The National Council of Teachers of Mathematics (NCTM) has developed a comprehensive set of principles, standards and expectations that standardizes the learning goals and methods that should be used to measure student achievement in mathematics. The standards focus on specific, clearly defined expectations in student learning based on the popular outcome-based model of education theory. They provide equity and accessibility for all students and reliable modes of assessing and delivering math learning. They also advocate for those who may struggle in learning mathematics.
The Principles
The six principles developed by NCTM are comprehensive and decisive, and take the guesswork about curriculum out of the equation for both teachers and students. And, according to these principles, all students regardless of backgrounds, abilities, or challenges, can learn higher level mathematics. The overarching themes of the principles are:
- Equity: The principle of equity is an essential aspect of NCTM standards because, in order to achieve the goals, curriculum must be accessible and understandable to all students. Teachers must provide adequate and appropriate attention to those who are underserved or falling behind in math studies.
- Curriculum: Curriculum must be coherent, organized, and presented in a way that students can follow.
- Teaching: Teachers need to have the flexibility to meet the students on the level at which they are functioning, offering support to those who need it and challenging those who excel.
- Learning: Students must be willing to embrace the concept of active learning over memorization, taking the time to understand material conceptually.
- Assessment: Teachers must rigorously and accurately assess student performance and develop curriculum in response to students’ specific needs.
- Technology: Incorporating technology is essential in the teaching and learning of math, as it enhances learning
Teaching under the six principles of the NCTM model is dynamic and requires diligence to deliver the appropriate curriculum to the student.
Content Standards
Coupled with concepts of equity, NCTM standards set forth content expectations designed to present common foundations of mathematics to students at each grade level. They are broken down into five strands:
- Number and Operations
- Algebra
- Geometry
- Measurement
- Data Analysis and Probability
Each standard has two to four specific, clearly defined goals associated with it. The NCTM maintains that developing this knowledge serves individuals far beyond the classroom; it prepares them for life. For teachers, these guidelines organize their curriculum and order their interactions with students. For students, the guidelines offer clear expectations resulting in the satisfaction of working through each content classification.
Process Standards
According to the NCTM, the process standards “highlight the mathematical processes that students draw on to acquire and use their [mathematical] content knowledge.” This allows students to learn through the application of methods they can return to anytime they are approaching a difficult mathematic problem. These well-defined strategies also focus student attention on what is required of them and allow teachers to see where there may be a possible breakdown or obstacle for students.
Process Standards include:
- Problem Solving
- Reasoning and Proof
- Communication
- Connections
- Representation
The NCTM believes that these standards, principles, and goals are required to “produce a society that has both the capability to think and reason mathematically and a useful base of mathematical knowledge and skills needed in any walk of life” (NCTM). And, when the goals are appropriate, well-defined, and presented in a cohesive manner, both students and teachers benefit by having clear guidelines for tracking students’ progress and achievement.
Barry University’s online Master of Science in Curriculum & Instruction – Mathematics Education program prepares teachers to apply the NCTM standards and provides a foundation based on best practices in math pedagogy and theory.
Learn more about Barry University’s online Master of Science in Curriculum & Instruction – Mathematics Education program.
Sources:
National Council of Teachers of Mathematics: Principles, Standards, and Expectations
National Council of Teachers of Mathematics: Principles and Standards for School Mathematics
Reflections of a Second-Career Math Teacher: NCTM Standards for Mathematics
