Course Overview
What is basic about mathematics is that “it makes sense.” Every child, in her or his own way, should come to believe that mathematics makes sense and that she or he is capable of making sense of it. All children should leave school with the confidence of knowing that they understand mathematics and that they are able to do it.
(John A. Van de Walle [2005])
What is true, however, is that many children do not leave school confident in their understanding of mathematics. What is also true is that many teachers entering the profession do not feel confident in their understanding of mathematics and, therefore, do not feel confident in their ability to teach mathematics. This course is designed to mitigate both of these concerns.
To learn how to teach mathematics for understanding first requires an understanding of how students best learn mathematics. Consequently, the main emphasis of EDUC 475 is on the learner. How does a child learn? How does a child learn mathematics? How does one teach to promote such learning? Through a series of readings, online discussions, and assignments as a student in this course you will begin to make sense of what it means to teach mathematics for understanding, not through an emphasis on mathematics, but an emphasis on learning. Of course, this is not to say that you will not engage in mathematics. Mathematics is the context in which this discourse is set and will therefore be a significant part of every discussion.
The topics covered in EDUC 475 can be broken down into three sections: foundations, basic concepts, and practice. These themes are summarized below in the order in which they will be covered.
Foundations
- What it means to develop understanding in mathematics.
- What does it mean to do mathematics?
- Understanding the reform movement in mathematics.
Basic Concepts
- Early number concepts.
- Place value.
- Basic operations (+, –, ×, ÷).
- Whole-number computations.
- Basic facts.
- Number sense and estimation.
- Measurement concepts.
- Geometric thinking and geometric concepts.
- Probability and data analysis.
Practice
- Technology and school mathematics.
- Teaching through problem solving.
- Assessment.
- Inclusion and diversity.
- Planning for effective instruction.
Course Objectives
The objectives of this course are many. I outline them here in point form, in no particular order:
- Enjoy your experience within the course.
- Obtain an enriched understanding of what mathematics is.
- Develop an enriched understanding of what it means to learn and teach mathematics.
- Acquire the tools and techniques necessary to enact these enriched understandings within your classroom practice.
- Make sense of your own past experiences with mathematics.
- Develop a critical eye with which you can make better sense of mathematics classroom practices for the rest of your teaching career.
- Become a teacher who is comfortable working with students within the wonderfully unpredictable realm of mathematical problem solving.
Course Resources
Textbook
Elementary and Middle School Mathematics: Teaching Developmentally by John A. Van de Walle, Karen S. Karp, Jennifer M. Bay-Williams, Lynn M. McGarvey, and Sandra Folk, 4th Canadian Edition (2015).