Improving mathematics teaching and learning through and beyond Algebra is one of the most important challenges facing educators worldwide. The powerful capabilities of technology to engage students, support their cognitive effort, represent mathematics insightfully, and better connect teachers and students are important to addressing the Algebra challenge. To leverage technology effectively, teachers need an appropriate pedagogical model.
We propose a pedagogical model based on the concept of interactivity. By interactivity, we mean increasing the quality and frequency of back-and-forth interplay among the
teacher, her students, and the mathematical content at hand. Technology can enhance many forms of interactivity, especially when:
• students and teachers use technology to explore mathematical models, not just as a calculation tool,
and when:
• teachers use a shared display and instant feedback to increase students’ cognitive engagement, not only to demonstrate or assess.
Across these forms of interactivity, the most important goal is to increase student engagement centered on the doing and making sense of mathematics. Application of this principle leads to highly interactive mathematics classrooms, in which teachers:
1. engage their students in mathematically meaningful activities;
2. focus on mathematics with connections;
3. track what mathematics their students know and adapt accordingly;
4. make mathematics learning a shared responsibility of teachers and students.
Implementing a highly interactive mathematics classroom takes more than technology, it requires support for professional development and time for teachers to learn and adapt. For example, the new capability to instantly capture and display students’ screens can provide cognitive contrasts that drive learning, but only when the teacher uses classroom
discussions to probe the meaning of contrasting screens. We propose an implementation model that proceeds in stages, based on research data that shows what teachers typically
accomplish immediately, with experience and, eventually, as masters of the technology-rich classroom. By thinking in terms of not just technology but also a pedagogical model and
implementation in stages, schools can realize deepening benefits over time. Within the first year, schools can experience increased student achievement and more positive
student attitudes. Teachers see immediate benefits from knowing more about their students. Over time, with continued technological support and sustained professional development, schools can make progress in closing achievement gaps and introducing higher-order skills, such as mathematical problem solving, collaboration, and argumentation. Over many years, schools will develop master teachers who can lead further improvement in their regions, aimed at developing students’ passion to pursue and succeed in university level mathematics and on toward challenging STEM careers.