counting and cardinality. children’s first experiences with numbers will influence the way they...
DESCRIPTION
Pre-Number Concepts Early experiences that lead to the development of counting skills are known as pre-number concepts. They include Sorting and Classifying Subitizing Comparing PatternsTRANSCRIPT
Counting and Cardinality
Counting and Cardinality
Children’s first experiences with numbers will influence the way they deal with mathematics for the rest of their lives.
Pre-Number Concepts
Early experiences that lead to the development of counting skills are known as pre-number concepts. They include
Sorting and ClassifyingSubitizingComparingPatterns
Sorting and Classifying
Sorting and classifying activities in children’s mathematical development is critical.
Through these activities children learn to think analytically and develop logical thinking.
Sorting and Classifying
In order to sort and classify a group of objects, child must recognize what is called an attribute.
Children begin sorting and classifying by focusing on one attribute.
They need to describe the attribute with words that label the groups that have been sorted and placed together.
Subitizing
Subitizing is a way of instantly counting.
Perceptual subitizing – seeing a small group of items and knowing how many without counting.
Conceptual subitizing – recognizing the whole as a sum of its parts
The ability to subitize can be developed, and uses a student’s pattern recognition.
Dot plates, ten frames, dice, and dominoes are good tools to help students develop subitzing.
Subitizing
Comparing
Comparing two objects helps students recognize different attributes and learn comparative terms.
This pencil is longer than that pencil This chair is taller than that chair The red paper is larger than the yellow paper This book is heavier than this book
Comparing
The concepts of “more”, “less”, and “the same” are basic relationships students must understand to mathematics.
Which group of toys has more?
Seriating is the process of focusing on an attribute and then arranging or ordering a set of objects according to that attribute.
Before asking children to order a set of three or more objects, you should have them compare two objects so as to recognize different attributes and comparative terms.
Seriating
Patterns
Children need the opportunity to explore all types of patterns that occur around them.
Patterns
Repeating Patterns
Patterns
Growing patterns
Estimating
Estimates are approximations rather than exact quantities.
The meaning of the term estimate can be developed by referring to the word about.
“About how many gumballs are in the jar?”
Early Counting
One to one correspondence – the matching of one counting word with one object.
Prior to developing counting capabilities, children can compare sets by using a one-to-one correspondence strategy.
This involves learning to pair up objects such as 1. Putting one cookie on each plate
2. Finding out if there is enough books for each student in the class
3. Drawing tally marks for each object
Early Counting
Conservation of Number – the number of objects does not change when the objects are rearranged.
Counting on – continue counting up from a given number
Counting back- continue counting down from a given number.
Skip counting – sets stage for multiplication
Early Counting
When the children count, do they use the appropriate counting sequence?
Do their errors appear to be random or to they consistently make the same errors?
Do they count each object once and only once, or do they lose the idea of one-to-one correspondence as they count?
Do they remember the number they counted to?When asked to get a certain number of objects, do they
count correctly or do they count past the number they need?
Representing Numbers
Numbers can be represented in four ways:1. Concretely2. Pictorially3. Symbolically 4. Orally – using number words
Learning to write numerals is similar to learning to write the letters of the alphabet.
Representing Numbers
5 five
Number Sense
Number Sense is “good intuition about numbers and their relationships”.
As students work with numbers they gradually develop flexibility in thinking about numbers which is a hallmark of number sense.
Number Sense
Number sense develops as students Understand the size of numbers Develop multiple ways of thinking about and
representing numbers Use numbers as referents Develop accurate perceptions about the effect of
operations on number.
Number Sense
It takes time and lots of experiences for children to develop a full understanding of number that will grow and develop into more advanced number related concepts.
Number concepts are intimately tied to the world around us. Application of number relationships to real world settings marks the beginning of making sense of the world in a mathematical manner.
Number Sense
Teachers support the development of understanding number by presenting planned and focused experiences and by interacting with the children as they work.