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Psychology is one of the important foundations of education as it essentially covers scientific studies on human development and cognitive processes. When contextualized in the area of mathematics education, it enables us to understand how learners develop an understanding of quantities and the cognitive processes involved in acquiring skills and enduring understanding of mathematical concepts and processes.
Nature of Mathematics Learners
In his paper, Psychological Foundations in Teaching Mathematics, Marlow Ediger emphasized the need for every Mathematics teacher to study various theories in psychology in order to understand the learners and in order to give them maximum support in learning Mathematics. He argued that Mathematics teachers should develop an understanding of theories of learning in Mathematics which include B.F. Skinner’s Operant Conditioning, James Popham’s Behaviorism, Robert Gagne’s Task Analysis, Jerome Bruner’s Structure of Knowledge, Jean Piaget’s Developmental Psychology, and John Dewey’s Utilitarian Mathematics.
B.F. Skinner puts emphasis on a highly structured curriculum wherein the learners achieve the objectives with fewer errors when they are arranged in ascending level of difficulty. Popham, on the other hand, believed that Mathematics instruction should be driven by measurements defined by a set of behaviorally stated objectives. Gagne provided a more open-ended approach than those of Skinner’s and Popham’s. For Gagne, the objectives written by the teachers should be arranged in ascending order of complexity. Bruner emphasized that pupils on any grade level attain structural ideas in Mathematics while Piaget argues the importance of providing lessons and materials to the learners according to their level of maturity. Dewey, who is known for his pragmatic philosophy in education, advocated a problem-solving approach where the learners identify and solve problems that are pragmatic.
When you expose a student to mathematical concepts and processes that are too complex for his/her level, it could lead to frustrations. Instead of learning Mathematics at the finest of its beauty and application, we could end up tormenting the child's potential to love Mathematics and embrace the many learning opportunities embedded within the subject. The content of Mathematics should be arranged according to the readiness of the student. Personally, as a teacher, I like to assess my students' readiness for the content when I handle tutorial sessions. This will allow me to understand the student's readiness and the type of materials that I should be providing. When I notice that a student is having difficulty understanding complex concepts, I look back to the foundation of the child. One's inability to factor polynomial expressions in Algebra could be a result of the students' lack of mastery in multiplying polynomials which is an essential learning requisite in understanding factoring.
While the question "Why do we teach Mathematics?" can be answered by the philosophical foundations of Mathematics Education, the question "How should we teach Mathematics?" can be answered by the psychological foundations of Mathematics. Thus, mathematics pedagogy as embedded in every Mathematics Curriculum is highly influenced by the psychology behind Mathematics Education.
In the Philippines, the Department of Education emphasized the twin goals of mathematics at the basic education level which are critical thinking and problem-solving. On the other hand, Singapore's Ministry of Education sets its mathematics curriculum's sole target to developing mathematical problem-solving. These targets can be attained by a definite set of skills, attitudes, contents, and other factors that are carefully built together in order to form a cohesive framework in the teaching and learning of mathematics.
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Understanding the framework of Mathematics Education in the context of the Philippines and Singapore, we can see how psychology forms part of the holistic framework. According to Eideger, the goals of the Mathematics curriculum are to engage the learners in the process of critical thinking and creative thinking through solving problems that are relevant and exploring creative ways to solve these problems. Ediger also made mention an array of teaching approaches and strategies to engage the learners in the process. Some of these strategies are induction, deduction, differentiated instruction, provision of extrinsic and intrinsic motivation to sustain the learners’ interest, and maintaining a sundry of persona to eradicate monotony in the class. These are all intertwined in the Mathematics Education frameworks of the Philippines and Singapore.
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In the Philippines, we grow up in a society where Mathematics is considered difficult if not impossible and that developing anxiety towards Mathematics is almost a norm. With a stigma attached to Mathematics, it is a necessity for every Mathematics teacher to develop a deeper understanding of Mathematics and its underlying pedagogical principles in order to effectively communicate it to the learners and lead them to the wonders of Math.
Ediger’s idea that Mathematics teachers need to guide learners to engage in higher levels of cognition when using meaningful materials for learners is relevant in the times wherein Mathematics is sometimes perceived as a subject composed merely of formulas and sets of defined processes. In such a case, learners are taught to memorize formulas and steps in solving problems instead of engaging them in critical thinking and creative thinking. A popular misconception about Mathematics is that it is a subject that does not require so much creativity due to well-defined rules and algorithms and that there is always singularity when it comes to arriving at the right answer. However, Ediger emphasized how creative thinking can be practiced in Mathematics by allowing the learners to explore various algorithms and have them familiarize the diversity of the solution. Comparing the various algorithms also enhances critical thinking and the learners’ ability to transfer knowledge in other situations such as solving real-life problems.
The various learning theories presented in the article shed light on the current practices in Mathematics teaching. Teaching Mathematics for a long period of time without any update or refresher on the pedagogical principles would make one forget the very motivation for doing these practices in Mathematics Curriculum and Instruction. Honestly, as I repeatedly wrote down various curriculum maps and instructional plans the past years, I somehow forgot the very reason why we had to structure our curriculum and lesson plan in such a way. All I know was it has always been the standard set by various accreditation bodies in order to ensure that we get to our respective targets. However, as I read through the various theories in the article, it gave me moments of eureka that, after all, these are the bases of how we have been structuring our curriculum and our lesson plan.
In conclusion, I strongly recommend all Mathematics teachers read the full article to gain significant insights on how the Mathematics curriculum is designed and why instructional plans are structured that way.