Table of Contents

Unit 1: Teaching and Learning the Standards for Mathematical Practice

1.2.2 Connecting Content and Practice: Points of Intersection

Girl at projector As discussed previously, the SMP do not exist in isolation; doing and using mathematics involves connecting content and practice. The content standards are based on procedure and on understanding — both are stressed equally.

According to the CCSS for Mathematics, “Expectations that begin with the word “understand” are often especially good opportunities to connect the practices to the content.”

Refer to page 29 of California’s CCSS for Mathematics document for an example of such a standard: Grade 4, Number and Operations — Fractions; Standard 3a: “Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.”

As stated in the CCSS for Mathematics,

Students who lack understanding of a topic may rely on procedures too heavily...In short, a lack of understanding effectively prevents a student from engaging in the mathematical practices. In this respect, those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice. Without understanding, a student may rely on procedures and may not represent problems coherently, justify conclusions, apply the mathematics to other situations, use technology mindfully to work with the mathematics, explain the mathematics accurately to other students, step back for an interview, or deviate from a known procedure to find a shortcut.”

A certain level of understanding is needed in order to employ the SMP to deepen learning. In this standard (Grade 4, Number and Operations—Fractions, Standard 3a), over-reliance on an algorithm may make it impossible for a student to explain, for example, why reference to the same whole is necessary when adding fractions or to build on notions of equivalence or knowledge of unit fractions to justify a solution. Therefore, the concepts delineated at these points of intersection are important as is providing time, resources and focus for their development. Setting the points of intersection as a priority can only lead to improved teaching and learning of mathematics.