New Paradigms for Mathematics Instruction

The roles of both the instructor and the students are also redefined in the new learning environments. The instructor is no longer the "expert" pouring knowledge into the "novices," or a "coach" who shows students how to do things. The instructors role is to participate in curricular decisions and then guide students doing important mathematics. That is, conceptual based mathematics that uses modeling, is descriptive of real life, involves the analysis of data, requires consideration of assumptions, and involves writing logical arguments and conclusions. This implies that every instructor knows the mathematical world with both breadth and depth. The instructor's role is to facilitate learning by providing a stimulating environment and access to a variety of resources.

Students are no longer viewed as the "recipients" of information, who can absorb knowledge as if by osmosis. Students are expected to engage in the learning process and to establish partnerships with each other and with the instructor.

Why is the Paradigm Shifting in Mathematics?

-- Understanding the Nature of Learning Mathematics.

Traditionally, we have made the assumption that the learning of mathematics is a vertical ladder: one must learn one rung before moving to the next. What we know now is that this is not true. Uri Treisman, mathematics professor at the University of Texas at Austin, has said that mathematics is a "bushy bush" with many branches, not a vertical ladder. We have been withholding from our students the power and enjoyment of mathematics because we make them climb the ladder. In reality, once you have a small set of skills, you can go in many different directions, use your skills, apply your knowledge, and see the utility, power, and even beauty of mathematics.

-- Understanding Student Learning.

Perhaps we now have a better understanding of students and how they learn. The mathematics community acknowledges that student learning needs to be active, collaborative, and meaningful. Research evidence supports that cooperative learning can be appropriate and effective in the learning of mathematics.

-- Technological Tools.

We have access to technological tools that can enable the shift. The traditional approach to the teaching of mathematics has been primarily analytical, the manipulation of symbols. Now a hand-held calculator or computer can even manipulate symbols. Technological tools (i.e., calculators and spread sheets) allow us to approach mathematical concepts graphically and numerically. The power of graphing tools is changing how and what we are teaching. These tools enable us to connect students back to real applications

-- Diversity of Learners.

Our student population is diverse; students have different goals and purposes for taking mathematics courses. Mathematics education is for "all" students and not for an elite group. Our national and international need is for a literate citizenry who has the mathematical skills to function productively in an information-based society. The College Sciences Education Board reminds us, a quality mathematics education for all students is essential for a healthy economy."

-- Societal Pressures are helping mathematics education change.

As a society we are in the information age, which is definitely changing the way we think and, hence, the way we learn. Every message we get from society, from businesses, from the government is that we, as educators, must prepare students to function in the information age.

The feminist movement has changed our understanding of how some people learn. Research indicates that some people are more comfortable learning in a collaborative environment, want to understand the concepts rather than just apply formulas, and need to create their own meaning in mathematics. The information presented has to make sense so they can put it into their own words and fit it into their own world.

The citizenry is beginning to get very involved in community life, both local and global. The "me" era seems to be over. People now want to make commitments to solve the world problems. This has opened the doors to the use of real-life applications in mathematics, issues such as environment, toxic waste, population growth, can be used when presenting concepts and solving problems.

Challenges Facing the Paradigm Shift

-- Facilitating Student Change.

Even if as educators we acknowledge and accept the new learning models, we need to help students understand the learning shift so they can become efficient and effective participants in an active learning environment. We must be aware that some students will not/do not want this shift. Many want a passive environment, where the instructor, as "the expert," lectures and the student passively listens and hopes s/he can regurgitate back enough content to pass the course. Sometimes we believe that what we have done in the past is the right way to doing things. Students are not different.

Students who may have difficulty with the new environments are those who have been successful in the traditional settings; those who are successful symbol manipulators; those who thrive in a competitive environment; those who "want" a passive environment; and those who cling to the ways they have been taught in the past.

-- Providing Instructor Support.

Comprehensive faculty/staff development is one of the keys to a successful paradigm shift to a new mathematics learning and teaching environment. Teachers need support as they begin to function in the new environment. As Treisman has said, "We are asking teachers to teach content they have not learned in ways they have never experienced." Teachers need to be taught new content through interdisciplinary applications, i.e., population models from biology, supply and demand models from economics, etc., and the new teaching strategies, such as writing for learning, use of technology, cooperative learning, and alternative assessment. An environment that promotes collegiality should be provided so that instructors are in contact with fellow educators who are experts in other disciplines.

-- Enabling System Changes.

We must rethink how our system is structured and how it functions. The traditional role of teachers and curriculum developers should be revised. The concepts of loading, learning units, meeting times, length of meeting times, hours per week, etc., must be redefined.

The system has to change to allow for interdisciplinary teaching in active and collaborative learning environments with appropriate technological support. Faculty must be given time and resource support to learn, to attempt pilot projects, to evaluate, and to reflect.