Teaching HCF and LCM Using Virtual Manipulatives

Teaching HCF and LCM Using Virtual Manipulatives

In this paper, we discuss the use of virtual manipulatives in teaching the concepts of Highest Common Factor (HCF) and Lowest Common Multiple (LCM). With

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About Teaching HCF and LCM Using Virtual Manipulatives

PowerPoint presentation about 'Teaching HCF and LCM Using Virtual Manipulatives'. This presentation describes the topic on In this paper, we discuss the use of virtual manipulatives in teaching the concepts of Highest Common Factor (HCF) and Lowest Common Multiple (LCM). With. The key topics included in this slideshow are . Download this presentation absolutely free.

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Slide1TEACHING HCF ANDLCM USING VIRTUAL MANIPULATIVES By: Norazlinawati Hj A. Magon (11M8128) Safiah binti Hj Yakup (11M8129) Didinawati binti Hj Zunaidi (11M8131)

Slide2Introduction• The new National education system 21 st  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 2

Slide3Emphasis  use of ICTUse of ICT in concept development Technology assisted instruction Problem solving Modelling Interactive learning www.brainybetty.com 3

Slide4Background• This research investigated whether the use of virtual manipulative could improve pupils’ achievement and attitudes in mathematics. • 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 4

Slide5Background• The software ‘Factor Tree’ was used to help the pupils to learn the topics found to be difficult for pupils.   • Reasons of using Virtual manipulatives to teach the Factors and Multiples : a) Provide learners with visual images. b) It can be manipulated as physical manipulatives and provide students opportunities for constructing mathematical knowledge. c) To promote effective teaching. www.brainybetty.com 5

Slide6Background• Benefits of using Virtual manipulatives  : a) It can help students visualize relationships and engage students learning actively. b) Useful to help the students to understand better. c) It will arouse students’ interest in learning mathematics. d) Pupils can work out the answer faster by using the virtual manipulatives. www.brainybetty.com 6

Slide7Background• Benefits of using Virtual manipulatives : e)  It can help students visualize relationships and engage students learning actively. f)   Useful to help the students to understand better. g)  It will arouse students’ interest in learning mathematics. h) Pupils can work out the answer faster by using the virtual manipulatives.   www.brainybetty.com 7

Slide8Research Questions• Is there any improvement in students’ achievement or scores in answering questions on factors (HCF and LCM) after using Virtual Manipulatives? • Is there any changes in students’ attitude towards mathematics and technology after using Virtual Manipulatives? www.brainybetty.com 8

Slide9Literature 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 9

Slide10Literature 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 is useful to introduce new concepts to all students www.brainybetty.com 10

Slide11Literature 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 11

Slide12Literature 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 12

Slide13Literature Review• Virtual manipulatives :    1) allow teachers to allow 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 13

Slide14Methodology• The researchers used quantitative and qualitative methods:     a) pre- and post-tests     b)questionnaires on attitudes towards mathematics     c) feedback on using the virtual manipulatives     d) informal observation of pupils attitude in class    e) Teacher’s reflection form www.brainybetty.com 14

Slide15Methodology• The researchers used one intact class for the study. There were twelve boys and sixteen girls in the sample. • The researchers worked together with the class teacher in delivering the lessons. www.brainybetty.com 15

Slide16Findings and Results• The researchers found that initially out of 28 Year six pupils, the majority were not able to correctly find the LCM and HCF of given set of numbers. www.brainybetty.com 16

Slide17Findings 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  activity. www.brainybetty.com 17

Slide18Findings and Results• The  researchers  found  that Cohen’s  effect  size,  d   =  0.3, indicating  a  small  effect  at  the  62 th percentile www.brainybetty.com 18

Slide19Findings and Resultswww.brainybetty.com 19 Table 1 shows the alpha reliability of the 10 items is 0.803 which is rounded to two decimal places is 0.80, indicating that the scale had good reliability. An alpha of 0.80 or above is considered satisfactory.

Slide20Findings and Resultswww.brainybetty.com 20 Results of pre-test shows most pupils have scores of 0 or no correct answers. The mean score is 0.07 (0.007%) 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.

Slide21Findings and Resultswww.brainybetty.com 21 Table  2  shows  that  female  pupils  ( M =4.00,  SD   = 2.98)  performed  better  than  male  pupils  ( M   =  3.18, SD   =  2.48).  Cohen’s  d =0.3  indicated  small  effect.

Slide22Conclusion• Face validity and content validity, 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 split-half reliability of the ten-item scale was 0.75, indicating that the scale had good reliability. www.brainybetty.com 22

Slide23ConclusionOn attitude toward mathematics : • 75% like learning mathematics. • 69% (19) said mathematics is fun to learn. On Feedback on Virtual Manipulatives • 90% of the students like virtual manipulatives; find it easy to play; know how to find the prime factors, LCM and HCF using the manipulatives; and they enjoy the lesson. www.brainybetty.com 23

Slide24ConclusionTeacher reflection form: • The benefits of using the virtual manipulatives as: a) useful to help pupils to understand better b) arose pupils’ interest in learning mathematics c) pupils can work out the answers faster • 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 24

Slide25ConclusionTeacher reflection form: • 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. • She also stated that the new method (using the software) in finding the GCF (HCF) and LCM is simple and easy to understand. • The software is also only need simple working to get the answer. www.brainybetty.com 25

Slide26Conclusion   From the mean scores of 0.007% 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 26

Slide27Recommendations• 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 27

Slide28Recommendations• 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 28

Slide29Recommendations• Related Technological Activities to Factors and Multiples • http://www.mathgoodies.com/factors/fa ctor_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/factort rees.html www.brainybetty.com 29

Slide30Bibliography• 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 30