Part B notes Flashcards
(30 cards)
1
Q
Describe the theory of constructivism
A
- Based on the notion that learners play an active role in ‘constructing’ their own meaning
- Knowledge is constructed from (or shaped by) experience
- Acknowledges that although learning is a personal interpretation of the world , the ‘environment in which learning is taking place’ and ‘learning that requires social interaction’ is vital
- Constructivist approaches require learners to be active and confident in themselves and their abilities. Students have to admit there are gaps in their knowledge or understanding
- Emphasises problem solving and understanding
- Uses authentic tasks, experiences, settings and assessments
2
Q
Who are two social constructivists and what do they say?
A
Lev Vygotsky- - Zone of proximal development- need assistance from an adult to surpass a certain point
Barbara Rogoff- Learning requires the active involvement of the learner
3
Q
According to constructivists, what is the role of the teacher?
A
- Adapt the curriculum to students’ “needs”
- Help negotiate goals and objectives with learners
- Pose problems of relevance to students
- Emphasis hands-on real world experiences
- Seek and value students’ points of view
- Provide the social context of content
4
Q
According to constructivists, what is the role of the students?
A
- Be a member of a community of learners
- Collaborate among fellow students
- Learn in a social experience- appreciate different perspectives
- Take ownership and voice in learning process
5
Q
Who has theories in mindsets? What do they believe?
A
- Yeager and Dweck (2012)
- Entity theory world- measuring your ability (caring about not looking ‘dumb’
- Incremental world- about learning and growth, everything is seen as being helpful to learn and grow. It is a world of opportunities to improve
6
Q
List and describe the four proficiency strands
A
- Reasoning= Explaining choices and why though processes were
- Understanding= procedural understanding- being able to follow steps to get the answer
- Problem solving= Being able to get the answer without knowing how to do it at first
- Fluency= Being able to get the correct answers- it does not rely on speed but accuracy
7
Q
How should teachers attempt to achieve the proficiency strands?
A
- If we are seeking fluency, then clear explanations followed by practice will work.
- If we are seeking understanding, then very clear and interactive communications between teacher and students will be necessary
- If we want to foster problem solving and reasoning, then we need to use tasks with which students can engage, which require them to make decisions and explain their thinking
8
Q
List and describe the steps of the planning cycle
A
- Planning- knowing your students and where they are at
- Teaching- Are multiple intelligences being addressed? Does the lesson provide for differentiation?
- Assessment
- Diagnostic assessment (where at)
- Formative assessment (ongoing and providing feedback),
- Summative (End of topic)
- Evaluation- determines the effectiveness of teaching and learning through analysis of evidence
9
Q
What is subitising?
A
Suddenly recognising
10
Q
What are the two types of subitising?
A
- Perceptual subitising- the immediate recognition of numbers up to 4
- Conceptual subitising- remaining numbers up to 10 can be recognised in terms of their subitised parts
11
Q
Whose are the counting principles?
A
Gelman and Gallistel’s five counting principles
12
Q
Describe Gelman and Gallistel’s five counting principles
A
- The one to one principle- each object receives one count and only one count
- The stable order principle- Counting words are always said in the same order
- Cardinal principle- the last number spoken names the quantity for that set
- The order-irrelevance principle- the order does not affect the count
- The abstraction principle- any set of objects can be counted as a set, regardless of whether they are the same colour, shape size etc.
13
Q
What are the stages of counting?
A
- Count all
- Count on
- Count on from larger
14
Q
What are the phases of place value?
A
- Unitary value
- Placement of values in the number string (e.g. 37 is after 36)
- Quantity value
- 36= 30+6
- Column value
- 36 is seen as 3x10 and 6x1
15
Q
List the properties of operations
A
- Commutative property (addition, multiplication)
- The order in which steps are performed makes no difference to the outcome
- Associative property (Addition, multiplication without brackets)
- Allows three or more factors to be added in any order
16
Q
List the properties of zero and one
A
- Additive property of zero
- Adding zero to any number leaves it unchanged (456+0=456)
- Multiplicative property of zero
- Multiplying a number by 0 gives 0
- Multiplicative property of one
- Multiplying a number by 1 leaves it unchanged
17
Q
What is the model on technology called?
A
The SAMR (Substitution, Augmentation, Modification, Redefinition) model
18
Q
Describe the SAMR model
A
- Substitution- tech acts as a direct tool substitute with no functional change
- Augmentation- tech acts as a direct tool substitute with a functional change
- Modification- Tech allows for significant task redesign
- Redefinition- tech allows for the creation of new tasks, previously inconceivable
19
Q
Define problem solving
A
Solving a question when there is no immediate and obvious solution first knowing how to answer the question
20
Q
Who has a model for problem solving and what is it called?
A
Polya’s four-step model for problem solving
21
Q
Describe Polya’s four-step model for problem solving
A
- Understand the problem (See)
- Devise a plan (plan)
- Carry out the plan (do)
- Look back (check)
- (extra step- publish/share ideas!)
22
Q
What is the Newman Analysis?
A
- Anne Newman (1977) identified that students may have difficulty:
- Reading the words,
- Understanding what they have read,
- Transforming what they have read so as to be able to form a course of action
- Following through on procedures, or
- Encoding the result of a procedure to answer the question
23
Q
Describe the CRA model
A
- Concrete- uses hands-on physical (concrete) models or manipulatives to represent numbers and unknowns
- (visual)- technological
- Representations- draws or uses pictorial representations of the models
- Abstract- involves numbers as abstract symbols of pictorial displays
24
Q
What is needed for a range of learners to understand content?
A
- A rich variety of representations is needed:
- Experience based scripts of real world events or dramatic play
- Manipulative materials
- Pictures and diagrams
- Spoken language
- Written symbols in number sentences
25
List some resources that can be used to teach mathematics concepts
- Dice games are good for subitising
- Work stations
- Games are good because they are entertaining
26
Define numeracy
- Being numerate involves having fluency in mathematical skills and knowledge; a clear understanding of the contextual requirements; the disposition to choose and use mathematics confidently; and a critical appreciation of how mathematics can be used
- Numeracy involves the ability to apply number and computational skills to everyday purposes, together with the ability to interpret the quantitative information that pervades everyday life (Westwood, 2008)
- Maths used in circumstances other than mathematics class
27
Why is numeracy important?
- Numeracy prepares students to manage the requirements of everyday life efficiently, in a range of situations that involve the use of mathematics e.g. Shopping, cooking etc. and school leavers in finance
- Numerate individuals are also able to participate more effectively and successfully in wider community and social spheres
- The growth of a socially just society depends upon individuals gaining appropriate levels of numeracy
28
How are maths and numeracy different?
- Mathematics conveys the power of conceptualising and abstracting; numeracy conveys the power of context and practicality
- Mathematics does not need to consider the real world as it can focus purely on abstract constructs and ideas regardless of their potential applications; numeracy is the application of mathematics in authentic contexts
- Mathematics is organised using categories from the past; numeracy focuses on the way quantitative knowledge is used in the information age
- Mathematics is most encountered in educational institutions; numeracy is mostly in the world around us.
- Numeracy comprises not only mathematics skills, but also the way in which they are used. This involves marrying the mathematical meaning of the symbols and operations to their contextual application, and thinking simultaneously about both.
29
Being numerate requires...
- Being numerate
- Numeracy technician (begins understanding)
- Numeracy participant (begins understanding)
- Numeracy user
- Numeracy analyst.
- Being numerate within a context involves a blend of three types of know-how: mathematical, contextual and strategic. Contextual know-how requires an understanding of how the mathematics is shaped by the context.
- Being numerate involves having:
- A fluency in mathematical skills and requisite knowledge
- A clear understanding of the contextual requirements
- The disposition to choose and use the mathematics appropriate to the context with confidence (involves the use of representational, physical or digital tools)
- A critical appreciation of how mathematics can be used, and misused, in order to question or judge the appropriateness of its use.
30
Define critical numeracy
- Critical numeracy
- Critical numeracy is the ability to make discerning decisions about everyday issues that involve the use of mathematics
- According to Stoessiger (2002), there are four main aspects to being critically numerate. These are;
- Being able to critique mathematical information
- Being able to interpret or decode mathematical situations
- Using mathematics in a self-reflective way
- Using mathematics to operate more powerfully in the world
