The Future of Mathematics Education
The Big Question/s:
What do we know about Mathematics in NZ Schools?
Why do many students do not succeed in Mathematics?
What needs to be done to confront obstacles with the subject?
Will technology be an effective instructional medium for Maths education?
Learning Goals:Geometry and arithmetic--thinking and calculating--are not only paradigms of school mathematics but also caricatures of mathematics in the minds of parents. Today, for quite different reasons, neither goal is especially relevant. Although most children learn to calculate well enough, calculators have made this hard-learned skill virtually obsolete. And although high school students still study proofs in geometry, little learned there-and little is all it is-transfers to clarity of thought in other important areas of life.
To help today's students prepare for tomorrow's world, the goals of school mathematics must be appropriate for the demands of a global economy in an age of information.
Social Constructivist Approach: Teacher will always evaluate students’ prior knowledge at the beginning of a lesson. Teacher will guide students to restructure their existing ideas. Teacher gives opportunities for students to apply their ideas. Teacher will guide students to make reflections. Social constructivisms stress the need for collaboration among students and practitioners. Mutual dependence or positive interdependence. Each member is responsible for completing the assigned tasks, mastering the material and explaining the work to the class, group members sit together to discuss and teach what they know to other members, students need to develop listening, respecting others, sharing responsibility.
Reform and Controversy in Maths Education: To begin, there are two terms in this controversy which both sides seem to agree upon their definition. They are "traditional maths" and reform math (modern maths). Modern maths involves a type of curriculum intended to help children discover, understand and integrate knowledge through the independent exploration of mathematics. It is also about how children learn and how to enable students to reach the content goals that are set for them by their teacher. It is hardly ever described as a math curriculum which initially allows students to discover mathematical concepts on their own and then reinforce them with repetition and practice. It has garnered a broad but shallow consensus among the two sides of the controversy and has obviously become a point of conflict which has to win.Traditional maths that is common when today's adults and elders were in school and suggests that children mimic mindlessly what teachers model with the hope that somehow the mimicry will lead to learning. Modern maths have the desire to make math fun and interesting. Teachers let technology, manipulatives, group work/cooperative learning and the use of realistic situations act as the means to the end.
Parents and traditionalists have taken the stance they have in believing there is no place for "modern math" in a mathematics curriculum. These people believe that any change is bad and that mathematics should be taught the traditional way - because that's how they learned it so "their children and grandchildren should learn it the same way. They also feel that widespread testing on computation skills will keep us on the straight and narrow path. Traditionalists have no place for problem-solving of real-world situations in a mathematics curriculum. Traditionalists believe mathematics to be a set of rules, skills and facts that need to be learned, maintained, and drawn upon when and if necessary. Other traditionalists understand mathematics to be "a unified (but static) body of knowledge, with all the parts logically connected, there to be discovered by humans. In essence, the traditionalists support the behaviorist theory of learning which is based on stimulus-response theory. Hence, the teaching is very directive and the classroom is extremely teacher-centered.
Modern Maths is one in which students engage in purposeful activities that grow out of problem situations, requiring reasoning and creative thinking, gathering and applying information, discovering, inventing, and communicating ideas, and testing those ideas through critical reflection and argumentation. On the other hand, the modern maths follows the cognitive theory of learning. Because of this, their teaching is very indirect and the classroom is notably student-centered.
One underlying issue in the controversy, which can be seen as a problem of understanding, is what each side is using as their definition of mathematics.
Effective Instructional Technology for Maths Education: Today, classroom teachers may not have personal experience with the technology and present an additional challenge. In order to integrate technology-based activities and projects in their curriculum, teachers first need to find the time to learn to use the tools and understand the terminology required for participation in projects or activities. They must have the ability to use technology to improve student learning, and to strengthen personal development training.
Educational technology enables students to improve the skills and concepts through multiple representations and advanced visualization. Its benefits include greater accuracy and speed in data collection and graphics, real-time display, the ability to collect and analyze large volumes of data and collaboration data collection and interpretation and presentation of results more varied. The technology is also engaged students higher-order thinking, builds strong problem-solving skills, and develop understanding of the concepts and procedures, when used appropriately.