Associations About Associations with color are defined, in part by Faber Birren the author of Color Psychology and Color Therapy by our senses, language, objects or formsand personality characteristics. This section presents the results of color associations and how they compare to other published studies.
Teaching Fractions with Understanding: In her studies of children learning about rational numbers, Grace Lopez-Charles [see Note 1 below] has identified some different perspectives through which children see fractions. This article starts looking at some of those perspectives, firstly by considering what happens in situations where learners are trying to create equal shares.
From sharing using halves learners move to partitioning using other divisions, such as fifths or sixths. This results in the need to develop understandings of equivalence which is discussed in the second section of this article. Finally, we look at some ways of teaching fractions more effectively that arise from Grace's work.
Equal shares Working with halves This strategy appears to be based upon halves because children are confident with this concept. Using this method, the child starts Thesis navigation bar splitting each region or composite unit into two parts. So, sharing three chocolate bars between four children would be achieved by first halving all the bars.
In this case four of the halves can be shared with one whole bar two halves remaining. The parts of the third bar are halved again and can now be shared.
If a fair share was not possible at this point further halving would take place. At this point a teacher might ask the child "How much has each person got? Stuck on counting In fragmenting the child treats the parts as individual unit items.
No conceptual distinction is being made between the 'two' as in number of pieces and the 'two' pieces as fractions of each unit, or the whole three bars that is being shared.
These children are aware of the fragments as only individual unit items. The complexity here is also whether the 'whole' refers to the individual bars, in which case each child gets three-quarters of the bar, or the 'whole' refers to the three bars.
In this latter case the answer would be "A quarter of the chocolate". Here a teacher would be trying to emphasise that we cannot always successfully describe quantity by counting.
It would be necessary for portions to be equal in size for counting to offer a way forward. Partitioning Even young children can partition regions or composite units approximately equally among two or three recipients.
The issue here becomes one of equivalence. This highlights a question for teachers about how they might raise awareness of those equivalences. This might be achieved through questions inviting learners to describe the same fraction in different ways or by identifying problems with equal answers.
This is based on a ratio concept and Grace argues it also indicates a deeper understanding of fractions. As in the previous example, a child indicating that the uncoloured fraction of the square is three-quarters, is simplifying the denominator and numerator to give an equivalent fraction, without losing the value of the fraction, though some information is lost.
What impact might this have on how we teach children to understand fractions better? Ideas for teaching fractions When teaching fractions in schools, the emphasis is often on situations where the object can easily be cut, folded, split or coloured in equal parts.
Although there is some need for this sort of activity, children should be exposed to a wide variety of situations, some where such folding or splitting strategies will not be successful.
In experiencing a variety of situations where fractions can be found, learners will have the opportunity to reflect and abstract critical relations in different contextual situations.
In other words, children must see a whole in all its representational forms. This will aid them in developing a more robust grasp of the concept of a fraction.
Grace describes some of these situations in terms of properties of being discrete or continuous, definite or indefinite see below.
Thus the aim is to engage in working in situations that offer opportunities to explore fractions in each of these situations. Discrete wholes - sweets, marbles, cherries, beads etc. Continuous wholes - cakes, chocolate bars, pizzas etc.
Definite wholes - where the extent of the whole is clear, for example: Indefinite wholes - where the extent of the whole is not clear, for example we do not know how long the pattern extends in either direction in the image below: In developing a sound understanding of the part-whole concept of fractions, it is necessary for teachers to present situations of fair sharing, where the child is expected to reason out the consequences of different actions.
For example with the very young, it might be necessary to begin with a number-free approach; Show the children some sweets; question them: Encourage the children to make meaningful comparisons e. Does everyone get more or less than a whole pizza?This paper was written by Joe Hallock in and was the final deliverable for his undergraduate thesis at the University of Washington.
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