The Challenge for Students
As students work through the free-response questions on an AP Statistics exam, they are asked to respond in a variety of ways. Some of the questions are fairly straightforward, but other, more difficult questions challenge students to turn their perceptive insights into effective solutions. This article explains why these questions are challenging, and suggests some strategies that can help students express their ideas more clearly and successfully.
A common type of question asks students to reach a conclusion or make a decision based on the statistical evidence presented. The writing needed to complete a response to these types of questions is not like a typical essay assignment where students have to develop a thesis, offer supporting evidence from a number of sources, and wrap up their work with a concluding paragraph. It is also not quite like the typical short answer question where a few words or a phrase might suffice to answer a very directed question. The writing task is somewhere in between, more than a single idea, but not needing the extensive development of an essay.
Practical Steps for Students
As the first step, students should formulate a clear and unambiguous answer to the question posed before they begin to write. Tell students to read the problem carefully, reach a conclusion, think again about their conclusion, and write it down. It may be helpful at this point to underline or circle the key phrases or clues that lead them to their conclusions.
The next step is to present evidence that supports the conclusion, using the facts in the problem that support it. The underlined words or phrases often provide the correct language. There may be several facts presented in the problem that are pertinent. If so, it is best to decide which are the most relevant and quote those first.
There may also be some parts of the problem that push towards a different conclusion. It may be a judgment call as to which wins out; if there is contradictory evidence, it is helpful to mention this as well. The final and indispensable step is to connect the facts—which have been written down as supporting evidence—to the conclusion reached.
Students should also state why the given facts led them to their conclusion. If they state some contradictory evidence, then part of the explanation should be why the chosen conclusion wins out. At least some part of this connection, if not all, is usually some statistical concept that you introduce into the solution that provides necessary linkage. It is this unveiling of the necessary concept that really brings home their point forcefully (to the delight of the Reader!).
This final step—making the necessary connection—is where many students lose credit in a situation in which they fully understand the problem, have identified a correct conclusion, and have presented the correct supporting evidence. The Reader will judge the response complete when it also contains an explanation of why the facts that are quoted support the conclusion. Too many students leave the conclusion and the evidence disconnected, and most scoring rubrics will demand that they be explicitly connected to receive full credit.
Two Common Question Prompts
Among the most common question prompts are two variations on the type of question discussed above. The first asks students to make a choice between two alternatives. Some students will make a correct judgment and write eloquently about the strengths of the favored alternative, addressing the three parts outlined above: They state their choice, they present sound evidence, and they explain why the evidence supports their chosen alternative using a valid statistics concept. But in these comparison problems, a common mistake is to only address one of the alternatives.
If faced with a comparison and choice, students must do two things: 1) explain why their choice is strong, and 2) explain why the other alternative is inferior. Scoring rubrics consistently demand both alternatives be considered to get full credit, and the format above can be used to guide the response to each part.
The second variation includes a phrase like “using your answer to part (a), explain why...” It is essential that the evidence stated includes or references the preceding answer, either by number or concept. The final linking step must also relate this answer to the key statistical concept of the problem if full credit is to be awarded.
Here’s a summary of the method that I recommend to my students:
- Read the problem carefully, and think about the question. Do you know the correct answer? Are you sure? Do not second-guess yourself, but be careful not to jump to conclusions, either. Write down your conclusion in a single, straightforward sentence.
- What evidence do you find in the problem that supports your answer? In several sentences at most, provide the details of the problem setting that are relevant.
- Why does the evidence you state support the conclusion? Using an appropriate statistical concept, show the connection between your evidence and the conclusion you reached.
I also make an analogy based on how criminal prosecutors operate on various popular television shows. As a prosecutor makes his or her case, there are similar stages to go through. First comes an opening statement where the lawyer will claim that the defendant is guilty, then a stage where evidence which incriminates the defendant is presented, and finally, a closing statement where the prosecutor makes sure that the jury sees how the evidence presented affirms the claim of guilt that began the trial. These are the same three parts of the method discussed above.
Colleagues Can Help
Along with the difficulty that students often face in making their writing clear and succinct, there is a second challenge: Many teachers of AP Statistics are not accustomed to teaching students to write. Most have come to teaching statistics from teaching mathematics. They are often not very experienced in teaching students how to write and may not themselves be confident writers. If you find yourself in this category, I hope that you can find colleagues at your school who may be able to help you. Think of successful history, social studies, or science teachers. Their tests and quizzes more routinely include examples of questions that demand writing similar to that used in AP Statistics, and they can often be useful coaches and allies for you.