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Mathematics and ICT
National Numeracy Strategy
National Curriculum for Mathematics
National Numeracy Strategy
emphasis on mental mathematics
building a network of understanding by making connections between
existing ideas importance of discussion of
mathematical ideas
National Numeracy Strategy
these principles belong to a 'constructivist' approach to learning, but much use of ICT for mathematics has followed a 'behaviourist' approach repetitive drill programs to practice
calculation
National Curriculum for Mathematics Data Handling
database spreadsheet and charts
Shape and Space, Movement and Angle turtle graphics
Number Patterns spreadsheet turtle graphics
Data Handling
KS 2 (small part in KS 1) it is more important to
understand why we collect data than to learn to mechanically turn data into a bar chart
Data Handling
the model:pose the question
analyse & represent
data
interpret data
make deductions
collectdata
Data Handling benefits of IT in data handling
allows children to try out different representations of the data, leading to better understanding of
the meaning of the data set how to interpret data
helps children to understand how to construct graphs and chart, including handling scale
Shape and Space, Movement and Angle
turtle graphics gives understanding of heading and angles shape units of measurement breaking large tasks into small steps
Shape and Space, Movement and Angle
turtle graphics introduces the idea of functions (KS3/4)
turtle graphics develops skills in estimating orientation and heading problem solving
Shape and Space, Movement and Angle
developing from the concrete to the abstract playing turtle floor turtle (Roamer) screen turtle
Logo / Turtle Graphics
applications in curriculum NC ICT and NC Technology
problem solving control
NC Mathematics shape and space, movement and angle
Logo / Turtle Graphics
origins MIT
Seymour Papert Harold Abelson
theories of learning education and disaffected pupils
Number Patterns
KS 1 " . . . explore, record, explain and
predict basic number patterns " KS 2
" . . . progress to interpreting, generalising . . . expressed initially in words and then using letters as symbols "
Number Patterns Variables
definition of a variable: something whose value can change
difficulty children have with abstraction (algebra and those xs and ys)
" . . . there is good evidence, supported by commonsense observation, that young students see the world as built of objects and events, not as variables."
(Ogborn, J. Modelling with the computer at all ages. Portugaliae Physica, 21 (3/4), 1992)
IT and using variables
where spreadsheets turtle graphics
IT and using variables
concrete abstract variables in classroom displays
day and date weather and temperature whose turn to . . . feed gerbils . . . give
out books
IT and using variables concrete abstract
reinforce variable concept by method of display
container and value name the container use removable card for value easy to change easy to understand concept
importance of discussion
Spreadsheets and Variables each cell is potentially a variable formulas combine the variables simple explorations
guess the formula are the formulas equivalent ?
e.g. A3 + A3 and A3 * 2 formulas with more than one step
e.g. A3 * 2 + 3 relationships between number
patterns e.g. triangular numbers
Variables in Turtle Graphics
parameters to procedures e.g. development of drawing a
square1. the series of, for example, FD 100
and RT 90 commands2. create a new Turtle command
(procedure) called SQUARE3. draw a square by issuing the
SQUARE command
Variables in Turtle Graphics
parameters to procedures e.g. development of drawing a square
4. modify the SQUARE command by adding a 'run parameter' for the length of a side
TO SQUARE :SIDE FD :SIDERT 90etc
5. draw squares of different sizes by issuing the SQUARE command with different run time values
SQUARE 150SQUARE 200