STANDARDS FOR MATHEMATICAL PRACTICE

MARIE GRACE L. GARCIA There are varieties of expertise that mathematics educators at all levels should seek to develop in their students, and these are called standards for mathematical practice.

These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education.

Students have to be taught the standards of problem solving, reasoning and proof, communication, representation, and connections.

They should also learn the strands of mathematical proficiency like adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).

When we see our students struggling in math, we should teach them to make sense of problems and persevere in solving them.

Students should be able to explain to themselves the meaning of a problem and look for entry points to its solution. They analyze givens, constraints, relationships, and goals. Then, they make conjectures about the form and meaning of the solution, and plan a solution pathway rather than simply jumping into a solution attempt. They should monitor and evaluate their progress and change course if necessary.

Young students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Let them. Mathematically proficient students, on the other hand, check their answers to problems using a different method, understanding the approaches of others to solving complex problems and identify correspondences between different approaches.

Elementary students use objects, drawings, diagrams, and actions in constructing arguments. These can make sense and be correct, even though they are not generalized or made formal until later grades.

Later on, students will learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

Students who lack understanding of a topic may rely on procedures too heavily. Because they don’t have a flexible base from which to work, they may be less likely to consider analogous problems, represent problems coherently and justify conclusions.

Lack of understanding effectively prevents a student from engaging in mathematical practices.

author is Teacher Pampanga --oOo-The I at Dolores National High School, Magalang,