Part 1
1. Relevance of 1-4 Scenario and Dot Colouring
The number learning this experience supports children to notice, explore, and/or talk about: is
· Use of number sense to identify a connection between quantities of the shop items and numbers of counters to give as payment
· Application of stable order principle to name numbers in the right sequence when making pages of a book
· Identification of the number mentioned last (cardinality) to know how many counters are lined up or included in a pattern
· Using ordinality to make a book’s cover page the starting point when stapling the pages of a book together
2. Importance of Number Knowledge (Above) for Learning of Number and Mathematics
The number knowledge mentioned are important for the following reasons:
Number Sense
Number sense is crucial for children who are learning mathematics, as it enables children to understand the language used when giving instructions in this area. It becomes the basis for mathematics success by enabling children to know the association between counting and quantity. The foundation created in counting and quantity builds number flexibility in children as they continue learning mathematics. The overall role of number sense is to enable children work with numbers.
The concept helps children to know about quantities, understand comparison words (less, more, smaller, etc.), and identify order of things (first, second, last, etc.). Number sense also helps children to recognize the connection or relationship of items within a group and in explaining the symbols used when referring to quantities. Knowledge of number sense, thus, enables children to read and understand mathematics instructions.
In other words, number sense improves mathematics literacy by enabling children to read and understand the meaning of words used to issue instructions. Children slowly begin to understand the role played by mathematics in real world and gain the ability to apply it to make sound judgements or solve problems. For instance, children with solid number sense do not face challenges when dealing with basic mathematics operations like multiplication and addition. Number sense expertise also helps children to easily complete tasks related to measuring and working with money.
Stable Order Principle
Is part of the number sense, and one of the initial counting concepts taught to children. In fact, most children become familiar with stable order, or how numbers follow each other, prior to gaining understanding of the meaning of numbers and their symbols. Teaching children the stable order principle helps them to know the sequence followed when counting numbers.
Even better, the order remains the same in all mathematical operations. Grasping this principle helps children to easily understand the other concepts within number sense. For teachers, the use of stable order helps to control the range of numbers children within the various age range should understand. That is, the teacher provides a list of counting words that is a long as the number of objects they should count at that given level. The stable order, thus, helps to ensure that a child fulfills all the counting requirements of a given age.
The principle is also important guide when planning mathematics lessons for children because it helps educators to select appropriate words and vocabulary to use when teaching. In this way too, the children get to understand the mathematics words that match their level of understanding. A child may have to read the order of numbers and reverse for quite some time before gaining a complete understanding, but at the end the child develops deeper knowledge of quantity and counting.
Cardinality
Children who master this concept can easily recognize the number of objects in a given group by simply looking for the last number. Cardinality knowledge improves the speed with which children solve basic mathematics tasks. For instance, a child who already remembers the last number reached when counting items of a group may not recount the set of objects when transferring them into a different location. This lessens the time taken to complete the counting and grouping.
Moreover, children that understand cardinality do not struggle when matching given numbers to set of items. They know that the last number, not last item, mentioned when counting items of a group represents the group’s magnitude. Cardinality knowledge, thus, relies on subitising to help children match the last number within a counting sequence with quantity of the set. This concepts also adds to the understanding of quantity and counting. The teaching of cardinality also introduces children to other vital number concepts.
First, the children must learn about the order of numbers and consistently use them to be able to count items in a particular group (stable order principle). Again, children get to know that even unlike items can form a set (abstraction) and that the outcome of counting objects in a group remains the same regardless of the order of counting (order irrelevance principle). While cardinality principle teaches children to accurately count items in smaller sets, their success with the smaller groups improves their ability to tackle more complex counting tasks.
Ordinality
This principle helps a child to recognise the number assigned to the first item in a set. A crucial number concept that children learn from ordinality is comparison. That is, a child must understand that 3 is smaller than 5 but comes after 2. For a child to fully understand this comparison, they must understand the sequence of numbers as explained in the stable order principles. In this way, ordinality principle encourages children to understand stable order. Learning ordinality also improves knowledge of cardinality concept as a child identifies both the smallest and the largest numbers in a set before picking the one that should come first.
It is evident that a child acquires cardinality and ordinaliy concepts simultaneously. When planning for mathematics teaching and learning, for instance, a teacher must recognise the first and last numbers to include in the list. The children who use the list for learning mathematics end up identifying the starting point (ordinality) as well as the quantity that represents the group’s quantity or magnitude (cardinality).
Part 2
1. Mathematics Words
· Pattern
· Order
· Shape
· Compare
· Match
2. Two questions
I chosen questions numbers 3 and 6.
3. Questions and Selected Number Concepts
The two questions will support understanding of ordinality principle as they require the children to count numbers, beginning with the first value and progressing in the correct sequence. In question 3 a child must identify the number that comes first when arranging the pages of a book, and question 6 involves counting which also involves identification of the name or symbol of the first number. Along with first number, the children must take note of the last number in both questions. By identifying the number on the book’s last page or the name of the number assigned to the last dot, the children exercise cardinality principle.
A factor that children should notice when handling activities in either question is that the numbers follow a certain sequence which never changes. When arranging the pages of the book, for instance, the children must identify the symbols and names of numbers that follow the one assigned to the first page and the one that appears before the symbol or name indicated on the last page. Children must, therefore, understand the stable order principle to complete tasks in questions 3 and 6. That is, a child that has difficulty understanding the stable order will not arrange the numbers of the book pages correctly. Similarly, this type of child will be unable to accurately count the number of dots he or she has coloured.
Children should have a strong sense of numbers to fulfil the requirements of each of the questions. The first aspect of number sense that is vital in this context is matching quantity and counting. This mostly applies to question 6 where a child should know when the number of coloured dots is the same as the stated number. Connecting quantities with counting will as well enable children to recognise the first and subsequent numbers of the book’s pages, in question 3. Comparison is another aspect of number sense that will enable the children to arrange numbers from the smallest to the biggest, and vice versa, in question 3 so as to find out how numbers follow each other. Such understanding will also help when counting coloured dots per triangle in question 6. Number sense is even more important for recognition of number names and symbols, which children must know before working on questions 3 and 6.
