D1.2 Collect data through observations, experiments, and interviews to answer questions of interest that focus on a single piece of information; record the data using methods of their choice; and organize the data in tally tables.
Skill: Collecting Data
Once students have identified the situation, they are ready to move on to the data collection stage. Since this stage can be complex for young students, they will need teacher guidance. The following is a two-step approach:
- plan the data collection;
- collect and record data.
Plan the Data Collection
Proper planning of data collection is the best way to ensure that the data collected will be meaningful and will answer the question of interest that prompted the survey. When planning, it is important to consider:
- the target population;
- the type of inquiry;
- the data sought;
- the method to be used for data collection.
Target Population
Students should plan their inquiry with the target population in mind. For example, if a survey is administered to students in the classroom, it is relatively easy to access that population to collect data. It is then a matter of planning when to conduct the survey. However, if the survey is administered to students in another classroom, it is necessary to discuss this with the teacher in that classroom to determine when and how the data will be collected. In the Primary and Junior Divisions, teachers should support students in these efforts.
When a survey is to be administered to a very large group (for example, the entire school), it is possible to limit the survey to a smaller number of people. This is called a sample. In the Primary Division the size of the target population is usually small so students do not have to worry about selecting a sample.
Type of Inquiry
In the first step of the inquiry process, students have identified the problem situation and formulated a question of interest that they will attempt to answer. In doing so, students have generally determined whether they will conduct an inquiry through a survey, observation or experiment.
The choice of inquiry will affect planning. For example, if students have chosen a survey, they need to plan how best to conduct the survey (for example, oral or written questionnaire). For other types of inquiries, they need to plan carefully how to collect the data to ensure that the data are accurate and valid (for example, how to make the observations, how to conduct the experiment).
Types of Data
Students need to determine whether they will be collecting qualitative or quantitative data, and whether the data is primary or secondary data. While students do not need to know this terminology, they do need to know the difference between these kinds of data in order to better plan their investigation. The table below provides a summary of each of these kinds of data.
| Type of Data | Definition | Examples |
|---|---|---|
| Qualitative data | Data represented by words. |
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| Quantitative data | Data represented by numbers. |
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| Primary data | Data collected directly from the target population by the person or team conducting the inquiry. |
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| Secondary data | Data collected by a person or organization other than the person conducting the inquiry (for example, researcher, company, association). |
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Data Collection Method
When planning an inquiry, students must devise a method that will be effective in collecting data. Deciding on a method of collecting data using concrete, semi-concrete or pictorial materials contributes to the development of statistical literacy.
Collect and Record Data
After planning the data collection, students should gather the necessary materials and organize them in a way that will facilitate the inquiry. Then they proceed to collect the data using the planned method. During this time, teachers circulate and encourage them to think about the inquiry process by asking questions such as:
- Is the investigation going according to plan?
- Are you getting the kind of data you expected? If not, what can you do to correct the situation?
- Are you sure you will get data for the entire target population? Why?
- Is the data collection method efficient and easy to use?
- How will you record the data collected?
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 67-71.
Skill: Recording Data
Data recording can be done either after data collection or as the data is collected. As with data collection, it is important to allow students to choose a mode of recording data before suggesting some of the more conventional methods of recording.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 71.
When students use different modes of data recording, it is important to encourage them to evaluate the effectiveness of their methods and compare them to highlight the advantages and disadvantages of each. To do this, educators can ask them questions such as:
- Do you find this method of recording data efficient? Why? (It's not really efficient because it takes a long time to draw all the objects.)
- Does this data recording take all data into account? How do you know? (Yes, because each student's answer is written directly next to their name on the list. That way, we're sure we won't forget anyone.)
- What do all of these methods have in common? (In all of these methods, each piece of data is represented by a drawing or symbol of some kind, which ensures that no data has been missed.)
- What is different about these methods? (In some cases, the same symbol is always used, while in others, different symbols are used.)
- Are there any methods that you find easier to interpret than others? Why? (For example, students might say that some methods seem easier to interpret because each piece of data is clearly represented in a table according to the category it belongs to. It is then easy to see which category contains the most data. However, other methods would need to have the data reorganized a bit before they could be analyzed.)
As students develop an understanding of what makes a data recording mode effective, educators can model the use of any of the following conventional methods:
- the simple table;
- the tally table.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 74.
Skill: Organizing Data
Once students have identified the situation and collected data, they need to organize it.
Why Organize the Data?
Gal (2002) indicates that data are organized for the purpose of analyzing or communicating information. Since the purpose of an inquiry is to find an answer to one or more questions of interest, it is very difficult to determine answers if data are presented in a haphazard fashion. Effectively organizing collected data will present it in ways that summarize and highlights information revealed in the data, communicate key features of the data, and facilitate interpretation of the data.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 62.
Knowledge: Question of Interest
In planning their investigation or probability experiment, students should first ensure that they have a clear understanding of the situation. This can be done by clarifying the problem and formulating one or more questions that can be answered with data. Students should also consider, to the extent possible, some of the factors that may affect the outcome, or variability, of the investigation or experiment.
Clarify the Problem
Before solving a problem situation, teachers should ensure that the problem is understood by all students. They can check this understanding and, if necessary, help them clarify the problem by facilitating an exchange of ideas about the situation.
Formulate Questions
Once you have a good understanding of what you are looking for or what you would like to know, you can start planning the inquiry. The first step is to clearly formulate the question of interest, that is, the question that clarifies the intention of the inquiry. A question of interest is a question that can only be answered from variable data. Thus, the question ”How many children are there in your family?“ is not a question of interest since the answer is fixed (for example, three children) and does not depend on variable data. On the other hand, the question ”How many children per family are there among the students in the class?“ is a question of interest since to answer it, we must first collect data on the number of children in each student's family. In light of the answers obtained, we can then conclude, for example, that in the majority of the students' families, there are two children.
Konold and Higgins (2003) argue that in the inquiry process, students' first challenge is to turn a general question into a question of interest. Teachers need to help students understand the importance of framing the question of interest correctly and ensuring that it accurately reflects what is being sought.
Students should also learn to recognize that the choice of question of interest affects the type of inquiry that will subsequently need to be conducted. The following are some examples of questions of interest that students might address in the Primary Division, each with the type of inquiry it suggests.
| Question of Interest | Type of Inquiry |
|---|---|
| What are the three favourite varieties of apples of the students in Mrs. Pommerleau's class? | Survey |
| How many servings of vegetables and fruits do the students in the class eat in a day? | Observation |
| How many bounces does a table tennis ball make when dropped from a height of one metre? | Scientific experiment |
| If a Styrofoam cup is dropped, is it more likely to land upright, upside down, or sideways? | Probability experiment |
| Which month of the year has the most precipitation? | Secondary data collection |
As the Mathematics Curriculum illustrates, students develop the ability to formulate survey questions over the years. For example, in Grade 1, students are asked to write survey questions that require a yes or no answer (for example, ”Do you like cats?“). Then, through Grade 4, they are asked to formulate survey questions with a limited number of answers.
Teachers can help students develop the skill of formulating a survey question by asking questions such as:
- Is the question easy to understand?
- Should it be reworded to better target the type of response desired?
- Should the number of possible different answers be limited?
- Will the expected answers allow us to answer the question of interest?
In summary, to help students develop the ability to formulate a question of interest or a survey question, teachers should lead them to:
- clarify the problem;
- specify the information that is needed to solve it;
- ensure that the question of interest and the survey question generate this type of information;
- think about the possible interpretations of their questions;
- ensure that the survey question is consistent with the issue of interest and generates a limited number of responses.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 59-64.
Knowledge: Data Collection Through Observation
For 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.
- We note the number of cars passing through an intersection during a given time interval.
- Every day for a week, we note the time at which we go to bed and the time at which we get up.
In planning data collection through observation, it is necessary to plan where, when, what, and sometimes how to observe (for example, recognizing that a car is or is not making a complete stop at an intersection, distinguishing a complete stop from an incomplete 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.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 46.
Knowledge: Data Collection Through Experiments
For data collection through experiments, the data comes from a hands-on scientific activity that requires adherence to certain preset parameters and, often, the use of precise measurement techniques and tools.
Example
For data collection of a probability experiment, a team spins a spinner 15 times and notes, with a check mark (√), each outcome in the appropriate place in a table.
Image Three rows: one for the yellow key, which has six check marks, another for the blue paperclip, which has two check marks, and a third for the red scissors, which has seven check marks. Roulette wheel divided into three parts: the first one showing a yellow key, the second one red scissors, and the third one blue paperclip.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 72.
Knowledge: Survey
A survey is the most common type of inquiry used by students in the Primary Division. It requires the formulation of one or more questions to be asked during the survey. These questions are usually closely related to the question of interest. For example, the question of interest, ”What are the three favourite varieties of apples in Ms. Pommerleau's class?“ could be answered with a survey question, ”What is your favourite variety of apple?“ The wording of the survey question depends largely on the type of information sought. In a survey, there are generally four types of information: preference, quantity, size, and general information.
| Type of Information | Sample Questions | Information Sought |
|---|---|---|
| Preference |
Do you like to read adventure stories? Which of the following 15 activities is your favourite? |
These questions invite respondents to express a personal choice. |
| Quantity |
How many buttons are there on your coat? Of the following 15 activities, how many would you like to participate in? |
These questions seek count information, often in response to a question beginning with “how many”. |
| Size | How many seconds does it take you to complete the 100 metre race? | These questions target data relating to units of measurement. |
| General Information |
Do you have a cat at home? In which country were you born? |
These questions target a variety of information that is not quantitative in nature and does not reflect a preference on the part of the respondents. |
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 62.
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 1 students are asked what kind of music they prefer.
In planning a survey, it is important to write the survey questions well to ensure that they are clear and objective. It is also important to anticipate the responses that may be given and sometimes to 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. 47-48.
Knowledge: Tally Table
The tally table allows you to quickly record data from an inquiry within pre-designated categories by placing a single symbol (for example, letter, checkmark, line) for each piece of data in the appropriate column or row. These symbols are usually placed horizontally in an orderly fashion to facilitate counting.
The tally table usually contains:
- a title;
- several columns or rows designated by categories;
- recording data in each category using the same symbol.
When the number of symbols within each category is relatively large, counting them becomes more difficult and the risk of error is greater. In such cases, the stroke recording strategy is more effective. This strategy consists of drawing a vertical stroke to represent each of the data and, for the fifth data item, drawing an oblique stroke on the four preceding strokes. It is therefore easier to count the strokes since one can count in steps of 5.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 76-77.