D1.2 Collect data through observations, experiments, and interviews to answer questions of interest that focus on qualitative and quantitative data, and organize the data using frequency tables.
Skill: Collecting Data
Planning and conducting data collection provides meaningful data.
The inquiry process is a comprehensive one that involves four steps: identifying the situation, collecting the data, organizing the data, and interpreting the results.
Once students have clarified the problem and formulated one or more questions of interest, they should plan and carry out a data collection. It is important to consider the different types of inquiries, the different kinds of data, and the difference between population and sample when planning the data collection. Involving students actively in planning the data collection encourages them to make thoughtful choices and to look critically at the entire inquiry process.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 44.
Questioning
It is important to provide students with a variety of opportunities to plan a data collection. By interviewing students throughout this stage, educators help them to better understand the importance of choosing the type of inquiry and the type of data that are most appropriate for the question of interest, as well as identifying the population and, if necessary, the sample to be surveyed. Doing so supports students in developing critical thinking skills, which will be very useful in the fourth step of the inquiry process.
Here are some ideas for questions that teachers can use to guide students through the data collection planning process:
Type of Inquiry:
- What type of inquiry is most appropriate for your question of interest? Why?
Type of Data:
- What kind of data will you collect?
- Does this kind of data lend itself well to your question of interest? Why or why not?
- If you are going to use secondary data, where will it come from? Is this source reliable?
Target Population:
- What is your target population?
- Is this the group that is the focus of your investigation?
Methods (Where, When, How):
- Where will you conduct your investigation?
- When will you conduct your investigation? Why is this a good time? If it were conducted at another time, would the results be the same?
- How will you go about getting the data you need?
- How will you record the results of your inquiry?
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 57-58.
Skill: Organizing Data
Organizing data and representing it in tables and graphs helps communicate information for interpretation. Once students have identified the situation and collected data, they need to organize the data.
Why Organize Data
Gal (2002) indicates that data obtained by an inquiry are organized for the purpose of analysis or reporting. Since the purpose of the inquiry is to find an answer to one or more questions of interest, it is very difficult to base this answer on data that are presented in a disorganized fashion. By organizing the data collected, it is possible to present them in a way that summarizes them, highlights some of the information they contain, communicates their main characteristics and facilitates their interpretation.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 62.
Knowledge: A Question of Interest
A question of interest is a self-selected question for which data must be collected. The question may deal not only with preference, but also with magnitude, quantity or general information.
Source: Ontario Curriculum, Mathematics Curriculum Grades 1-8, 2020, Ontario Ministry of Education.
Knowledge: Types of Inquiry
Data Collection Through Observation
In a data collection through observation, one records what one sees or does.
Examples
- We count the number of birds we see in the schoolyard at specific times.
- The number of cars passing through an intersection during a given time interval is noted.
- We count the number of times we go to the sports center in a month.
- We note, every day for a week, at what time we go to bed and at what time we get up.
In planning to collect data through observation, it is necessary to plan where, when, what, and sometimes how to observe (for example, how to distinguish between a car making an incomplete stop at an intersection and a car making no stop). It is also possible to plan whether all observations will be made by one person or whether they will be made by several people at the same time to ensure better reliability.
Data Collection by Means of an Experiment
In a data collection by means of an experiment, the data are derived from a hands-on, scientific activity that requires adherence to certain preset parameters and often the use of precise measurement techniques and tools.
Examples
- At specific intervals, plants are measured for growth, with some receiving a small amount of nutrients, some receiving a larger amount, and some receiving no nutrients, to see if nutrients are contributing significantly to plant growth.
- Every 30 seconds, we take the temperature of any liquid that has been heated to 100°C and left to cool down. We repeat the experiment with different liquids in order to compare the speed at which they cool down.
When planning an experiment, the scientific approach must be used and the reliability of the data collection method must be ensured. Variables that may render the results invalid must be controlled for and neutralized.
Data Collection Through Surveys
When conducting a survey, data are collected by asking a number of individuals about a particular topic. The questions often take the form of a questionnaire that can be answered in writing or orally.
Examples
- Students in the class are asked how many hours they spend watching television each week.
- Grade 6 students are asked what kind of music they prefer.
In planning a survey, it is important to write the survey questions carefully to ensure that they are clear and objective. It is also important to anticipate the responses that may be given and sometimes group them into categories.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 46-48.
Knowledge: Frequency Table
A frequency table helps organize the data from an inquiry and summarizes it quantitatively, making it easier to construct a bar graph and develop an answer to the question of interest. For example, students in the class take a survey to find out how everyone woke up this morning. There are four response choices: A parent woke me up, I woke up by myself, My alarm clock woke me up, and Other means. Students complete the survey by checking the appropriate response on an individual sheet of paper and then the responses are tabulated. The result of this tabulation can be represented by a frequency table; the Number of Students column is the frequency.
| Mean of Waking Up | Number of Students |
|---|---|
| A parent woke me up. | 7 |
| I woke up by myself. | 4 |
| My alarm clock woke me up. | 8 |
| Other means | 3 |
| Total | 22 |
In the situation where students take turns answering the survey orally, a tally table can be used for recording the data.
| Mean of Waking Up | Count | Number of Students |
|---|---|---|
| A parent woke me up. |  |
7 |
| I woke up by myself. |  |
4 |
| My alarm clock woke me up. |  |
8 |
| Other means |  |
3 |
| Total | 22 |
In some situations, one may want to group the data in the frequency table according to various categories. For example, the data obtained from the survey on the number of pieces of trash found in the students' lunch boxes can be summarized in a frequency table as follows.
| Number of Waste | Frequency |
|---|---|
| 0 | 0 |
| 1 | 1 |
| 2 | 2 |
| 3 | 2 |
| 4 | 1 |
| 5 | 5 |
| 6 | 6 |
| 7 | 2 |
| 8 | 1 |
| 9 | 0 |
| Total | 20 |
This table contains ten answer choices, but the frequency of several choices is only 1 or 2. Therefore, it may be more useful to group the data two by two as in the following table.
| Number of Waste | Frequency |
|---|---|
| 0 to 1 | 1 |
| 2 to 3 | 4 |
| 4 to 5 | 6 |
| 6 to 7 | 8 |
| 8 to 9 | 1 |
| Total | 20 |
This table can be considered more useful and easier to deal with because it summarizes the data into five categories instead of ten. For example, it quickly reveals that almost half of the students have 6 or more pieces of trash in their lunchbox. However, if the goal of the survey is to determine how many students have no garbage in their lunchboxes, this table is not very useful since it is impossible to tell if they have 1 or no students who completed the school's Green Committee Challenge of the Month. So, building a frequency table can generate useful and interesting classroom discussions. In addition to guiding students on how to construct a frequency table, educators should discuss with students the possible choices and facilitate discussions about the benefits and limitations of each table.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 67-70.