• The pacing of this lesson matches the traditional lesson flow. For a 45 minute class:
  • Day 1: Lesson Starter, Activity, Discussion Question
  • Day 2: Lesson Synthesis, Practice, Mastery Check
• For block periods (90-minute class periods), this lesson can be completed in one day.

• Begin with the Lesson Starter to formatively assess students’ comfort level with the CODAP platform. If students display a variety of proficiency levels with interpreting the display, it may be beneficial to partner those who need support with another student who shows more facility with it. This partnering may provide opportunities for some students who have not traditionally been leaders in the classroom to step into that role.
• Each student should have a printed copy of the student handout, which includes a tinyurl link to the customized CODAP page. Each student should also have access to an internet enabled device, preferably with a screen 10” or larger.
• Students begin by making predictions about the relationships between variables. Then, they follow the guided questions in their handout, which walk them through fitting their own linear regression models in CODAP.

Instructional routine: Ten-Minute Talk. The lesson provides space for students to jot down their thoughts on the prompt, before discussing with a partner and engaging in whole group discussion. You can find more background on implementing a Ten-Minute talk here.

Purpose & Background: This Lesson Starter is designed to provide formative assessment that guides facilitation of the CODAP activity in this lesson. Students see both a data table and a CODAP screen image. Student responses will provide insight as to whether they are able to interpret the CODAP output or may need additional support. The data displayed in the Lesson Starter come from the same college debt data set that students will use during the main portion of the lesson. The x-variable is graduation rates, and the y-variable is student loan default rates. By withholding the college debt context (i.e. deleting the axis labels from the graph), the Lesson Starter allows students to observe and analyze numeric trends in the data set first, before they consider more contextualized and complex analyses during the main part of the lesson.

First, download this lesson's handout key and read through its Discussion Question section. Then, check out our model discussion norms and the additional background notes below.

• As time allows, prompt students to conjecture about why graduation rates and net tuition may be confounded. In particular, why do schools with high graduation rates also tend to have high tuition levels? One possible theory: High-quality colleges have robust support for students and high graduation rates. High-quality colleges may also charge more for the extra services and value that they provide to students. So, college quality may influence both graduation rates and tuition levels simultaneously. Ultimately, the highest quality colleges – which have both high graduation rates and high tuitions – may prepare their students best for the workforce, helping them avoid student loan default. So, these relationships can explain why high graduation rates and high tuition levels tend to be associated with low student loan default rates.
• There are other possible theories that could explain this confounding relationship. For example, students from high-income backgrounds may be more likely to graduate from college, since they may not have to work a job outside of school and may be able to afford private tutors. In addition, students from high-income backgrounds may be able to afford attending more expensive colleges. Finally, students from high-income backgrounds may not need to take out student loans as often as their peers, since their families may be able to pay the cost of tuition out-of-pocket. So, colleges that serve students from predominantly high-income backgrounds may simultaneously have high graduation rates, high tuition levels, and low student loan default rates.

• The data set in this lesson is a sample from the Department of Education’s College Scorecard database. Clarification of column headings (variables) and background information on each variable can be found in this document. This data was originally downloaded in December of 2022, and it describes information from the 2020-2021 school year.
• The data provided in this lesson was randomly selected from this complete dataset, filtered to be a manageable size for students and to clearly demonstrate the trends that analysis of the complete data would provide.
• In exploring the relationship between tuition and default rates, students may notice that the y-intercept, 8.6, indicates that even if college were free (after scholarships/discounts), we’d still predict an 8.6% student loan default rate. Students may wonder how such a statistic could be true. Because there are net tuition values in the full data set that are nearly 0, this prediction isn’t heavily extrapolated. Rather, guide student thinking toward the costs of going to college beyond tuition (e.g. housing, books). With student loans potentially being applied to such expenses, default on loans is still possible, even at low tuition values.

• In the Activity, students first create a dotplot using the explanatory variable: net tuition. They describe the characteristics of this variable. Then, they add the response variable (default rates) to the y-axis, and CODAP transforms the graph into a scatterplot. This sequence provides the opportunity to compare and contrast the types of analyses that are possible with univariate data (center, unusual features, shape, spread) and with bivariate data (direction, unusual features, form, strength).
• CODAP is one of many software platforms that can generate linear regression models. Its main instructional advantage is that it allows students to manipulate and visualize data with simple mousepad drag-and-click sequences. It also allows students to explore the structure of raw datasets, allowing them to see individual data values and sort by variables in data tables. As students begin to work with much larger datasets or more complex models in future coursework or in the workplace, they may start using coding-based statistical platforms – which have a tougher learning curve, but are ultimately more powerful. The two coding languages used most often for data analysis are R and Python.