Module summary

This marks the end of the module on representing and comparing fractions in elementary mathematics teaching. This module focused on the following core elements of elementary teaching:

• Mathematics: fraction representation, definition, comparing and equivalence
• Student thinking: students’ ideas about and approaches to working with fractions
• Teaching practice: using representations in classroom teaching
• Learning from practice: protocols for learning from images of blackboards and other public recording space

Many of the understandings and skills developed in this module are applicable beyond the teaching of fractions. For example, components of the mathematics in this module, such as the concept of equivalence and the use of definitions, arise in other mathematics topics. Representations are central across mathematics, so skill in connecting, narrating, and using public space is useful in almost every mathematics lesson. Analyzing tasks to unpack the mathematics and to anticipate student thinking are productive strategies for planning any lesson. Further, on-going learning in and from practice further develops the ability to support the learning of all students and to improve the quality of the mathematics they learn.