the function minverse. Since the mathematical process involved in solving the equations remains the same regardless of the size of the matrices, the pupils can be taken to a higher level of working, dealing with examples from real-life situations. By finding instances such as this, where ICT allows pupils to go beyond what they are normally capable of in the classroom, the teacher is making effective use of ICT as expected and required by 10/01.
Databases for handling data
The basic processes in Handling Data require pupils to be able to sort information into groups. The NNS encourages the use of Carroll Diagram, Venn Diagram and Sorting two-dimensional shapes as ICT support materials in the primary classroom. Other software for this age group includes Counting Pictures 2 (produced by Black Cat) and can be used to introduce the idea of databases at a simplistic level. Teachers can use existing topics and fields to collect data within the classroom—for example, the class database can be restricted to gathering data on pupils’ hair colour and eye colour only. Using an interactive white-board and an optical (or wireless) mouse, each pupil can select the data relating to themselves by passing the mouse around the room. The class data can then be sorted and patterns observed using charts.
In more advanced databases, pupils will also use the Sort facility to arrange data in ascending or descending order. Pupils should be encouraged to establish the link between ascending and alphabetical order or increasing numerical order, while descending order is the reverse. The use of searches on single or multiple criteria can be applied to the data when testing hypotheses. The application of criteria will often demand the use of mathematical terminology or symbols such as ‘greater than’ or >, ‘less than or equal to’
or <=, and the Boolean operators: not, and and or when using multiple criteria.
Depending on the software package being used, additional information such as mean, mode and median may also be available from the data. Packages such as SPSS offer the full range of statistical approaches. However, this software would only be suitable for Advanced-level analysis in biology, geography or mathematics coursework. The most commonly used database software in schools (aside from integrated databases such as Works and MS Access) is Pinpoint. It comes in two forms, Junior Pinpoint for primary schools and Pinpoint 3 for post-primary pupils. Pinpoint allows the pupils to work through each stage, completing a survey using a built-in facility for creating a questionnaire, electronic storage of the results, a range of analytical facilities and charting options, plus the electronic production of a report that integrates the tables of data and the charts in an editor. The questionnaire design can include a number of different data types as defined by the pupils. When analysing the results, the use of Boolean operators can be used to extract subsections of data for analysis, such as gender or age groups. Cumulative frequency curves can be produced and the median and semi-interquartile ranges can be calculated and included in the report. Bar charts, line graphs and correlations are all available as ways of representing the information and drawing conclusions.
Work of this nature is best completed as a group task over an extended period of time.
If linked to a local issue related to the environment, shopping, parking facilities in the town or road safety, there could be a real audience for the final report. Using this approach will allow pupils to design and complete a survey under realistic conditions. By suggesting a real audience for the report, the pupils will be able to take into account the level of language to be used, the importance of accuracy and sound interpretation of facts rather than hypotheses, and the use of a clear structure and presentation in the final report.
Graphs in Omnigraph
The Omnigraph software is often used for introducing graphs to children. However, it is not limited to pre-GCSE and many investigations have been created for use in Advanced-level mathematics. It can be used either as part of a classroom demonstration or for pupil-centred ICT work in the Computer Room. As an introduction to the topic of straightline graphs, teachers can use Omnigraph to draw a number of graphs of the form y=n and x=n (where n is any number). Based on the features of these graphs, the pupils should be able to answer questions and draw conclusions about the lines. Words such as parallel, horizontal and vertical should be used and a worksheet containing blank axes for the pupils to draw their observations and suggestions for the shape of other lines of the same format will provide a suitable means of checking the pupils’ understanding of the main features of the task.
A similar process can be used for lines of the form y=mx+c. By keeping m fixed and changing c, pupils will notice that the intercept of the graph and the y-axis changes with c. Next examples can be used where c is fixed and m changes (positive numbers only), so that the pupils see the slope or gradient of the line changing. By repeating the last example with negative values for m, the pupils should be able to predict the shape of graphs of the form y=mx for positive and negative values of m.
Graphs of the form y=ax2+b can also be produced quickly and accurately so that the role of a and b can be investigated for positive and negative values. It is quite possible that less able pupils will be able to understand and discuss these patterns as work of this nature is purely observational, requiring only the ability to notice patterns.
The benefit of using ICT for graphing is that it allows the pupils to visualise the mathematical process without spending large amounts of time plotting points and joining them together. The patterns can be viewed easily from the software and the key teaching points can be reinforced through questioning the pupils regularly. The inclusion of ICT in the lesson or series of lessons in this topic offers the less able pupils access to work normally reserved for the more able students or older students. Variations on the sine and cosine functions can also be covered using a visual approach.
Using graphics calculators
The work described in the above section can also be illustrated using graphics calculators.
By pre-setting the values for m and c in the example y=mx+c, the recursive facility will display a series of lines representing each graph specified in the range using the same axes. Pupils will be able to identify the patterns on the graphics calculators in the same way as they did in Omnigraph. A similar approach can be used for graphs of the form:
y=ax2+b. Dick (1996) highlights the importance of graphics calculators to work within