Are You Focused?

Common Core State Standards Curriculum must be focused and coherent. For over a decade, research studies of mathematics education in high performing countries have pointed to the conclusion that the mathematics curriculum in the United States must become substantially more focused and coherent in order to improve mathematics achievement in this country. Fewer topics should be taught in each grade, but taught thoroughly. When a concept appears in a subsequent grade level, it is always at a higher level. Mastery of grade-appropriate concepts eliminates the need for repetition year after year. Fractions are not taught in first grade, to allow students the time they need to master the whole number concepts that form the basis of fractions. Fractions are introduced in second grade, which covers what a fraction is. In third grade, students cover equivalent fractions and fractions of a set. Fourth grade deals with mixed fractions and addition of simple fractions. Finally, fifth grade moves on to addition, subtraction, and multiplication of fractions as well as division of fractions by whole numbers. Each grade level addresses an increasingly complex facet of fractions, and draws on the mastery of concepts that has been developed in previous years. This is the coherence and focus that the Common Core State Standards call for. Teach to mastery is structured for mastery learning. Rather than repeating topics, students master them in a grade level, and subsequent grades develop them to more advanced levels. Students continue to practice all the operations with whole numbers in every grade in the context of problem solving and deep applications. Focus on number, geometry, and measurement in elementary grades

Mathematics experiences in early childhood settings should concentrate on (1) number (which includes whole number, operations, and relations) and (2) geometry, spatial relations, and measurement, with more mathematics learning time devoted to number than to other topics. In first grade, students learn the teen numbers and math facts through place value. In all the grades, operations are taught with place value materials so students understand how the standard algorithms work. Even the mental math that is taught uses understanding of place value to model how mental arithmetic can be understood and done. Curriculum must include both conceptual understanding and procedural fluency. The Standards for Mathematical Content are a balanced combination of procedure and understanding. One hallmark of mathematical understanding is the ability to justify in a way appropriate to the student’s mathematical maturity. Instruction should model and enable students to solve problems, as well as justify their solutions. In addition to journal questions and other explicit opportunities to explain their thinking, students are systematically taught to use visual diagrams to represent mathematical relationships in such a way as to not only accurately solve problems, but also to explain their thinking.