Introduction

achieved by the end of the unit. They also decide what evidence will be gatheredfrom students to demonstrate the successful attainment of the required learning,and they determine the criteria that will be used to ascertain levels of achievement.Sometimes the evidence at the end of a unit can be a student’s representation andexplanation of a concept using a geoboard, pattern blocks, or another manipulative.It need not be a long, complex task based on a scenario.In making a unit or short-term plan for mathematics, teachers need to consider thefollowing questions:• How will I determine the prior knowledge that my students bring?Often the use of an introductory activity from a previous grade or unit can behelpful in determining students’ level of understanding of a concept. Anothereffective strategy can be brainstorming or mind mapping the concept. Forexample, the teacher might ask: “What do you know about two-dimensionalshapes? Write and draw everything you know.”• What are the conceptual understandings and procedural knowledge(key concepts) that I want students in my class to know at the end ofthis unit?Teachers need to become familiar with the key concepts underlying the expectationsoutlined in the relevant strand of the mathematics curriculum and shouldstructure their lessons around those key concepts.• How will I structure a series of lessons (subtasks) to help my studentsexplore and learn these concepts?Over the course of the lessons in a unit, teachers should use a variety of opportunitiesfor shared, guided, and independent mathematics. This does not mean thatall three instructional approaches must occur in each lesson, but that there shouldbe a balance of all three over the series of lessons. All students benefit fromopportunities to learn along with others (shared mathematics), to learn in aguided situation (guided mathematics), and to learn on their own (independentmathematics). See Chapter 4: Instructional Approaches.Lessons should focus on problem-solving tasks and include multiple opportunitiesfor students to use manipulatives, pictures, and charts in modelling mathematicalconcepts and demonstrating their understanding of concepts. The lessons in a unitshould also include multiple opportunities for students to communicate throughtalk with their peers and with the teacher, and include opportunities for studentsto connect their conceptual understanding with mathematical procedures.Finally, teachers need to establish criteria for the successful completion of tasks.50 A Guide to Effective Instruction in Mathematics, Kindergarten to Grade 6 – Volume One