Enhancing the Teaching and Learning of Early Statistical Reasoning in European Schools SOCRATES-COMENIUS Action Project 226573-CP-1-2005-1-CY-COMENIUS-C21 Scenario 2 Partners: ARISTOTLE UNIVERSITY OF THESSALONIKI
COPYRIGHT Copyright 2006 EarlyStatistics Consortium consisting of: Cyprus College (CC), Cyprus Sor Trondelag University College (HiST), Trondheim, Norway University of Thessaly (UTH), Volos, Greece Aristotle University of Thessaloniki (AUTH), Thessaloniki, Greece Universidad de Cádiz, Departamento de Didáctica (UCA), Cádiz, Spain This document may not be copied, reproduced, or modified in whole or in part for any purpose without written permission from the EarlyStatistics Consortium. In addition to such written permission to copy, reproduce, or modify this document in whole or part, an acknowledgement of the authors of the document and all applicable portions of the copyright notice must be clearly referenced. All rights reserved. This document may change without notice.
ACTIVITIES In the analytic program of elementary school there are some parts that concern Probabilities and Statistics. In the end of this section we include the relative parts from the students book and the schoolteacher s book. The importance of activities for the comprehension of mathematical concepts and processes has been recognized more widely. Teaching probabilities and statistics using activities, is likely the most suitable (most efficient) method. Particularly today, in the era of growth of information systems, the organisation of such activities gives the possibility of using computers in Statistics education. Moreover, the statistics and probabilities concepts are suitable for the enhancing of collective work in the school class, for the assignment of individualised work, for the planning of the total frame of energies and the entrusting of individual duties and competences in this frame. For example, in order to organise and complete a sampling research or census, a series of duties should be assigned to a group of people. After the selection of the research object some people should undertake the preparation of essential materials (questionnaires, maps, etc), others should undertake the data collection, others data validation, others should undertake data entry and others data analysis and presentation of the results. It is not essential that these groups of people are distinguished (the teams can have common members) and everyone can take part in all stages. However, it is essential to assign individual work to teams and individuals, because everyone dealing with everything is not effective. Such an example constitutes the overall activity about the "TV attendance" that is reported analytically in this paper. Moreover, we mention certain more specialised activities that were drawn for the cognitive level of orders of elementary school. 1st ACTIVITY: Everything we want to learn about our social environment. I learn my class, I present myself. This activity is designed for students of the first two classes of elementary school and it aims to the comprehension of variable, the concept of relative frequency, the graphic representation with simple tables of frequencies and simple plots. The children should comprehend that everyone does not have the same characteristics; everyone does not have the same preferences for daily activities. Moreover, they should become able to distinguish measures of centre (mode) - what they prefer most, what hair colour dominates etc - so that they are led to simple forecasts and conclusions. For instance, if most children in the class prefer orange juice, on my birthday at school I should mainly offer orange juices and I should avoid offering orange juices, lemonades and other refreshments in equal quantity. Respectively from the relative frequency they can have more conclusions (the second in preference refreshment is lemonade etc). March 2006 S2 Page 3
This activity is organised in 4 instructive hours and it includes: 1 hour Presentation - example. The book of B class gives a characteristic example with the separation of children depending on the kind of refreshment that they prefer. The teacher can present this example or a proportional one (e.g. the season of the year we have our birthday) at this instructive hour. If this example is presented in a place where children can move around (e.g. in the courtyard of school) it will cause their additional interest and help them dissociate mathematics from the school class and make them move lively. Transporting the results in the table - in the school class - we give the dimension of transport and abstraction that is required. 1 hour Design and Data collection In this instructive hour the characteristics (variables) that will be measured and recorded are selected after discussion. Here the teacher should direct the children so that they select all types of variables (categorical, ordered and quantitative), variables objectively measurable (hair colour, height, etc) and variables subjectively measurable (beloved course, beloved food, etc). At least 2 variables from each type should be selected. At the same time, we encourage data collection at an individual level, where each child records the data that we selected for him/her. In the end of this hour we collect all data and we categorize them. 2 hours Analysis-presentation In these two hours the children are separated into groups and each group processes one or two variables. We take care to aggregate variable values so that there are not a lot of categories (if e.g. we measure the height in cm it is appropriate to group the values in a scale i.e. tall mediocre - short, if we measure hair colour we code them in a scale of basic colours - black, blond, red, brown -, if we measure preference of food we should code based on one or two particular components - meat, fish, chicken, pastas, vegetables, etc - or preparation way - fried, roast, in the oven etc. We distribute to each group all the recording sheets - preferably coded - and tell them to deal with two variables, i.e. to make a table of frequencies and a simple bar chart. In the first class we present the results the last two hours and cause discussion on their annotation. In the second class the treatment and the presentation is appointed to the children themselves. Parallel activity or the initial phase of the choice of variables can start with the prompt to present the children (each one) elements about themselves and their preferences, using reason, form, drawing, materials e.t.c. This phase can help, particularly in the first class, in the choice of variables and in recording or coding of the prices. March 2006 S2 Page 4
2nd ACTIVITY: Changes in space and in time. Presentation of the preferences of the current and the previous generation It is addressed to students of the third and fourth class and aims at the comprehension of variable, the significance of relative frequency, graphic presentation with simple tables of frequencies and simple forms, at the faculty of choosing and recording of information. The children should comprehend that all do not have the same characteristics or the same preferences for daily activities. They should comprehend that these characteristics change in space (they differ from region to region) and in time (they differ from generation to generation). They should moreover, be able to distinguish metres of place (prevailing price, median) - what they most prefer, which hair colour dominates, which is the medium height, weight e.t.c.- so that they will be led to simple forecasts and conclusions concerning space and time, by observing the changes that have taken place. They should be able to select information depending on their use. This activity is organised in 4 instructive hours and includes: 1 hour Presentation-example. Selecting certain sizes or tables (e.g. populations at region between successive general inventories) we can present the picture of region or country in the past and today. Commenting what was happening in our own season (when we were studying to the elementary school) we can give an example of the follow-up changes. Thirdly, in the book there are examples of difference in space (B and C class, two fruit stores) and discrimination in time (month of travel). 1 hour 1.1.1 Generalisation of elements In this instructive hour the characteristics (variables) that will be measured are selected after discussion and are recorded for the parents and the students. Here the teacher should direct the children so that select all the types of variables (category, provision and quantitative), variables objectively measurable and variables subjectively measurable. At least 2 variables from each type should be selected. We end up with a leaf of recording in which the variables that will be measured have been fixed with clarity and the questions have been clearly formulated so that the single recording is ensured. At the same time we point out that elements for the child and his parents based on the questionnaire will be recorded. March 2006 S2 Page 5
2 hours 1.1.2 Treatment-presentation In these two hours the children are separated into groups and process one or two variables in each group. We have attended to group the prices of variables so that a lot of categories do not exist. We give to each group all the leaves of recording - preferably coded - and tell them to deal with two variables,i.e.draw a table of frequencies and one simple bar chart for each one. Moreover, in a presentation report simple conclusions of comparison in time should be recorded. This can become with the comparative presentation "then-parents", "now-students" A leaf of recording could contain: Emission of television Type of music Game Extracurricular activities Food Sum of money (pocket money) Clothes Place of holidays Sport e.t.c. The question that corresponds with the recording can be: - Dad, which was your favourite food when you were my age? - Mum when you were the same age which game did you play more often? Recording the answers of the parents each child assembles a volume of individual data which with special treatment presents the changes between generations. It should be pointed out that in order to compare these sizes they should be corresponded in a single unit (e.g. relative frequency). It is possible that simple tables of double entry will come up e.g. Then Place of Holidays Sex Mountain Sea No Holidays Boy Girl Now Place of Holidays Sex Mountain Sea No Holidays Boy Girl March 2006 S2 Page 6
Parallel activity or the initial phase of the choice of variables can take place with the prompt to present the children (each one) elements from their season which they consider important to maintain in the history with reason, form, drawing, materials e.t.c. so that people in the future will find them and which elements we would like to know from a previous season (e.g. Ancient Greece, Byzantium, Revolution 1821, e.t.c.). This activity can help to the comprehension of changes in time, as if the same information is asked from a school of other prefecture or other country to help comprehend the changes in space. 3rd ACTIVITY: Collection and treatment of data-information. It is addressed to students of the fifth and the sixth class. The stages of organisation and concretisation are respective to those reported analytically in the example. Instead of the leaf of primary data that results from the television program, a leaf of primary data can be used to record for a period of one week elements from two meals, a lunch and a dinner of each day in the following table: Food Hour Satisfaction Number of individuals Frequency Place Duration Lunch Lunch Lunch Lunch e.t.c. In the variable "food" we record the kind of food, in the "hour" we record the hour when we started eating, in the "satisfaction" how much we enjoyed food (a lot, relatively, little, by no means), in the "number of individuals" how many individuals ate with us, in the "frequency" how often we have this food, in the "place" where we have lunch (cooker, dining room, room of television, outside in restaurant-tavern, in a friend s house, in a relative s house e.t.c.) and in the "duration" how much time it took us to complete our meal. From the primary data a leaf of recording-computer background that is used for the coding of elements results. Each student transports the primary material coded prices in this leaf during the 2 nd instructive hour. The "food" is referred as the main "dish". As we have mentioned before it can be coded based on the main component (look "we and the world", book of "Education of health"), the area in intervals of hour (e.g. 13-14, 14-15, 15-16, e.t.c.). In the next two hours the students in groups deal with two variables. (Look the example) March 2006 S2 Page 7
Team A Team B Team C Team D Team E Team ST Type-satisfaction Type-frequency Type-place Duration (time) concerning the day Place-satisfaction Type concerning the discrimination of dinner (middayevening) A/A Mac Day Dinner Type Food Area Satisfaction Number of individuals Frequency Place Duration Sunday Sunday Monday Monday Tuesday Tuesday Wednesday Wednesday Thursday Thursday Friday Friday Saturday Saturday March 2006 S2 Page 8
4th ACTIVITY: Collection and treatment of data-information. It is addressed to students of the fifth and the sixth class. In this activity we do not collect information from our direct environment but from forms and sources. This activity presupposes that the students have access in similar sources of information (municipal library, collections of newspapers, e.t.c.) The time period of collection and the thematic unit of information should be determined. For example we can determine that for the time interval of January 99from the available newspapers and magazines all the elements with regard to economic sizes will be assembled. Forms of activity For time interval of one week, the students assemble from newspapers, magazines, other forms, other electronic sources, all the statistical diagrams, tables that are contained in them. They evaluate, categorize thematic, comment and present their conclusions and the processed information. The students can be separated into groups teams depending on the titles of the newspapers and magazines and the time duration. A pair e.g. can record from the "Free press" of the same month, another from the Sunday newspapers of the same month, another from the "Free Press", other from the local newspapers and so on. Alternatively, a specific newspaper can be recorded for a bigger interval (if there are 26 children, each one will have to read two weeks a year so that all the year will be covered). Respectively, the teacher can assemble material from newspapers and/or magazines and prepare the course based on it and asking from the children some moment (after the second course) to bring their own elements. Here, we present the significances and the diagrams that are included in the material of the fifth and sixth class with the use of real examples and daily sources. This leads to the presentation of a teaching lesson plan with the apposition of materials, objectives and course of teaching. March 2006 S2 Page 9