The
Pacific Standards for Excellence in Mathematics represents the Pacific
mathematics educators' response to the Curriculum and Evaluation Standards
for School Mathematics (National Council of Teachers of Mathematics, (NCTM)1989).
As the Pacific Mathematics Leadership Team, we identified goals for the
Pacific region. We also reviewed the NCTM document with the Pacific region's
environments, cultures, and needs in mind. Relevant recommendations were
adapted from the NCTM document or new standards were created especially
for the Pacific region.
The goals for the Pacific Standards for Excellence in Mathematicswere established with the whole child in mind. They represent what is necessary for our children to be successful in a technological world that changes very quickly, often in ways we could not envision. We must, therefore, educate our students, so that they are capable of meeting new challenges.
The goals of the Pacific standards reflect qualities needed for success in an ever-changing world.
The study of mathematics includes intellectual and aesthetic pursuits. Intellectually, students investigate and explore problem-solving tasks in numerical, statistical, geometrical, and algebraic contexts. Rather than the memorization of step-by-step methods, these tasks encourage students to make their own conjectures and test their hypotheses. New mathematical understandings build on their findings from these explorations. Most importantly, however, students communicate their understandings in their own language instead of language from the textbook. The content knowledge is thus richer and more meaningful to students.
Aesthetically, students discover relationships between the environment and geometrical and numerical concepts. The representation of mathematical concepts in nature and the environment connects learning for children. Additionally, students gain a respect for the beauty of mathematical reasoning, as they engage in problem-solving tasks that are motivating.
The problem-solving focus represented in the standards and associated activities will help students to function in an ever-changing workplace. Even though the problem-solving tasks are mathematical, the solution strategies are used in everyday situations that require decisions to be made. Predicting, sorting out needed from unimportant information, and analyzing solutions in the context of a situation are important characteristics of decision making.
As the Pacific Mathematics Leadership Team drew up the standards, our vision for our students guided our thinking. We first looked at the needs of a demanding work force and society to determine the characteristics of a successful citizen. From there, we identified three goals.
Goal 1: Mathematically literate workers can:
Goal 2: Lifelong learners can:
Goal 3: Informed decisions are made by students who:
Students can productively contribute to society as mathematically literate workers, lifelong learners, and informed decision makers.
The Leadership Team was also aware that, for students to accomplish the three goals, all students must have access to important mathematics. Students should not be separated into groups that receive different content or for whom there are different expectations. We, therefore, added a fourth goal to these standards.
Goal 4: Open mathematics to all students, so that they have opportunities to:
These goals are characterized by dramatic shifts in mathematics education related to content, instruction, and assessment. The content that was once reserved for the top few is now accessible to all students and includes such topics as probability, statistics, discrete mathematics, transformational geometry, functions, and algebra. The instructional methods use student language as the means to develop ideas about the topics. Finally, students demonstrate their mathematical understandings in a variety of ways including projects, journal writings, problem creations, and discussion.
These shifts will require teachers to rethink their concepts about how students learn and what instructional methods promote learning. Lecture and practice have long been the primary instructional approach in mathematics from elementary through secondary classes. The result has been students who are dependent upon the teacher to supply the "correct" method to solve problems and who have little creativity in nonroutine problem solving. With new demands on our students as they enter the work force, we must restructure our schools to provide experiences in mathematical content that extend beyond what has traditionally been a part of mathematics classes.