Semester 1 Exam Revision Flashcards
What three factors determine the mathematics being taught in schools?
- The needs of the subject (natural progression between ideas, new opportunities/challenges posed by new technology)
- The needs of the child (developmental readiness, past experiences)
- The needs of society (accountability of schools for students’ performance, skills which benefit future workers, equity of opportunity for all students)
What are the five ways you can view mathematics as a body of knowledge?
- As a study of patterns and relationships
- As a way of thinking
- As an art, characterised by order and internal consistency
- As a language that uses carefully defined terms and symbols
- As a tool
What is subitising?
Instantly recognising the number of objects in a small group, without counting.
What does ‘seriate’ mean?
To arrange in a series
What are the three stages young children go through as they learn to count?
- Prenumber concepts (classification, making/describing patterns)
- Early number development (conservation of number, subitising, comparing numbers of items to identify more/less)
- Counting
What is conservation of number?
The realisation that a given number doesn’t vary (eg, 9 blocks in a long line aren’t more than 9 blocks in a short line)
What four things must happen for counting to work?
- Each object gets one (and only one) number name (one-to-one correspondence)
- The number name list must be used in a fixed/stable order (1,2,3,4 not 1,4,7,10)
- The order in which the objects are counted (eg, L-R or R-L) doesn’t matter (order irrelevance rule)
- The last number name used gives the number of objects counted (cardinal principle)
What is the difference between rote counting and rational counting?
In rote counting, the child can recite number names, but lacks one of the four basic skills of counting (one-to-one correspondence, number names used in a fixed order, order irrelevance rule, last number said gives the number of objects counted). In rational counting, the child uses all four skills.
What sorts of thing should a child be doing once s/he has mastered basic counting, but before starting work on the four operations?
Counting on, counting back, skip counting
In Australia, how is the word ‘numeracy’ usually used?
To describe the ability to apply maths in context (eg, in choosing which mathematical processes to use to compare phone plans from different companies)
What are the five facets of number sense?
- An understanding of number concepts
- Development of strategies for handling numbers
- Computation (number facts)
- Ability to use numbers flexibly to make mathematical judgments (because when you start using maths in the real world, there’s often multiple ways of solving a problem)
- Ability to see the utility of using numbers (ie, seeing that maths has a point, and can be useful)
What is a procept?
Something in maths which represents both a process and a concept (eg, 5 is a procept, representing both the process of counting 1,2,3,4,5 and the concept of ‘fiveness’.
What is a cardinal number? Give an example.
A cardinal number answers the question ‘How many?’
Eg, ‘There are three dogs in the park.’
What is an ordinal number? Give an example.
An ordinal number tells the order of a series of things.
Eg, ‘Petrus was the second man to take the throne name Valerius.’
What is a nominal number? Give an example.
A nominal number provides a label or classification.
Eg, ‘Glenn McGrath had the number 11 on his ODI shirt when he played for Australia.’
