Math — Developing Fraction Sense Essay Example

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  • A brief description of the purpose of the essay/paper

Main body

  • Number sense and numeracy

  • Fraction sense’ and how is it related to number sense and numeracy

  • Important things children should know relating to fraction

  • Factors that can impact on students developing fraction sense’

  • Misconceptions around fractions that can be developed by children and how
    they be addressed


Important points from the pape


This paper seeks to account for the development of fraction sense. The first of the paper covers number sense, which is the intuitive feel for numbers and their various applications. People who understand numbers and can use them in daily life experiences are said to be in possession of number sense. The paper then would address numeracy, as a central part of math knowledge e.g. houses number sense, measurement, and data sense. This section will be followed by fraction sense and the important things that a child should know about fraction senses. The other part of the paper lays emphasis on the different factors that affect development of fraction sense. The end tackles misconceptions around fractions that can be developed by children and approaches to address them.

Number Sense

In a study by Lindquist (2004), number sense is a perceptive feel for numbers in addition to their various uses and interpretations. It further captures the capacity to calculate accurately and efficiently, spot errors, and distinguish validity of results. The classes of people who have the number sense are in a position to understand numbers and subsequently use them as a tool in daily living. Moreover, people with good number sense are able to identify relative magnitudes of numbers and establish benchmarks that can be used to measure common objects and situations in the surrounding environment.

There are five specific components that characterize the number sense: number meaning, relationship, magnitude, their operations and referents for numbers and quantities (Bullock, 1994). These skills are vital given that they contribute to general intuition concerning numbers and further construct a foundation for advancing the skills. A good number system is evident among students who are proficient in mental calculation, computational estimation, making judgment on relative magnitude of numbers, and recognize place value concept.

A sense of number begins at very early age such that children at the age of two years are able to identify one, two, or three objects before they count with understanding (Gelman, 1978). The renowned psychologist Piaget referred such ability as “subitising.” As a child develops until the age of four, a group of four can be automatically identified without necessarily counting. The skill depends on the capability of the mind to form mental images of patterns and correlate them with a number. As an example, six dots arranged in two rows of three can be easily identified because of familiarity. This is based on the understanding that three added to three makes six. Before a child begins schooling, such an understanding has already begun and ought to be nurtured since it lays a foundation for development of complex mental calculations.

It is fundamental to note some of the teaching strategies that promote development of number sense. A teacher can present objects such as dices or cards in various arrangements in order to prompt various mental strategies (Steen, 2001). An example is presenting six cards in a group of four and a pair invites a student to combine four and two to arrive at six. In a situation where the group of four is not subitised, a child may see it as two and two and two that combines to make up six. From this example, different arrangements call upon a student to use varied strategies in order to reach an end. These strategies vary from one person to another. Initially, objects used are movables to allow a child manipulate the object into various groups. Games can also be employed in an attempt to reinforce and develop ideas and procedures, which were previously introduced to a child.


This is the ability to reason while using numbers and other mathematical concepts. A person who is literate numerically is capable of managing and responding to the mathematical demand of life. Some of the characteristics of numeracy include number sense, operation sense, computation, measurement, geometry, probability, and statistics (Booker, 1997). Numeracy furnishes an individual with skills necessary to function well in schooling. Besides, a student is equipped to handle challenges beyond the school.

Numeracy involves central part of mathematical knowledge e. g number sense, measurement, and data sense that varies with experiences and needs. Secondly, numeracy revolves around critical application of math in a particular context to realize a desired outcome. Finally, numeracy capture actual processes and strategies required to communicate what has been done and reasons for such deeds (Siemon, 2001).

Fraction sense

This is the intuitive feel for fractions. Fractions are often used as an approach of describing parts when a whole is divided into parts. The whole can be one length or shape. Before a child develops the concept of fraction, number sense acts as its foundation. A child will be able to develop a sense of fraction after first describing relative magnitude of numbers by drawing a comparison with common benchmarks. At the same time, the child must first give simple estimates, order a set of numbers, and find a number between numbers. These are just the basics of number sense, which ought to be developed by a student before progressing to gain the sense of fractions.

To demonstrate this relationship between number sense and fraction sense, ½ can be used as a benchmark for estimating relative size of fractions. From participating in this task, a child makes use of number sense to estimate and understand relative sizes of fractions. At the onset of the lesson, a child begins by identifying fractions close to ½ while giving an explanation (BS, 1997). The student then progresses to confirm whether some fraction additions are more or less than one. At the end, the learner extends the knowledge to similar but open-ended task.

Given that numeracy is knowledge of numbers and operating with them, the concept is important in fraction sense since the ideas can be used to work with denominators and numerators. A child who has a strong numeracy is able to solve numerical problems including money, measurement, and time. Often, numeracy is utilised during operation with numbers, utilising measurement in various purposes, solving geometric problems, and managing data and probability. Similarly, a student who is said to have developed the fraction sense should be in a position to apply the knowledge in daily life.

While teaching fraction sense, a teacher’s focal point is on a number of objectives. One of the objectives is for the student to uncover, and separate fractional parts of whole. Secondly, the student should create fractions using data covering on lengths. At the same time, student is supposed to divide geometrically grids into various parts to produce fractional pieces. Finally, the student will apply fraction sense in daily experiences or challenges.

Important things that a child needs to know about fractional sense

The first point that a child should note about fractions is that a problem can be solved from different angles. This is in recognition of the fact that even though fraction problems have a single answer, there can be several ways to arrive the ultimate answer. The child should be familiar with the fact that learning fractions goes beyond finding solutions to mathematical problems. It as well entails applying them in daily experiences to solve problems and further find solutions to new problems faced.

The second factor to be remembered by children is that wrong answers sometimes are helpful. Accuracy has to be noted as an important factor in any mathematical calculations. Where a child reaches a wrong answer during a fraction task, such a result can be used to help a child figure out why the mistake was made. With the help of a teacher or a parent, a child is assisted to understand concepts underlying the problem and to learn to deploy reasoning skills to arrive at the right answer. To illustrate this important factor, a child might be asked to explain how the problem was solved. This explanation will give a hint on specific part of fraction concepts that should be improved. An example is a situation where a child misses to find the least common multiple when adding fractions.

Thirdly is the value of advising a child to be taking risks. This is where a child tries to handle a fractional problem by making several attempts. A child is allowed to explore various avenues that can be employed to solve a specific fraction problem. As the child progresses with the assignment, a teacher or rather a parents encourages the student to expose what is in the mind. This observable fact will strengthen fractional skills consequently leading to independence of thinking.

The final element that a child must attempt to gain is the ability to do mathematics and fractions in own head. It is quite clear that mathematics and fractions are not restricted to pen and paper. A student ought to attempt to do math calculations in the mind. Normally, the skill is applied when doing mathematical calculations in stores, restaurants or any other business environment. At this stage, a child should know that a mental calculation enhances the strength of mathematics. There is need also for a child to make certain that strong grounding in math operations e.g. fraction concepts improves the use of calculators.

Factors that can influence students developing fraction sense

Intellectual ability of a learner affects capacity of a learner to develop fraction sense. This factor is also evident in a class where students learn differently. Some children learn better by seeing or doing things while others learn better by seeing. In the same vein, development of fraction sense is affected by intellectual ability of the learner. In a family set up, even children in similar learning environment can learn at different rates and in varied ways.

The number sense affects development of fraction sense given that knowledge of numbers is vital when working with numbers. More often, students have strong focus on numbers, which creates difficulties when deriving relative size of fractions. In the daily experience of a child, a large number means more. If this concept is transferred to fractions, development of fraction sense will be negatively affected. It is imperative to note that inverse relationship between number of parts and their sizes must be a creation of an individual student.

Students’ common misconceptions about fractions

The first misconception is students believing that both numerators and denominators can be treated as whole numbers, which are separate (Booker, 1997). On frequent occasions, students add or subtract numerators and a denominator of two fractions as a result failing to be acquainted with the idea that denominator defines size while numerator represents number of this part. This misconception can be handled by presenting several meaningful problems. The practices would help a student deduce that treating numerators and denominators is not appropriate and can amount to deception. One example to deal with this misconception is where a student has ¾ of an orange and proceeds to give 1/3 of it to a friend. From this, it is evident that subtracting directly denominator and numerators gives an inappropriate answer.

Failing to find a common denominator while in the process of subtracting or adding two fractions is the second misconception. This is where a student fails to convert fractions to a common and equivalent denominator before proceeding with either addition or subtraction. Similarly, a student can change the value of denominator without making corresponding change to the numerator. The misconception can be dealt with by utilizing the number line and other additional visual demonstrations, which show equivalent fractions.

Thirdly is where a student believes that whole numbers should be manipulated when working with fractions greater than one (Bullock, 1994). In this scenario, a student fails to understand concepts of mixed numbers. Related with this is a thought that whole numbers have same denominator as a fraction in question e.g. 4-3/8 is the same as 4/8-3/8. It is the responsibility of the teacher to help students make a distinction between mixed fractions and improper fractions.

The forth misconception is touches on students who eave the denominator unchanged during addition and multiplication of tasks. Students have been noted to leave fractions with common denominator unchanged during the multiplication process. This can be dealt with by giving an explanation on fractions multiplications using unit fractions. An educator can demonstrate that ½*1/2 is similar to ½ of ½, which gives the result of 1/4 i.e. a smaller value.


This essay began by elaborating on number sense and numeracy that acts as building block for fractional sense. It is evident from the literature that numeracy sense is the subset of fractional sense. The paper the progressed with an in-depth discussion on important things children should know relating to fraction sense. This was followed by an analysis of factors affecting development of fractional sense. Lastly, students’ common misconceptions about fractions were given necessary attention.

Reference List

Board of Studies. (1998). Effective Assessment for Mathematics — Levels 4 to 6,

Melbourne: Longman.

Bullock, J. O. (1994), «Literacy in the Language of Mathematics», the American Mathematical Monthly, 101 (8): 735–743.

Booker, G., Bond, D., Briggs, J. & Davey, G. (1997). Teaching Primary Mathematics. 2nd Edition. Melbourne” Longman Cheshire.

Fischer, F. (1990). A part-part-whole curriculum for teaching number to kindergarten. Journal for Research in Mathematics Education, 21, 207-215.

Gelman, R. & Gallistel, C. (1978). The Child’s Understanding of Number. Cambridge, MA: Harvard University Press.

Lindquist, M. M., Lambdin, D. V., Smith, N.L., & Suydam, M. N. (2004). Helping children learn mathematics. 7th Ed. Boston, MA: John Wiley & Sons.

Siemon, D, Virgona, J, & Corneille, K (2001) Middle Years Numeracy Research Project

Final Report. Department of Education and Training

Steen, L. A. (2001), «Mathematics and Numeracy: Two Literacies, One Language», the Mathematics Educator, Journal of the Singapore Association of Mathematics Educators, 6 (1): 10–16.