Abstract: Research findings have not yet formally established that Computer-Aided Instruction (CAI) offers a significant improvement over conventional method of teaching. However, in a meta-analysis of 254 comparative Computer-Assisted Instruction studies, Kulik and Kulik found that the students of varying ability levels all displayed significant positive learning gain when using CAI had better examination score, better attitude toward instruction and computers. This covers a wide range of concepts on how to use Microsoft package to solve mathematical problems graphically. Spreadsheet package is used in giving step-by-step solutions to graphical problems with emphasis on Microsoft Excel. The computerised learning activities in this study will supplement conventional instructions of acquiring skills and thus enhances effective students learning.

INTRODUCTION

The outcry of dismal performances of students in mathematics at external examinations like Cambridge, Senior School Certificate organised by West African Examinations Council (WAEC), National Examinations Council (NECO), Universities Matriculation Examination (UME) and Polytechnic and Colleges of Education Examination (PCE) has been on the increase. Many factors have been identified by mathematics educators for the poor students’ achievement in mathematics. Research on student’s learning has revealed that orientations to learning affect learning outcomes. The perceptions of the learning environments especially that of assessment has also been shown to have a strong influence on the orientations to learning (Entwistle and Entwistle, 1991, 1992; Entwistle et al., 1993; Entwistle, 1995). Examinations and tests sometime hamper students attempt to achieve personal understanding because they only show the final outcome but fail to reveal the individual change that has taken place (Tynjala, 1997). Effective teaching and learning of mathematics could only be achieved through introduction of various innovations and skills that are learners-centred to teaching of mathematics. No single method of teaching has been found to be effective. The computer however is considered as the best educational technology in this 21st century. The reason, simply as Chauhau observed is the ability of the individual to act purposefully, think rationally and deal effectively with his environment.

The introduction of computer education under pre-vocational electives at the Junior Secondary School (JSS) level and vocational electives at the Senior Secondary School (SSS) in the National Policy on Education (NPE) is a good development towards enhancing greater learners’ participation in the classroom (Federal Republic of Nigeria, 2004). Computer has been noted to facilitate learning of mathematics and other subjects. Jegede (1991) taught Senior Secondary School Biology students with the help of computer and found that their attitude towards the subject improved after the lesson. Matthews (1990) also discovered that the use of Computer-Assisted Algebra System Package had a desirable effect on the learning and teaching of calculus. This study, therefore, aims at demonstrating how Microsoft Excel could be used in effectively teaching and solving mathematical problems graphically.

MATERIALS AND METHODS

A number of techniques are used in mathematical modelling. Mathematical models can provide concise and unambiguous description of decision problems. Moreover, they enable problems to be explored and investigated through mathematical analysis (Goodwin, 1998). Mathematically, numerical values can be represented in graphical form.

Microsoft Excel is one of the Microsoft Office Suite programs. It is one of the examples of spreadsheet packages apart from QuatroPro and Lotus 1-2-3. Microsoft Excel is an application package meant for solving both statistical and mathematical problems. Spreadsheet program allows the users to present values in graphical form. Graphs in spreadsheet are called Charts. There are different types of chart in spreadsheet. This includes column, bar line, pie, scatter, area, etc.

Charts are used to show proportions of each value in the data set. Data are grouped into related data points. These groups are called data series. When you create a chart with Excel, the categories are plotted along the horizontal or X-axis while the values are plotted along the vertical or Y-axis. Data series originate from single worksheet rows or columns. Each data series in a chart is distinguished by a unique colour or pattern. You can plot one or more data series in a chart except for pie charts.

Charts are created in Excel using Chart Wizard located on the Standard Toolbox. The ChartWizard is a series of dialog boxes that guides you through the steps required to create a new chart or modify settings for an existing chart. When creating a chart with the ChartWizard, one can specify the worksheet range, select a chart type and format and specify how one want ones data to be plotted. One can also add a legend, a chart title and a title to each axis and other chart options.

RESULTS AND DISCUSSION

The object of a graph (short for graphic) is to convey information rapidly and easily. Graphs appear in newspapers, magazines and business publication and take various forms (Durell, 1975).

Before you can draw a chart in Excel, the numbers that compose the chart must be entered in a workbook. There are five general steps in defining a chart. These steps are:

Table 1:	Tourism survey in six geopolitical zones in Nigeria

These five steps should be performed in this order. It is important to know that a chart is linked to the workbook data. Therefore, subsequent changes made to the workbook are automatically reflected in the chart. That is the chart that depends on the data in the workbook where a change is made will also change.

Example 1: A Tourism Centre conducted a survey on the average monthly use of tourist centres located in the six geo-political zones in Nigeria between 2000 and 2003. The worksheet below shows the detail of the attendances in the period (Table 1).

The values in the survey can be transformed into graph. To produce a bar graph showing the number of attendants for each of the zone in 2000-2003 follow these procedures:

Changing the pattern of the bars: In the above chart, each zone has four bars representing each year under review. It is important to note that each bar representing the same year in each of the zone is of the same pattern. Whenever any bar in the chart is selected by single clicking it, those bars representing the same year is equally selected simultaneously. However, the pattern of those bars can be changed. To effect the change, carry out these procedures:

Repeat the same procedures for other three groups of bars representing other years.

Changing chart type: The above chart type (Bar graph) can be changed automatically using the same set of data without necessarily going through series of procedure earlier itemized. To change the chart type, the procedures are:

Pie chart: Pie charts are used to show relative proportions of the whole for one data series only. Data series are a group of related data points.

In the tourism survey, we can produce the pie chart for the data relating to the outcome of the survey. To deal with pie chart, only data in a single row or column could be used. In the example, each cell in the range F5:F10 shows the total attendances for each zone for the period under review. Hence this cell range would be used for pie chart. Follow these procedures to produce the pie chart:

The pattern in each sector of the pie chart can be changed as discussed earlier in bar chart.

Exploding pie chart: Pie chart or graph can be exploded to highlight certain values. To explode pie chart simply means pulling out the slices or sectors in the pie. For example, we might want to explode the zone that has the highest percentage. This will explode only one slice in the pie chart. The procedures are as stated below:

These procedures will shown the result. To explode all the slices, click and hold on the pie and then drag away the pie from the centre of the chart. To collapse or bring the exploded slices to normal, click and hold on the exploded slice. Then drag back to the centre of the chart.

Quadratic chart: Spreadsheet chart techniques can also be used to plot mathematical quadratic graphs.

Example 2: Plot the graphs of y₁ = x² – 5x+4 and y₂ = x – 2 on the same axes between -1≤x≥6. The values of independent variable (x) and dependent variables (y₁ and y₂) look like the table below when entered on worksheet (Table 2). To transform the data in the spreadsheet to a desire XY chart, the procedures to follow are:

Table 2:	Values of dependent and independent variables

The roots (or solutions) of the quadratic equation and the point of intersection between the two graphs can be found using the chart by reading the values accurately.

Line chart (Trigonometry): The line chart can be used to produce the trigonometry values. Excel has most of the mathematical and trigonometric functions built into it. If you need to use the sin, cos, tan functions, they can be typed into any cell and invoke the appropriate function to find their values. By default, the trigonometry value of any angle in spreadsheet is in radian. To calculate trig functions in degrees you must convert them otherwise excel will calculate them in radians. The formula that converts an angle in radian to degree is: = sin (angle*pi ()/180). The values of sin θ, cos θ and tan θ (in degree) for the range of angle 0≤θ≥360 at interval 30° look like the Table 3 when entered into a worksheet. To find the sin, cos and tan values for the angles, the procedures are:

The output is shown in Table 4. The value of tan 90° or tan 270° is infinity (∞). So, these should adequately be effected manually on the worksheet.

Example 3: Using the same scales and axes, draw the graphs of y₁ = 3 sin²x and y₂ = 2cos²x for values 0°≤x°≤ 180° at interval of 15°. Use graph to deduce the solution of the equation 2cos²x = 3sin²x. To solve the above stated problem, the first step is to create a table of values in form of a worksheet as shown in Table 5.

Table 3:	Range of independent variable values (θ)

Table 4:	Computed values of dependent and independent variables

Table 5:	Range of independent variable values (θ)

Table 6:	Computed values of dependent and independent variables

Procedures:

It should be noted that the learner must acquire the skill of converting angles in radian to degree.

Moreover, adequate understanding of the skills resulting the rudiments of solving graphical problems using computer approach.

CONCLUSION

Acquiring basic skills through the use of computer has really justified the inclusion of Computer Aided Instruction (CAI). As it can be seen above, some concepts including graphical problems perceived by many to be too difficult to learn can be taught using Spreadsheet package (MS-Excel). Perceived difficult topics by students in mathematics could be simplified for easy learning with the use of computer software packages such as Geometrical Sketch Pad, Microsoft Excel and Microsoft Word etc.

RECOMMENDATIONS

The researchers are in agreement with Etukudo’s (2002) recommendations that:

ACKNOWLEDGEMENTS

Researcher hereby acknowledge all the researchers of the publication cited as references in this study.