in elementary school, students embark on the long path to the fluent rational
number reasoning that they need to succeed in high school mathematics (algebra
and beyond). The path begins with reasoning with multiplication and
division—with whole numbers. But later on, as middle grades and high school
teachers know, division and multiplication—of fractions—seems to become a beast
that few students can tame: the troll lurking under the bridges along the road
to success in algebra.
This course on Division and Multiplication of Whole Numbers introduces a learning trajectory approach to students’ multiplicative reasoning, exploring a stronger conceptual basis for multiplicative reasoning, so that, eventually, multiplication and division of fractions is an extension of multiplication and division of whole numbers, instead of a new and mystifying monster of its own. Together we explore how students begin to recognize contextual problems and model with multiplication and division problems, to properties and number facts, and back again with increasing understanding. And we identify where some of the key misconceptions are hiding.
We recommend this course for elementary and middle grades educators seeking to understand student multiplicative reasoning—how students make their own mathematical distinctions when reasoning with multiple contexts for multiplication and division—helping their students move beyond repeated addition early, instead of too late.
View Full Series Description Video
View Informational Videos on Learning Trajectories and the Common Core
|Course Outline||Major Goals for Participants||The MLT Team||Acknowledgments|
|The MOOC-Ed Learning Experience||Frequently Asked Questions||Privacy and Terms|
The MLT MOOC-Ed series is brought to you by the GISMO Research Group at the Friday Institute for Educational Innovation at NC State University, led by Dr. Jere Confrey and Dr. Alan Maloney. The MLT team will provide instructions, suggest resources, contribute to discussions, and answer questions from course participants in each lesson in the course.