matsuura, & Glenn Stevens

2017 STEM for All Video Showcase
Title: Assessing Secondary Teachers' Algebraic Habits of Mind

Presenter(s): Sarah Sword, Courtney Arthur, Al Cuoco, Miriam Gates, Ryota Matsuura, & Glenn Stevens

2016 STEM for All Video Showcase

Title: Assessing Secondary Teachers' Algebraic Habits of Mind

Presenter(s): Ryota Matsuura, Al Cuoco, Glenn Stevens, & Sarah Sword


Assessing Secondary Teachers' Algebraic Habits of Mind (Collaborative Research: Stevens)

This collaborative project is developing instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement.

Partner Organization(s): 
Award Number: 
1222496
Funding Period: 
Wed, 08/15/2012 to Sun, 07/31/2016
Full Description: 

Boston University, Education Development Center, Inc., and St. Olaf College are collaborating on Assessing Secondary Teachers' Algebraic Habits of Mind (ASTAHM) to develop instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. MHoM is a critical component of mathematical knowledge for teaching at the secondary level. Recognizing the need for a scientific approach to investigate the ways in which MHoM is an indicator of teacher effectiveness, the partnership is researching the following questions:

1. How do teachers who engage MHoM when doing mathematics for themselves also bring MHoM to their teaching practice?

2. How are teachers' engagement with MHoM and their use of these habits in teaching related to student understanding and achievement?

To investigate these questions, ASTAHM is developing two instruments: a paper and pencil (P&P) assessment and an observation protocol that measure teachers' knowledge and classroom use, respectively, of MHoM.

The work is being conducted in two phases: (1) an instrument-refinement and learning phase, and (2) an instrument-testing and research phase. Objectives of Phase 1 are to gather data to refine the project's existing instruments and to learn about the bridge factors that impact the relationship between teachers' knowledge and classroom use of MHoM. Specific research activities include: administering the pilot P&P assessment to 40 teachers, videotaping Algebra instructions of 8 teachers, performing initial testing and refinement of the instruments, and using the data to analyze the bridge factors. Phase 2 is a large-scale study involving field-testing the P&P assessment with 200 teachers, videotaping 20 teachers and studying them using the observation protocol, collecting achievement data from 3000 students, and checking P&P content validity with 200 mathematicians. With these validated instruments in hand, the project will then conduct an investigation into the above research questions. Lesley University's Program Evaluation and Research Group (PERG) is the external evaluator. PERG is assessing ASTAHM's overall success in developing valid and reliable instruments to investigate the extent to which a relationship exists between teachers' MHoM and their classroom practice, as well as student achievement. Evaluators are also investigating whether users' coding guides for both instruments enable field-testers to effectively use and adequately score them.

This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement. The MHoM construct is closely aligned with the Common Core State Standards-Mathematics (CCSS-M); especially its Standards for Mathematical Practice. For example, both place importance on seeking and using mathematical structure. Thus the instruments this project produces can act as pre- and post-measures of the effectiveness of professional development programs in preparing teachers to implement the CCSS-M. Mathematics teacher knowledge at the secondary level is an understudied field. Through analyses of the practices and habits of mind that teachers bring to their work, ASTAHM is developing instruments that can be used to shed light on effective secondary teaching.


Project Videos

2019 STEM for All Video Showcase

Title: Studying Teachers' Mathematical Habits of Mind

Presenter(s): Sarah Sword, Eden Badertscher, Al Cuoco, Miriam Gates, Ryota Matsuura, & Glenn Stevens

2017 STEM for All Video Showcase
Title: Assessing Secondary Teachers' Algebraic Habits of Mind

Presenter(s): Sarah Sword, Courtney Arthur, Al Cuoco, Miriam Gates, Ryota Matsuura, & Glenn Stevens

2016 STEM for All Video Showcase

Title: Assessing Secondary Teachers' Algebraic Habits of Mind

Presenter(s): Ryota Matsuura, Al Cuoco, Glenn Stevens, & Sarah Sword


CAREER: Learning to Support Productive Collective Argumentation in Secondary Mathematics Classes

Research has shown that engaging students, including students from underrepresented groups, in appropriately structured reasoning activities, including argumentation, may lead to enhanced learning. This project will provide information about how teachers learn to support collective argumentation and will allow for the development of professional development materials for prospective and practicing teachers that will enhance their support for productive collective argumentation.

Award Number: 
1149436
Funding Period: 
Sun, 07/01/2012 to Sun, 06/30/2019
Full Description: 

Doing mathematics involves more than simply solving problems; justifying mathematical claims is an important part of doing mathematics. In fact, proving and justifying are central goals of learning mathematics. Recently, the Common Core State Standards for Mathematics has again raised the issue of making and critiquing arguments as a central practice for students studying mathematics. If students are to learn to make and critique arguments within their mathematics classes, teachers must be prepared to support their students in learning to argue appropriately in mathematics. This learning often occurs during class discussions in which arguments are made public for all students in the class. The act of creating arguments together in a classroom is called collective argumentation. Teachers need to be able to support students in productively engaging in collective argumentation, but research has not yet shown how they learn to do so. This project will document how mathematics teachers learn to support their students in engaging in productive collective argumentation. The research team will follow a cohort of participants (college students majoring in mathematics education) through their mathematics education coursework, observing their engagement in collective argumentation and opportunities to learn about supporting collective argumentation. The team will continue to follow the participants into their first two years of teaching, focusing on how their support for collective argumentation evolves over time. During their first two years of teaching, the research team and participants will work together to analyze the participants' support for collective argumentation in order to help the participants develop more effective ways to support collective argumentation.

Research has shown that engaging students, including students from underrepresented groups, in appropriately structured reasoning activities, including argumentation, may lead to enhanced learning. This project will provide information about how teachers learn to support collective argumentation and will allow for the development of professional development materials for prospective and practicing teachers that will enhance their support for productive collective argumentation.

Core Math Tools

This project is developing Core Math Tools, a suite of Java-based software including a computer algebra system (CAS), interactive geometry, statistics, and simulation tools together with custom apps for exploring specific mathematical or statistical topics. Core Math Tools is freely available to all learners, teachers, and teacher educators through a dedicated portal at the National Council of Teachers of Mathematics (NCTM) web site.

Lead Organization(s): 
Partner Organization(s): 
Award Number: 
1201917
Funding Period: 
Sun, 01/15/2012 to Mon, 12/31/2012
Project Evaluator: 
David Barnes, NCTM
Full Description: 

Core Math Tools is a project from Western Michigan University that meets the urgent need of providing mathematical tools that students can use as they explore and learn mathematical concepts that are aligned with the Common Core State Standards in Mathematics (CCSSM). The developers have repurposed and modified tools originally designed for an NSF-funded curriculum project (e.g., Core-Plus Mathematics), creating a suite of tools that supports student learning of mathematics regardless of the curricula choice. Core math Tools is Java-based software that includes a computer algebra system(CAS, interactive geometry, statistics, and simulation tools together with custom apps for exploring specific mathematical and statistical topics. The designers provide exemplary lessons illustrating how the software can be used in the spirit of the new CCSSM. The goal of the project is to provide equitable and easy access to mathematical software both in school and outside of school. The tools are available to all learners and teachers through the web site of the National Council of Teachers of Mathematics (NCTM). The web site includes feedback loops for teachers to provide information about the tools. By using the NCTM website, the tools can be downloaded for use by teachers and students. The dedicated portal on the NCTM website allows supervisors to use the tools in professional development, teachers to use the tools as an integral part of instruction, and students to use the tools for exploring, conjecturing, and problem solving.

Gateways to Algebraic Motivation, Engagement and Success (GAMES): Supporting and Assessing Fraction Proficiency with Game-Based, Mobile Applications and Devices

This project is designing digital games for middle school students that will help them prepare for success in Algebra. The games are intended to help students gain a deep understanding of measurement and fraction concepts that are critical as they begin to learn algebra. The project studies students' development of fraction concepts, their engagement in the tasks, and the use of hand-held devices as a useful platform for games.

Award Number: 
1118571
Funding Period: 
Mon, 08/15/2011 to Wed, 07/31/2013
Full Description: 

The Gateways to Algebraic Motivation, Engagement and Success (GAMES) project is designing digital games for middle school students that will help them prepare for success in Algebra. The games are intended to help students gain a deep understanding of measurement and fraction concepts that are critical as they begin to learn algebra. The design of the games is based on research on learning fractions and research on engagement. The researchers at Virginia Polytechnic Institute and State University are studying students' development of fraction concepts, their engagement in the tasks, and the use of hand-held devices as a useful platform for games. They are providing valuable information on how students develop fraction concepts and contributing to the development of a learning trajectory that will guide the teaching of measurement and fraction concepts.

The design of the games is based on engagement states that are known to facilitate learning, with specific attention to cognitive, behavioral, and affective domains. The mathematical framework driving the games is based on how students learn fraction concepts. Most grade 6 students think of fractions from a part-whole conception, but this is not an adequate base for developing algebraic concepts. The games help students develop splitting concepts by moving through activities that focus on sequencing, partitioning, and iterating. The games are designed for iOS platforms that provide ease of engagement and data collection flexibility.

The project offers a variety of products ranging from theories to games. The research is building a conceptual framework that identifies features of engagement that lead to learning, and contributing to the development of a learning trajectory related to fraction concepts. The work will produce a scalable model for developing and using digital games to increase engagement and learning of middle school students. In addition, three games and associated tasks are being developed for use with current curricula to enhance students' understanding of fractions and prepare them for learning algebra.

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