Welcome to this four-part series on Measurement and Spatial Sense. In this series we explore:
● What it means to measure - milestones and misconceptions;
● The meaning of a unit and our metric system;
● An understanding of scales and measurement tools;
● The movement between spatial geometric relationships and measurement formulas.
Videos, readings, tasks and discussion prompts guide the learning, inform conversations, and invite you to test these ideas with students to apply and deepen the learning. Move through the four parts at your own pace. It's not a race so feel free to take your time and linger in areas that you find most rewarding. Perhaps not surprisingly, it's typically more enjoyable to learn with a friend or a team so consider who you might invite to join you.
Thank you for your interest in this topic and your willingness to work through these ideas. We hope you enjoy the learning and find it useful as we work to strengthen mathematics achievement and well being for all.
Craig and Patrick
Session 1: What does it mean to measure?
What exactly is measurement? And why do students, from elementary to secondary, find it so challenging, especially when it is used so often in daily life? Building on some of the thinking from the Small and Northern Board project, this session uses video, online facilitation and google sharing environments to describe key measurement milestones that develop across the grades, examine how measurement differs from counting and explore some rather shocking – but all too common – misconceptions that student may hold because they have lost measurement’s connection to spatial reasoning.
It seems basic enough, but deeply understanding the meaning of a unit lies at the heart of understanding what it means to measure. And it’s not as straightforward as we might imagine! In this session we will explore big ideas underpinning the concept of a unit and some strategies to help students move from comparing to measuring. We will look at the role of accuracy, precision and estimation, the challenge of gaps and overlap, the differences between standard and non-standard units and relationships between and among our metric system – all from a spatial perspective.
Tired of seeing students do the protractor shuffle as they try to figure out the measure of an angle? Shocked at hearing that well over half of our grade six students have significant difficulties measuring a length when given a broken ruler? Maybe it’s because using a measurement tool is far more complex than we thought and for many students there are critical concepts missing in their understanding. This session will delve deeper into this idea and have us build our own scales and measuring devices in order to better understand and help students use the tools of the measurement trade.
In the minds of many people – and students – measurement comes down to memorizing disconnected formulas. And that’s unfortunate because any formula is really just the final “ah ha moment” of recognizing very cool spatial relationships that exist among shapes and between attributes. Together we will explore these relationships and strategies for how students can reduce their myriad of area and volume formulas to a singular idea.