# Idea formation and abstraction

## 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:

1. Formation (Ideation)
2. Refinement
3. Decomposition
4. 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
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.

#### Step 2: Refinement

Learning outcome
Students convert ideas to workable problems with measurable solutions
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.

#### Step 3: Decomposition

Learning outcome

Groups decompose problems into sequential steps
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.