Materi penataran di QITEP Chance and Dat
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:
What is the question being asked?
How do I want to organize the data set?
1
Which presentation is best to use to analyze the data?
If so, which average do I want to use and what will it tell me about the data set?
Do I want to determine an average or the range of the data?
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.
-
Represent data (e.g. line plots, bar graphs, coordinate graphs).
-
Compute the mean, median, or mode and the range of a data set.
-
Understand the distinction between categorical data and numerical data and identify
which graphs and statistics may be used to represent each kind of data.
2
-
Make informed choices about which graph or graphs and which of the average (mean,
median, mode) and range may be used to describe a data set.
3
Activity 1:
Experience of problem
The trainer would pose a problem e.g. „We are going to
Whole class (allow 20 minutes) investigate the characteristics of these QITEP trainees.
What information should we collect and Why?
Mathematical activity
Brainstorm and list trainees‟ ideas in each group. They
Groups (allow 20 minutes)
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
Discuss and compare appropriateness and efficiency of
Whole class (allow 10 minutes) methods used.
Mathematical activity
Refine plans and methods. Carry out data collection
Groups (allow this to take up to Record and collect information. Encourage the trainees to
40 minutes)
devise and refine their own methods of recording.
Have groups make posters of their data using
Communicating Results
Reflect on what was found out, methods used for data
Groups and whole class (allow
collection and recording. Comment on how
40 minutes).
informative/persuasive the reports are.
Discuss what general principles of this investigation can be
gathered from this experience.
4
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.
Note: Most of the ideas/this writing in this handout were taken from the books of Lappan et.al.
5
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)
Measurement tools (standards and non-standars)
Markers with various colors
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
experience.
6
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.
Stand up in a row from person who has the most corn to the less.
7
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?
Materials: cubes (10 each of 6 different colors per group)
8
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 mean of a data set?
What is the mode 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.
Note: Most of the ideas/this writing in this handout were taken from the books of Lappan et.al.
9
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:
What is the question being asked?
How do I want to organize the data set?
1
Which presentation is best to use to analyze the data?
If so, which average do I want to use and what will it tell me about the data set?
Do I want to determine an average or the range of the data?
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.
-
Represent data (e.g. line plots, bar graphs, coordinate graphs).
-
Compute the mean, median, or mode and the range of a data set.
-
Understand the distinction between categorical data and numerical data and identify
which graphs and statistics may be used to represent each kind of data.
2
-
Make informed choices about which graph or graphs and which of the average (mean,
median, mode) and range may be used to describe a data set.
3
Activity 1:
Experience of problem
The trainer would pose a problem e.g. „We are going to
Whole class (allow 20 minutes) investigate the characteristics of these QITEP trainees.
What information should we collect and Why?
Mathematical activity
Brainstorm and list trainees‟ ideas in each group. They
Groups (allow 20 minutes)
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
Discuss and compare appropriateness and efficiency of
Whole class (allow 10 minutes) methods used.
Mathematical activity
Refine plans and methods. Carry out data collection
Groups (allow this to take up to Record and collect information. Encourage the trainees to
40 minutes)
devise and refine their own methods of recording.
Have groups make posters of their data using
Communicating Results
Reflect on what was found out, methods used for data
Groups and whole class (allow
collection and recording. Comment on how
40 minutes).
informative/persuasive the reports are.
Discuss what general principles of this investigation can be
gathered from this experience.
4
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.
Note: Most of the ideas/this writing in this handout were taken from the books of Lappan et.al.
5
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)
Measurement tools (standards and non-standars)
Markers with various colors
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
experience.
6
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.
Stand up in a row from person who has the most corn to the less.
7
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?
Materials: cubes (10 each of 6 different colors per group)
8
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 mean of a data set?
What is the mode 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.
Note: Most of the ideas/this writing in this handout were taken from the books of Lappan et.al.
9