What are the issues that commonly cause students’ natural abilities and love for mathematics to fade to difficulty and dislike? This course will examine the skills and concepts that form the foundation for understanding mathematics. In addition, it will examine the elements of instruction that have been found to nurture young students’ innate mathematical curiosity, confidence and ability. A primary cause of students’ dislike and/or difficulty with mathematics is that they see little relationship between skills too frequently taught in isolation and the fast-paced, high-interest lives they plug into. Even at this early age, students need to experience mathematics as important, fun and a natural part of their explorations. For this reason, topics in geometry, measurement, data analysis and representation and real-world problem solving are integrated into the three components of this course.
Component One: Counting. The first component builds from a child’s innate ability to distinguish quantities and to react when the number of objects in a small collection has increased or decreased. Normally, this ability develops into counting objects, rote counting, representing these ideas with numbers and operation symbols and a basic understanding of place value. When a student is not showing normal progress developing these skills and understandings, skillful teachers are quick to intervene with research-based strategies that are discussed in this component.
Component Two: Operations of Addition and Subtraction. This component continues with counting strategies as students learn to count-on and count backwards until they develop an understanding of the operations of addition and subtraction. As students grow in their knowledge of place value and ability to manipulate larger numbers, they use these skills to measure, analyze and display data, and to solve problems that bring relevance to their studies.
Component Three: The Foundations of Problem Solving. This final component focuses on the application of these skills and understandings to problem solving. If mathematics is to be valuable to students, it must be a tool to help them explore and make sense of their world. Although all instruction should be presented in the context of a meaningful problem to be solved, this component will focus on strategies to build this important part of a student’s mathematical foundation.