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Conceptual-Framework.pptx
- 1. Chapter 1: Problem Solvingand The Conceptual Framework of the K to 12 Mathematics Curriculum
- 2. K – W– L K (What I know) W (What I want to know) L (What I Learned) 1. 2.
- 3. Learning outcomes: At theend of the lesson students are expected to: Describe the conceptual framework of the k to 12 mathematics curriculum. Explain the pedagogies in teaching Mathematics in their own words. Illustrate the concept of Spiral Approach Observes accuracy and honesty in performing the task
- 4. Nature of Mathematics Mathematicsis a core subject of basic education that encompasses life at any stage.
- 5. Its importance goesbeyond the lesson and the school. It provides learners with the answers to many questions about the world they live in.
- 6. It plays avital role in many fields including natural science, social sciences, engineering finance, and many more. Its application to these fields makes use of new mathematical innovations in which new disciplines are developed.
- 7. Checkpoint! Think of instancesin which Mathematics plays a vital role in your day-to-day life.
- 8. The Conceptual Framework ofthe K to 12 Mathematics Curriculum
- 9. CONCEPTUAL FRAMEWORK an analyticaltool with several variations and contexts. It can be applied in different categories of work where an overall picture is needed.
- 10.
- 11. The Conceptual Framework ofthe K to 12 Mathematics Curriculum
- 13. Twin Goals CRITICAL THINKINGPROBLEM SOLVING
- 14. intellectually disciplined processof 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. CRITICAL THINKING Scriven and Paul (1987)
- 15. finding a wayaround a difficulty, around an obstacle, and finding a solution to a problem that is unknown. PROBLEM SOLVING Polya (1945 & 1962)
- 16. problem solving focusesthe student attention on ideas and sense making rather than memorization of facts develops the student’s s belief that they are capable of doing mathematics and that mathematics makes sense
- 17. teaching through problemsolving is fun and when learning is fun, students have a better chance of remembering it later. it provides ongoing assessment data that can be used to make instructional decisions, help students succeed, and inform parents
- 18. Checkpoint! What is therelationship between critical thinking and problem solving?
- 19.
- 20. learners construct knowledge ratherthan just passively take in information. CONSTRUCTIVISM
- 21. The learner constructsand clarifies meaning in terms of their own understanding and cognition, supporting changes in conceptual perspective. REFLECTIVE LEARNING
- 22. the process wherebyknowledge is created through the transformation of experience. EXPERIENTIAL AND SITUATED LEARNING
- 23. students are encouragedto construct their own knowledge through a self- directed learning process—essentially “instructionless” learning DISCOVERY AND INQUIRY – BASED LEARNING
- 24. the instructional useof small groups to promote students working together to maximize their own and each other's learning COOPERATIVE LEARNING
- 26. Number and Number Sense CONTENTS Measurement GeometryPatterns and Algebra Statistics and Probability
- 27. Knowing and understanding SKILLS ANDPROCESSES Estimating, Computing, Solving Visualizing and Modelling Representing and Communicating
- 28. SKILLS AND PROCESSES Conjecturing,Proving, Reasoning and Decision – Making Applying and Connecting
- 29. Accuracy VALUES AND ATTITUDES Creativity ObjectivityPerseverance Productivity
- 30. Manipulative Objects MATHEMATICAL TOOLS MeasuringDevices Calculators and Computers Smartphones and Tablet PCs Internet
- 31. Beliefs CONTEXTS Environment Language Culture Learner's PriorKnowledge and Experiences
- 33. THE K TO12 MATHEMATICS CORE LEARNING AREA STANDARDS
- 34. The learner demonstratesunderstanding and appreciation of key concepts and principles of mathematics - using appropriate technology in problem solving, critical thinking, communicating, reasoning, making connections, representations, and decisions in real life.
- 35. numbers and number sense measurement wholenumbers up to 20, basic concepts on addition and subtraction time, location, non-standard measures of length, mass and capacity K
- 36. geometry Patterns and algebra statisticsand probability (basic attributes of objects basic concept of sequence and number pairs data collection and tables K
- 37. numbers and number sense measurement wholenumbers up to 100, ordinal numbers up to 10th, money up to PhP100, addition and subtraction of whole numbers, and fractions ½ and ¼ time, non-standard measures of length, mass, and capacity GRADE 1
- 38. geometry Patterns and algebra statisticsand probability 2- and 3- dimensional objects continuous and repeating patterns and number sentences tables, pictographs, and outcomes GRADE 1
- 39. numbers and number sense measurement wholenumbers up to 1000, ordinal numbers up to 20th, money up to PhP100, the four fundamental operation of whole numbers, and unit fraction time, length, mass, and capacity GRADE 2
- 40. geometry Patterns and algebra statisticsand probability basic shapes, symmetry, and tessellations continuous and repeating patterns and number sentences tables, pictographs, and outcomes GRADE 2
- 41. numbers and number sense measurement wholenumbers up to 10 000; ordinal numbers up to 100th; money up to PhP1 000;the four fundamental operations of whole numbers. conversion of time, length, mass and capacity, area of square and rectangle GRADE 3
- 42. geometry Patterns and algebra statisticsand probability lines, symmetry, and tessellations continuous and repeating patterns and number sentences tables, bar graphs, and outcomes GRADE 3
- 43. numbers and number sense measurement wholenumbers up to 100 000, multiplication and division of whole numbers, order of operations, factors and multiples, addition and subtraction of fractions, and basic concepts of decimals including money time, perimeter, area, and volume GRADE 4
- 44. geometry Patterns and algebra statisticsand probability lines, angles, triangles, and quadrilaterals continuous and repeating patterns and number sentences tables, bar graphs, and simple experiments GRADE 4
- 45. numbers and number sense measurement wholenumbers up to 10 000 000, order of operations, factors and multiples, fractions and decimals including money, ratio and proportion, percent time, circumference, area, volume, and temperature GRADE 5
- 46. geometry Patterns and algebra statisticsand probability polygons, circles, solid figures sequence and number sentences tables, line graphs and experimental probability GRADE 5
- 47. numbers and number sense measurement divisibility,order of operations, fractions and decimals including money, ratio and proportion, percent, integers rate, speed, area, surface area, volume, and meter reading GRADE 6
- 48. geometry Patterns and algebra statisticsand probability plane and solid figures sequence, expression, and equation tables, pie graphs, and experimental and theoretical probability GRADE 6
- 49. numbers and number sense measurement geometry setsand real number system conversion of units of measurement sides and angles of polygons GRADE 7
- 50. Patterns and algebra statisticsand probability algebraic expressions and properties of real numbers as applied in linear equations and inequalities in one variable data collection and presentation, and measures of central tendency and variability GRADE 7
- 51. geometry Patterns and algebra statisticsand probability axiomatic structure of geometry, triangle congruence, inequalities in a triangle, and parallel and perpendicular lines factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables probability of simple events GRADE 8
- 52. geometry Patterns and algebra parallelogramsand triangle similarities and basic concepts of trigonometry quadratic equations and inequalities, quadratic functions, rational algebraic equations, variations, and radicals GRADE 9
- 53. geometry Patterns and algebra circlesand coordinate geometry sequences, series, polynomials, polynomial equations, and polynomial functions GRADE 10 statistics and probability combinatorics and probability, and measures of position
- 54. Quarter Grade Level G1 G2G3 G4 G5 G6 Q1 Number & Number Sense Number & Number Sense Number & Number Sense Number & Number Sense Number & Number Sense Number & Number Sense Q2 Number & Number Sense Number & Number Sense Number & Number Sense Number & Number Sense Number & Number Sense Number & Number Sense
- 55. Quarter Grade Level G1 G2G3 G4 G5 G6 Q3 Number & Number Sense Geometr y Patterns and Algebra Number & Number Sense Geometry Patterns and Algebra Number & Number Sense Geometry Patterns and Algebra Geometry Patterns and Algebra Measureme nt Number & Number Sense Geometr y Patterns and Algebra Measure ment Geometr y Patterns and Algebra Measure ment
- 56. Quarter Grade Level G1 G2G3 G4 G5 G6 Q4 Measure ment Statistics and Probabilit y Measure ment Statistics and Probability Measurem ent Statistics and Probability Measureme nt Statistics and Probability Measure ment Statistics and Probabilit y Measure ment Statistics and Probabilit y
- 57. Quarter Grade Level G7 G8G9 G10 Q1 Number & Number Sense Patterns and Algebra Patterns and Algebra Patterns and Algebra Q2 Measureme nt Patterns and Algebra Patterns and Algebra Geometry Patterns and Algebra Patterns and Algebra Geometry
- 58. Quarter Grade Level G7 G8G9 G10 Q3 Geometry Geometry Geometry Statistics and Probability Q4 Statistics and Probability Statistics and Probability Geometry Statistics and Probability Statistics and Probability
- 59. Math Concept: TheSpiral Approach The Mathematics K to 12 curriculum is seamless. This ensures smooth transition between grade level and a continuum of competencies through spiral progression where learning of knowledge, skills, values, and attitudes increases in depth and breadth.
- 60. Math Concept: TheSpiral Approach There is also continuity of competencies and standards from elementary to secondary level through a unified curriculum framework.
- 61. Math Concept: TheSpiral Approach The unified standards and competencies ensure integration of what learners learn across grade levels and across learning areas for a more meaningful learning. Below is an example of spiraling of concepts about Numbers and Number Sense and Geometry from Kindergarten to Grade 3.
- 62. Kindergarten Grade 1Grade 2 Grade 3 Numbers and Numbers Sense Demonstrate understanding of key concepts of sets and the relationship between numbers and quantities up to 20. Demonstrate an understanding of key concepts of numbers. Demonstrates an understanding of the concepts of whole numbers up to 1000 Demonstrate an understanding of key concepts of numbers
- 63. Kindergarten Grade 1Grade 2 Grade 3 Geometry Begins to identify the common attributes of an object and the common 2 to 3 dimensional objects in the environment. Demonstrates an understanding of 2- dimensional and 3- dimensional shapes. Demonstrates an understanding of 2dimensional and 3dimensional shapes. Demonstrates an understanding of 2dimensional and 3dimensional shapes.
- 64.
- 65. ACTIVIT TIME! Instruction: Bringout 1/2 sheet of paper and answer the following activities. 1. Describe the conceptual framework in the k to 12 mathematics curriculum in your own words. At least 5 sentences.
- 66. ACTIVIT TIME! 2. Choose2 pedagogies and explain why these should be given more emphasis in teaching Mathematics. 3. Create a spiral and input the lessons that should be discussed in statistics from Grade 6 to Grade 8 on the spaces between the curves. Below your drawing/illustration, explain the spiral concept.