math education

1. Misconceptions In
Mathematics Education :
Misconception of Fraction
among Year Four Pupils at
Primary School

2. • Mathematics is a subject that is always given special attention in schools. This is
because mathematics is related to many other fields and disciplines.
• many students find it difficult to learn mathematics in school, and it is often
considered as a difficult subject to learn.
• Therefore, it is not surprising that many students consider mathematics as a
challenging subject, and as a result, students have little interest in learning
mathematics.
• Like most other subjects, students also make misconceptions in mathematics.
• According to Mohyuddin and Khalil (2014), mistakes and misconceptions occur
when students make inappropriate generalizations about an idea.
• Based on this statement, it is believed that students should possess a strong
mathematical foundation to help them learn mathematics effectively.
Misconceptions In Mathematics Education :
Misconception of Fraction among Year Four Pupils at Primary
School

3. • There are various definitions of misconceptions put forward by different
researchers, many failed to distinguish between errors and misconceptions.
• Ojose (2015) defined misconceptions as misunderstandings that result from
incorrect interpretations.
• Korey and Bal (2002) pointed out that misconceptions constitute of wrong
clarifications that most students accept as correct.
• Li, Julihi, and Eng (2017), who defined misconceptions as misunderstandings of ideas
or concepts while errors reflect incorrect applications, concepts, theories, or
formulas.
• Brodie (2014) argued that most misconceptions stem from incorrect previous
knowledge.
• Ocal (2017) suggested that teachers should correct the misunderstandings of basic
mathematical concepts before introducing a new concept.
Misconceptions In Mathematics Education :
Misconception of Fraction among Year Four Pupils at Primary
School

4. • “Fractions” is a subtopic in Numbers and Operations. In Primary Year 4 (10-year-old),
pupils learn about concept, comparing/ordering, equivalence, addition, subtraction,
multiplication, division and problem solving in fractions.
• This topic often occurs, there are four things that students often do when answering
addition and subtraction fraction operation questions, namely systematic errors,
random errors, negligence errors and not knowing how to answer fraction questions
(Braithwaite et al., 2021).
• Finding from Dhlamini & Kibirige (2014), tells that mistakes and misconception may
related but they are in two different types of mistakes; systematic and unsystematic
mistakes.
• Saragih (2011) found that the students did not master the topic since they only
memorise the formula, examples of questions and similar exercises.
Misconceptions In Mathematics Education :
Misconception of Fraction among Year Four Pupils at Primary
School

5. • Misconception will lead pupils to not mastering fractions, thus making this subject less
favourable (Trivena et al. 2017).
• A good example supporting this fact is when students were offered an arithmetic
problem such as { + = }, students approached the problem by adding numerators
(1+2) and denominators (5+6), resulting to ( ) as their answer (Xu et al., 2021). These
misconceptions can be seen in almost all schools globally, including the Malaysian
students.
Misconception of Fraction
Misconceptions In Mathematics Education :
Misconception of Fraction among Year Four Pupils at Primary
School
1
5
– 2
6
–
–
11
3

6. Misconceptions In Mathematics Education :
Misconception of Fraction among Year Four Pupils at Primary
School
• One of the aspects that can improve students' understanding is through the use of
effective teaching aids (Rohaeti et al., 2020).
• The use of teaching aids is very important so that teachers can explain things more
accurately and clearly compared to oral explanations only. This can ensure that the
delivery of teaching and learning can be implemented more effectively (Rohaeti et al.,
2020).
• The use of aids can change the teaching and learning methods of the teacher for the
better and give internal motivation to students to learn something (Gaetano, 2014).
• However, teachers still maintain teaching practice with the method of reviewing training
answers, lectures and individual exercises while conducting math classes. This is because
they are more focused on improving academic achievement (Mariani & Ismail, 2013).

7. The Bar Model Concept with the Butterfly Method :
A Way To Enhance Student Ability In Addition And Subtraction Fraction.
• The Butterfly Method is a visual and an alternative method for teaching the addition and
subtraction of fractions where diagonal and horizontal multiplication of denominators
and numerators are applied (Rosli, Han, Capraro, & Capraro, 2013).
• The Bar Model concept is a technique where bars are drawn as a whole, divided into
equal pieces, and defined by the denominator (Madani, Tengah, & Prahmana, 2018).
• The Bar Model algorithm helps students to visualize and a useful tool to understand the
concept of addition and subtraction of fractions (Thirunavukkarasu & Senthilnathan,
2014).
• Bar modelling is a technique of representing any Mathematics problems pictorially,
which has been popularised by the Singapore Mathematics teaching method (Emeny,
2014).
• The Butterfly Method will leave a mental picture of the algorithm that can be easily
applied (Miller & Obara, 2017).

8. 6
5
9
7
3
2
10
5
=
2
1
to add and subtract fractions with Model Bar concept.

9. • The Butterfly Method is a visual and an alternative method for teaching addition and
subtraction of fractions where the diagonal and horizontal multiplication of the
denominators and numerators are employed as well as to work out a visual way by
drawing the Butterfly on both of the fractions with different denominators.
• According to Cardone (2015), fractions can be compared, added, or subtracted by
shading the bars on the Bar Model, whereas the total bars represent the common
denominator.
• By applying Bruner’s constructivism theory, students will construct their
understanding of adding and subtracting fractions by using the Bar Model concept.
• Cardone (2015) advised teachers to help students not to rote memorize procedures
and attempt any shortcutting tricks, but to use Bar Models to make connections with
the concepts of understanding fractions.
• Teachers should teach with animated visual Manipulatives in order to show the
splitting of Bar Models, and this will help students to visualize or to see the
relationship of the Bar Model with the Butterfly Method in evaluating the given
fractions.
CONCLUSION………..