The current goal of mathematics education in the United States is for all students to learn how to participate in and use mathematics to solve problems by the time they finish high school. Authentic participation in and the use of mathematics to solve problems requires making conjectures based on measurements, patterns, and structure found in the physical world, the social world, and in the discipline of mathematics itself. Much like the work of professionals in the other STEM fields, mathematicians must make claims based on evidence and then clarify their logic with justifications. The claims and conjectures must withstand rebuttal and peer review, thus participation in mathematics requires interaction with other members of the community.
We developed the Argument-Driven Mathematics (ADM) instructional model as a tool for mathematics teachers. Teachers can use ADM to transform the way they teach so students view mathematics as a dynamic field of knowledge and a tool to more effectively inquire about their surroundings. ADM investigation are grouped under three broad categories: (1) pure math investigations, where students answer mathematical questions because math is an interesting field in and of itself; (2) natural world investigations, where students use mathematical concepts and practices to answer a question grounded in the life, physical, or Earth sciences; and, (3) social world, where students use mathematical concepts and practices to answer a question related to their social, political, and/or economic surroundings. ADM also requires students to learn how to obtain the information they need, communicate what they know and how they know it, and evaluate the mathematical thinking of others. Argumentation, which is the process of proposing, supporting, critiquing, and refining claims based on evidence, is the foundation of all ADM investigations. ADM, as a result, makes math more authentic for students, grounds mathematics in open questions, and most importantly helps students learn the mathematical concepts and practices they are required to learn to a higher degree than they do in a typical course.
ADM is a way of teaching that can be integrated into any grade 6-12 mathematics curriculum. The ADM instructional model consists of 8 stages. Each of these stages gives students an opportunity to participate in different mathematical practices and use key concepts. The stages of ADM are the same for each investigation so students have an opportunity to improve over time. The 8 stage structure of ADM also makes it easy for schools or districts to adopt it as a way to increase student achievement in mathematics or literacy because it can be used across grades and subject areas.
We developed ADM using current research about how people learn mathematics and ways to improve classroom instruction. We also field-tested and refined this instructional approach inside numerous classrooms as part of our research projects. If you are looking for a way to give students more opportunities to learn how to “figure things out” inside the classroom instead of just “learning about things” in mathematics, ADM provides a way for you to make this shift.
All the instructional materials that a teacher needs to begin using ADI in her or his classroom.