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TEACHING HCF AND LCM USING VIRTUAL MANIPULATIVES

TEACHING HCF AND LCM USING VIRTUAL MANIPULATIVES. By: Norazlinawati Hj A. Magon (11M8128) Safiah binti Hj Yakup (11M8129) Didinawati binti Hj Zunaidi (11M8131). Presentation Outlines. Introduction Background Research Questions Literature Review Methodology Findings and Results

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TEACHING HCF AND LCM USING VIRTUAL MANIPULATIVES

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  1. TEACHING HCF AND LCM USING VIRTUAL MANIPULATIVES By: Norazlinawati Hj A. Magon (11M8128) Safiah binti Hj Yakup (11M8129) Didinawati binti Hj Zunaidi (11M8131)

  2. Presentation Outlines • Introduction • Background • Research Questions • Literature Review • Methodology • Findings and Results • Conclusion • Recommendations www.brainybetty.com

  3. Introduction • The new National education system 21st century in Brunei Darussalam promotes the use of technology in teaching and learning of mathematics in schools. • The mathematics curriculum supports the developments in children by placing clear emphasis upon the sensible use of ICT in classroom (CDD, 2008 p.9) www.brainybetty.com

  4. Emphasis use of ICT www.brainybetty.com

  5. Background • This research investigated whether the use of virtual manipulative could improve pupils’ achievement in mathematics and perception in using virtual manipulative. • The researchers explored the use of technology in the teaching and learning of factors and multiples in Year 6. • The researchers used free virtual manipulative software obtained online from http: //nlvm.usu.edu/. www.brainybetty.com

  6. Background The National Library of Virtual Manipulatives is "an NSF funded project to develop interactive online learning units for 3-12" (NLVM Web site 2006). Many of the 200+ virtual manipulatives found at the National Library of Virtual Manipulatives are embedded into "eModules" which are fully developed lesson plans for implementation in to the classroom. The site allows teachers to create accounts for the purpose of developing virtual classrooms in which students can go through the activities laid out for them. The resources are developed by a variety of contributing authors and teachers are encouraged to perform "field tests" to provide feedback to the developers (NLVM Web site 2006). www.brainybetty.com

  7. Background • The software ‘Factor Tree’ was used to help pupils to learn the topics found to be difficult for them. • Reasons of using Virtual manipulatives to teach the Factors and Multiples : • Provide learners with visual images. • It can be manipulated as physical manipulatives and provide students opportunities for constructing mathematical knowledge. • To promote effective teaching. www.brainybetty.com

  8. Background • Benefits of using Virtual manipulatives: • It can help students visualize relationships and engage students learning actively. • Useful to help the students to understand better. • It will arouse students’ interest in learning mathematics. • Pupils can work out the answer faster by using the virtual manipulatives. www.brainybetty.com

  9. Research Questions • Are there any improvement in pupils’ achievement or scores in answering questions on factors (HCF and LCM) after using Virtual Manipulatives? • Do female and male pupils differ significantly in their mathematics achievement (post-test)? • Does pupils’ perception on virtual manipulatives affect their achievement in the post-test? www.brainybetty.com

  10. Literature Review • Abstract concepts are essential to understanding and performing mathematics. They are also a source of difficulty for many students who struggle with mathematics, many of whom find even basic mathematics concepts difficult to understand. www.brainybetty.com

  11. Literature Review • A popular approach to help students understand abstract concepts is the use of manipulatives. • Manipulatives enable students and teachers to represent concretely the abstract concepts that they are learning in mathematics class and to link these concepts to prior knowledge. • Manipulatives are useful to introduce new concepts to all students www.brainybetty.com

  12. Literature Review • For the most part, classroom use of manipulatives has involved concrete, or physical, manipulatives. However, with the advent of the World Wide Web, there is a new category of manipulatives. • Virtual manipulatives are basically digital “objects” that resemble physical objects and can be manipulated, usually with a mouse, in the same ways as their authentic counterparts. www.brainybetty.com

  13. Literature Review • Virtual manipulatives are a relatively new technology and are modeled after existing manipulatives such as base ten blocks, coins, blocks, tangrams, spinners, rulers, fraction bars, algebra tiles, geoboards, geometric plane and solids figures.  • They are usually in the form of Java or Flash applets. www.brainybetty.com

  14. Literature Review • Virtual manipulatives : 1) allow teachers for efficient use of  multiple representations and 2) to provide concrete models of abstract mathematical concepts for learners of mathematics. • Research suggests that students may also develop more connected understandings of mathematical concepts when they use virtual manipulatives (Moyer, Niezgoda, & Stanley, 2005) www.brainybetty.com

  15. Literature Review The concepts and skills to be learned from the virtual manipulatives activities (in teaching the Factors and Multiples) are: • Can make connections between the concepts, extension and generalizations in order to solve the problems. • Identify prime and composite numbers. • Find factors and multiples of whole number less than 100 and identify which are prime or composite. • Identify common factors of a set of whole numbers. www.brainybetty.com

  16. Literature Review The concepts and skills to be learned from the virtual manipulatives activities (in teaching the Factors and Multiples) are: • To manipulate and change the representations, thus increasing exploration possibilities to develop concepts and test hypotheses • Know how to use technology. • Learn by using factor tree method through games. • To develop their relational thinking and to generalize mathematical ideas www.brainybetty.com

  17. Literature Review • Reimer and Moyer ( 2005) studied a small group of third-graders learning about fractions with the use of virtual manipulatives. They concluded that, "Student interviews and attitude surveys indicated that the virtual manipulatives (1) helped students in this class learn more about fractions by providing immediate and specific feedback, (2) were easier and faster to use than paper-and-pencil methods, and (3) enhanced students' enjoyment while learning mathematics" (Reimer & Moyer 2005, p. 5-6). • However, the authors do admit that the small class size and specific demographics fail to make the findings applicable to a broader population (Young 2006, p.4). www.brainybetty.com

  18. Literature Review • Crawford and Brown (2003) explored teacher's rationale for choosing virtual manipulatives over alternative forms of instruction. • They provided a group of in-service teachers with Roblyer and Edwards' (2000) "Elements of a Rationale for Using Technology in Education" to use as a guide as they were given time to explore the virtual manipulatives available at the National Library of Virtual Manipulatives. • The teachers then shared their ideas and thoughts on the virtual manipulatives through an online survey developed by the researchers. • The results showed a variety of teacher thoughts, in which most teachers thought they could be beneficial. However, many teachers also mentioned concerns about classroom management and superiority of other methods (Young 2006, p.4). www.brainybetty.com

  19. Methodology - instruments • The researchers used quantitative and qualitative methods: a) pre- and post-tests (10 items based on PSR format questions) b) feedback on using the virtual manipulatives (Likert Scale consisting of 7 items: all positive items) www.brainybetty.com

  20. Methodology - instruments The researchers used quantitative and qualitative methods: c) informal observation of the lessons. d) Teacher’s reflection form www.brainybetty.com

  21. Methodology - instruments • Face validity, content validity and reliability • The test items were shown to our lecturer to be checked and finalized. • The items were constructed based on Primary School Examination (PSR) format questions. The final questions were checked by the Year 6 mathematics teachers before given to the pupils. • The alpha reliability of the 10 items is 0.803, which rounded to two decimal places is 0.80, indicating that the scale had good reliability. www.brainybetty.com

  22. Methodology- samples • The researchers used one intact class for the study. There were twelve boys and sixteen girls of Year 6 in the sample. • The researchers worked together with the class teacher in delivering the lessons. www.brainybetty.com

  23. Methodology- samples • The researchers found that at the beginning, out of 28 Year six pupils, majority were not able to correctly find the LCM and HCF of given set of numbers. www.brainybetty.com

  24. Methodology- ImplementationLesson Activities • Day 1: Pre-test, demonstration showing how to use factor tree (virtual manipulatives) and worksheets. • Day 2: showing how to use virtual manipulatives to find HCF and LCM and worksheets. • Day 3: post-test and pupils’ feedback on using virtual manipulative www.brainybetty.com

  25. Findings and Results • Initially the pupils were quiet, listening to a demonstration by the class teacher and then later the researchers noticed that the students were enthusiastic and deeply engaged with the activities in the lessons. www.brainybetty.com

  26. Findings and Results • The researchers found at the end of the study, Cohen’s effect size, d = 1.83, indicating a large effect at the 96.4th percentile. www.brainybetty.com

  27. Findings and Results Table 1 shows the mean score for pre-test and post-test of 28 pupils. The mean score for pre-test = 0.07 and post-test = 3.68. There is a significant difference in the mean scores between the pretest and posttest at p < 0.025 level (2-tailed). The pupils performed significantly better in their posttest scores. This implies that the use of virtual manipulative (Factor Tree) may be effective in enhancing pupils’ academic performance. www.brainybetty.com

  28. Findings and Results Results of pre-test shows most pupils have scores of 0 or no correct answers. The mean score is 0.07 (0.7%) out of 10 questions. Result of post-test shows most pupils have scores of 3 or 4 correct answers. The mean score is 3.68 (36.8%) out of 10 questions. www.brainybetty.com

  29. Findings and Results Table 2 shows that female pupils (M=4.00, SD = 2.98) performed better than male pupils (M = 3.18, SD = 2.48). But Cohen’s d=0.3 indicated only small effect. www.brainybetty.com

  30. Findings and Results www.brainybetty.com

  31. Conclusion On Feedback on Virtual Manipulatives • 86% of the students like virtual manipulatives. • 61% find it easy to work with. • 50% know how to find the prime factors. • 64% know how to find the LCM using virtual manipulatives. • 68% know how to find the HCF using the manipulatives. • 79% like the topic (Factors and Multiples). • 82% enjoy the lesson. www.brainybetty.com

  32. Conclusion On Feedback on Virtual Manipulatives • But from an analysis of the post test papers done by the pupils, the researchers found out that only 41.1% of the pupils were able to find the correct answers to the questions on prime factors. • 38.6% were able to give the correct answers to HCF questions; and only 20.7% were able to find the correct answers to LCM. • However, from the pre-test papers these are an increase from only 1.4% of giving correct answers to HCF and LCM questions respectively and 0% in prime factors. www.brainybetty.com

  33. Conclusion According to the teacher’s feedback: 1. The virtual manipulatives is: • useful to help pupils to understand better • arose pupils’ interest in learning mathematics • pupils can work out the answers faster 2. The objectives of the lesson were achieved as the pupils could use the virtual manipulatives software effectively in answering the questions given www.brainybetty.com

  34. Conclusion 3. The software also worked in developing the lesson plan as pupils use the virtual software in expressing a given number as a product of prime factors. 4. She also stated that the new method (using the software) in finding the GCF (HCF) and LCM is simple and easy to understand. 5. The software only needs simple working to get the answer. www.brainybetty.com

  35. Conclusion • From the mean scores of 0.7% correct responses in the pre-test and 36.8% in the post-test, it can be seen there is an improvement in student’s achievement in answering questions on factors (HCF and LCM) after using virtual manipulatives. www.brainybetty.com

  36. Conclusion • Although Virtual Manipulatives seems to be a promising tool for teachers in assisting their teaching and learning processes of mathematics, the effectiveness of these manipulations is basically reliant on teachers themselves and their instructional designs. • Thus further research on the effectiveness of using Visual Manipulatives by teachers and in their instructions should be further studied. • In addition, development and implementation of Virtual Manipulatives online and in secondary education should also be further explored. www.brainybetty.com

  37. Recommendations • In order for manipulatives to benefit learners, manipulatives that permit children to use informal method should be selected. During the used of manipulatives pupils must be in control and be allowed to think at their own solutions. • Manipulatives should never be used in a rote manner. After the pupils have interacted freely with the manipulatives, pupils should be encouraged to reflect and explain their solutions. In this way the learner can understand and analyse errors (Clement, 2000) www.brainybetty.com

  38. Recommendations Related Technological Activities to Factors and Multiples • http://www.mathgoodies.com/factors/factor_tree.asp • http://www.math-play.com/Factors-and-Multiples-Jeopardy/Factors-and-Multiples-Jeopardy.html • http://www.toonuniversity.com/flash.asp?err=499&engine=14 • http://www.mathplayground.com/factortrees.html www.brainybetty.com

  39. References • Crawford, C. & Brown, E. (2003). Integrating Internet-based Mathematical Manipulatives Within a Learning Environment. Journal of Computers in Mathematics and Science Teaching. 22(2), 169-180.   • Curriculum Development, Ministry of Education, Brunei Darussalam (2008). Framework and Guidelines for Curriculum and Assessment Mathematics Year 4.  • Moyer, Niezgoda, & Stanley (2005). Learning Mathematics with Virtual Manipulatives. Retrieved March 3, 2012 from http://www.cited.org/index.aspx?page_id=151. Cited Research Centre. www.brainybetty.com

  40. References • National Library of Virtual Manipulatives (2006). Retrieved March 3, 2012 from http://nvlm.usu.edu/en/nav/vlibrary.html. Utah State University. • Reimer, K., & Moyer, P.S. (2005). Third-Graders Learn About Fractions Using Virtual Manipulatives: A Classroom Study. Journal of Computers in Mathematics and Science Teaching. 42(1), 5-25.   • Young, D. (2006). Virtual Manipulatives in Mathematics Education. Retrieved April 24, 20012 from http://enlvm.usu.edu/ma/nav/doc/intro.jsp. • Yuan, Y. (Dec, 2009).Taiwanese elementary school teachers apply web-based virtual manipulatives to teach mathematics. Journal of Mathematics Education, 2 (2), 108 - 121. www.brainybetty.com

  41. THE ENDTHANK YOU FOR YOUR ATTENTION!!! www.brainybetty.com

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