STRAND: CHANCE AND DATA
PROJECT: DATA ABOUT QITEP TRAINEES
Sitti Maesuri Patahuddin
Introduction:
A basic knowledge of statistic and data analysis is a necessary life skill. Newspapers, television, internet, books bombard us with statistical data. Students need experience in both consuming and creating data that is represented in several different forms, including tables, graphs, and statistics. Exploring statistics as a process of data investigation involves a set of four interrelated
components:
- Posting the question: formulating the key question(s) to explore and deciding what data to collect to address the question(s).
- Collecting the data: deciding how to collect the data as well as actually collecting it. - Analyzing the data: organizing, representing, summarizing, and describing the data and
looking for patterns in the data.
- Interpreting the results: predicting, comparing, identifying relationships and using the results from the analyses to make decisions about the original question(s).
What should teachers do to help students in learning statistics and data analysis? - Help them to engage in the process of data investigation
- Help them to represent data
- Help them to explore concepts, ways of describing data such as: the shape of distribution, what is typical in the data, measures of centre, range; variability in the data
- Help them to develop a variety of strategies
Therefore, in this lesson, the participants should be encouraged to ask questions about situations that involve data analysis:
Which presentation is best to use to analyze the data? Do I want to determine an average or the range of the data?
If so, which average do I want to use and what will it tell me about the data set?
How can I use graphs and statistics to describe a data set or to compare two data sets in order to answer my original questions?
Teachers have many favorite activities that they know children will enjoy and engage with, for example:
‘We are going to go out to the school gate and tally the traffic that passes the school so that we can make a graph’
Children do seem to enjoy this type of activity but they never „own‟ it. They‟ve been told what to do and why and how to record their findings. Most of the purpose and need to think
mathematically has been taken away from them.
In this section, the trainees are expected to generate their own questions and make them match their own interest or curiosity. They will also be involved in making the decisions as to what and how to record as well as presenting data. If the similar activity is applied to the children, we hope that students will become involved in the topic and therefore motivated.
Objectives:
The trainees will carry out statistical investigation to answer this question: What are some of characteristics of a typical QITEP trainee?
Mathematical highlights:
- Understand and use the process of data investigation by posing questions, collecting data, analyzing data, and making interpretations to answer the participants‟ question.
Activity 1:
Experience of problem
Whole class (allow 20 minutes)
The trainer would pose a problem e.g. „We are going to investigate the characteristics of these QITEP trainees. What information should we collect and Why?
Mathematical activity
Groups (allow 20 minutes)
Brainstorm and list trainees‟ ideas in each group. They decide what information to collect and how to record their findings.
These characteristic may include:
- Physical characteristics (For example, age, height, or eye color)
- Family and home characteristics (For example, number of brothers and sisters, or number of television sets) - Behaviors (For example, hobbies or number of hours
spent watching televisions) Communicating results
Whole class (allow 10 minutes)
Discuss and compare appropriateness and efficiency of methods used.
Mathematical activity
Groups (allow this to take up to 40 minutes)
Refine plans and methods. Carry out data collection Record and collect information. Encourage the trainees to devise and refine their own methods of recording.
Have groups make posters of their data using Communicating Results
Groups and whole class (allow 40 minutes).
Reflect on what was found out, methods used for data collection and recording. Comment on how
informative/persuasive the reports are.
Discussion:
Participants could discuss:
The types of teaching that they have encountered that would not facilitate students to achieve the goal of teaching.
The possible answer:
- Give the student data. Asking students to find the measure, such as, mean, median, modes, without helping the students to make these concepts meaningful for them. - Ask student to present data using a particular graph as required by teachers. Teacher
sometime gives the interval of the data. It means that students do not have enough space for them to make think and to make decision about the best way to present data.
Discuss the type of teaching that could help students construct their own understanding about statistic.
Discuss about the characteristic of realistic mathematics education involved in this activity.
References:
Lappan, G., Fey, J. T., Fitzgerald, W. M. , Friel, S. N., Phillips, E. D. Connected Mathematics: Data About Us.Statistics. Teacher‟s Guide. Prentice Hall: Glenview.
Worksheet
Project : Investigation about the characteristics of a typical QITEP trainee
Time : 3 x 50‟
Materials needed:
Large chart paper (a few sheets per group of students) Markers with various colors
Measurement tools (standards and non-standars) Calculators as needed
Task:
We are going to investigate the characteristics of these QITEP trainees. What information should we collect and why?
1. In each group, brainstorm and list your ideas. Decide what information to collect and how to record your findings. Prepare your presentation for a whole class discussion.
2. Discuss and compare appropriateness and efficiency of methods used.
3. Refine your plans and methods then carry out data collection. Record and collect information. Refine your own methods of recording.
4. Each group must prepare a poster of their data and the conclusion of their investigation. Reflect on what was found out.
Reflect methods used for data collection and recording.
Comment on how informative/persuasive the reports in the posters are. 5. Discuss what general principles of this investigation can be gathered from this
STATISTIC
Sitti Maesuri Patahuddin
Introduction
In this section, we are going to explore concepts that relate to average or the measures of center: mode, media, mean. Remember that an average is a value used to describe what is typical about a set of data. An average can be thought of as a measure of center.” The mode and the median are two types of averages you have used quite a bit. The mode is the value that occurs most frequently in a set of data. The median is the value that divides a set of ordered data in half. Activity 2 and 3 is to explore the concept of median, mode, and mean.
Objectives:
- To understand the mean as a number that “evens out” or “balances” a distribution.
- To find the mean of a set of data
- To reason with a model that clarifies the development of the algorithm for finding the mean.
Mathematical concept: median, mode, and mean
Material:
Manipulatives: corn, unit cubes, or any manipulates that can be counted and shared among the participants, a flag (to write a number on it)
Activity 2
1. The class is divided into two groups.
2. In each group: the participants conduct the activities below.
Each person takes a handful of corns and count their amount. Write down the number of corn in your own flag.
The person(s) who are standing in the middle of the row highlight his/her flag. This number is the median of the data as it gives the middle value of the data set.
Find the number that occurs most frequently. We call the value that occurs most frequently the mode of the data set.
For every body in the group, find another people in your group and share your corn to make the same amount of corn or the difference is only one.
Make sure that any pair in each group has the same number of corn or their difference is one.
What is the mean of the number of corn in a group of QITEP trainees.
Activity 3: What do we mean by mean?
1. Divide the class into groups of 6 people.
2. Make a set of cube towers to show the size of each household. Each tower should be a single color and different from the colors of the other towers.
3. Arrange the towers in order from smallest to largest. What is the mode and the median of the data set (number of people in households of your group)
4. Find the average by “evening-out” the number of cubes in each tower. This means that you need to move cubes from one tower to another.
5. Since each tower was originally a single color, now, look at the tower from which towers the “moved data” came.
6. Each household has an average of …. people. This number is called mean. Whole class discussion:
What is the median of a data set? What is the mode of a data set? What is the mean of a data set?
Give examples, the uses of mode, median, and mean in a daily context.
References:
Lappan, G., Fey, J. T., Fitzgerald, W. M. , Friel, S. N., Phillips, E. D. Connected Mathematics: Data About Us.Statistics. Teacher‟s Guide. Prentice Hall: Glenview.
