Teaching & Learning



  • Mathematics is not about numbers, equations,
    computations, or algorithms: it is about understanding.
    — William Paul Thurston
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     Image of Dice with Math Operators

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  • The National Council of Teachers of Mathematics (NCTM) has identified six principles for school mathematics. The following information is an excerpt from Executive Summary: Principles and Standards for School Mathematics available on the NCTM website.
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Excellence in mathematics education requires equity—high expectations and strong support for all students.

All students, regardless of their personal characteristics, backgrounds, or physical challenges, can learn mathematics when they have access to high-quality mathematics instruction. Equity does not mean that every student should receive identical instruction. Rather, it demands that reasonable and appropriate accommodations be made and appropriately challenging content be included to promote access and attainment for all students.

A curriculum is more than a collection of activities; it must be coherent, focused on important mathematics, and well articulated across the grades.

In a coherent curriculum, mathematical ideas are linked to and build on one another so that students’ understanding and knowledge deepen and their ability to apply mathematics expands. An effective mathematics curriculum focuses on important mathematics that will prepare students for continued study and for solving problems in a variety of school, home, and work settings. A well-articulated curriculum challenges students to learn increasingly more sophisticated mathematical ideas as they continue their studies.

Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well.

Students’ understanding of mathematics, their ability to use it to solve problems, and their confidence in doing mathematics are all shaped by the teaching they encounter in school. To be effective, teachers must understand and be committed to students as learners of mathematics. They must know and understand deeply the mathematics they are teaching and be able to draw on that knowledge with flexibility in their teaching tasks. Teachers must be supported with ample opportunities and resources to enhance and refresh their knowledge.

Students must learn mathematics with understanding, actively building new knowledge from experience and previous knowledge.

Research has solidly established the important role of conceptual understanding in the learning of mathematics. By aligning factual knowledge and procedural proficiency with conceptual knowledge, students can become effective learners. They will be able to recognize the importance of reflecting on their thinking and learning from their mistakes. Students become competent and confident in their ability to tackle difficult problems and willing to persevere when tasks are challenging.

Assessment should support the learning of important mathematics and furnish useful information to both teachers and students.

When assessment is an integral part of mathematics instruction, it contributes significantly to students’ mathematics learning. Assessment should inform and guide teachers as they make instructional decisions. The tasks teachers select for assessment convey a message to students about what kinds of mathematical knowledge and performance are valued. Feedback from assessment tasks helps students in setting goals, assuming responsibility for their own learning, and becoming more independent learners.

Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students’ learning.

Students can develop deeper understanding of mathematics with the appropriate use of technology. Technology can help support investigation by students in every area of mathematics and allow them to focus on decision making, reflection, reasoning, and problem solving. The existence, versatility, and power of technology make it possible and necessary to reexamine what mathematics students should learn as well as how they can best learn it.