Learning Goals
At the end of this page, you should feel comfortable performing these skills:
- Identify statistical investigative questions.
- Identify survey questions.
- Write a survey question that takes a numerical response.
- Write a survey question that takes a non-numerical response.
video placement
[Intro — a 3-instructor video that gives perspective on the benefit to the student of completing this What to Know preview assignment as pre-work for the Forming Connections in-class activity. This will be the first “flipped” learning piece the students will encounter. Providing the reasons for it will go a long way to providing student buy-in for an assignment they might otherwise consider as “having to teach myself the material.”] Note that this video should be as brief as possible, under 1.5 minutes if possible.
From DC Instructor notes for in-class 1B (the piece immediately prior to this one):
- This course will challenge students in terms of content and also in terms of expectations of students as learners. You can expect a variety of emotional reactions: excitement about a “different” way of learning math; anxiety about something that is unfamiliar; or resentment that you are not “teaching” them in the way to which they are accustomed.
- Students are most willing to work hard and try new things when they understand the reason for it. Therefore, throughout the course, look for opportunities to explain to students why you make certain instructional choices or why activities are designed in a certain way. These explanations are valuable in addressing student frustration.
Since we cannot depend on instructors unfamiliar with the materials setting up the rationale carefully during the previous class before assigning this WTK page to students, having this 3-instructor video placed here at the beginning will serve that purpose. Otherwise, it will serve to reinforce the instructor’s in-class delivery.
Some ideas for how to approach the reasoning:
- This video would introduce this WTK as the first of a regular WTK page that delivers precisely the information students will need for the activity that follows.
- Engaging with the rich multimedia on this page should be presented as a benefit that will make the class-work and the graded work less challenging.
- When students come together in their groups in FC, those that have completed the WTK will positioned to comfortably tackle questions that ask them to think deeply about concepts in sophisticated ways.
- When informed students work with similarly informed classmates, they will be empowered to build their own knowledge under the guidance of their instructor, increasing their own success and contributing to the learning community in a way that helps, not hinders everyone’s success.
[Finish the video with a brief statement about the goals for this activity: to distinguish between statistical questions and survey questions, and between survey questions that take numerical and non-numerical responses.]
Note: The video(s) on this page don’t have to be deep discussions of statistical concepts. The material on this page is not complex. For example, the FC activity will introduce the words categorical and quantitative. Here, the only goal is to provide a brief and gentle introduction into statistical questions/survey questions and numerical/non-numerical data as a way to provide a brief and gentle introduction into WTK pages in general.
Preparing for the Forming Connections Activity
During your first Forming Connections activity, you completed a diagram to illustrate the statistical process surrounding a research objective as consisting of four stages: 1) formulating an investigative question; 2) collecting data; 3) analyzing the data; and 4) interpreting the results.
[insert an image of that process. A basic example exists in the instructor page for 1A]
The process naturally renews as interpretation of the analysis generates further questions for researchers. In this section of the course, we’ll spend some time learning about the characteristics of investigative questions and what sort of data is appropriate to try to answer them. Answer the questions on this page to learn what you’ll need to know to successfully complete the upcoming activity.
In the upcoming Forming Connections activity, you will need to consider the connection between the first two steps of the statistical problem-solving process—formulating statistical investigative questions and collecting/considering the data. Specifically, you will need to identify statistical investigative questions and survey questions and anticipate the responses to survey questions. Let’s learn about these ideas now in preparation for that activity.
Statistical Questions
A statistical investigative question is a question that can be used as the starting point for an investigation that involves data collection and data analysis. For example, “Is there a relationship between students’ phone use in class and their grades?” To answer this question, you would need to survey a group of students and ask them about their phone use and their grades. You would then analyze the data using appropriate graphical displays and summary statistics and interpret the results.
In Forming Connections [1A], you learned that variability plays a key role in the statistical process. Statistical investigative questions always anticipate variability. For example, if you surveyed a group of students, you would expect them to vary in terms of their phone use and their grades. On the other hand, “What is the square root of 9?” does not anticipate variability, so it is not a statistical investigative question. If you surveyed a group of people, each one would give the same answer.
Investigative questions vs survey questions
In practice, statistical investigations involve more than one type of question. The question “How many problems did you answer correctly on your most recent statistics test?” would be answered with a single numerical value, so it is not a statistical investigative question. However, it is a survey question that could be used to collect data from many students. We would expect the answer to vary from student to student. Well-constructed survey questions are often an important part of the statistical process.
- Statistical investigative questions are the questions a researcher wants to investigate. They ask about the tendencies and likelihoods associated with a population or phenomenon.
- Survey questions are the questions researchers ask in order to collect data, which is expected to vary from individual to individual. Survey questions may collect numerical or non-numerical data.
See the following video for a demonstration of how to think about the differences between these types of questions.
video placement
[Worked example video — a 3-instructor video on how to identify statistical investigative questions and survey questions. Also include how to tell if a question will take a non-numerical or a numerical answer (like questions 3 and 4). This video should be brief, < 1 minute.]
Now check your ability to distinguish between statistical investigative questions and survey questions by answering Questions 1 and 2. Remember that if the answer to a question could be looked up and would never vary from individual to individual, it would be neither a survey nor an investigative question.
question 1
Which of the following are statistical investigative questions? There may be more than one correct answer.
- a) How tall is the tallest mountain in the United States?
- b) Do standing heart rates tend to be higher than sitting heart rates?
- c) What is the sum of all the whole numbers between 0 and 10?
- d) What is your favorite subject in school?
- e) What proportion of college students live on campus?
- f) How many members does your household have (including pets)?
question 2
Which of the following are survey questions that could be used to collect data? There may be more than one correct answer.
- a) How tall is the tallest mountain in the United States?
- b) Do standing heart rates tend to be higher than sitting heart rates?
- c) What is the sum of all the whole numbers between 0 and 10?
- d) What is your favorite subject in school?
- e) What proportion of college students live on campus?
- f) How many members does your household have (including pets)?
Numerical vs non-numerical data
Recall that survey questions can take numerical or non-numerical data as responses. You’ll see in the upcoming activity that there are statistical terms for these kinds of data, which you may recall from a previous math class. For now, focus on the type of question that would anticipate a particular response. For example, the question, “how many siblings do you have?” would take a numerical response but the question, “do you own a car?” would not. Answer Questions 3 and 4 to assess your understanding of anticipating the responses to survey questions.
Question 3
Write a survey question that would be answered using a numerical value.
question 4
Write a survey question that would not be answered using a numerical value.
Summary
This summary section will appear at the end of all the What to Know pages to help you assess your readiness for the upcoming Forming Connections activity.
In this What to Know page, you’ve learned that a statistical investigative question is one that anticipates variability and could lead to data collection and analysis. You also learned that survey questions are questions used in the data collection process and that, while they can be answered with a single response for each individual asked, they are expected to vary from individual to individual. Finally, you anticipated the response to a survey question by writing one that would take a particular kind of answer: numerical or non-numerical. Let’s summarize these skills and tasks by identifying the Questions in which they were located.
- In Questions 1 – 2, you identified statistical investigative questions and survey questions.
- in Question 3 – 4, you anticipated the responses to survey questions.
If you feel comfortable with these ideas, it’s time to move on to Forming Connections in the next activity!
