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