The Known Equation and the Mathematical Standards and Best Practices

The Known Equation
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The Known Equation
Mathematical standards and best practices are very important as they establish a standardized approach to teaching and learning. Having a standardized way of teaching ensures that every student passes through the same learning experience to reduce the likelihood of some students having undue advantage over others. One effective way of establishing mathematical standards and best practices is by introducing performance assessments in every learning institution. Performance assessments help foster authentic learning, reduce misconceptions, and encourage flexibility and student-centered learning that are critical to the success of their lives in school and in real life.
Mathematical Standards and Best Practices
1 Conceptual Understanding
Conceptual understanding is the first standard and best practice in performance assessment of mathematical concepts. It refers to a functional understanding of mathematical ideas. Students who follow this standard know more than facts and methods (National Research Council, 2001). They understand the context in which the mathematical equations and concepts are useful, which enables them to apply the knowledge and connect it to new ideas they come across.
2 Procedural Fluency
The second standard is procedural fluency. It refers to knowledge of equations, concepts, and procedures and how and when to use them appropriately (National Research Council, 2001). Procedural fluency requires that students have sound knowledge of mathematical concepts and skills that they can use to perform operations with accuracy and flexibility.
3 Strategic Competence
Third, strategic competence refers to the ability to determine what a problem is and solve it using mathematical concepts. This standard is also called problem solving and problem formulation according to the National Research Council (2001). This standard prepares students to formulate problems in real life and solve them using mathematical concepts.
4 Adaptive Reasoning
Fourth, adaptive reasoning is the most important aspect in mathematical application. The National Research Council (2001) posits that adaptive reasoning is the capacity to think logically and formulate relationships between situations and concepts. It is based on careful consideration of alternatives and justifying the conclusions using mathematical knowledge, concepts, procedures, and solutions.
5 Productive Disposition
The last standard and best practice is productive disposition. It involves seeing sense in mathematical models and equation, and perceiving them as useful and applicable in real life (National Research Council, 2001). Productive disposition enable students to have positive attitude towards math, which inspires their ability and willingness to grasp all the facts, concepts, and procedures.
Performance Assessment Design of Pythagorean Theorem
Title: Pythagorean Theorem
Content Areas:
* Pythagorean Theorem
* Fermat’s Last Theorem
Standard/Proficiencies Assessed:
* Conceptual Understanding – Does the student understand the basic principles of the Pythagorean and Fermat’s Last Theorems?
* Procedur...