Conceptual Framework of Mathematics PDF

# Conceptual Framework of Mathematics ## Objectives: - Understand the conceptual framework of mathematics education in the Philippines. - Identify the different skills needed to develop critical thinking and problem solving. - Define and understand the different theories to learn the different ski...

# Conceptual Framework of Mathematics ## Objectives: - Understand the conceptual framework of mathematics education in the Philippines. - Identify the different skills needed to develop critical thinking and problem solving. - Define and understand the different theories to learn the different skills in mathematics. - Compare the different standards from kinder level to grade level. ## Conceptual Framework The conceptual framework is visualized as a five-point star with the title "Critical Thinking and Problem Solving" in the center and the following points: - **Content:** - Numbers and Number Sense - Measurement - Geometry - Patterns and Algebra - Statistics and Probability - **Experiential and Situated Learning** - **Reflective Learning** - **Constructivism** - **Cooperative Learning** - **Discovery and Inquiry-Based Learning** - **Contexts:** - Language - Culture - Learner's Prior Knowledge & Experiences - **Skills and Processes:** - Knowing and understanding - Estimating, computing and solving; visualizing and modeling - Representing and communicating - Conjecturing, reasoning, proving, and decision-making - Applying and connecting ## Mathematics is a Skill Subject - Mathematics from k-10 is a skills subject. - It is all about quantites, shapes and figures, functions, logic, and reasoning. - Mathematics is also a tool of science and a language complete with its own notations and symbols and "grammar" rules, with which concepts and ideas are effectively expressed. ## Twin Goals of Mathematics The twin goals of mathematics in the basic education levels, K-10, are Critical Thinking and Problem Solving. - **Critical thinking** (Scrivin and Paul, 1987) is the intellectually disciplined process of actively and skillfully conceptualizing, applying, analyzing, synthesizing, and/or evaluating information gathered from, or generated by, observation, experience, reflection, reasoning, or communication, as a guide to belief and action. - **Mathematical Problem Solving** (Polya, 1945 & 1962) is finding a way around a difficulty, around an obstacle, and finding a solution to a problem solving ## Content Areas in Mathematics - There are five content areas in the curriculum, adopted from the framework prepared by MATHTED & SEI (2020). ### Numbers and Number Sense - Includes concepts of numbers, properties, operations, estimation, and their application. ### Measurement - Includes the use of numbers and measures to describe, understand, and compare mathematical and concrete objects. - It focuses on attributes such as length, mass and weight, capacity, time, money, and temperature, as well as applications involving perimeter, area, surface area volume, and angle measure. ### Geometry - Includes properties of two and three-dimensional figures and their relationships, spatial visualization, reasoning, and geometric modelling and proofs. ### Patterns and Algebra - Studies patterns, relationships, and changes among shapes and quantities - Includes the use of algebraic notations and symbols, equations, and most importantly, functions, to represent and analyze relationships. ### Statistics and Probability - Develops skills in collecting and organizing data using charts, tables, and graphs; understanding, analyzing and interpreting data; dealing with uncertainly; and making predictions about outcomes. ## Skills and Processes - The specific skills and processes to be developed are: - Knowing and understanding - Estimating, computing and solving; visualizing and modeling - Representing and communicating - Conjecturing, reasoning, proving, and decision-making - Applying and connecting ## Values and Attitudes - The following values and attitudes are to be honed as well: - Accuracy - Creativity - Objectively - Perseverance - Productivity ## Tools in Mathematics Education - We recognize that the use of appropriate tools is necessary in teaching mathematics. - Manipulate objects - Measuring devices - Calculators and computers - Smart phones and tablet PCs - The internet ## Learning Principles and Theories - The framework is supported by the following underlying learning principles and theories: - Experiential and Situated Learning - Reflective Learning - Constructivism - Cooperative Learning - Discovery and Inquiry-based Learning ### Experiential and Situated Learning - **Experiential Learning** (David Kolb) is learning that occurs by making sense of direct everyday experiences. - **Experiential Learning theory** defines learning as: the process whereby knowledge is created through the transformation of experience. - **Knowledge** results from the combination of grasping and transforming experience: (Kolb 1984, p. 41) - **Situated Learning** (Lave and Wenger) is learning in the same context in which concepts and theories are applied ### Reflective Learning - **Reflective Learning** refers to learning that is facilitated by reflective thinking. - It is not enough that learners encounter real-life situations. - **Deeper learning** occurs when learners are able to think about their experiences and process, these allowing them the opportunity to make sense of and derive meaning from their experiences. ### Constructivism - **Constructivism** is the theory that argues that knowledge is constructed when the learner is able to draw ideas from his/her own experiences and connect to new ideas. ### Cooperative Learning - **Cooperative Learning** puts premium on active learning achieved by working with fellow learners as they all engage in a shared task. ### Discovery Learning and Inquiry-Based Learning - **Discovery Learning and Inquiry-Based Learning** (Bruner, 1961) support the idea that students learn when they make use of personal experiences to discover facts, relationships, and concepts.