This unit plan is intended to prepare AP Statistics students in the New Haven Public Schools district for the rigorous free response section of the AP Statistics exam. This section of the exam consists of six open-ended questions that require students to interpret statistical results clearly and accurately in the context of data. Many students enrolled in AP Statistics at the school where I teach struggle to communicate statistical results in a coherent manner and use statistical vocabulary in an appropriate context. This might be because historically, students have not had as much experience writing in mathematics courses as they have had in other core academic courses. Regardless of the reason, students have to overcome obstacles related to writing in order to pass the AP Statistics exam. At this stage in their academic careers, students begin to express concerns about how they will pay for higher education. Students who will be dependent on merit-based financial aid could potentially have their financial burdens eased by performing well on the exam. If a student scores a 3 or higher on the AP Statistics exam, one could potentially receive college course credit, avoid excessive tuition fees, increase one’s chances of being admitted to a university, or be eligible for college scholarships.
The free response questions on the AP exam typically prompt students to use statistical results to defend arguments. For instance, on the 2015 AP exam, students were given two boxplots summarizing sample employee salary data from two different accounting firms, Corporation A and Corporation B. Students had to imagine that both corporations offered them a job for $36,000 a year as an entry-level accountant. Students then had to use the information in the boxplots to justify why they would accept a job at either corporation. This problem generated a lot of discourse when presented to my students as a warm-up prior to their AP exam. Students came up with their own unique reasons why Corporation A or Corporation B would be a more enticing option, backing up their claims with measures such as the range, lower quartile, mean, median, or maximum salary of an individual working for each corporation.
This problem resonates with all students, including those who demonstrate lower levels of engagement with topic information through poor attendance in class or a low level of self-efficacy in mathematics. The reason for this resonance is due to the topic’s real-world relevance. Deciding whether the financial benefits of one job opportunity outweigh those of another is a task many individuals will inevitably encounter. The problem was also met with satisfaction by the students because it allowed them to perform a task similar to that of a professional statistician. Professional statisticians often use data to inform decisions that impact the lives of others. The final reason the AP practice problem hooked all students into the lesson for that day was because they were able to exercise creativity when formulating their responses. The problem had more than one possible answer, so it alerted students to the idea that data can have multiple interpretations or can even be used to benefit a particular perspective, agenda or party.
Many students dislike mathematics because they believe that their success in the subject is solely contingent upon correct execution of procedures and formulas. Students who have difficulty memorizing algorithms or arithmetic facts tend to perform poorly on mathematics assessments. Teachers exert little to no control over how much studying students do for tests or quizzes when they are at home. However, teachers can provide students with in-class experiences that increase their retention of skills and concepts. Implementing a curriculum unit that encompasses the positive components of the AP Statistics practice problem (real-world relevance and opportunities for student choice) can help teachers achieve this goal. Individuals selectively remember experiences that they find meaningful. With this in mind, a teacher can present statistical concepts in a meaningful way by having students learn about them in the context of issues that have consequences for everyone. This interdisciplinary curriculum unit will allow students to apply statistical concepts to understand attitudes towards the controversial practice of gene-editing using CRISPR-Cas9 technology. By the end of the unit, it is expected that students will demonstrate mastery of the following AP Statistics curriculum objectives:
- Use an appropriate random sampling method to select participants for a survey.
- Design a survey that contains non-biased questions.
- Describe the shape, center, and spread of a univariate data distribution.
- Use a contingency table to calculate conditional probabilities.
- Use a contingency table to determine whether an association exists between two variables of interest.
- Calculate and interpret a confidence interval for a true population proportion in the context of real-world data.
- Conduct a hypothesis test to determine how closely a sample statistic estimates a population parameter.
This curriculum unit is also intended to build community within a school. The lessons contain activities meant to foster connections between students who might not have previously interacted. Moreover, students will have opportunities to share newly-acquired knowledge about gene-editing with their peers.