Body measurements, databases and spreadsheets in the Mathematics Classroom
Pupils are provided with information about how the Chagga people from Tanzania used to make their beehive-shaped dwellings, see Africa Counts (C. Zaslavsky, 1973). They are then provided with information about how different cultures used body measurements as their units of length.
Further information is supplied from the work of the Roman, Vitruvius, about his views on the proportions of the body. The pupils then have to collect a number of body measurements from each other. They will have to consider the best way to take measurements, as well as decide on an appropriate degree of accuracy. The information is then typed into either a spreadsheet or a database (occasionally both). Once the typed data has been checked, the pupils then interpret the data. They will have to produce some, or all, of a suitable measure of central tendency; an appropriate measure of spread; a chart; and a way to compare two variables.
Discipline, subject : mathématiques
Public : cycle d'orientation
Sek I, BWK
lower high school
Department of Education
Keele University, Keele
STAFFORDHIRE ST5 5BG
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Pédagogie, pedagogy : Pupils had to measure various parts of their body and enter the information into both a database and a spreadsheet. They then had to examine the data in both the database and the spreadsheet in one of a number of ways. For some pupils this work was used as an introduction to scatter graphs; another group had to compare the difference between using a database with using a spreadsheet; another class looked for correlation between lengths of different body parts.
Apprentissage, learning : Method of data collection was important, with thought being given to appropriate level of accuracy, given the equipment used, and ensuring consistency of method of measuring. Once measurements were collected pupils had to examine the data using either, or both, of the spreadsheet and database to produce some of the following statistics: a suitable measure of central tendency (such as mean, mode, median); an appropriate measure of spread (range, inter-quartile range, standard deviation); a chart to illustrate the information (bar chart, pie chart, line graph, histogram, cumulative frequency); and a way to compare two data sets (scatter graph, line of best fit, correlation).
Enseignement, teaching : The aim varied according to the class, their age and ability and their experience of mathematics.
Examples included: to gain understanding about how to standardise when taking measurements; to understand the benefits of using a spreadsheet or a database; to be able to decide when to use a
particular measure of central tendency; and to investigate the different types of scatter graphs that might arise from sets of data.
Technique : Database used was GRASS - a graphics, sorting and searching program available for some IBM
PCs, BBC and Archimedes computers, though any database program with charting features would do. The spreadsheet EXCEL was also used - this does have database features, but they are rather difficult for many pupils to use. Later versions of EXCEL (from version 5 onward) are much easier to use than earlier versions. It is necessary that the teacher, or the pupils check the data, to ensure that it has been entered correctly (data verification).
Société, society : Pupils have to be aware of the feelings of others when taking body measurements. In the UK pupils will become aware that although for most of the time boys are, on average, taller than girls, this will not be the case for children aged between 10-12, when girls are, on average, taller than boys.
Culture : Pupils were provided with information taken from Africa Counts (C. Zaslavsky, 1973) about the Chagga people in Tanzania and the way they used to decide on the size of their traditional dwellings. In addition, they were provided with information about Vitruvius' book (De Architectura) which gives his comments on body proportions from the first century BC. Information was provided about measurements that were common to societies in different parts of the world.
Institution : Measuring apparatus, a single computer and the software (at least one spreadsheet or database with charting facilities).
Logistique : A single computer is all that is required, especially for data entry. For data interpretation one computer can be used if pupils take it in turns to use the computer, however, it can be much more effective if pupils have one computer between two pupils.
Remarques, remarks : This activity, designed by the author, has been used with considerable success by the author in many classrooms and on training courses. It has subsequently been used and adapted by others, to suit their own pupils. It is a remarkably simple idea which brings together work in mathematics and statistics, information about common measurements in different cultures, details about the history of mathematics, and uses of information technology.