Information to Describe and Become Outstanding Professional Mathematics Educators

Introduction

This article focuses on mathematics and pedagogy related to what professional math teachers need to know to teach and learn mathematics. While a professional educator's knowledge base and conceptual framework model generally includes, What teachers and students need to know. It leaves the specifics of that knowledge and how best to teach different ideas to be delineated elsewhere. The focus here: is to explore how professional math educator's identify what is essential for math literacy and how it fits with the development of a professional educator's knowledge base and conceptual framework to facilitate mathematical learning.

How to develop as a professional math educators

Two basic things are needed:

  1. A process for professional math development. A process that guarantees genuine planning and decision making that combines our understandings with current research and wisdom of practice to verify or improve the decision we make to teach and have a positve affect on our student's development of mathematical literacy. This includes a considerable amount of information to use to make the numerous and complex decisions professional educators make to facilitate mathematical literacy.
  2. A description of the mathematical knowledge, processes, and dispositions necessary for professional educator to know to facilitate mathematical literacy. (mathematical knowledge base and mathematical conceptual framework)

What process?

A process to inquire and reflect on what outstanding teachers know and do to facilitate student learning and the dispositions necessary to be successful.

A reflective cycle begins with a person's present understandings and practices.

We must know and describe the beliefs, assumptions, and philosophies, that are the basis for our goals and how to use these ideas to base our reasoning for the selection of our practices and assess the consequences of those practices to benefit students.

Further it notes how decisions are informed by research and wisdom of practice. It is through reflection on the differences and similarities that lead us to seek and implement beneficial change or not to meet the needs of our students.

This model suggests how we, educators, use a learning cycle as a process to explore focus questions to facilitate our professional development. Professional development cycle

What do professional educators need to know and be able to do?

There are three kinds of knowledge professional math educators use when making decisions:

All three are important, our focus here is on how math educators facilitate mathematical literacy. To do so, consider these focus questions derived from the professional development model:

  1. What is mathematics?
  2. What do people need to know to use mathematics - be mathematically literate?
  3. How do we assess what people know about mathematics - math literacy?
  4. How do children, adolescents, and adults learn mathematics - become math literate?
  5. How do we facilitate peoples understanding of math literacy?
  6. How do we improve our understanding of mathematics and how do we help others improve their understandings?

The missing details?

The big ideas represented in these questions are enormous and how we answer them is our professional mathematics conceptual framework. The details and its systematic organization has been described in many publications. Outstanding teachers have much of this information stored in their memory so they can make decisions on the fly to facilitate mathematical learning. If we don't acknowledge and systematically study and learn about these big ideas, then our decisions will be poorer and students less likely to learn.

Therefore, outstanding math educators construct a comprehensive understanding of pedagogy and how to use this understanding to facilitate math literacy. The amount and quality of information a person has in both areas directly relates to the quality and number of choices available for their decision making. Which in turn increases or decreases the likelihood of success for our students and ourselves as educators.

Let's consider what a comprehensive view of math content in a mathematical conceptual framework would include ...

What is Mathematics?

Define Mathematics and Mathematical Literacy

If we define mathematics as a body of knowledge accumulated by human activity to organize and interpret reality with the use of numbers, symbols, and relationships, then, we should ask: does that definition capture the importance of doing mathematics as a necessary activity to understand the world?

Does it center the definition on the importance of the knowledge of doing mathematics for mathematically literacy? Authors of the Young Mathematicians at Work series emphasize the importance of mathematics as a human activity of organizing and interpreting reality mathematically by using the verb Mathematizing through out their writings.

This list of math definitions includes a variety of definitions of mathematics to review. I would suggest that we must select one that includes a powerful representation for the doing of mathematics and its use to explain the world.

A person's mathematical literacy is an individual's ability to use mathematics in the real world.

Once a definition is selected, the next step is to identify what a mathematically literate person needs to know and do to be mathematically literate.

Mathematical content:

Many people and groups have worked for years to identify mathematical content. Groups such as: the National Council of Teachers of Mathematics (NCTM), Project 2061, State governments separately and collectively represented in the Common Core State Standards of Mathematics and others.

The content in these documents can be classified into big categories such as:

Math Knowledge Base

The National Council Teachers of Mathematics (NCTM) organizes their standards with two big categories - mathematical processes and mathematical content. Each with five sub categories:

Common Core State Standards - Organize their categories into two big areas: Standards for Mathematical Practice and Standards for Mathematical Content.

Project 2061 (AAAS) - Initial source - Science for All Americans. YES, I know the title is science, but it includes mathematics as well as other areas besides science.

Each of us has our own ideas of what mathematics is (mathematical literacy). Whether we have it in a mental map or outlined on paper or electronically.

Therefore, if we haven't document our ideas, we should. We don't have to create it from scratch. We can review the documents above or other and use them as is, or cut and paste to create our map or outline of what we believe needs to be known and done to be mathematically literate. Our mathematical conceptual framework for mathematical literacy. To do so will allow us to teach more effectively and confidently.

My mathematical conceptual framework is outlined with categories adapted from NCTM and AAAS: big ideas: dispositions, processes, & content. Written as concepts and outcomes necessary to be mathematically literate. We can be use it to reflect on our mathematical knowledge to plan and facilitate student's mathematical literacy and to edit it as we develop professionally as described in our professional development model.

While being mathematically literate is necessary to teach mathematics, the real reason we develop as teachers is to teach, which brings us to planning and teaching to facilitate math literacy.

Continue exploring professional development with these resources on how people learn math, how to plan, and how to teach mathematics.

Dr. Robert Sweetland's notes
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