Formal VocabularyLearners may be drowning in the language of fractions, even before thinking about their properties.do not behave like ‘normal’numbersFractions sometimes represent an amount, something that can be visualised,and sometimes an operation, e.g. 3/4 can mean a shape with 3 equal piecesshaded out of 4; it can mean the result of dividing 3 by 4, or part of aninstruction to find, say, 3/4 of 16.They mamy master it perohindi
Factual knowledge (memorization) contributes little to accurate student performanceMath is cumulative Weak foundation = poor future performancelistening to the teacher and completing their ownWorksheets the main way of learning?- maghanapng picture
“There is evidence that the development of students’ understanding of fractions is greatly enhanced by students’ developing their own representations of fraction ideas including pictorial, symbolic and spoken representations to clarify their thinking.”
Typically this is the only representation taughtStudent understanding of rational numbers (a huge and complex subject in mathematics) is based on a tiny foundationProvide exposure to other types of interpretations Ignoring other ideas leaves incomplete understandingStudents must be able to do more than just manipulate symbols
In part–whole situations, which aretypically used to introduce fractions inprimary school, the denominatorindicates the number of equal parts intowhich a whole was cut and thenumerator indicates the number of partstaken: for example, if a chocolate barwas cut into 4 equal parts and Sarah ate1, Sarah ate1/4 of the chocolate.
A clock face shows clearly what halves and quarters look like, and can beextended to other fractions with discussion about why some are easier toshow than othersPaalala:One of 3/8 pie and 3 of 1/8 pies have different meanings even though the final quantity are the same. This can be understood by introducing the concept of unit fraction.Wag langpuro pie chart:pwedenama, hnyung hats
All too often learners think of ‘fractions’ as being a discrete (and often difficult)topic that has no real connection with any other area of maths.They should have plenty of experience doing this toexplore the connections, rather than trying to learn these by rote.
Get cooking. Teach kids simple measurements such as 1 cup, 1/2 cup, 1/4 cup, 1/3 cup. Let them experiment with measuring solids and liquids. Show them how three 1/3 cup measure equals 1 cup, by allowing them to pour different ingredients. Ask them to find out how many 1/4 cup measures it would take to fill a 1 cup measure. Reverse the experiment, and challenge them to discover how many 1/4 cups they can take out of a one cup measure.
Many learners identify fractions as an area of maths that they find difficult,despite often using concepts of sharing effectively in their daily lives.
Learners may group together different representationsof the same fraction: in a picture, in words, on a number line, as a decimal.They may classify them according to their size, or classify statements aboutfractions as true or false
In the article you have to imagine things like how many people would make up a quarter of the population. It's a bit like dividing England into four areas, one area would be a quarter of the population. It's a big amount. Or, another way of looking at it is to imagine a crowd of people and imagine lines dividing them into quarters.
A tape measure andsome sketching can check the truth of these rules.
How to Teach Fractions
Problem Fractions = one of the most difficult concepts for children to grasp Notation of fractions Formal vocabulary Learners may be able to draw and label fractions correctly, but not be able to put them in order of size, or use them to solve problems. Do not behave like ‘normal’ numbers
How to Teach Fractions It is important that learners think about relationships between fractions, rather than just trying to memorize methods for processing them. FACTUAL CONCECPTUAL FACTUAL We should move towards a more holistic approach when teaching fractions.
Teachers’ Mistakes Syntactic vs. Semantic emphasis Technical procedures instead of understanding/meaning Adult- vs. Student- centered approach Ignore ‘prefactional’ knowledge Adult concepts are very different from children’s Confusing representation
Multiple Representations Students given multiple explanations can have… Greater conceptual understanding Transfer knowledge to tasks not directly taught to them
Different Interpretations for the Fraction ¾ (Lamon, 2001) Provide exposure to other types of interpretations Ignoring other ideas leaves incomplete understanding
Multiple Representations Learners need to be familiar with multiple representations of fractions, and should always be given more than one representation. 1/3 of the class are boys.
Multiple Representations Use a variety of mediums to illustrate the same fraction Sharing Cakes Clock Manipulatives
Multiple Representations What fraction of the hats are red?
Multiple Representations What fraction of the circles are blue?
Multiple Representations Pictorial representations of a particular fraction may be of different sizes and different shapes. For example, don’t always use shaded sections of circles. When you divide things into fractions it doesn't matter how you do this as long as the parts are all equal in size.
Multiple Representations Use manipulatives when introducing fractions. Practice cutting different shapes into fractions.
How to teach Fractions Students learn more if they actually enjoy the activity, have a chance to discuss what they do, explain their work, and reach a shared understanding. Conceptual Understanding
Making connections Integrate into other math topics solving money problems sharing a bill comparing prices calculating journey times
Making Conncetions Cooking checking the weight of ingredients
Making Connections Interpreting data in pictograms and bar charts Using a metre rule Measuring a room Comparing each other’s heights
Making Connections Ask learners to think of some fractions they encounter in an everyday context
Classifying Fraction Classifying different representations of fractions, or statements about them, can be a very effective method of encouraging learners to reflect on and discuss their properties
Evaluating statements about fractions Learners are given some generalisations about fractions, perhaps printed out on separate cards, and are asked to choose whether they consider these to be ‘always’, ‘sometimes’ or ‘never’ true, and to justify their choices, with examples and convincing explanation.
Links outside the classroom Many learners do not use their understanding of fractions outside the classroom, and are unwilling or unable to transfer it to ‘real life’ problems. Encourage children to give names to the fractions they see in everyday life. Did your family have meatloaf for dinner last night? How many pieces was it cut into? How many pieces did you eat? Encourage kids to share.
Links outside the classroom The proportions of the human body provide links with art, and with dressmaking/tailoring. Artists assume the eyes are half-way down the face, the nose half-way between the eyes and the chin.
Fraction Quotes A man is like a fraction whose numerator is what he is and whose denominator is what he thinks of himself. The larger the denominator, the smaller the fraction. —Leo Tolstoy “We live but a fraction of our lives” — Henry David Thoreau
Games Fraction War Game Show (Jeopardy) Fairytales Fraction Blackjack