Information and procedures for describing and becoming an outstanding professional Mathemtics educator
(last update Monday, March 5, 2007)
How can I develop as a professional mathematics teacher?
The answer is complex and requires linking many ideas together to create big important and powerful ideas. When these ideas are recalled later an explosion of ideas is triggered that allows access to information previously constructed and carefully connected in a logical consistent manner according to present beliefs and understandings. The amount and quality of information accessed in this explosion is directly related to the kinds and number of solutions available when decisions are required and the likelihood successful results will be achieved. If sufficient time is not invested in selecting, weeding, and connecting ideas a hodgepodge of ideas is like junk in a drawer and selecting an idea to use is like playing the lottery, results depend on luck or odds that are stacked against success. An example of a mapping with five big ideas and connections for a professional educator.
The big powerful ideas for the educator are on the left. There are five of them. They are the same five ideas that is the core of what educators need to know about and do. The following questions and answers connect to one or more of those five as it relates to a professional educator and more specifically a professional mathematics educator.
What is it that professional mathematics educators need to be able to know and do?
The immediately obvious and singular answer is usually know mathematics. Then sometimes as an after thought a person might add and probably something about teaching and learning (pedagogy) mathematics. So a place to start is with mathematics.
What is mathematics?
There are many defininitions of what is included in mathematics. A simple notion is using numbers to explain the world. A person could argue that number operations and all the other ideas used in mathematics is nothing more than an attempt to represent what we have observed and provide an explanation to understand it.
Isn't it more complicated than that?
Not much. Mathematics, at its naked beginnings, is the attempt to explain something in the world with numbers. Thinking and reasoning about quantities, and using them to represent and explain events and observations. Anyone reading this, has done that successfully for many years in a variety of ways. Mathematics is NOT the formulas students have memorized, or equations used to guide rockets with men inside to the moon, or PI calculated to millions of decimal places. It is the process used to communicate patterns in the world and events with numerical representations and explanations. Ideas on -> subject knowledge.
What is needed?
To continue professional development two basic things are used: 1. a procedure for professional development and 2. a description of the knowledge, skills and attitudes professional mathemtics educators exhibit.
A procedure to inquire and reflect on what outstanding mathemtics teachers know and do to facilitate student learning, and the attitudes that are helpful to achieve that success. The procedure is to reflect on your present understandings and practices, describe what they are and the rationale for the selection of each practice, and its consequences for students. This information can be compared to what other professional mathematics educators know and do and by reflecting on the differences and similarities a person can decide a course of action. The process --> mapped.
How can I start?
Generate questions or ideas about what mathemtics educators should know, be able to do, and what attitudes will increase their likelihood of success. Next organize the list into categories. Five categories can be created using the following questions: If any questions of ideas do seem to fit within these areas, one of two things can be done. First, another category can be created or second, one of the existing categories can be broadened. Below an example of how the second is accomplished is discussed for the first two.
Categories Based on Possible Focus Questions
What is mathematics? What is mathematical literacy? How do children, adolescents, and adults learn mathematics and become mathematical literate? How is mathematical literacy assessed? How is mathematical literacy facilitated? How do mathematics teachers develop professional?
What do I know or can find out about what outstanding teachers know or do for each of these?
Of course if you are or will take a mathematics methods class, that is much of what is hoped to be accomplish. However, professional educators continually strive to understand more in each of these areas during their careers. It would be nice if all of these could be dealt with simultaneously the way that a teacher seems to be doing when he or she is in the act of teaching. However, since most humans focus on one idea at a time each will be studied singularly also. However, keep in mind that they are not isolated. All are constantly coming together simultaneously in the classroom.
Forget mathematics and think about mathematical literacy?
The adventure includes a quest to know in detail many dimensions of mathematical literacy. Yes, mathematical literacy. A defintion of mathematics can set us in the appropriate direction, but unless that definition is a list of all the core mathematical ideas and at least hints at what each can do, how it can be achieved, when it has been useful and when it might be useful again, then it isn't sufficient for what professional educators need to know. The National Council of Teacher of Mathematics (NCTM) and Project 2061 both uderstood this and created documentation to describe mathemtical literacy and contnue to create and collect information on how to achieve it. The NCTM Standards Documents and Project 2061 Science for All Americans attempt to describe mathematical literacy. So the more useful and powerful question is: what is mathematical literacy? Definitions can still be used, but they are now a subcategory of mathematical literacy. Doing this reduces the categories from six to five.
Information at this link provides a way to explore different dimensions of mathematical literacy and the similar and different categories used in different documents by different people and organizations. A professional educator upon hearing mathematical literacy will have a brain explosion that results in linking dimensions with categories through generalizations, concepts, and facts. A brain burst should include dimensions of content, processes, attitudes, and perspectives. With content categories of number value, geometry, algebra and patterns, data analysis, and probability. Processes of inquiry to include how to create and identify problems, represent them mathematically, use a problem solving heuristic and strategies to solve problems. Attitudes to include curiosity, persistence, skepticism, open-minded, and wonderment. Perspectives to include connections of mathematics within mathematics and to the real world. Kinds of patterns and events that can be better communicated and understood with mathematics and the different wasy to represent them.
What do outstanding teachers know about how children, adolescents, and adults become mathematically literate and what can prevent that from happening and how do they use that knowledge?
-> Learning theory -> Inquiry -> Development ->
Sequences of understanding and other content links at these directories ->
-> data analysis/ probability -> geometry/ spatial reasoning -> measurement -> number values -> patterns and algebra <-
How do outstanding teachers facilitate mathematical literacy?
-> questioning -> instructional strategies -> directions -> learning cycle -> cooperative learning -> commonknowledge construction theory ->
How do outstanding teachers sequence and assess mathematical understandings?
-> assessment -> accommodation for learning and assessment ->
How do outstanding teachers continue to develop professionally?
-> ideas -> principled procedure mathematics ->
All this information will help to develop a mathematics education position paper and portfolio.
Dr. Robert Sweetland's Notes ©