Rigorous Mathematical Thinking
A Revolution in Mathematics Instruction

Rationale

The prevailing culture in American mathematics education is driven by a perceived need to rapidly cover expansive amounts of content with an acute focus on the product of covering material rather than the process of structural learning. The institutional culture of American education has time and again reduced rich and fresh ideas into dry elements of dull routine. Nearly all instruction in mathematics education classrooms today features procedural, algorithmic demonstrations with an exclusive expectation that students must mimic the mechanics to arrive at some meaningless answer. The revolutionary approach in Rigorous Mathematical Thinking is radically different, nurturing students to engage in vigorous structural thinking to construct deep conceptual understanding.  RMT teaches students to think about their thinking in order to learn how to learn.

RMT is an instructional process that consists of the following elements:
Ongoing rigorous engagement of all students in thinking about thinking and learning how to learn (cognition and metacognition).

 Intentionally and explicitly guiding and nurturing students to appropriate the tools of mathematics as instruments separate and distinct from mathematics content.  Each of these tools has a structure which dictates its unique function or functions. These functions of the tools contribute to constructing aspects of mathematical concepts and are driven by cognitive and metacognitive processes. Thus, each tool is a mathematical psychological tool. Examples are number line, place value systems, table, x-y coordinate plane, equations, and the language of mathematics.

 Guiding and nurturing students into conscientiously practicing the use of each tool, through its instrumentality for carrying out its function or functions. This instrumentality is to organize and orchestrate the cognitive and metacognitive processes and channel them into systemically constructing deep mathematical conceptual understanding.

Genuinely and constantly seeking to compel each student to become a proactive agent in building his/her thinking and learning by having each to draw from his/her culture and prior experiences and employ these as “supporting material and processes� to create and apply mathematical knowledge.

Proactively engaging students in the full cycle of mathematics investigation:  representation, manipulation, and validation, by  helping students appropriate the tools, language, and culture of mathematics.

Guiding students to experience the intrinsic beauty of mathematics while building their intrinsic motivation for mathematical thought.

Target Populations

1. Students from 2nd grade – 12th grade, college students, students pursuing
    graduate and professional degrees, and adults of all ages.
2. Teachers who need to develop a deeper understanding of mathematical
    concepts, processes, and engage in constructing insights.
3. Teachers who want to be trained and certified to teach through RMT.
4. Workers who need training and retooling for technological firms.
5. Companies, firms, and organizations who need to improve productivity,
    creativity, and innovative capacities for their employees.
6. Governmental agencies who need to improve productivity, creativity, and
    innovative capacities for their staff.