Developing Mathematical Knowledge and Skills through the Awareness Approach of Teaching and Learning

摘要

Every object we think of or encounter, whether a natural or human-made, has a regular or irregular shape. In its own intrinsic conceptual design, it has elements of mathematics, science, engineering, and arts, etc., which are part of the object’s geometric shape, form and structure. Geometry is not only an important part of mathematics, but it is also an important part of daily life. However, geometry is challenging for some students, even high-achieving students. One way to help students understand geometry and its relevance in life is to engage students to discover them cognitively, then to research and identify them in real world examples and then to relate them to past, present, and future innovations that improved our way of thinking about ourselves and the world around us. This interdisciplinary activity uses the Developmental Awareness Approach of Teaching and Learning (DAATL) to help students discover principles, acquire knowledge, and learn mathematical concepts including surface area, volume, dimensions, regular and irregular plane figures, solid polygons (regular polygons and polyhedra), thinking design, and graph making, etc. It is designed to help students become acquainted with the most useful and familiar parts of mathematical geometry and its application in daily life through connections with disciplines such as science, engineering, art, design, and social studies. The Development Awareness Approach of Teaching and Learning (DAATL) capitalizes on student's natural curiosity, inclination to comprehend as well as students love of drawing, doodling, painting, thinking and talking. Throughout the learning process, students are engaged in authentic learning activities by real and concrete doing with clear purposes, thinking analytically, and evaluating their understanding of texts and ideas orally, in drawing, and in writing. This approach of teaching and learning has been tried and modified to ensure maximum effectiveness of acquiring understanding of the intended learning concepts. The activities can be used with students in elementary school up to 2-year college levels.