Principles and Strategies in Teaching Mathematics MATH-116-WEEK-2-3.pptx

Lecture

1. Underlying Principles and Strategies

2. Teaching Principles in Mathematics

3. Learning Principles in Mathematics

4. Learning Principles in Mathematics Mathematics is a subject that requires logical thought, and trains students to think critically and creatively. It provides students with the essential skills in reasoning, decision-making and problem solving to help them make sense of many aspects of our rapidly changing world.

5. Learning Principles in Mathematics Mathematics can be our gateway for national progress. That’s because Filipino students with strong mathematical knowledge will help ensure the country’s economic survival. Mathematics can provide a strong foundation that prepares our youth to pursue higher education and be part of the country’s technologically-oriented work force in the future. Therefore, it’s necessary to teach children the fundamental ideas of numbers and number concepts. This will help them become more proficient in computing and problem solving.

6. Learning Principles in Mathematics Principle 1 : Being mathematically competent means more than having the ability to compute and perform algorithms, and mathematical procedures. A mathematically competent student does not only know how to compute and perform algorithms, but is also able to pose and solve mathematical problems, and apply mathematical skills and reasoning in other subjects and everyday experiences.

7. Learning Principles in Mathematics Principle 2 : The physical and social dimensions of a mathematical environment contribute to one’s success in learning mathematics. Students need a learning environment that is safe, clean and allows plenty of movement and exploration. An ideal mathematical environment is one that is well equipped with tools for learning mathematics.

8. Learning Principles in Mathematics Principle 3 : Mathematics is best learned when students are actively engaged. Students must be engaged in the learning activities planned by the teacher for them to learn faster. Therefore, students cannot expect to learn by simply watching their teacher solve problems on the board. Students must bear the responsibility of being actively engaged in order to maximize their learning potential. They ought to join in class discussions, ask questions, argue and reason out so that they see the many different aspects of mathematics that they are studying.

9. Learning Principles in Mathematics Principle 4 : A deep understanding of mathematics requires a variety of tools for learning. Following from Principle 3, mathematical tools allow students to be actively engaged in learning mathematics and deepen their understanding. These tools include manipulative and hands-on materials that can be effective for developing, clarifying and applying mathematical concepts. These materials should be carefully integrated into the instructional process.

10. Learning Principles in Mathematics Principle 4 : A deep understanding of mathematics requires a variety of tools for learning. Technology offers a variety of tools that must be used judiciously. The use of technology should be driven by the needs of the students as learners of mathematics and should be used when it aids the learning process. It should not be regarded as a substitute for students’ understanding of quantitative concepts and relationships.

11. Learning Principles in Mathematics Principle 4 : A deep understanding of mathematics requires a variety of tools for learning. When properly used, tools, such as measuring instruments, scientific and graphing calculators, and computers with appropriate software, can contribute to a rich learning environment. For example, calculators should be used with caution; elementary students should be able to perform basic arithmetic operations independent of calculator use .

12. Learning Principles in Mathematics Principle 5 : Assessment in mathematics must be valued for the sake of knowing what and how students learn or fail to learn mathematics. Assessment is an essential component of mathematics learning. Whether the assessment is carried out by teachers or external groups and during or all throughout the learning period or at the end of it, results are useful to both teachers and students. It is through assessment, formal or informal, that students know how much mathematics they have learned and how much more they need to know.

13. Learning Principles in Mathematics Principle 5 : Assessment in mathematics must be valued for the sake of knowing what and how students learn or fail to learn mathematics. Assessment tools must be varied in order to understand the different dimensions of students’ learning. While exams and quizzes have a place in measuring skills, knowledge development and acquisition, many aspects of mathematical learning could be more effectively measured by other means.

14. Learning Principles in Mathematics Principle 6 : Students’ attitudes and beliefs about mathematics affect their learning. Like with any type of learning, students have to maintain wholesome attitudes and positive beliefs about mathematics. Students should develop the attitude that engagement in mathematics is essential and that perseverance, persistence, reflection, self-assessment and self-confidence are keys to success.

15. Learning Principles in Mathematics Principle 6 : Students’ attitudes and beliefs about mathematics affect their learning. Students can learn from each other; cooperative work develops a spirit of camaraderie , teamwork and common purpose . Working with other students exposes students to multiple ways of solving and working with mathematics.

16. Learning Principles in Mathematics Principle 7 : Mathematics learning needs the support of both parents and other community groups. Studies have shown that parental and home support contribute to students’ success in learning mathematics. Families should project positive attitudes and beliefs toward mathematics and the learning of it.

17. Learning Principles in Mathematics Principle 7 : Mathematics learning needs the support of both parents and other community groups. Community support for mathematics learning is also as valuable. It is through the community that students could see how mathematics is alive and utilized, particularly in day-to-day activities, such as making purchases.

18. Learning Principles in Mathematics Principle 7 : Mathematics learning needs the support of both parents and other community groups. Communities could provide useful resources and other means for students to enhance their learning. To enhance students’ understanding of applications of mathematics, schools rely on local communities for fieldwork and site visits. These activities expose students to the realities of everyday mathematics at work.

19. The goals of mathematics education at the basic education level remain, more or less, the same: “To provide opportunities for students to develop skills and attitudes needed for effective participation in everyday living and prepare them for further education and the world of work so that they make worthwhile contributions to the society at large”. Filipinos must do better in mathematics and science if we want to be able to compete globally.

20. Constructivism in Mathematics teaching

21. Introduction The Constructivist Learning Theory states that learning is an active process of creating meaning from different experiences. In other words, students learn best by trying to make sense of something on their own with the teacher as a guide

22. Introduction DepEd (2016) specifically noted constructivist theory as the backbone of the curriculum Knowledge is constructed when the learner is able to draw idea from his/her own experiences and connect them to new ideas

23. Constructivism Constructivism was conceptualized by educational theories Jean Piaget. He believed that young children learn by doing, constructing knowledge from experiences rather than from adults telling them about their world The method most likely to truly educate students is the one in which they experience in their world

24. Constructivism It is appropriately so applied in teaching mathematics since math is cumulative, vertically structured discipline. One learns new math by building on the math that has been previously learned

25. Constructivism Brooks & Brooks (1993) listed the following characteristics of constructivist teaching: 1. Constructivist teachers invite student questions and ideas 2. Constructivist teachers accept and encourage students’ invented ideas 3. Constructivist teachers encourage student’s leadership, cooperation, seeking information, and the presentation of the ideas

26. Constructivism Brooks & Brooks (1993) listed the following characteristics of constructivist teaching: 4. Constructivist teachers modify their instructional strategies in the process of teaching based upon students; thought, experience, and/or interests 5. Constructivist teachers use printed materials as well as experts to get more information

27. Constructivism Brooks & Brooks (1993) listed the following characteristics of constructivist teaching: 6. Constructivist teachers encourage free discussions by the way of new ideas inviting student questions and answers 7. Constructivist teachers encourage or invite students’ predictions of the causes and effects in relation to particular cases and events

28. Constructivism Brooks & Brooks (1993) listed the following characteristics of constructivist teaching: 8. Constructivist teachers help students to test their own idea 9. Constructivist teachers invite students’ ideas before the student is presented with the ideas and instructional materials

29. Constructivism Brooks & Brooks (1993) listed the following characteristics of constructivist teaching: 10. Constructivist teachers encourage students to challenge the concepts and ideas of others 11. Constructivist teachers use cooperative teaching strategies through student interactions and respect, sharing ideas, and learning tasks 12. Constructivist teachers encourage students to respect and use other people’s ideas

30. Constructivism How is a constructivist classroom different from a traditional classroom? In the constructivist classroom, the focus shifts from the teacher to the students. The classroom is no longer a place where the students are seen as empty vessels to be filled by the teacher. In a constructivist classroom, the students are actively involved in their own learning. the teacher functions as a facilitator who guides, prompts, and helps students to develop and assess their own understanding

31. Constructivism The table below compares the traditional classroom to the constructivist one. Traditional Classroom Constructivist Classroom Curriculum Curriculum begins with the parts of the whole, emphasizing basic skills Curriculum emphasizes big concepts, beginning with the whole and expanding to include the parts Teacher’s role Teachers disseminate information to students; students are recipient of knowledge Teachers have a dialogue with students, helping students construct their own knowledge Students’ role Students work primarily alone Students work primarily in groups

32. Summary The constructivist learning theory states that learning takes place when we build on what students already know. Moreover, it is student-centered, allowing the students to take ownership of their own learning

33. Dale’s Cone of Experience

34. What is Dale’s Cone of Experience? a pictorial device used to explain the interrelationships of the various types of audio-visual media, as well as their individual “positions” in the learning process. Useful in selecting instructional resources and activities (is as practical today as when Dale created it)

35. Principle of Dale’s Cone of Experience The cone is based on the relationships of various educational experiences to reality (real life), and the bottom level of the cone, "direct purposeful experiences," represents reality or the closest things to real, everyday life The opportunity for a learner to use a variety or several senses (sight, smell, hearing, touching, movement) is considered in the cone

36. Principle of Dale’s Cone of Experience Direct experience allows us to use all senses Verbal symbols involve only hearing The more sensory channels possible in interacting with a resource, the better the chance that many students can learn from it Each level of the cone above its base moves a learner a step further away from real- life experiences.

37. Principle of Dale’s Cone of Experience Motion pictures (also television) is where it is on the cone because it is an observational experience with little or no opportunity to participate or use senses other than seeing and hearing Contrived experiences are ones that are highly participatory and simulate real life situations or activities Dramatized experiences are defined as experiences in which the learner acts out a role or activity

38. Verbal Symbols principal medium of communication bear no physical resemblance to the objects or ideas for which they stand Disadvantage : highly abstract

39. Visual Symbols chalkboard/whiteboard, flat maps, diagrams, charts fits the tempo of presentation of idea, topic or situation very easy to procure and prepare Limitations: lack of ability to use the media size of visuals simplification of visual materials leads to misconceptions

40. Recordings, Radio, Still Pictures attention – getting, particularly projected views Limitations : *size of pictures or illustrations * expensiveness of projected materials and equipment, *timing difficulties between radio shows and classroom lessons

41. Television and Motion Pictures a solution to time and space constraints provides “windows to the world” effective for presenting movement, continuity of ideas or events substitute for dangerous direct learning experiences

42. Television and Motion Pictures Limitations : Expensive viewing problems timing with classroom lessons misconceptions about time, size, and ideas

43. Exhibits present objects or processes otherwise impossible inside the classroom exposure to new ideas, discoveries, inventions problems that may be encountered: too little space time – consuming maintenance

44. Demonstrations visualized explanation of an important fact or idea or process may require nothing more than observation or students may be asked to do what has just been shown how to do Disadvantage: ideas or processes might not be interpreted or conceived very well to all learners

45. Field Trips undertaken primarily for the purpose of experiencing something that cannot be encountered within the classroom a rich experience in learning about objects, systems, and situations

46. Field Trips Disadvantages: time-consuming expensive high exposure to danger /accidents inadequacy of the community’s resources

47. Dramatized Experience help get closer to certain realities that are no longer available at first hand stirring and attention getting participant learns to understand intimately the character he portrays teaches cooperative work

48. Dramatized Experience Disadvantages: time consuming without commensurate results participation is limited to few individuals

49. Contrived Experience an “editing” of reality substitutes for confusing or unmanageable first – hand experiences easier to handle, manipulate or operate

50. Contrived Experience Disadvantages: simplification leads to misconceptions, distorted views, and incomplete pictures of reality no freedom to handle expensive or fragile models, mock – ups, specimens, etc.

51. Direct and Purposeful Experience unabridged version of life itself direct participation with responsibility for the outcome the basis for the most effective and lasting learning Disadvantage : not all things can be learned through direct, first hand experiencing

52. Dale (1969) explained that the broad base of the cone illustrated the importance of direct experience for effective communication and learning . Especially for young children, real and concrete experiences are necessary to provide the foundation of their permanent learning.

53. Dale’s Cone of Experience continues to influence instructional designers today in both theory and practice. For example, Baukal , Auburn, and Ausburn built upon Dale’s ideas in developing their  Multimedia Cone of Abstraction ,

54. the implications of Dale’s Cone have been misunderstood or misapplied. For example, Dale’s Cone has been used to maintain that more realistic and direct experience is always better. However, Dale (1969) demurred, writing that, “Too much reliance on concrete experience may actually obstruct the process of meaningful generalization ” (p. 130). Also , Dale noted that providing realistic learning experiences may not be efficient in terms of cost, time, and efforts. Instead, Dale suggested that teachers should balance combinations of concrete and abstract learning experiences

55. Pie Graph on Senses and Perception

56. Retention Rate Levels Learning is an active process. Retention level practically increases as students are actively involve in various learning activities. Researchers found out that the most effective approaches – resulting in 75% and 90% retention rates, respectively – are learning by doing and learning by teaching others

57. Experiential Learning Environments

58. Dale (1969) described learning as a “fourfold organic process” (p. 42) which consisted of needs, experiences, incorporation of the experiences, and the use of them. To promote permanent learning, Dale asserted that teachers should help students identify their  needs  for learning and set clearly defined learning goals related to their needs. A learning experience must be personally meaningful with respect to students’ backgrounds and developmental stages and the nature of the experience should be logically arranged to help students  incorporate  new knowledge with what they already have.

59. Later, students should have opportunities to practice and try out their new knowledge in real life as well as in learning contexts. Thus , effective learning environments should be filled with rich and memorable experiences where students can see, hear, taste, touch, and try.

60. Dale (1969) articulated the characteristics of rich experiences . In a rich experience: students are immersed in it and use their eyes, ears, noses, mouths and hands to explore the experience, students have a chance to discover new experiences and new awareness of them, students have emotionally rewarding experiences that will motivate them for learning throughout their lives, students have chances to practice their past experiences and combine them to create new experiences, students have a sense of personal achievement, and students can develop their own dynamic experiences .

61. In Dale’s perspective (1972), most students in schools did not learn how to think, discover, and solve real problems. Rather, students were forced to memorize facts and knowledge in most schools, and as a result, any knowledge they acquired was inert in their real lives. For this reason, he argued that we should have revolutionary approaches to improve the quality of educational learning environments. To build learning environments infused with rich experiences, Dale argued for the development of new materials and methods of instruction.