The Common Core standards for mathematical practice focus on numbers and geometry. Elementary students are required to have a working knowledge of whole numbers, as well as the four basic mathematical operations and how they relate to each other. Students also must understand the basic concepts of geometric measurement, as well as spatial relationships. By gaining understanding of these basic ideas, students set a foundation they can continue to recall throughout their mathematical studies -- and their adult lives as well.
The Common Core standards require students to quickly analyze problems, identify how to solve them and reach a logical solution. The standards use language such as “precision,” “structure,” and “regularity.” In other words, students must be consistent in their mathematical thinking and be able to identify and utilize mathematical patterns. For example, a third-grade student who understands the concept of multiplication arrays should be able to quickly comprehend how to find the area of a rectangle. By being able to focus their attention while also noticing patterns in other math-related areas, students form a real-world understanding of mathematical concepts.
The revised Bloom’s Taxonomy shows simple recall and remembering to be only the first step toward becoming an independent learner. The Common Core standards support this notion: “There is a world of difference between a student who can summon a mnemonic device to expand a product such as (a + b)(x + y) and a student who can explain where the mnemonic comes from.” For example, many students struggling to learn the multiples of nine may rely on a mnemonic in which they use their fingers to find the answer. By holding up all 10 fingers then folding down the third finger for 9x3, the two fingers to the left of the one folded and the seven to the right mean the answer is 27, and so forth. Two problems arise when using this trick: It doesn't work when multiplying nine by anything higher than 10, and it definitely does not reinforce any mathematical thinking. With the new standards in place, educators need to be careful not to teach meaningless tricks to struggling students; in fact, the students who are having trouble with certain material would benefit more from gaining a true understanding of the abstract ideas relevant to the topic than from learning a simple trick that may or may not always work.
The Common Core standards take a project-based learning approach to teaching math. Although textbooks and word problems remain an important part of instruction, teachers should utilize them only as diagnostics for understanding. Again, the goal is for students to apply, analyze and evaluate information, culminating in a creation that exhibits true understanding of mathematical concepts. A student who can create a birdhouse using geometric knowledge demonstrates a much deeper understanding than a student who can identify the area of a birdhouse given its dimensions. In cultivating a classroom of students who explore math concepts rather than simply memorizing math facts, teachers increase their students’ future chances of success in occupations that require higher-level thinking and problem-solving skills.