A DRK-12 math project
Collaborative Research: Enhancing Middle Grades Students’ Capacity to Develop and Communicate Their Mathematical Understanding of Big Ideas Using Digital Inscriptional Resources
The Inscriptions Math Project is a four-year, $3 million project funded by the National Science Foundation (NSF). The project explores how the use of digital inscriptional resources can improve middle school students’ mathematical understanding. Using a problem-centered math curriculum, a digital learning platform is being developed to assist these students in learning collaboratively.
A major goal of this project is to help middle school students deepen and communicate their understanding of mathematics. Research has indicated that having students work together and share ideas enhances their learning experience. As they do this, students use inscriptions--external representations of thinking, such as equations, diagrams, tables, or charts. This project will support students in collaboratively constructing, manipulating, and interpreting shared representations of mathematics using digital inscriptional resources. The proposed research activities will enhance the understanding of math learning and make it easier to design learning environments that:
support students in using inscriptions in collaborative settings
improve learning of mathematics
track students’ conceptual growth of big mathematical ideas over time.
Why do we need the Inscriptions Math Project?
Research shows that conceptual understanding depends upon a student's capacity to represent knowledge and make sense of their inscriptions. These capacities noticeably develop in social settings where meanings of the work are publicly shared and negotiated. However, very little is known about how this type of learning is used in middle school mathematics. Learning more about how middle school students represent their knowledge through inscriptions will be of great benefit to researchers, teachers, and curriculum developers in designing more effective ways to support students in learning math.
The Inscriptions Math Project builds on a problem-centered math curriculum that is among the most widely used and studied in the nation. This project also makes use of a digital platform that will host all of the tools developed. Additionally, the research activities will take place in schools with a wide range of diversity in gender, race, ethnicity, economic status, and disability. Therefore, the project has the potential to make problem-based learning accessible and effective for even more students than the already-effective print curriculum. Knowing how to improve support for students will also help to produce a population of mathematically literate citizens that is reflective of the wider STEM community.
Representations often refer to the information in material form on paper or the computer screen, such as written text, graphical displays, tables, equations, diagrams, maps, and charts. However, the term “representation” is vague and unclear because it also refers to a learner’s internal or mental thought.
Inscriptions refer to external representations of thinking that exist in material form where meanings are developed in social settings. They are constantly changing and improving.
The eight characteristics common among inscriptions are that they:
are easily able to be sent and received
do not change when being sent or received
are easily embedded into different contexts
are easily modified
are easily combined and superimposed with other inscriptions
can be reproduced at low economic, cognitive, and temporal cost
are easily merged with geometry
are often translated into other inscriptions.
Research in other subjects has overwhelmingly shown that use of inscriptions fosters collaborative learning, but more research is needed for math education. This project is developing a suite of inscriptional resources for this purpose.
The Digital Learning Environment
A digital learning environment allows students to use inscriptions more effectively by giving them ways to capture and archive thinking that makes sense. Students will be able to make notes on their work to help sort and reference the mathematical thoughts for future use. This feature will also support students’ learning of big math ideas over time because retrieval will be easier. Also, the learning spaces will support collaborative practices where students can share and build upon each other's work.
The digital work spaces will allow students to:
organize and map their ideas
generate and manipulate representations using a variety of different tools
incorporate work from others
link representations together
disseminate their work into their individual, group, or class spaces.
These spaces will benefit teachers as well. They will be able to observe the work, monitor each student’s contribution to group work, and select work to be uploaded to the class space for use in summary discussions.
The digital inscriptional resources will be freely available online for researchers and schools, making them accessible to a wider audience.
Researchers will work closely with teachers to design and implement these tools and materials. Teacher participants will review and test the developed resources and provide feedback to the team on the tools’ feasibility and use in classrooms. The project will also have a professional development meeting each year. There, teachers will engage in activities that:
introduce the digital learning space and its features
provide an overview of problems and mathematical reflections
compare the print and digital versions of the units
plan for implementation
suggest additional resources.
This project plans to use the problem-centered Connected Mathematics3 curriculum. The Connected Mathematics Project (CMP) has worked over 25 years to design, develop, field-test, evaluate, and disseminate student and teacher materials for a middle school math curriculum. CMP focuses on the investigation of mathematical ideas embedded in problem situations, explored through inquiry, classroom discourse, and collaboration. Results of peer-reviewed studies into use of the materials show that, compared to their peers using traditional math curricula, students in CMP classrooms typically do as well on assessments of procedures and skills, and score significantly higher on problems requiring modeling, mathematical reasoning, and/or articulating their thinking.
Connected Mathematics3 is clearly having an impact on middle school mathematics, but it can be made even better. Right now, it makes use of the student notebook, which isn’t always the most efficient way to store, access, and share information. This makes it the perfect curriculum to try to go all digital. Researchers have chosen seventh grade as their focus because the students have had at least one year of inquiry-based instruction, and because eighth grade poses issues of tracking when students are transitioning to high school courses.
The project plans to use the following units: Comparing and Scaling: Proportional Reasoning, Stretching and Shrinking: Understanding Similarity, and Moving Straight Ahead: Linear Relationships. Each unit has three or four investigations, each of which contains 2-5 problems. A unit is typically enacted in 4-6 calendar weeks. The units were chosen because proportional reasoning is a connective theme in all of them.
The teachers participating in this research already have experience implementing the Connected Mathematics3 curriculum in non-digital form. This means that they are already familiar with its philosophy and learning goals, which will remain unaltered by this project. They have also attended professional development activities related to implementing the curriculum or have experience facilitating teacher professional development activities at the regional and national level. Their knowledge of the curriculum makes them an asset to the development of the digital tools, and no time will have to be spent training new teachers to implement the curriculum.
This project makes use of an existing full-format digital platform designed specifically for educational research purposes. The Concord Consortium’s Lightweight Activity Runtime and Authoring (LARA) environment and its associated teacher portal were developed under funding from prior NSF-supported projects. The Inscriptions Math Project will use and extend this existing portal environment to develop inscriptional tools and enable students to access both individual and shared spaces. This platform provides a firm foundation for the development work of the project, so researchers can focus on extending the functionality to meet their needs. Because the portal is housed on Concord Consortium’s website, the materials will be widely accessible to students and teachers across the nation.
CREATE for STEM is partnering with the Program for Mathematics Education (PRIME) at MSU and the Concord Consortium (CC) in this collaborative effort. The project team represents a unique collaboration among experts in mathematics and science curriculum design and research, educational research, and technology learning environments.
Elizabeth Difanis Phillips - PI, PRIME
Chad Dorsey - PI, CC
Joe Krajcik - Co-PI, CREATE
Kristen Bieda - Co-PI, CREATE
Alden Edson - Co-PI, PRIME
Valerie L. Mills
Participating school districts:
Battle Creek Public Schools (Battle Creek, MI)
Phoenix Elementary School District #1 (Phoenix, AZ)
Bellingham School District (Bellingham, WA)
Portland Public Schools (Portland, MI)
Falmouth Public Schools (Falmouth, ME)
Clarke-Shawnee Public Schools (Springfield, OH)
Traverse City Area Public Schools (Traverse City, MI)
Lansing Christian School (Lansing, MI)
Ann Arbor Public Schools (Ann Arbor, MI)
This project will run from September 1, 2016 - August 21, 2020.
Year 1 - Prototype Testing
Year 1 will primarily focus on the development and usability testing of the developed resources for a small set of problems. This is the first phase of the development, testing, and revision process. Individuals and small groups of students will use the inscriptional resources to explore mathematics problems. By focusing on their interactions within the digital learning space and on how students provide evidence of their learning using the tools, researchers will learn how to better support students in the learning process.
Year 2 - Trial Testing
Year 2 will focus on the development and usability testing of connected sequences of problems, rather than focusing on individual problems. Researchers will examine similar questions as in Year 1, but the emphasis will be on features that span individual problems and investigations. During this phase, researchers will learn more about how students use these inscriptional resources to interpret the evidence of their learning over time.
Year 3 - Pilot Testing
Year 3 will focus on piloting units consisting of connected sequences of investigations and problems in a small number of classrooms. In other words, researchers will focus on entire classes where students produce, discuss, and refine their inscriptions of their thinking. The team will collect both qualitative and quantitative data from four teachers/classrooms at each site. They will also collect iterations of the inscriptional work students incorporate into their reflections and assessments to examine if students’ understanding of big mathematical ideas becomes more sophisticated over time. All of the units are anticipated to be completed during this phase.
Year 4 - Field Testing
Year 4 will field test multiple units in a variety of classrooms to further extend the work of the previous phases. Researchers will continue to focus on understanding student inscriptions and the related social practices, in addition to further refining the digital tools. At the end of the project, the team will have research results that will indicate evidence of student learning in a digital learning environment from a wide range of classrooms and a set of inscriptional resources that has been vetted by teachers and students from various settings and backgrounds.
The project team will be preparing conference papers and journal articles on the learning research at every phase in the research process. All of the relevant research tools will be made available through the most effective means possible. The digital inscriptional resources will be freely available online for researchers and schools and will be hosted on Concord Consortium’s website. Finally, classroom artifacts of student thinking and related findings will be available at teacher workshops, conferences, and project websites.
The Inscriptions Math Project incorporates design-based implementation research. This process is based on collaboration among researchers and practitioners and focuses on iterative analysis, design, development, and implementation. Something that is iterative involves multiple cycles of development, testing, and revision. For this project, the research process includes four design phases that will study how students use the digital learning space and related inscriptional resources.