To address our students' struggles with transposition of formulae a 3-hour intensive refresher course was developed at MTU. This approach is based on a peer discussion/instruction method and presents the topic in the following progression:

• developing the concept of an equation and balancing equations (supported by peer discussion);
• addressing misconceptions about handling equations (supported by peer discussion);
• teaching, through explicit instruction, manipulating equations and basic principles of transposition;
• addressing relevant algebraic misconceptions (supported by peer discussion);
• teaching and practising the transposition of harder (more convoluted) formulae.

The teaching sequence comprises a three-lesson plan where Lesson 1 focuses on the main concepts and fundamentals of balancing equations: motivation for transposing formulae; the concept of an equality and balancing scales; inverse operations; common conceptual misconceptions.

The objectives of Lesson 2 are to review and reinforce algebra pre-requisites of transposition (simplifying expressions, distributive law, non-linearity of exponents), to discuss the relevant misconceptions and to present the general approach to rearranging equations. This class also addresses the difficulty of “where to start” which is a common stumbling block with weaker students.

Lesson 3 is dedicated to dealing with harder (more convoluted) formulae involving the use of the distributive law, a subject appearing on both sides of the equation and fractions. Purposeful practice using students’ discipline specific formulae here aims to help students master the skill.

Explore a detailed lesson plan and  student handouts (Handout 1, Handout 2 and Handout 3) with exercises and some concept questions. Also visit the page with more concept questions suitable for peer discussions. PollEverywhere is one of the platforms that can be used for polling students on concept questions.