Transcript 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
Conclusion
Recommendations
www.brainybetty.com
2
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
3
Emphasis use of ICT
Technology
assisted
instruction
Interactive
learning
Use of ICT in
concept
development
Problem
solving
Modelling
www.brainybetty.com
4
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
5
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
6
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 :
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
7
Background
• 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
8
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
9
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
10
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
11
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
12
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
13
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
14
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
15
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
16
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-andpencil 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
17
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
18
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
19
Methodology - instruments
The researchers used
quantitative and qualitative
methods:
c) informal observation of the
lessons.
d) Teacher’s reflection form
www.brainybetty.com
20
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
21
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
22
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
23
Methodology- Implementation
Lesson 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
24
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
25
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
26
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
27
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
28
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
29
Findings and Results
www.brainybetty.com
30
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
31
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
32
Conclusion
According to the teacher’s feedback:
1. The virtual manipulatives is:
a) useful to help pupils to understand
better
b) arose pupils’ interest in learning
mathematics
c) 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
33
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
34
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
35
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
36
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
37
Recommendations
Related Technological Activities to
Factors and Multiples
• http://www.mathgoodies.com/factors/fa
ctor_tree.asp
• http://www.math-play.com/Factors-andMultiples-Jeopardy/Factors-andMultiples-Jeopardy.html
• http://www.toonuniversity.com/flash.asp
?err=499&engine=14
• http://www.mathplayground.com/factort
rees.html
www.brainybetty.com
38
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
39
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
40
THE END
THANK YOU FOR YOUR
ATTENTION!!!
www.brainybetty.com
41