Slice Fractions

The word fraction is derived from the Latin word fractus meaning broken (Fraction, n.d.).  Although there may have been instances of fraction use all over the world prior; it is not surprising that fractions were first used consistently by Egyptians in about 1000BC (Fraction, n.d.).  A different notation and method were used; however, the same modern day answers were achieved (Fraction, n.d.).  Greeks began using fractions around 540BC during the time of the well known philosopher, Pythagoras (Fraction, n.d.).  Indian Jain mathematicians wrote Sthananga Sutra, which listed the topics of mathematics studied in India in 150BC (Fraction, n.d.).  The first modern expressions of fractions appeared in about 500AD in the works of Indian mathematician, Aryabhatta, in 628AD via the works of Indian mathematician, Brahmagupta, and Bhaskara in 1150AD (Fraction, n.d.).  The works of these mathematicians represented fractions as we know them today; however, without a bar between the numerator and denominator (Fraction, n.d.).  Use of the horizontal fraction bar that we use today was first seen in the works of a Muslim mathematician from Morocco known as Al-Hassār in 1200AD (Fraction, n.d.).  This same notation is later seen in the works of Leonardo Fibbonacci in the 13th century (Fraction, n.d.).  A persistent use of fractions over the past 4000 years demonstrates both the importance as well as usefulness of fraction concepts to progression of the human species.

According to Bruce, Chang, Flynn, & Yearly (2013), fractions have historically presented challenges to education specialists due to “difficult-to-learn and difficult-to-teach concepts” (Bruce et al, 2013) involved.  These difficulties present themselves in all stages of education, from Primary school students through to College level students (Bruce et al, 2013).  It is most concerning; however, that difficulty in understanding fractions persists into adulthood having immense effects on professions such as “medicine and health care, construction and computer programming” (Bruce et al, 2013).  Furthermore, careers in science, technology, engineering, and mathematics (STEM) all require strong foundations in fraction concepts.  Students who are uncomfortable with fractions may be reluctant to choose career paths involving mathematics, greatly reducing opportunities later in life.  As Bruce et al (2013) points out, implications in medicine due to an inadequate understanding of fractions can be greatly detrimental.  “Pediatricians, nurses, and pharmacists were tested for errors resulting from the calculation of drug doses for neonatal intensive care infants.  Of the calculation errors identified, 38.5% of pediatricians’ errors, 56% of nurses’ errors, and 1% of pharmacists’ errors would have resulted in administration of 10 times the prescribed dose” (Grillo, Latif, & Stolte, 2001, p.168; Bruce et al, 2013).  The sheer importance of a solid foundation in difficult concepts such as fractions is reason to provide children with early opportunities to embrace such concepts.

Because mathematics is a subject which builds upon previous knowledge, an inability to grasp concepts in understanding fractions can serve to hinder student ability in further mathematics education (Bruce et al, 2013).  “Learning fractions is probably one of the most serious obstacles to the mathematical maturation of children” (in Charalambous & Pitta-Pantazi, 2007, 293; Bruce et al, 2013).  Cognitive processes such as proportional reasoning and spatial reasoning are important in the ability to grasp fraction concepts, while fraction concepts are pertinent in later mathematics concepts such as algebraic reasoning and probability (Bruce et al, 2013), thus fraction concept synthesis is an immensely important step in achieving higher mathematics success. Difficulty in teaching fraction concepts lies partially in the fact that fractions are not typically an overt part of daily life; however, by including opportunities for children to experience fractions in daily life we increase their understanding of fractions even prior to or as a supplement to formal education (Bruce et al, 2013).

Slice Fractions is an application developed by Ululab for children ages 5-12; however my son loved this game and did well with it when he was only three and still loves it at age five.  The University of Quebec at Montreal (UQAM) conducted a research study on the game in a school classroom of year 3 students in which Slice Fractions was found to “significantly improve students’ performance in a very short amount of time” (Slice Fractions, n.d.).  By partitioning students into three groups, one receiving only traditional teaching, one only playing the Slice Fractions game, and one receiving both treatments, researchers were able to test students to measure the amount of learning that took place (UQAM, n.d.).  “The two groups who used Slice Fractions showed greater and more significant improvement in performance than the students who received only traditional teaching” (UQAM, n.d.).  Available in 13 languages and costing only $2.99, Slice Fractions is well worth the cost.

The application covers Common Core concepts such as (Slice Fractions, n.d.):

  • part-whole partitioning
  • numerator/denominator notation
  • fraction equivalence
  • fraction ordering
  • fraction subtraction
  • Common Core State Standards*

And proves enjoyable for children due to key features such as (Slice Fractions, n.d.):

  • learn fraction concepts without words
  • guide an adorable mammoth
  • collect funky hats
  • solve innovative physics puzzles

In addition the application has earned numerous awards for its innovative success (Slice Fractions, n.d.):

  • Best of 2014 – App Store, Apple
  • Apple Editor’s Choice – App Store Apple
  • Best Original Digital Content 2015 – Youth Media Alliance
  • Best New Interactive Media 2015 – Numix
  • Best Family Friendly Game 2014 – Indie Prize Showcase Awards
  • Gold Medal Winner 2014 – International Serious Play Awards
  • Editor’s Choice for Excellence in Design – Children’s Technology Review
  • Winner of a Parent’s Choice Gold Award 2014
  • Solver Winner 2014 – National Parenting Publications Awards
  • Best Game Audio Nomination 2014 – Indie Prize Showcase Awards

A persistent use of fractions over the past 4000 years demonstrates both the importance as well as usefulness of fraction concepts to progression of the human species.  Furthermore, there is an increased need for students who are successful in STEM related areas.  Providing children with opportunities to engage with fractions in daily life is pertinent to successful education in these areas.  The belief that play cannot be educational should be discarded.  There is no reason why learning shouldn’t be fun.  Allowing children to acquire knowledge through enjoyable play supports a love of lifelong learning and gives parents peace of mind knowing that their children are engaged in purposeful play.

*Common Core State Standards: 

  • CCSS.Math.Content.2.G.A.2: Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.
  • CCSS.Math.Content.2.G.A.3: Partition circles and rectangles into two, three, or four equal shares […]. Recognize that equal shares of identical wholes need not have the same shape.
  • CCSS.Math.Content.3.NF.A.1: Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
  • CCSS.Math.Content.3.NF.A.3: Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
  • CCSS.Math.Content.4.NF.A.1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
  • CCSS.Math.Content.4.NF.A.2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2.[…] Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
  • CCSS.Math.Content.4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
  • CCSS.Math.Content.4.NF.B.3: Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
  • CCSS.Math.Content.4.NF.B.3.B: Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
  • CCSS.Math.Content.4.NF.B.3.C: Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction.

References:

Bruce, C., Chang, D., Flynn, T., & Yearly, S. (2013). Foundations to Learning and Teaching Fractions: Addition and Subtraction. 1-54. Retrieved January 16, 2017.

Fraction. (n.d.). Retrieved January 16, 2017, from https://en.wikipedia.org/wiki/Fraction_(mathematics)

Slice Fractions. (n.d.). Retrieved January 16, 2017, from http://ululab.com/slice-fractions/

UQAM researchers demonstrate effectiveness of educational video game Slice Fractions. (n.d.). Retrieved January 16, 2017, from https://salledepresse.uqam.ca/communiques-de-presse/general/7162-uqam-researchers-demonstrate-effectiveness-of-educational-video-game-slice-fractions

The Slice Fractions App can be found here.  

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