Welcome to the wonderful world of mathematics for young children! It is a world of creativity
and imagination. This course examines key concepts, strategies and skills in early childhood mathematics curriculum. Topics include constructive way of learning mathematics, general principles of teaching mathematics, early Number concepts and Number sense, Estimation and mental computation, Algebraic Reasoning, Data and Chance; Geometry; Measurement; Numeration and Order; Patterns, Sequences; Operations; and Reference Frames. There will be an emphasis on problem-solving, reasoning and proof, communication and representation of ideas. The course also addresses state and national standards in early childhood mathematics, and discusses uses of manipulative and technology in the classroom.
There has been a body of research that indicates that teachers’ beliefs about mathematics and their knowledge of how students learn mathematics can influence their teaching effectiveness. This class will focus on students’ learning of mathematics. The view of mathematics that will be taken in this course is different from that with which many of you have grown up. Rather than viewing mathematics as a collection of rules to be followed, we will view mathematics as a creative and cooperative endeavor that students can only come to understand by building upon their existing knowledge. Furthermore, mathematical concepts are not learned in a single day, but rather develop over time. This course will not complete your education in learning how to teach mathematics. Rather, it is but one stage in a continuing evolution of yourself as a mathematics teacher. By the end of this course, it is my hope that you will begin to see yourself as an intelligent consumer of mathematics education and will have developed the ability to ask the important questions that will guide you in developing the mathematics curriculum for the students you teach.
B. COURSE GOALS/OBJECTIVES
1. Integrate the National Council of Teachers of Mathematics and the New York State Standards regarding the teaching and learning of early childhood mathematics, and plan instruction that follows these recommendations [NYS v,vii,ix, INTASC 1,3,4,7,8,9, ACEI 1,2D; NAEYC 1,4];
2. Review and study topics in the b-2 mathematics curriculum and their development in the elementary school program [NYS v,vii,ix, INTASC I, 3, ACEI 2D; NAEYC 1,4];
3. View mathematics as a science and process of making sense of the world around them [NYS ix, INTASCI 1, ACEI 2D; NAEYC 1,4];
4. Integrate a wide variety of activities and manipulative materials that engage students in reflective thought [NYS v,vii, INTASC I,3,4,8,9, ACEI 3C; NAEYC 1,4];
5. Identify classroom teaching/learning problems and to propose possible solutions
[ NYS v,vii, INTASC 3,7,8, 9, ACEI 2A,2D; NAEYC 1,4];
6. Engage in designing activities and assessing student achievement [NYS v,vii, INTASC I,3,4,7,8,9, ACEI 2A, 4; NAEYC 1,4];
There are three “big” ideas I hope that you take from this course:
1. School mathematics is the science and process of making sense of things. Mathematics is a verb: it involves investigating, verifying, exploring, explaining, discovering, conjecturing, describing, etc.
2. The most significant factor in helping children learn mathematics is to provide tasks or activities where children are actively engaged in reflective thought.
3. Mathematics is fun and enjoyable, both to learn and teach. It is not boring nor does it consist of mindless and tediously repetitious tasks.