Mountain Climbing Analogy


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This is the paper entitled "Effects of the Mountain Climbing Analogy to the Performance and Attitude of the First Year University students in Basic Mathematics"

the paper together with its data gave an insight on the viability of this teaching approach as a substitute to the teacher-centered traditional classroom environment.

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Mountain Climbing Analogy

  1. 1. The Effects Of Mountain Climbing Learning Analogy On The Achievement And Attitude Of The First Year University Students In Basic Mathematics Methusael B. Cebrian College of Education Capitol University
  2. 2. <ul><li>What is mountain climbing learning method? </li></ul><ul><li>- It is a learning method widely used in Japan that Focuses on enhancing the ability of the students to understand their newly created knowledge thru improved communicability of the students in mapping the knowledge they have created in the classroom. </li></ul>
  3. 3. <ul><li>What is Mountain Climbing Analogy? </li></ul>- It is a holistic approach to instruction implementation that promotes an active learning, cooperative and student-centered environment, integrating various teaching concepts to support the development of the students higher order thinking in mathematics.
  4. 4. <ul><li>Similar to actual mountain climbing, the analogy contends that learning must only occur as a continuation of a previous knowledge, achieved actively and collaboratively and retained as a result of learning by doing. </li></ul>
  5. 5. <ul><li>Key Factors of the strategy: </li></ul><ul><li>Knowledge creation process is a spiral one (Nonaka 1998) . </li></ul><ul><li>Previous learning experiences are connected and integrated to the new one. </li></ul><ul><li>It is a Student-Centered Learning. </li></ul><ul><li>Students will have a meaningful learning if they are doing or engaged to it. This is also called learning by doing (John Dewey). </li></ul>
  6. 6. <ul><li>It is an active and dynamic process. Interaction is the key to learning. Interaction not just from peer-to-peer or teacher to learner but also with the materials such as books, handouts and lectures. </li></ul><ul><li>Reaching the top of the mountain is not an individual effort. It is a TEAM effort. </li></ul><ul><li>Learners do not compete with each other, but rather they compete with their own past performances. </li></ul><ul><li>Learners have to engage in collaborative and cooperative effort. Both on the part of the teacher as the facilitator in the learner’s knowledge creation and the student’s themselves, working together creating their own knowledge based on experience. </li></ul>
  7. 7. <ul><li>The rope used by the learners in the mountain climbing analogy, represents the role of the teacher. </li></ul>
  8. 8. <ul><li>The teacher doesn’t have to push the learners to reach the top or learn but rather serve only as the link between the bottom of the mountain or lower knowledge to the top of the mountain or higher knowledge. The teacher serves only as facilitator in whole process. </li></ul>
  9. 9. <ul><li>Teaching Concepts and Strategies used: </li></ul><ul><li>Active Learning </li></ul><ul><li>Problem-Based Learning </li></ul><ul><li>Cooperative Learning </li></ul><ul><li>Discovery Learning </li></ul><ul><li>Constructionism </li></ul>
  10. 10. <ul><li>Active Learning (Meyers and Jones (1993)) </li></ul><ul><li>define active learning as learning environments that allow “students to talk and listen, read, write, and reflect as they approach course content through problem-solving exercises, informal small groups, simulations, case studies, role playing, and other activities. </li></ul><ul><li>-- all of which require students to apply what they are learning”. </li></ul>
  11. 11. <ul><li>Problem-Based Learning (PBL) </li></ul><ul><li>Is a student-centered instructional strategy in which students collaboratively solve problems and reflect on their experiences. Organized in small groups, the learners, accompanied by an instructor or facilitator deals with problems that enables them to construct knowledge with an initial guidance of the teacher, and then guidance is faded as learners gain expertise (Merrill, 2002). </li></ul><ul><li>It is also known as scaffolding. </li></ul>
  12. 12. <ul><li>Cooperative Learning </li></ul><ul><li>is a systematic pedagogical strategy that encourages small groups of students to work together for the achievement of a common goal. </li></ul>
  13. 13. <ul><li>Discovery learning (Bruner, 1960) </li></ul><ul><li>is an inquiry-based, constructivist learning theory that takes place in problem solving situations where the learner draws on his or her own past experience and existing knowledge to discover facts and relationships and new truths to be learned. </li></ul>
  14. 14. <ul><li>Constructionist learning </li></ul><ul><li>Is inspired by constructivist theories of learning which propose that learning is an active process wherein learners are actively constructing mental models and theories of the world around them. </li></ul><ul><li>Constructionism holds that learning can happen most effectively when people are actively making things in the real world. </li></ul>
  15. 15. <ul><li>Objectives of the Study </li></ul><ul><li>This study aims to </li></ul><ul><li>To Determine the Effects of the Mountain Climbing Learning Analogy on the performance of the students in Mathematics. </li></ul>
  16. 16. <ul><li>To Compare the Pretest and Posttest scores between the Experimental Group and the Control Group, and determine whether there are significant differences in the performance of the students. </li></ul><ul><li>To Determine the Attitudes of the students towards Mathematics. </li></ul><ul><li>To Provide recommendations based on the outcome of the study. </li></ul>
  17. 17. <ul><li>Methodology </li></ul><ul><li>Subjects of the Study </li></ul><ul><li>Subjects of the study were the two classes of first year university students from the College of Education of the Capitol University under the basic mathematics curriculum who were enrolled during the first semester of the school year 2008-2009. </li></ul>
  18. 18. <ul><li>Methods Used in the Study </li></ul><ul><li>This study used the quasi experimental design. </li></ul>
  19. 19. <ul><li>Instruments Used </li></ul><ul><li>The achievement test was constructed covering the following topics: Uses of percent in business, cost and markup, selling price and margin, commission, interest (simple, ordinary, compound). </li></ul><ul><li>This test was face-validated, item-analyzed, and revised by the researcher. The achievement test consisted of 25 items. </li></ul>
  20. 20. <ul><li>This study focused on two groups, Experimental and the Control group. </li></ul><ul><li>One class, the experimental group, was subjected to an experimental treatment and the control group was subjected to the traditional method. </li></ul><ul><li>The experimental class has 27 students while the control class has 14 students. The topics used in the treatment were part of their lessons in the finals. </li></ul>
  21. 21. <ul><li>To measure the students’ attitude, an Attitude Scale was given which consisted of 25 statements where respondents can either express their favorable or unfavorable feelings towards mathematics. </li></ul><ul><li>It is only given at the end of the two weeks treatment together with the posttest, the students’ agreement or disagreement to the statement is encircled on the 5-point scale. </li></ul>
  22. 22. <ul><li>The scale values for the responses to the statements are: </li></ul><ul><li>1 – Strongly Agree </li></ul><ul><li>2 – Agree </li></ul><ul><li>3 – Not Sure </li></ul><ul><li>4 – Disagree </li></ul><ul><li>5 – Strongly Disagree </li></ul>
  23. 23. <ul><li>Statistical Measures Used </li></ul><ul><li>The mean was computed using the formula: </li></ul>
  24. 24. <ul><li>To know the dispersion of the scores of the given test, standard deviation SD, was computed using the formula: </li></ul><ul><li>Where: </li></ul><ul><li>X i = is the score obtained by each student </li></ul><ul><li>N = is the total number of the respondents </li></ul>
  25. 25. <ul><li>To test for the homogeneity of the population variance Levene’s Test was used. </li></ul><ul><li>This served as the basis for the use of the T-test for unequal samples with unequal variance. </li></ul><ul><li>Levene’s Test is more robust in accurately presenting the equality of the population variances, thus ensuring that the right T-test formula is used for the succeeding determination and interpretations of data. </li></ul>
  26. 26. <ul><li>Formula for Levene’s Test : </li></ul><ul><li>Where; </li></ul><ul><li>W is the result of the test; </li></ul><ul><li>k is the number of different groups to which the samples belong, </li></ul><ul><li>N is the total number of samples, </li></ul><ul><li>N i is the number of samples in the i th group, </li></ul><ul><li>Y ij is the value of the j th sample from the i th group, </li></ul>
  27. 27. <ul><li>T test for unequal samples with unequal variance was used; </li></ul><ul><li>Where: </li></ul>
  28. 28. <ul><li>Where: </li></ul><ul><li>_ </li></ul><ul><li>X 1 = the mean score of the control group </li></ul><ul><li>X 2 = the mean score of the experimental group </li></ul><ul><li>n 1 = the number of respondents in the control group </li></ul><ul><li>n 2 = the number of respondents in the experimental group </li></ul><ul><li>S 2 = variance of the samples </li></ul><ul><li>D.F. = degrees of freedom </li></ul><ul><li>S x 1 x 2 = is the unbiased estimator of the variance of the two samples </li></ul>
  29. 29. <ul><li>All computations are manually solved with the use of Ti-83 Calculator, Microsoft excel with data analysis pack and verified using the Statistical software, SPSS. </li></ul>
  30. 30. <ul><li>PRESENTATION AND ANALYSIS OF DATA </li></ul>
  31. 31. <ul><li>Pretest and Posttest Scores in the Achievement Test of the Two Groups </li></ul>Scores Experimental Group Control Group Pretest Posttest Pretest Posttest F % F % F % F % 21- 25 16 – 20 11 – 15 6 – 10 1 - 5 2 19 5 1 0 7.4 70.4 18.5 3.7 0 15 12 0 0 0 55.6 44.4 0 0 0 4 5 5 0 0 28.6 35.7 35.7 0 0 4 6 3 1 0 28.6 42.9 21.4 7.1 0 Total 27 100 27 100 14 100 14 100 Mean 16.88889 20.07407 16.5 18.28571 S.D 2.736271 2.894636 4.327906 4.286447
  32. 32. Pretest Scores of Experimental and Control Group
  33. 33. Comparison of Pretest differences of the Two Groups Groups Mean S.D. Computed t Critical Region Remarks Experimental 16.89 2.74 0.353 -1.729 < t > 1.729 No significant difference Control 16.5 4.33
  34. 34. Posttest Scores of Experimental and Control Group
  35. 35. Comparison of Posttest differences of the Two Groups Groups Mean S.D. Computed t Critical Region Remarks Experimental 20.5 6.25 2.1 -1.734 < t > 1.734 There is significant difference bet. The two groups. Control 18.28 18.3
  36. 36. Comparison of Pretest and Posttest means of Both Groups
  37. 37. Comparison of Mathematical Attitudes of the Two Groups GROUPS Mean S.D. Computed t Critical Region Remarks Experimental 2.7664 0.478077 0.62 -1.721 < t > 1.721 No significant difference Control 2.656 0.654994
  38. 38. SUMMARY OF FINDINGS, CONCLUSIONS. <ul><li>Based on the statistical analysis, the following findings and conclusions were drawn. </li></ul>
  39. 39. <ul><li>There was a significant difference between the Achievement Test of the Experimental and Control group. </li></ul><ul><li>This means that the Mountain Climbing Learning Analogy Method can be an effective teaching strategy compared to the traditional method. </li></ul><ul><li>Mathematical attitudes of the students between the two groups are found to have no significant difference. It is neither positive nor negative. </li></ul>
  40. 40. RECOMENDATIONS <ul><li>Based on the findings and conclusions of the study, the researcher recommends that: </li></ul><ul><li>Similar or parallel studies be conducted in the Capitol University to identify topics in mathematics where the mountain climbing learning analogy method could be more effective than other techniques. And identify how best a teacher can employ the strategy without placing additional burden on them. </li></ul>
  41. 41. <ul><li>Employ teaching strategies that focuses on mastery learning and help reduce the stigma of fear in mathematics through student-centered environment. </li></ul><ul><li>Support an environment that is warm and supportive, so that students will feel confident working as groups because they are not competing with each other but with their own performances. </li></ul>
  42. 42. <ul><li>The mountain climbing learning analogy method may be used as a classroom strategy side by side or alternately with other equally effective and time-tested teaching strategies whenever the need arises. </li></ul><ul><li>Explore possibilities of employing the strategy on other subjects. </li></ul>