For DepEd_Mathematics PResentation ELLN.pptx

math presentation

1. On Teaching and Learning Mathematics : Developing & Assessing Math Skills Prof. Leonor Ercillo Diaz, PhD. UP College of Education

2. Outline of the Session How do the K-3 children learn Mathematics? What do they have to learn in Mathematics? (a look into standards, content & competencies) How do we teach and assess Mathematics skills?

3. How do Kids Really Learn Math Is Math a set of answers to questions? Is Math a process of investigation and exploration? Are kids allowed to actively work with materials & ideas? Is short-term success the goal? Do we aim for long term understanding?

4. How do Kids Really Learn Math Is there much rote learning involved? Are we allowing kids to think and figure things out ? Is the goal for future application? Is our purpose immediate application? Are the steps in solving specified by the teacher? Are the students also allowed to discover the steps?

5. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Action Learning is Reaction Learning is Process

6. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Action Cognitive/Constructivist Bruner - Modes of Reality  Enactive - action on reality on concrete ways w/o the need for imagery, inference, or words

7. Math Materials

8. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Action Cognitive/Constructivist Bruner - Modes of Reality  Enactive  Iconic – pictorial need to represent reality; internal imagery that stands for a concept  Symbolic –abstract, arbitrary systems of thought

9. The Gap

10. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Action Cognitive/Constructivist Vygotsky  Zone of Proximal Development The area where the child cannot solve a problem alone but can be successful under adult guidance or in collaboration with a more abled peer.

11. Zone of Proximal Development Upper Limit Instruction through guidance or assistance Lower Limit

12. Break Time: Storytime What are some things that you want more of? Find out why the character says “More for Me”. What does he want more of? At the end of the story, guess the age of the character.

13. Think Back Why does the character say “More for Me”. What does he want more of? Guess the age of the character. What grade is he in? Why do you say so? What are his characteristics?

14. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Action Cognitive/Constructivist (Piaget) Stages of Development  Sensorimotor – actions on objects  Preoperations – actions on reality  Concrete operations -  Formal Operations

15. Pre-operations Stage Egocentrism Centration Irreversible Thought Static Thought

16. Preoperation Concrete Operational Egocentrism Centration Irreversible thought Intuitive thought Lack of : conservation class inclusion transitive interference Can see others have diff. viewpoints Decentration Reversible Thought Dynamic Thought Conservation Class inclusion Transitive Interference

17. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Reaction Behaviorist Reinforcement Theory  Immediate feedback  Programmed learning

18. Immediate Feedback Activities

19. Immediate Feedback Activities

20. Immediate Feedback Activities

21. Information Processing How we encode, store and retrieve information Thought Processing Learning Styles

22. Rewind Time! Which of the next two activities do your pupils answer easier?

23. Activity One

24. Activity Two

25. Information Processing Thought Processing Strategies used to organize and classify new information or skills to obtain order out of a confusing series of stimulus events.

26. If this is your answer……

27. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Process Information Processing Thought Processing  Field-dependent (Simultaneous processing) requires stimulus materials to be presented all at once, seeing the whole before its parts; look for patterns to break down the whole into its respective parts to arrive at a solution

28. If this is your answer…..

29. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Process Information Processing Thought Processing  Field-independent (Successive processing) requires stimulus to be presented from 1 component to the next, leading from detail to detail until the whole is seen; build parts into the whole to arrive at solution

30. Thought Processing Field dependent Field independent

31. Thought Processing Field dependent Field Independent

32. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Process Information Processing Learning Styles Perceptual Factors – Preference for materials presented through one or more of the 5 senses  Visual  Auditory F Tactile

33. Learning Styles: An Overview Perceptual Time Mobility Stimuli Elements Physical

34. Learning Theories with Implications for Math Instruction ( Hatfield, et.al. 1997 ) Learning is Process Gardner’s Multiple Intelligences Nine intelligences

35. Nine Intelligences (Gardner)

36. Learning Theories with Implications for Mathematics Instruction (Hatfield, et.al. 1997) Learning is Action Learning is Reaction Learning is Process Cognitive/Constructivist Behaviorist Information Processing Bruner Modes of Reality  Enactive  Iconic  Symbolic Vygotsky  Zone of Proximal Development Piaget Stages of Development  Sensorimotor  Preoperations  Concrete operations  Formal Operations Reinforcement Theory  Immediate feedback  Programmed learning Thought Processing  Field-dependent (Simultaneous processing)  Field-independent (Successive processing) Learning Styles Perceptual Factors  Visual  Auditory Tactile Gardner Multiple Intelligences

37. Good job! 

38. Standards Kinder The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 20, basic concepts on addition and subtraction); geometry (basic attributes of objects), patterns and algebra (basic concept of sequence and number pairs); measurement (time, location, non-standard measures of length, mass and capacity); and statistics and probability (data collection and tables) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations and decisions in real life.

39. Standards Grade 1 The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 100, ordinal numbers up to 10th, money up to PhP100, addition and subtraction of whole numbers, and fractions ½ and 1/4);geometry (2- and 3-dimensional objects); patterns and algebra (continuous and repeating patterns and number sentences); measurement (time, non-standard measures of length, mass, and capacity);and statistics and probability (tables, pictographs, and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

40. Standards Grade 2 The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 1 000, ordinal numbers up to 20th, money up to PhP100, the four fundamental operations of whole numbers, and unit fractions); geometry (basic shapes, symmetry, and tessellations); patterns and algebra (continuous and repeating patterns and number sentences);measurement (time, length, mass, and capacity); and statistics and probability (tables, pictographs, and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

41. Standards Grade 3 The learner demonstrates understanding and appreciation of key concepts and skills involving numbers and number sense (whole numbers up to 10 000; ordinal numbers up to 100th; money up to PhP1 000;the four fundamental operations of whole numbers; proper and improper fractions; and similar, dissimilar, and equivalent fractions); geometry (lines, symmetry, and tessellations); patterns and algebra (continuous and repeating patterns and number sentences); measurement (conversion of time, length, mass and capacity, area of square and rectangle); and statistics and probability (tables, bar graphs, and outcomes) as applied - using appropriate technology - in critical thinking, problem solving, reasoning, communicating, making connections, representations, and decisions in real life.

42. Content: K-3 Numbers & Number Sense Measurement Geometry Patterns & Algebra Statistics & Probability

43. Building the Concept of Number Counting Rote Counting Rational Counting Writing Numerals

44. Numbers and Counting Rote counting saying from memory the names of the numerals in order. Rational counting attaching the number names in order to items in a group to find out the total number of items in the group.

45. Counting

46. Place Value

47. Estimation

48. Operations of Whole Numbers

49. Addition: Connecting Level

50. Addition: Symbolic Level

51. Addition: Other Forms

52. Addition Sentences

53. Addition Exercises

54. Subtraction

55. Subtraction

56. Subtraction: Other Forms

57. Addition & Subtraction: Number Sentences

58. Number Sense of Fractions

59. Geometry

60. Shapes What objects do we use to teach shapes?

61. Shapes

62. Shapes

63. Shapes

64. Shapes

65. Shapes : Enrichment

66. More Shapes

67. Introducing a Lesson on Geometry

68. Patterns & Algebra

69. Patterns Patterning includes auditory, visual, and physical motor sequences that are repeated. Patterns may be : formed, verbally described, copied, created and extended

70. What should come next?

71. Patterns Patterns have to be repeated at least twice ….

72. Patterns

73. Patterns

74. Other Patterns 3, 5, 7, 9, ____ 1Z, 2Y, 3X, ___, ___, 6U 10, ___, ___, ___, ___, 60, 70 1000, 2000, 4000, ____, 16 000 100, 110, 130, ___, 250

75. Measurement

76. Measurement Days, Months Understanding the calendar Time Length Mass: Capacity Area

77. Measuring Length: Non Standard Units

78. Estimating Length

79. Use of standard units Comparison using standard units Conversions Problem Solving

80. Statistics & Probability Graphs Children can put into a picture form the results of classifying, comparing, counting and measuring activities.

81. Introduction to Graphs

82. Introduction to Graphs

83. Introduction to Graphs

84. Use of Graphs: Application

85. Statistics

86. Graph of Pets

87. Birthday Chart