Enhancing Fraction Understanding: A Multiple Representation Approach

This essay discusses the effectiveness of using a multiple representation approach to teach fractions and operations with fractions in middle school. It emphasizes how combining mathematical symbols with representations like circles, rectangles, and number lines aids in visualizing fractions and relating them to whole numbers. The approach fosters an interactive environment where students can manipulate fractional parts, promoting a deeper understanding of equal proportions and various mathematical operations. Furthermore, it enhances learners' efficacy, cognitive skills, reasoning, and innovative thinking. The essay also highlights the importance of incorporating students' interests into the representations and enhancing qualitative and quantitative reasoning. It concludes that the multiple representation approach can significantly improve students' interest and performance in fractions, especially when combined with different instructional methods and practical exercises. Desklib provides access to similar assignments and study tools to support student learning.

Using a multiple representation approach to understanding fractions and operations with
fractions 1
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Using a multiple representation approach to understanding fractions and operations with
fractions 2
Using a multiple representation approach to understanding fractions and operations with
fractions
In elementary school, fractions are one of the tough topics which challenge the students.
Different methods are used in the explanation of the fractions. The multiple representation
approach can be used to evade key challenges which students find while studying fractions. A
representation may be used to have different meanings in teaching mathematics. The common
definition for representation according to Seeger, Voight & Werschescion (1998) is
“...representation is any kind of mental state with a specific content; a mental reproduction of a
former mental state, a picture, symbol, or sign, symbolic tool one has to learn their language, a
something “in place of” something else”. Multiple representation approach is defined as a way of
providing the same information in different external mathematical representation. Although
some methods such as modern educational researches (MERs) have been successful in helping
students when learning fractions (Ainsworth, Bibby and Wood, 2010). Some key methods such
as multiple representation approach can be used to enhance the understanding of fractions and
operations with fractions better. Besides, the use of multiple representation approach ensures
that suitable content representation of the fractions is done and therefore guiding the students in
understanding the fractions and operations with fractions. This paper will analyze the
effectiveness of the use of the multiple representation approach in teaching fractions and
operations with fractions to middle school. In addition, this paper will include key
recommendations which can be included in this approach to ensure that students can get more
understanding of the fraction topic.

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The combination of the mathematical symbols with the multiple representation approach
leads to better and deeper understanding of fractions. The use of representations such as circles,
rectangles, number lines helps the student in their visualization of the fractions with the whole
numbers (Hohenwarter and Preiner, 2007). Having the visual representation helps the students to
understand how the fractions can relate to the whole numbers which they already know.
Learning fractions need the connection of the small parts and relating them to the bigger whole
numbers. When dealing with fractions, students find it hard to relate the different parts. The use
of multiple representations helps the students to have an easy time in relating these different
parts (Pantziara & Philippou, 2012). Different choices of representations are available which aid
the learners in relating the fractions. To implement this approach, to junior mathematics class,
the teachers can improvise different representation images which interest the learners.
In addition, to better understand the fractions, students need to have the freedom to
manipulate different fractional parts. The use of multiple representation approach gives the
learners this freedom for them to continue with exploration. Their active manipulation of the
various representations helps them to enhance their understanding (Hegarty and Kozhevnikov,
2009). The students can therefore divide, multiply, add and subtract different fractions. Allowing
the learners to have this freedom helps them to perform different mathematical operations with
the representations and thus increasing their innovativeness in dealing with the portions and
fractional parts. In addition, concepts such as drag and drop of different fractions help the
learners to relate the fractional parts to the whole numbers. Through this, the learners will be able
to understand the fractional parts and connecting to the numbers. The notional of equal
proportion is enhanced through the use of multiple representation approach in teaching fractions.

Using a multiple representation approach to understanding fractions and operations with
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The learners can, therefore, be able to relate which fractional parts are equal. The use of this
approach helps the student to develop a supporting connection between different parts (Schultz
and Waters, 2013). The learners are able to use the representations to connect the appearances of
fractions. This approach, therefore, creates an environment where the student can create different
representation parts and equate them to one another.
Moreover, when dealing with fractions and operations with fractions, an interactive
environment is needed. The multiple representations offer an interactive environment where the
students can try different operations of their choice in dealing with fractions (Mill, 2011). This
approach gives the student freedom to work different operations with the representations for
them to understand the topic. The interactive environment is, therefore, able to enhance the
creativity of the learners and therefore promoting their knowledge in dealing with fractions. This
environment helps the student to formulate what the fractions are in different situations. For
instance, they will be able to understand two parts of a whole block is the same as four parts of
two blocks. This helps the learners to be able to perform different fractional operations in such
environment (Hansen, Geraniou & Mavrikis, 2014). The use of this approach helps the student to
have proper integration by combining different representations to relate with whole numbers and
fractional parts.
Also, this approach is able to enhance learners efficacy and therefore able to facilitate
cognitive skills. Learning skills are needed to be developed at different stages for the learners to
get clear pictures of the topics. It is important for learners to have these skills and the multiple
representation approach is able to help the student to acquire these skills (Rau, Aleven &
Rummel, 2009). Fractional operations require key skills which will enhance dealing with fraction

Using a multiple representation approach to understanding fractions and operations with
fractions 5
problems. Multiple representation approach can enhance reasoning and thinking skills and
therefore able to improve the dealing with fraction problems. Innovation helps to come up with
new ways which are easy to deal with the different issues. The innovativeness will ensure that
learners will come up with other key skills while using the multiple representation approach.
This will enhance their understanding of the different fractional operations and enhance their
knowledge. In addition, these skills are likely to help the teachers in passing their knowledge of
the fractions to different students (Ainsworth, 2006). This aspect for the teachers will ensure that
different students are able to understand the topic without locking any other them outside.
In addition, the multiple representation approach is able to offer different new and
different instructional methods. According to Klein (2003); `Learning to create and interpret
representations using specific media such as texts, graphics, and even videotapes are themselves
curricular goals for many teachers and students` (p. 49). The different instruction methods will
be helpful for the teachers in achieving their goals in explaining the fractions to the students. The
various instructional methods are essential for the students to grasp the concepts of dealing with
fractions. Through these methods, the learners will be able to pick the most appropriate ways for
them to tackle issues and problems involving the fractions. Addition of vital instructional
practices is needed to enhance the understanding of the different concepts involving the
fractions.
Most importantly, the use of the multiple representation approach is able to enhance the
assessment of the students in the fraction topic. The fact that the learners can visualize the
fractional problems in their different ways ensures that their performance is enhanced (Plötzner,
Bodemer & Neudert, 2008). The students have options on representing the fractional in different

Using a multiple representation approach to understanding fractions and operations with
fractions 6
ways on which they have interest in. This ensures that the students are able to grasp the fractional
ideas and therefore enhancing their understanding of the topic. The assessment by Martinie &
Bay-Williams (2003), show that students who use the multiple representation approach have
high performance. The students are able to represent the fractions with different representation
which they have interests on. In addition, to enhance the understanding of the portion through the
use of the multiple representation approach, the teachers should be able to identify the interests
of the students during their junior classes. This will help the teachers to use a representation
which the students hold dear to and therefore enhance their understanding of the topic (Rau,
Aleven & Rummel, 2010). The teacher should, therefore, understand the hobbies of the students
and use representations which have indicators of these hobbies. This will ensure that the student
creates high interest in the fraction and fractional operation and therefore helping them to
understand the topic more.
In addition, enhancing qualitative and quantitative reasoning is important in
understanding issues when dealing with fraction and fractional operations (Tunç-Pekkan,
Zeylikman, Aleven & Rummel, 2010). The multiple representation approach is able to enhance
the acquisition of such reasoning for the learners. When used during the junior classes, the
method helps to strengthen the thinking of the students and helping them to understand the issues
of fractions. The use of the approach helps the student to conceptualize the ideas of fractions a
shift their meaning in reality (Alajmi, 2012). This improves the handling the fractional
operations well. In relation to this, the teachers should look at other essential means which will
enhance the reasoning of the student in relation to the fraction and fractional operations. To

Using a multiple representation approach to understanding fractions and operations with
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enhance the understanding of the topic to the junior classes, the teachers need to evaluate the
reasoning of the students when applying this approach.
The use of this approach in teaching mathematics to junior class may be achieved by
using different representation such as pictures, videos and manipulations in order to create
interests for the learners to understand the topics (Ainsworth, Bibby & Wood, 2002). When used
in fractions, the learners will have the much-needed curiosity which will inspire them to
understand fractional operations. The use of the multiple representation approach should be
enhanced by the teachers to ensure that the approach has interest to the students. The teachers
have to be innovative by combining different interests of the students to ensure that they create
the required motivation in fractional operations. The inspiration in the fraction will generate a
key situation where the students have the curiosity to solve and understand the fractional
operations (Martinie & Bay-Williams, 2003). Lack of inspiration has been missing in fraction
topic since most of the students feel it hard for them.
Using different representation models and practical exercises will be required for the
junior mathematic classes when implementing this idea. The junior mathematics class requires
the motivation to ensure that they have a positive attitude to fraction problems. In the past, lack
of motivation on some of these topics had created the friction of the student. This has been
lacking to the students who find it hard to understand the topic. Creating the motivation for the
junior classes will ensure that the student gets the required attitude to the student and enhance
their understanding of the fractional and fractional operations.

Using a multiple representation approach to understanding fractions and operations with
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According to my personal view, this approach is much needed to solve problems, which
most learners have experienced in fractional topics. The idea has been able to create different
dimensions under which I can view the fractions and its operations. This is able to make it easy
for me to understand fractional and fractional operations. This idea, therefore, needs much
attention from the teachers to ensure that the learners are able to get these different perspectives
which they can handle the topic. Creating different options for the learners in processing the
fractions will help in making the subject comfortable and thus enhancing their interest in it.
In conclusion, the multiple representation approach can be a useful method of ensuring
that the junior students have an apparent interest in fractions and fraction operations. This
approach is able to create motivation and attention to the student when their hobbies are
combined in the representations. This ensures that the teachers create the required curiosity and
interest to the student concerning the fraction topic. Besides, this approach focuses on enhancing
different skills for the junior students and equipping them with relevant reasoning. All these will
ensure that the students can solve the fractional problems with great thinking and skills.

Using a multiple representation approach to understanding fractions and operations with
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References
Ainsworth, S. (2006). DeFT: A conceptual framework for considering learning with multiple
representations. Learning and Instruction, 16(3), 183-198.
Ainsworth, S. Bibby, P. and Wood, D. (2010). "Information technology and multiple
representations: New opportunities – new problems," Journal of Information Technology
for Teacher Education 6, no. 1.
Ainsworth, S., Bibby, P., & Wood, D. (2002). Examining the effects of different multiple
representational systems in learning primary mathematics. Journal of the Learning
Sciences, 11(1), 25-61.
Alajmi, A. H. (2012). How do elementary textbooks address fractions? A review of mathematics
textbooks in the USA, Japan, and Kuwait.
Educational Studies in Mathematics, 79, 239–261.
Hansen, A. Geraniou, E. & Mavrikis, M. (2014). Designing interactive representations for
learning fractions. Paper presented at the British Education Research Association
Conference, London.
Hegarty, M., and Kozhevnikov, M. (2009). Types of Visual-Spatial Representations and
Mathematical Problem Solving. Journal of Educational Psychology v91, no 4 p.684 –
689.
Hohenwarter, M. and Preiner, J. (2007). "Dynamic mathematics with GeoGebra," Journal of
Online Mathematics and its Applications 7.

Using a multiple representation approach to understanding fractions and operations with
fractions 10
Klein, P. D. (2003). Rethinking the multiplicity of cognitive resources and curricular
representations: alternatives to `learning styles` and `multiple intelligences`. Journal of
Curriculum Studies, 35(1), 45-81.
Martinie, S.L., & Bay-Williams, J.M. (2003) Investigating students’ conceptual understanding of
decimal fractions using multiple representations. Mathematics Teaching in the Middle
School, 8(5), 244-248.
Mill, J. (2011). Body Fractions: A physical Approach to Fraction Learning. Australian Primary
Mathematics Classroom, v16 n2 p17-22.
Pantziara, M., & Philippou, G. (2012). Levels of students’ “conception” of fractions.
Educational Studies in Mathematics, 79, 61–83.
Plötzner, R., Bodemer, D., & Neudert, S. (2008). Successful and less successful use of dynamic
visualizations in instructional texts. In R. K. Lowe & W. Schnotz (Eds.), Learning with
Animation. Research implications for design. New York: Cambridge University Press.
Rau, M. A., Aleven, V., & Rummel, N. (2009). Intelligent Tutoring Systems with Multiple
Representations and Self-Explanation Prompts Support Learning of Fractions. In V.
Dimitrova, R. Mizoguchi, & B. du Boulay (Eds.), Proc. of the 14th International
Conference on AI in Education. Amsterdam: IOS Press, 441—448.
Rau, M; Aleven, V; & Rummel, N. (2010) Blocked versus Interleaved Practice With Multiple
Representations in an Intelligent Tutoring System for Fractions. 10th International
Conference of Intelligent Tutoring Systems (ITS), 413-422.

Using a multiple representation approach to understanding fractions and operations with
fractions 11
Schultz J. and Waters, M. (2013). "Why Representations?" Mathematics Teacher 93, no. 6. P.
448–53
Seeger, F., Voight, I. & Werschescio, V. (1998). Representations in the mathematics class-room:
reflections and constructions. In F. Seeger, I. Voight, & V. Werschescio, (Eds.). The
Culture of the Mathematics Classroom (pp. 308-343). Cambridge: Cambridge University
Press.
Tunç-Pekkan, Z; Zeylikman, L; Aleven, V; & Rummel, N. (2010). Fifth Graders’ Conception of
Fractions on Numberline Representations. The annual meeting of North American
Chapter of the International Group for the Psychology of Mathematics Education,
Columbus, Ohio.