# Idea formation and abstraction

## Contents

## Teaching data literacy: Module 1

Idea formation & abstraction

Data management cycle

The diagram above represents the data management cycle. As you can see, it describes an iterative process that begins with an idea and ends with a process of evaluation. It is circular because in a knowledge building environment, evaluation should lead to another set of ideas that keeps the process moving clockwise around the circle. This module deals with the first node in the cycle, idea generation. It has four parts. To begin, please read the following two articles written by Marla Sole and published in *The Mathematics Teacher*, a publication of the National council of Teachers of Mathematics.

- Sole, M. (2015). Engaging students: in survey design and data collection.
*The Mathematics Teacher, 109*(5), 334–340. [1]

- Sole, M. (2016). Statistical literacy: Data tell a story.
*The Mathematics Teacher, 110*(1), 26-32. [2]

For more articles visit the Course library

Finally, watch the following video from *Anywhere Math* entitled **Introduction to Statistics** that provides a brief example of the entire cycle. These articles and this video are appropriate for most K-12 students. Younger students may require some additional explanation.

Idea generation process

Idea formation and abstraction has four steps:

- Formation (Ideation)
- Refinement
- Decomposition
- Abstraction

The first three are appropriate for all levels. The fourth, abstraction, may require some support for younger elementary students. This is a linear process, as illustrated in the diagram above.

Step 1: Ideation

**Learning outcome**- Students learn to
*define*ideas that they can analyze with data **Tasks**- A.
*Choose*a topic to investigate- Group chooses a topic with teacher input appropriate to the age of the group

- B.
*Identify*measurable ideas associated with chosen topic(s)- 1. For each idea, students answer the following questions with teacher guidance appropriate to the age and prior knowledge of the students.
- a. Does analysis of idea require data?
- b. Is required data available to class conducting research?
- c. Does available time permit adequate analysis?
- d. Are student skills sufficient to conduct analysis?
- e. Does course have sufficient financial and technological resources to conduct analysis?

- 2. Repeat process for each idea until finding at least one that meets all criteria (a-e). If more than one passes all screens, class may select one or assign different topics to groups within class.

- 1. For each idea, students answer the following questions with teacher guidance appropriate to the age and prior knowledge of the students.

Step 2: Refinement

**Learning outcome**- Students convert ideas to workable problems with measurable solutions
**Tasks***List*problems to solve- Groups discuss ideas to
*distinguish causes and effects*of problems they need to solve to*diagnose*each idea. For example, suppose students are considering how many solar panels they would need to put atop their school to supply electricity for its operation. Problems would include determining how much power a solar panel produces, and how much electricity the school consumes.

- Groups discuss ideas to

Step 3: Decomposition

**Learning outcome**

- Groups decompose problems into sequential steps
**Tasks**- A.
*Identify*steps required to solve each problem. - B.
*Organize*steps in the order in which they need to take place. - C.
*Construct*a Problem Process Table (sample below) for each problem to use to*organize*the data required for each problem. - Continuing the with the solar panel example, this step would require students to
*identify*the sources of demand for electricity in their school. Since there are many, they would also have to begin to think about how they plan to go about collecting it. They would also have to learn about the different types of solar panels they might use to generate electrical power, and the different options that exist for installing them. As they identify each step, they list it in the process table. They will fill the rest of the table out when they organize and collect their data, the subject of Module 2.

Problem Process Table | |||||
---|---|---|---|---|---|

Step | Data description | Data format | Source | Storage | Preparation |

Step 4: Abstraction

**Learning outcome**- Groups develop theories, i.e. testable hypotheses, to analyze the problems they must solve to validate ideas.
**Tasks**- Abstraction is the first step in modeling. It is central to the process of analysis presented in Module 3. At this initial stage in the process, students
*formulate*possible explanations for the phenomena they observe that motivate their ideas. Teachers may need to direct this process very incrementally for elementary students. Students in middle school and above should be able to develop theories in group discussions. - The key point of this step is to introduce students to the idea of a "testable hypothesis." Students of any age can understand this idea if it is explained to them in terms that they understand. For example, even the youngest children could understand the following two hypotheses.
- The moon is made of cheese
- Peanut butter is better than tuna salad

- Only the first of these is testable. Since the first has been tested, teachers can report to their students that the hypothesis, stated more formally as "If the moon is made of cheese, then astronauts who travel to the moon will find it," is false, or more appropriately, has been rejected based on evidence. In contrast, the second statement is simply a matter of opinion. A teacher can transform this statement of opinion into a testable hypothesis by changing it to "Students prefer peanut butter to tuna salad" because this is testable, and students can collect data to determine if it true or not for a given population of students. The point is for students to learn how to turn problems into statements that they can test with data.

Assessing Module 1

- The four steps in this module address different aspects of Bloom's taxonomy.The first is a brain-storming exercise that requires creativity, a high level skill. As such, it provides a good opportunity to ask students if they understand that they created knowledge at some level as they formulated ideas to investigate. They will also have learned and therefore now
*know*that not all ideas require data, and that data may not exist or be available due to other constraints to test all measurable ideas. Grasping this concept enables them to avoid wasting time pursuing unattainable objectives. - The second step requires students to apply their knowledge and to "identify causes and effects" and to "develop a diagnosis" of their ideas. The first of these involves Bloom's concept of application; the second his concept of analysis. Soliciting comments from students about these activities may reveal whether or not they ignited some metacognitive activity.
- The third step is fairly mechanical and also falls into the application category of Bloom's taxonomy.
- The final step of
*hypothesizing*falls again into the analytical category. Students' formative assessments of this process should indicate an awareness of that activity.

Continue to Module 2 of *Teaching data literacy*: Data organization

Jump to Module 3 of *Teaching data literacy*: Static Data Analysis

Jump to Module 4 of *Teaching data literacy*: Dynamic Data Analysis

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