D1.5 Analyse different sets of data presented in various ways, including in logic diagrams, line plots, and bar graphs, by asking and answering questions about the data and drawing conclusions, then make convincing arguments and informed decisions.
Skill: Analyzing Sets of Data
To support students in developing skills to analyze data, educators need to engage their reasoning skills by asking questions that encourage them to look closely at the results of an inqury that are presented in a table or graph. In doing so, they will contribute to the development of their data literacy skills.
Gal (2002, p. 1-25) suggests that data analysis should be done from two points of view, that of the investigator and that of the reader. From the point of view of the investigator, the students analyze primary data, that is data that they themselves have collected within the framework of an inquiry. From the reader's perspective, students analyze secondary data, that is, data that has been collected by others. In this context, teachers can take the opportunity to present them with data that may relate to other subjects (for example, science and technology, social studies, physical education and health). They can even offer students data represented by types of graphs that are not the subject of study in the primary grades. In such a case, however, it is important to focus on the interpretation of the graph and not on its components and its creation.
When educators present a table or graph to students, they should give them enough time to reflect on the data and form a general idea, and then ask open-ended questions to help them translate their observations and ideas into their own words, and 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 glean from this graph?
Open-ended questions elicit a variety of responses, allowing all 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 of the Level |
|---|---|
| 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 make connections between them and read beyond it. In order to help students develop data analysis skills to make sense of data, teachers should ask them questions related to each of the three levels of comprehension. The following example provides a more detailed explanation of each level, as well as questions that could be asked in a data analysis activity.
Reading the Data
At this first level of comprehension, students can extract data from the table or graph without analyzing it in depth, so students are able to identify:
- the title of the table or graph;
- axes or categories;
- scale or key;
- class intervals;
- 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 et Higgins, 2003)
This level is more difficult to achieve because students must be able to
- 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, most, least;
- describe the likelihood of certain outcomes using expressions such as possible, impossible, certain;
- compare the length of the bars or columns of pictographs;
- make the connection between different ways of describing a relationship between data;
- compare data from one category to pooled data from two or more categories.
Reading Beyond the Data
At this third level of comprehension, students use several skills related to statistical literacy. They must:
- draw conclusions and justify them;
- make inferences and predictions;
- assess the credibility and logic of predictions and conclusions;
- recognize some information that the table or graph does not provide;
- review the steps in the inquiry process.
Skill: Drawing Conclusions, Formulating Arguments and Making Decisions From a Graph
Throughout the data analysis and results interpretation phase, teachers should engage students in making critical judgments about the representations of the data and the information that can be gleaned from them. Critical judgment allows students, for example:
- to determine whether a graph is a good representation of the data or whether it leads to false conclusions;
- to compare two graphs and determine if one is a better representation of the data than the other.
During the mathematical exchange, educators can use questioning to help students build their critical thinking skills. It is important to note, however, that critical thinking skills are at an early stage of development in the primary grades, 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.
As a result of examining and analyzing the data (three levels of comprehension: reading the data, reading between the data, and reading beyond the data), students will develop capacity to draw conclusions, formulate arguments, and make decisions about data they produce or read.
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 an inquiry 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 direction. Teachers must therefore lead students to answer the question of interest that prompted the inquiry 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.