D1.5 Analyse different sets of data presented in various ways, including in tally tables, concrete graphs, and pictographs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions.
Skill: Analyzing Sets of Data
In order to help students develop data analysis skills to make sense of data, teachers should ask them questions that encourage them to look closely at the results presented in a table or graph. This will support the development of the students' statistical literacy skills.
Gal (2002) suggests that the interpretation of the results should be done from two perspectives, that of the investigator and that of the reader. From the investigator's perspective, students investigate data that they themselves have collected in an inquiry and summarized in graphs or tables. They then interpret the data in order to answer the question of interest they posed at the beginning of the inquiry. From the reader's perspective, students are investigating data that is externally sourced, that is, collected by others. In this context, educators can take the opportunity to introduce them to data that relate to other subjects (for example, science and technology, social studies, physical education, and health).
When teachers present a table or graph to students, they should give them enough time to reflect on the data and form a general idea. Then teachers ask open-ended questions to help students express their observations and ideas in their own words as well as develop ideas from those of their peers. For example:
- What do you notice about this representation?
- What is interesting about this graph?
- What can you say about this data?
- What information can you get from this graph?
Open-ended questions elicit a variety of responses, allowing students to communicate their observations, descriptions, and conclusions in a general way.
Levels of Comprehension
Analyzing data represented by a table or graph involves three levels of comprehension: reading the data, reading between the data, and reading beyond the data.
| Level of Comprehension | Description |
|---|---|
| Reading the Data (Level 1) | Identify the data as represented by the table or graph. |
| Reading Between the Data (Level 2) | Compare and combine certain data in order to establish relationships between them. |
| Reading Beyond the Data (Level 3) | Infer or predict from implicit or explicit information drawn from the table or graph and draw conclusions. |
These three levels are hierarchical, meaning that students need to be able to read the data before they can read between them and read beyond the data. In order to help them develop data analysis skills, teachers should ask them questions related to each of the three levels of comprehension. The following provides a more detailed explanation of each level as well as questions that could be asked during a data analysis activity.
Reading the Data
At this first level of comprehension, students are able to extract data from the table or graph without analyzing it in depth. They are able to indicate:
- the title of the table or graph;
- axes or categories;
- the key;
- the frequency of each category.
Reading Between the Data
At this second level of comprehension, students see data less as “an amalgamation of personal data each with its own characteristics” than as “a set of collective data with new properties”. (Konold and Higgins, 2003).
This level is more difficult to achieve because students must be able to:
- see the graph as a collective data set that represents a whole;
- compare data using expressions such as more than, less than, as much as, or most;
- compare the length of the strips or columns of pictures;
- establish the link between the different ways of describing a relationship between data;
- compare data from one category with pooled data from two or more categories.
Reading Beyond the Data
At this third level of comprehension, students use several skills related to data literacy. They must:
- draw conclusions and justify them;
- make inferences and predictions;
- assess the credibility and logic of predictions and conclusions
- recognize information that the table or graph does not show;
- review the steps in the inquiry process.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 100-105.
Skill: Drawing Conclusions, Formulating Arguments and Making Decisions From a Graph
Throughout the data analysis and results interpretation phase, teachers can take advantage of various situations to encourage students to exercise critical judgment with respect to representations of the data and the information that can be derived from them. For example, critical judgment is needed for students to:
- determine whether a graph is a good representation of the data or whether it leads to false conclusions;
- compare two graphs and determine if one is a better representation of the data than the other.
During the mathematical exchange, teachers can use their questioning to help students develop their critical thinking skills. It is important to note, however, that these skills are in their infancy in the Primary Division, so teachers should keep the situations relatively simple.
Source: translated from Guide d’enseignement efficace des mathématiques, de la maternelle à la 3e année, Traitement des données et probabilité, p. 110.
After reviewing and analyzing the data (three levels of comprehension, reading the data, reading between the data, and reading beyond the data), students are expected to draw conclusions, formulate arguments, and make decisions.
Interpretation of the results allows for relevant conclusions to be drawn in order to answer questions of interest and to make informed decisions.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 89.
Decision-making is very important in the inquiry process because without decision-making, the process becomes meaningless. Why would anyone set up a survey and then collect, organize, and analyze data if they have no intention of drawing conclusions? In many cases, decision-making is limited to providing an answer to the original question. In other cases, it is about using the answer to decide whether to act in a particular way. Teachers must therefore lead students to answer the question of interest that prompted the survey or to make a decision based on:
- the relationships established between the data;
- the meaning they have derived from the data;
- the conclusions they drew from it.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 101.