MATH 5001, 5002, and 5003 are designed to work together with the mathematics methods courses EMAT 3400 and 3410. In combination, these courses are designed to prepare you to teach elementary school mathematics for understanding, as envisioned by the National Council of Teachers of Mathematics, and as described in their document Principles and Standards for School Mathematics.

Education is consistently cited as a top priority in this country, and improving mathematics education is consistently of special concern. Numerous groups and commissions have studied education and have made recommendations. One consistent conclusion is that the old ways of teaching and learning mathematics are simply not good enough for our advanced technological society: the depth of understanding of mathematics must be improved. The mathematical and scientific talent and potential of far too many children of all ethnicities and backgrounds is going untapped and underdeveloped. Many other countries are doing a better job of teaching children mathematics than we are, and we find ourselves needing to import scientists. The National Council of Teachers of Mathematics (NCTM) has studied extensively how to teach mathematics better in grades Pre-K &endash; 12, and has produced the document Principles and Standards for School Mathematics (PSSM) with recommendations for this purpose. This document is based on the available research, and it is based on the best advice of top teachers, of professors who train teachers, and of mathematicians. It is the best advice currently available, and therefore we must take it seriously. In order to teach to the vision presented in PSSM, prospective teachers will need a far deeper understanding of the mathematics they will teach than has been common in the past.

The new mathematics courses, MATH 5001, 5002, and 5003 have been designed to help meet the challenge of preparing elementary school teachers to teach to the standards of PSSM. These courses have been designed with the aid of faculty in Mathematics Education and in Mathematics; they are based on the currently available literature in mathematics education and on our experiences as teachers and learners. These courses are supported by the faculty in Mathematics, the faculty in Mathematics Education, and the faculty in Elementary Education. We are working together to give you a top quality preparation.

MATH 5001, 5002, and 5003 will examine in depth the mathematics concepts that are taught in elementary school. You will learn to understand and explain "why does it work this way?" or "why can't we solve it that way?" for a variety of situations involving elementary school mathematics. You will learn many different ways of thinking about a variety of mathematical situations. This kind of knowledge is crucial for the depth and flexibility of understanding that you will need in order to teach to the vision of the PSSM. Although you already know elementary school mathematics at a certain level, the courses will challenge you to think about and to explain the material in a new and deeper way. Please don't underestimate the importance of developing this new and deeper understanding. It is hard work to develop this understanding, so please be patient with yourself and with the courses. Even if you do not do well at first, do not give up or lose heart. Sustained effort does pay off and does lead to deeper understanding.

In order to achieve the depth of understanding we are seeking, and therefore, in order to succeed in MATH 5001, 5002, and 5003, you will need to engage yourself in the material and take responsibility for your own learning. Don't be shy about asking questions, but don't be put off if you are asked to continue thinking with a hint or a question. Be willing to try out ideas and to modify them if necessary. Learning for true depth of understanding requires that you be very active in seeking this understanding. Deep conceptual understanding cannot be achieved by passive absorption of the material. Be willing to "get messy and make mistakes". Don't give up when answers don't immediately come to you.

MATH 5001, 5002, and 5003 are not methods courses: they do not discuss how to teach mathematics to children. Despite this, the course material is directly relevant to teaching mathematics in elementary school; in fact, some of the class activities could be modified for use with children, while others examine misconceptions that you may encounter. Your methods courses, EMAT 3400 and 3410, will help you develop an understanding of children as learners and will help you join this understanding of children to the deep content knowledge you will develop in the math courses. Research shows that this kind of blended knowledge of content and pedagogy is important in order to teach for understanding. PSSM recognizes the need for this blended knowledge of content and pedagogy. Research also shows that in other countries where many children excel at mathematics, mathematics is much more likely to be taught for a conceptual understanding, and teachers are much more likely to possess a deep conceptual understanding of the material they teach.

Please be aware that even if your particular interests lie in teaching the youngest children, you will be certified to teach through 5th grade if you complete the Early Childhood Education program. This is true even if you are in the Pre-K&emdash;2 program. If you are in the special education program you will be certified through 12th grade. Furthermore, you may change your mind about what grade level you would like to teach, or you may wind up teaching a different grade level than you hoped for. Also, you should be prepared to challenge all the children you will teach. Therefore it really is important and relevant for you to achieve depth of knowledge in all the content of MATH 5001, 5002, and 5003, even if you may at times feel that you won't ever need this knowledge.

MATH 5001, 5002, and 5003 are our current best effort to provide you with top quality courses that will help prepare you for outstanding teaching. The courses are new and the methods we are using to teach these courses are new to most of us who teach them. We too must think about this material in a new way, we too must learn new ways to teach better for deeper understanding, and we too are challenged. We promise that we will strive to do our best to continually improve these courses and the way we teach them. We will appreciate constructive criticism. We ask that you also strive to do your best and to be open to a new and deeper way of thinking about mathematics.