Random Flashcards
What does it mean to be a facile student?
Facile or flexible students are at a stage where they can use their knowledge of number properties and number facts to come up with an answer. (Counting by ones is not a flexible strategy)
The contemporary teacher needs to bring more than mathematics knowledge to teaching mathematics they must also
Be able to show students that what they are learning can be applied to real life situations (making mathematics meaningful) using a range of different pedagogical strategies and approaches, language and literacy skills
Problem solving has a place in every classroom - explain
It gives meaning and relevance to maths, uses prior knowledge in unfamiliar situations, challenges students, they combine other skills and concepts to solve a problem, solving mathematical problems gives students skills to problem solve in other areas of their life
Jean Piaget theory
Children learn through investigation and adjusting new experiences to fit prior concepts and concepts to fit new experiences.
Schema - category of knowledge and process of obtaining that knowledge (a child has a schema abou t dogs - small, fluffy, 4 legs then meets a big dog so this new information is modified and the schema now includes big dogs)
Assimilation - taking in new information into our previously existing schemas
Accomodation - changing or altering our existing schemas when given new information
Equilibrium- maintaining a balance between assimilation (applying previous knowledge) and modifying to account for new knowledge (accomodation)
What are some problem solving strategies?
Create a table, make a drawing, think aloud, act it out, look for patterns, guess and check, identify unwanted info, work backwards,
List and describe the working mathematically processes at the centre of the Australian curriculum and NSW syllabus
Communication - students represent mathematical ideas in written, oral or graphical form using appropriate language, terminology etc
Problem solving - students develop ability to make choices, interpret, formulate, model and investigate problem situations and communicate solutions effectively
Reasoning - thinking, analysing, proving, etc. students are thinking mathematically when they explain their thinking, justify strategies etc
Polya’s problem solving technique
Understand problem
Devise plan (use strategies)
Carry out plan
Reflect
What is a rich task?
What is authentic assessment?
A rich task can be connected to different subjects using a range of teaching and learning methods (interdisciplinary)
Authentic assessment is when students apply their knowledge in real world tasks that demonstrate meaningful application of essential knowledge and skills
True problem solving is based on understanding the problem and inventing the maths needed to solve it. Teaching problem solving requires the three t’s…
Teaching for, teaching through and teaching about
Subitising is when students recognise learned patterns without having to individually count. How can you facilitate subitising?
Use die, tallies, dot cards
What strategies are useful for developing early number skills?
Subitising, anchoring to 5, counting out loud, ten frames, websites such as count me in
By reference to simple examples of at least two stages explain the importance of algebra in primary schools?
To be continued
Students draw on a range of different Stage 2 -
The syllabus has been modelled from constructivism theories such as Piaget and Vgostsky. Explain constructivism
Constructivism: people actively build or construct their knowledge of the world and of each other. Knowledge is actively constructed by students through reflection on their physical and mental actions (observing, identifying, generalising), learning mathematics should be a social progress as when students engage in social and physical aspects they construct robust understandings
Identify 3 problem solving strategies for problem solving. Outline each strategy and a classroom activity in which it could be used
Working backwards through the problem -
Guess and check -
Draw a table - a farmer has some ducks and some horses altogether the ducks and horses have 40 legs and 14 heads
