SDMAT04 Common Questions
Problem-centred approach
• Teacher poses problems that learners can’t solve w/ routine methods
• Teacher doesn’t teach before posing problem
• Learning occurs during tackling of the problem
• Learners can discuss
• Learners get to appreciate mathematical tools they learnt before
• Role of teacher:
o Not sole source of knowledge & don’t transmit knowledge to learners
o Appreciate that learners construct their own knowledge
o Make sure learners understand problem
o Make sure learners can use tools needed
o Create positive classroom atmosphere that’s conducive to learning
Modelling
• What is modelling?
o Mathematical construction designed to study a particular real-world system or
phenomenon
o Start with real-world situation then use equations, symbols, simulations or graphs to
represent the situation
• Representations in modelling
• Advantages of modelling
o Can use to predict what will happen in the future
o May explain why things behave in certain ways & how a change in variables affects
others
o Allows us to solve complex problems ∵ can represent problems that can’t be tackled
another way
o Help us describe real-world behaviour
• Limitations of modelling
o Can’t capture all info into model ∵ simplification of real-world
o Maths is complicated and not accessible to all (may be errors)
Lesson planning
• Importance of planning
o Establishes specific goals and ensures essential concepts, skills & processes are incl.
o Prepares teachers to instruct at level of understanding of learners
, o Helps teacher avoid mistakes and unnecessary repetition & can anticipate difficulties
o Curriculum delivered in logical sequence. Helps w/ time management
• Essential elements of planning
o Begin with maths
▪ Mention new ideas learners must construct
o Consider learners
▪ Accessible ideas but not straightforward
o Decide on a task
▪ Not too much detail
o Predict what will happen
▪ Predict difficulties and strategies to mitigate
o Articulate learner responsibility
▪ Learners should report/discuss ideas
o Plan the ‘before’ portion
▪ Present task and let learners brainstorm
o Plan the ‘during’ portion
▪ Plan for hints and give time frame
Validity vs reliability
• Validity
o Valid assessments are appropriate i.e. measure what they claim to measure
o Evidence from valid assessments is enough to prove competence
o Evidence is taken from anything related to the assessment
• Reliability
o Reliable assessments are fair i.e. results are consistent if another assessor conducts
the assessment, they’ll make the same judgements
o Comply w/ structural methods and procedures
Summative vs formative assessment
• Summative
o Conducted after learning period to evaluate overall competence
o Assesses how much was learnt
• Formative
o Conducted before learning to prepare teacher for learning
o Assesses learner’s prior knowledge
Key processes involving ‘doing’ maths
• Problem-solving
o Process by which we answer questions/deal with situations
o Involves formulating a strategy
• Reasoning and proving
o Involves justifying arguments and making sense of the world around
o Must verify correctness of their results
• Making connections
o Between existing knowledge and new ideas
o Must connect maths to real life situations
• Communication
Problem-centred approach
• Teacher poses problems that learners can’t solve w/ routine methods
• Teacher doesn’t teach before posing problem
• Learning occurs during tackling of the problem
• Learners can discuss
• Learners get to appreciate mathematical tools they learnt before
• Role of teacher:
o Not sole source of knowledge & don’t transmit knowledge to learners
o Appreciate that learners construct their own knowledge
o Make sure learners understand problem
o Make sure learners can use tools needed
o Create positive classroom atmosphere that’s conducive to learning
Modelling
• What is modelling?
o Mathematical construction designed to study a particular real-world system or
phenomenon
o Start with real-world situation then use equations, symbols, simulations or graphs to
represent the situation
• Representations in modelling
• Advantages of modelling
o Can use to predict what will happen in the future
o May explain why things behave in certain ways & how a change in variables affects
others
o Allows us to solve complex problems ∵ can represent problems that can’t be tackled
another way
o Help us describe real-world behaviour
• Limitations of modelling
o Can’t capture all info into model ∵ simplification of real-world
o Maths is complicated and not accessible to all (may be errors)
Lesson planning
• Importance of planning
o Establishes specific goals and ensures essential concepts, skills & processes are incl.
o Prepares teachers to instruct at level of understanding of learners
, o Helps teacher avoid mistakes and unnecessary repetition & can anticipate difficulties
o Curriculum delivered in logical sequence. Helps w/ time management
• Essential elements of planning
o Begin with maths
▪ Mention new ideas learners must construct
o Consider learners
▪ Accessible ideas but not straightforward
o Decide on a task
▪ Not too much detail
o Predict what will happen
▪ Predict difficulties and strategies to mitigate
o Articulate learner responsibility
▪ Learners should report/discuss ideas
o Plan the ‘before’ portion
▪ Present task and let learners brainstorm
o Plan the ‘during’ portion
▪ Plan for hints and give time frame
Validity vs reliability
• Validity
o Valid assessments are appropriate i.e. measure what they claim to measure
o Evidence from valid assessments is enough to prove competence
o Evidence is taken from anything related to the assessment
• Reliability
o Reliable assessments are fair i.e. results are consistent if another assessor conducts
the assessment, they’ll make the same judgements
o Comply w/ structural methods and procedures
Summative vs formative assessment
• Summative
o Conducted after learning period to evaluate overall competence
o Assesses how much was learnt
• Formative
o Conducted before learning to prepare teacher for learning
o Assesses learner’s prior knowledge
Key processes involving ‘doing’ maths
• Problem-solving
o Process by which we answer questions/deal with situations
o Involves formulating a strategy
• Reasoning and proving
o Involves justifying arguments and making sense of the world around
o Must verify correctness of their results
• Making connections
o Between existing knowledge and new ideas
o Must connect maths to real life situations
• Communication
