Lesson 5: So Many Questions

Objective:

Students will learn the features of a good statistical investigative question.

Materials:

Sticky notes

Vocabulary:

(statistical) investigative questions

Essential Concepts:

Statistical investigative questions typically begin with a vague general question, then develop into a precise question. The process of developing or creating a good investigative question is iterative and requires time and effort to get right. In her 2021 paper, What Makes a Good Statistical Question, Dr. Pip Arnold identified the following as features of a good investigative question:

(1) The variable(s) of interest is/are clear

(2) The group or population we are interested in is clear

(3) The question can be answered with the data

(4) The question asks about the whole group, not an individual

(5) The intention is clear (e.g., summary, comparison, association, time series)

(6) The question is one that is worth investigating, is interesting, and has a purpose

Lesson:

Entrance Slip (see Instructional Strategies in Teacher Resources): Each student should submit a ticket that displays the 4 components of the Data Cycle.
Inform students that they will learn about what makes a good investigative question. Ask them to recall the definition of an investigative question:

Investigative questions are questions that address variability and can be answered with data. They are questions we ask of the data. A good way to determine this is to ask: Do we need to see the data to answer the question?
Remind students of the two questions from the previous lesson, noting that one of the questions was an investigative question, and the other was not:
1. How old are you?
2. How old are the students in my school?
In pairs, ask students to analyze each question using the definition of an investigative question and come to an agreement about which one is an investigative question.
Using Agree/Disagree (see Instructional Strategies in Teacher Resources), ask a pair of students for their results. Discuss why the first question IS NOT an investigative question (there is only one possible value so there is no variability in the data) and why the second question IS an investigative question (not all students are the same age. The ages vary, so there is variability in the data).
Ask students to think of the data they collected about the stick figures (name, GPA, friends, sport, height, shoe). Inform them that the researchers used the following survey questions to collect the data:
1. What is your name?
2. What is your GPA?
3. How many friends do you have?
4. What sport do you play?
5. How tall are you in inches?
6. What type of shoe do you mostly wear?
Survey questions are another example of a type of statistical question, but with a different purpose to investigative questions. Survey questions are questions we ask to get the data.
Tell students that it is important to know exactly what survey questions were asked to collect the data before asking investigative questions. For example, we saw an image of a ball next to each stick figure but we don’t know if that represents a sport they like to watch, their favorite sport, or a team they are on.
In teams, ask students to create investigative questions that could be answered using the data collected about the stick figures. Introduce the sentence stem “I wonder…” to help students get started. Have the Recorder/Reporter record the questions on post-its.
Ask the teams to identify which variable(s) each question is investigating by having them circle the variable name(s) within their investigative questions.
Have the Task Manager organize their group’s investigative questions on the board, placing investigative questions that incorporate only one variable on the left-hand side of the board and investigative questions that incorporate two or more variables on the right-hand side.

Note: This sorting activity will help students begin to distinguish between different types of investigative questions.

Summary investigative questions are questions about a single variable.

Comparison investigative questions compare a numerical variable across groups.

Association investigative questions look for a relationship between paired numerical or paired categorical variables.

As a class, begin the process of transforming some of the summary investigative questions so that they have all of the features of a good investigative question. Here is an example to get you started:

Initial investigative question : I wonder who has the most friends?

Feature	Explanation
The variable(s) of interest is/are clear	Yes. The variable of interest is the number of friends.
The group or population we are interested in is clear	No. Teacher should ask: “Who did the researchers want to learn about?” These stick figures.
The question can be answered with the data	Yes. The researchers collected data on the number of friends.
The question asks about the whole group, not an individual	No. This question is about an individual stick figure. Teacher should ask: “How can we reword the question to include the whole group?” How many friends do ... have?
The intention is clear (e.g., summary, comparison, association)	It is clear that this is a summary investigative question (single variable), specifically the number of friends.
The question is one that is worth investigating, is interesting, and has a purpose	For students, this might be something interesting.

Reworded investigative question after going through the criteria: I wonder how many friends this group of stick figures have?

As a class, apply the same process to a few of the comparison and association questions.

Initial investigative question: I wonder if someone who plays a specific sport has more friends?

Feature	Explanation
The variable(s) of interest is/are clear	Yes. This seems to be a comparison investigative question comparing the number of friends within the sport played.
The group or population we are interested in is clear	No. Teacher should ask: “Who did the researchers want to learn about?” These stick figures.
The question can be answered with the data	Yes. The researchers collected data on the number of friends and the sport the stick figures played.
The question asks about the whole group, not an individual	No. The word someone gives the impression that we are interested in one observation.
The intention is clear (e.g., summary, comparison, association)	The intent is somewhat clear. This seems to be a comparison investigative question between the sport the stick figures played and the number of friends each stick figure had. Teacher should ask: “What is the variable that is being compared? Which groups within the sport variable are you comparing (all groups, specific groups)?”.
The question is one that is worth investigating, is interesting, and has a purpose	For students, this might be something interesting.

Reworded investigative question after going through the criteria:

I wonder if there is a difference in the typical number of friends the stick figures have based on the sport they play?

I wonder if these stick figures who play soccer tend to have more friends that these stick figures who play tennis?

Using the criteria of a good statistical investigative question, student teams will go back and modify their statistical investigative questions. Facilitators will ensure the team goes through the criteria for each investigative question. Task Managers will encourage everyone to contribute. Resource Managers will ensure all materials are easily accessible for recording and reporting. Recorders in each team will capture team members’ responses while the teacher circulates the room to check for understanding.
Ask the Reporters of selected teams to share their revised statistical investigative question(s). Students in the audience will listen to the presentations and provide feedback about each team’s statistical investigative question(s). Be sure to discuss disagreements before moving on to different questions.
Inform students that, in the next lesson, they will begin using the Data Cycle to learn about their food habits. To prepare for this, students should begin collecting the “Nutrition Facts” labels from foods/snacks they typically eat.

Class Scribes:

One team of students will give a brief talk to discuss what they think the 3 most important topics of the day were.

Homework

Ask students to bring at least 2 cutouts of the “Nutrition Facts” labels of the snacks they typically eat (e.g., chips, yogurt, blended drinks, etc.).

Note: An alternative to collecting “Nutrition Facts” labels is to print them from an online source and bring the printouts to class.