{"id":6428,"date":"2018-01-10T00:33:00","date_gmt":"2018-01-10T00:33:00","guid":{"rendered":"https:\/\/theteacherstudio.com\/2018\/01\/what-makes-teaching-fractions-so.html"},"modified":"2019-01-30T15:51:39","modified_gmt":"2019-01-30T15:51:39","slug":"what-makes-teaching-fractions-so","status":"publish","type":"post","link":"https:\/\/theteacherstudio.com\/what-makes-teaching-fractions-so\/","title":{"rendered":"What makes teaching fractions so challenging?"},"content":{"rendered":"

If you have followed me or seen any of my webinars, you know that I wholeheartedly believe that all students can learn math at a high level–and we, as teachers, need to constantly strive to refine our teaching strategies and methods so that we reach ALL students…no matter their starting point.\u00a0 This is especially true for fractions which can be one of the most challenging things we teach.\u00a0 This post begins a series about fraction instruction that I hope you find helpful and meaningful.<\/p>\n

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\nTo begin, I don’t think it would be surprising if I told you that a majority of intermediate grade teachers declare that fractions are one of (or THE) most challenging concept for them to teach–and for their students to learn.\u00a0 So why is this?\u00a0 And more importantly–what can we do about it?!\u00a0 These questions will be the foundation for this series of blog posts.\u00a0 We CAN make a difference in how we reach our students and deepen their fraction knowledge.<\/p>\n

What makes fractions so challenging to teach?<\/h2>\n

I have done some research (formal and informal) by looking at what the experts have said and by asking countless teachers in the trenches, and I think I have some answers as to what makes this topic so overwhelming for many.\u00a0 Why is this important?\u00a0 If we can identify the stumbling blocks, then we can start to chip away at them and begin to learn more about what WILL work and how we can overcome these obstacles.\u00a0 I am constantly on a quest to find ways to “make sense” of fractions for my students (which is what led to me creating a full fraction unit<\/a> to use with my students!)<\/p>\n

\u00a0Fractions are not always “concrete”.<\/h3>\n
Although we may start our fraction instruction with objects–perhaps paper folding or plastic fraction pieces–we too often move very quickly past these real-world models to paper and pencil computation.\u00a0 I’m going to argue that even drawings<\/b> of fractions fail to be concrete enough for some students with limited fraction sense.\u00a0 To many, this is just a circle with lines.\u00a0 The physical act of cutting, folding, and manipulating is so important for many.<\/div>\n
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To make matters more complicated–this is just the beginning!\u00a0 When we multiply whole numbers, we can make “groups of” objects, right?\u00a0 3 times 6 can be represented by 3 piles of 6 objects.\u00a0 Do we take the time to really make our more advanced fraction concepts such as multiplying and dividing concrete?\u00a0 Do students really “see” what happens when we multiply fractions (HINT:\u00a0 We can still model 3 groups of 1\/4 or 6 groups of 2\/3…and it can make a huge difference!).\u00a0 When we move too quickly to “bare numbers”, we make a lot of assumptions about what our students truly understand.<\/div>\n
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Fractions are numbers–really!<\/h3>\n
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Here’s another statement that seems a little obvious, right?\u00a0 Of course, fractions are numbers!\u00a0 But wait…try to get yourself into the mindset of a struggling student.\u00a0 We show them pictures of pizzas and candy bars cut into little pieces.\u00a0 We talk about the pictures in different ways…and we help students learn to “label” them as representing 1\/5 or 3\/8 or whatever the picture represents.\u00a0 Do we really help them understand that fractions allow us to represent real numbers–and even parts of numbers?\u00a0 That when we have a drawing of 3\/8, it means that we have LESS than a whole object or amount?\u00a0 That fractions allow us to show amounts BETWEEN whole numbers?\u00a0 This is a critical part of fractional understanding; the drawings we use to show fractions are merely representations of numbers from a number line.\u00a0 More to come in upcoming posts.<\/p>\n\n\n\n\n
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(These number lines are a part of my fraction number line resource–also part of my 10 resource fraction toolkit)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

The understanding of “unit fraction” is missing<\/h3>\n
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This leads me directly to this concept.\u00a0 The term “unit fraction” refers to a fraction with a<\/div>\n
“1” in the numerator…such as 1\/4, 1\/7, or even 1\/500.\u00a0 Understanding that this is “unit” of measure or amount is so critical.\u00a0 I like to interchange the terms “unit fraction” and “counting fraction” with my students because I really want them to understand that, just like whole numbers, unit fractions can be counted, added, subtracted, composed and decomposed–and more.<\/div>\n
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In the primary years, a great deal of time is spent counting whole numbers in different ways–by ones.\u00a0 By 5’s.\u00a0 By 10’s.\u00a0 We even practice counting backward which helps develop subtraction understanding.\u00a0 The same is true for fractions–and we really cannot make assumptions that all our students can do this automatically.<\/p>\n

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When we count fractional parts (“unit fractions”) using manipulatives, on number lines, and even orally, it helps build that understanding that fractions are numbers.\u00a0 It helps students begin to develop their sense of the relative size of fractions.\u00a0 It helps lead to a greater understanding of what happens when we count and get the same numerator and denominator (a new “whole”) and then count past that to make improper fractions and mixed numbers.\u00a0 When we can count fractions we start to see the additive nature of them…I have 2\/5 and I count up one more fifth and get 3\/5–and this is something that can often be missing in student understanding if time isn’t spent working on this.\u00a0 It really forms the foundation for addition and subtraction of fractions–and is truly an essential skill.<\/div>\n
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Fraction interventions<\/h3>\n
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In fact, this is one of the first interventions I do with students who are struggling. I get out a manipulative of some type (I linked to some of my favorites…note, these are affiliate links) and we practice counting.\u00a0 We notice what happens when we reach a “whole” and then beyond.\u00a0 We essentially “play” with these counting fractions and then begin to record our findings on paper and pencil. I will often pull these back out when reteaching is needed. Also, consider when you look for manipulatives that some have the fractional part written on them and others are blank–both are great, but make your decisions based on what you want to accomplish.\u00a0 Similarly, if you ONLY use circles or ONLY use fraction bars, students may struggle to generalize the learning.\u00a0 Even using tools like pattern blocks can be really helpful as you study basic fraction concepts.<\/p>\n<\/div>\n

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