topic 5 pre number concepts(conservation, group recognition, patterns)

STUDY GUIDE HDPS3503 Early Mathematics for Children

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Week 5

Topic 5: Pre Number Concepts (Conservation, Group Recognition, Patterns)

Readings

Read the stipulated pages and answer the study questions that follow:

Smith, S. S. (2008). Early childhood Mathematics (4th ed.). USA: Allyn &

Bacon.

Chapter 6: pp. 92 – 93; pp. 101 – 102

Chapter 9: pp. 140 – 147

Suggested Websites:

1. http://teacherweb.com/wa/nachesvalleyprimaryschool/msclark/

Subs.PDF

2. http://gse.buffalo.edu/fas/clements/files/Subitizing.pdf

3. http://www.suite101.com/content/subitizing-is-part-of-math-starting-in-

the-early-years-of-school-a223535

Study notes

In the previous topic, the mathematical relationships of matching, classification, comparing and ordering were examined and discussed at length. During this week, the discussion will be extended to include three other pre number concepts essential for developing deeper understanding of early Mathematics amongst young children. To complete the discussion on pre number concepts, you will need to focus on the concepts of conservation, group recognition and patterns in this topic. Let us look at the three related elements of pre number concepts: (a) Piaget’s Tests of Conservation: For a start, you need to consider and relate to Piaget’s Tests of

Conservation. As mentioned in the previous topic, matching is a prerequisite skill needed for dealing with the more difficult tasks of conservation. Piaget’s tests of conservation are used to assess children’s development at a later age. If you remember, children can only perform conservation tasks during the concrete operational stage


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(ages 7 – 11) according to Piaget’s learning theory of cognitive development discussed in Topic 2 of this Study Guide. In a nutshell, Piaget’s tests of conservation require children to make judgements about two sets of objects (number), two quantities of clay (mass) or liquid (capacity).

Piaget’s Test of conservation or invariance of number, that is, a given

number does not vary, is presented using suitable illustrations, with one diagram showing a one-to-one correspondence for two equal rows (sets) of counters and another displaying the same number of counters but with one row being more spread out. This is illustrated clearly in the text (Refer p. 92).

In the tests for quantity, liquid measure and clay are normally used.

These tests are more difficult compared to the test of conservation of number as they rely on continuous measurement rather than counting. According to Piaget, classification, order and seriation represent proper topics for the early childhood classroom in contrast to the view of Montessori and her supporters.

Next, take a look at the skill of group recognition in relation to the development of early mathematics concepts. (b) Group Recognition (Subitizing): Thinking in groups or seeing small sets instantaneously without having

to manipulate every item or count from the very beginning is emphasised as an important activity in developing number concepts later on. Instant or rapid visual recognition of groups of objects or sets is accepted as an important skill that is required for developing a good understanding of number concepts to be learnt.

Not much information concerning subitizing is given in the text by Smith.

You are thus encouraged to refer to other sources suggested as additional references or relevant websites for more information on the skill of subitizing. For instance, you may refer to the one given below:

http://teacherweb.com/wa/nachesvalleyprimaryschool/msclark/ Subs.PDF

Subitizing is defined as "instantly seeing how many", originating from a

Latin word meaning ‘suddenly’ and is a way of manipulating numbers, that is, recognising an amount or groups of objects through visualisation rather than by counting the items individually. The role of subitizing is seen as a developmental prerequisite to counting, underlaying number


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ideas and focusing on the whole as well as the unit. Subitizing is important because it includes visualisation in learning and creates a better understanding of mathematics and its relationships.

Two types of subitizing are identified/recognised:

(i) Perceptual Subitizing – Knowing instantly the number of dots rolled on a dice; and

(ii) Conceptual Subitizing – Breaking down the entire group of dots into smaller groups and still not counting the dots individually but recognising groups of dots according to their arrangements (e.g. rectangular, linear, circular or scrambled), then adding them together. For example, if six on the dice is rolled, a child might instantly recognise a group of three dots and add it to a second group of three dots.

Other examples of perceptual subitizing include "just knowing" the

domino's number by recognisng the number pattern as a composite of parts and as a whole. Spatial patterns, such as those on dominoes, are just one type of patterns that can aid in recognising groups or small sets of objects. More examples of conceptual subitizing comprise temporal and kinesthetic patterns, including finger patterns, rhythmic, and spatial-auditory patterns. Creating and using these patterns will help children to acquire the skill of group recognition or subitizing overall.

Read more about this concept at the following site – Suite101:

Subitizing is Part of Math Starting in the Early Years of School http://www.suite101.com/content/subitizing-is-part-of-math-starting-in-the-early-years-of-school-a223535#ixzz1JDDk5T00

According to Baroody, 1(987), "Subitizing is a fundamental skill in the development of children’s understanding of numbers". Thus, children can use pattern recognition to help them to discover essential properties of numbers, such as conservation and compensation. In general, seeing part-whole relationships using sight or abstract thinking (without counting) contributes towards developing number sense in children. Finally, a discussion on pattern recognition rightly follows. (c) Patterns (Copying a pattern, Finding the next one, Extending a

pattern, Making their own pattern): You are probably familiar with the meaning of Mathematics as a study

of patterns. Describing, constructing and making patterns require


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problem solving skills and is an integral part of learning Mathematics. Group recognition activities that involve thinking in groups can be refined by practising instant visual recognition of common number patterns, such as those found on number cubes, dominoes, dot pattern cards or ten frames. Patterns encountered in classifying and comparing provide several number-sense experiences. Recognising, labelling, and translating patterns are some examples of challenging early mathematical experiences. Three types of patterns are illustrated: repeating patterns, growing patterns, and relationship patterns.

Read about the four basic principles of pattern described in the text.

(Refer pp. 141 – 142). Smith informs that children explore pattern on four levels:

(i) Recognise pattern;

(ii) Describe a pattern;

(iii) Extend a pattern; and

(iv) Create their own pattern. To facilitate children to recognise patterns, teachers can first make a

pattern on the overhead or on a mat in front before getting them to perform a variety of actions to explore patterns. Patterns can be used in various ways to develop mathematical ideas. For instance, children can be asked to:

(i) Copy the pattern and call out the number without counting;

(ii) Find the next one;

(iii) Extend a pattern; and

(iv) Make their own pattern. Simple round materials for instance, checkers, poker chips, counters,

buttons, coins, or small cookies can be used to facilitate instant recognition.

Preschool children are usually given the opportunity to work with

patterns using various resources. Smith gives a detailed account of some examples of pattern activities at kindergarten and first grade level involving real objects, people patterns and pattern cards in the text. Read about these pattern activities to get more information and a better understanding of pattern activities suitable for developing Mathematics concepts in young children. (Refer Chapter 9: pp. 143 – 145).


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Based on the above discussion, it is recommended that kindergarten children should first be given the chance to recognise and describe patterns before being asked to do more challenging tasks such as extending a pattern by continuing a sequence until a particular item was not available, and creating their own patterns on a card.

In conclusion, it is imperative that you have a good grasp of all the pre

number concepts discussed to enable you to plan appropriate activities for

developing early Mathematics concepts in children effectively.

Study questions

1. Using suitable illustrations, describe and explain what is meant by

Piaget’s Tests of Conservation.

2. Explain what is meant by subitizing. Identify and differentiate between

two types of subitizing with the help of suitable examples.

3. Three types of patterns generally used for fostering early mathematical

experience: repeating patterns, growing patterns, and relationship

patterns. Illustrate each type of patterns named and explain how you

would guide young children to recognise, label and extend such

patterns.

4. Patterns consist of both numerical and nonnumerical patterns. Describe

and illustrate examples of nonnumerical patterns involving shape,

sound, colour, and position.

5. Pattern activities play an important role in guiding preschool children to

develop an understanding of early Mathematics concepts. Preschoolers

often work with patterns using real objects, people and pattern cards.

Create three patterns of your own using real objects, people and pattern

cards.

Glossary of important terms

1. Conservation – Pengabadian Conservation refers to the situation whereby things remain unchanged;

conservation of numbers is the understanding that the number of objects remains the same when they are rearranged spatially.


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2. Subitizing – Mengenalpasti secara serta merta Subitizing, coined in 1949 by E.L. Kaufman et al. refers to the rapid,

accurate, and confident judgements of number performed for small numbers of items. The term is derived from the Latin adjective subitus (meaning sudden) and captures a feeling of immediately knowing how many items lie within the visual scene, when the number of items present falls within the subitizing range. Number judgements for larger set-sizes were referred to either as counting or estimating, depending on the number of elements present within the display, and the time given to observers in which to respond (i.e., estimation occurs if insufficient time is available for observers to accurately count all the items present).

topic 5 pre number concepts(conservation, group recognition, patterns)

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