Pedagogical Shifts: A Framework in the Teaching of Mathematics across levels

Jenie R. Dimarucut

Mathematics is defined as a study of patterns and relationships; a way of thinking; an art, characterized by order and internal consistency; a language, using carefully defined terms and symbols; and a tool for sciences and other disciplines. With regards on these definitions, Mathematics teaching aims to develop problem solving abilities, reasoning abilities, conceptual and procedural knowledge, positive attitudes, and abilities to work and communicate with others. Also, the NCTM made its goals for mathematics Education, these goals include: to value mathematics, to reason mathematically, to communicate mathematics, to solve problems, and to develop confidence.

On the other hand, a lot of theories and approaches are concerned in teaching mathematics, one is the theory of Constructivism which is a philosophy of learning founded on the premise that, by reflecting on our experiences, we construct our own understanding of the world we live in. Each of us generates our won “rules” and “mental models” which we use to make sense of our experiences. Learning, therefore, is simply the process of adjusting our mental mode to accommodate new experiences. Constructivism is basically a theory on observation and scientific study about how people learn. It says that people construct their own understanding and knowledge of the world, through experiencing things and reflecting on those experiences. When we encounter we encounter something new, we have to reconcile it with our previous ideas and experiences. This may mean changing what we believe, or simply ignoring the new information, which we may consider irrelevant. In any case, we are active creators of our knowledge.

We also have the two contrasting approaches by Bernardo et al. (2003): The Transmissive Approach and Inquiry Approach. The Transmissive approach entails math as well as science as formalized collection of facts, concepts and procedures; it is a mastering concepts and replicating procedures and operations; a teacher controlled, initiation – reply – evaluation pattern; teachers are the authority or transmitter of knowledge; and students have the ability to follow procedural instructions to obtain correct answer. The Inquiry Approach implies science and math as modes of inquiry and problem solving; it is exploration, discovery, conjecturing, proving, problem posing, problems solving and collaboration; there is discussions and negotiations among the students and between students and teachers; teachers are facilitators of students’ inquiry learning; and students have the ability to explain and justify actions on science and math tasks.

Teachers should select the best approach in teaching mathematics considering the students’ needs and abilities. The Inquiry approach is advisable during instruction because after such lesson, students are able to generate his/her solutions to problems; apply problem solutions they learned to novel problems; and think of alternative solutions to one mathematical problem. With regard on these things, an effective teacher must provide an opportunity for students to discover concepts and procedures for themselves; let the students discover the meaning of mathematical concepts by discovery and explorations; let the students understand mathematical operations by exploring tasks; and take student preferences into account when planning lessons.

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The author is SST I at Sapang Bato National High School, Sapang Bato, Angeles

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