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 collect data

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 * relationships between number patterns e.g. triangular numbers

Variables in Turtle Graphics parameters to procedures e.g. development of drawing a square 1. the series of, for example, FD 100 and RT 90 commands 2. create a new Turtle command (procedure) called SQUARE 3. 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 :SIDE RT 90 etc 5. draw squares of different sizes by issuing the SQUARE command with different run time values SQUARE 150 SQUARE 200