Pedagogy in Action > Library > Developing Quantitative Reasoning > Designing Assignments

Designing Assignments


"[R]eal problems are messy and not amenable to unequivocal final answers...." Grant Wiggins in "'Get Real!' Assessing for Quantitative Literacy," Quantitative Literacy: Why Numeracy Matters for Schools and Colleges.

Jump down to: Keep your eye on your course goals | Backward-design your course and assignments | Be very clear on your goals | Set assignments in an explicit, real-world context | Plan your assessments and assignments | Tell students what you are up to

Introduction

The principles for designing strong quantitative reasoning (QR) assignments are similar to those for designing strong assignments of any other type. Because of this, much of what follows is drawn from John Bean's take on designing strong quantitative writing assignments.

There are a number of tips that are specific to teaching students to work with quantitative evidence in particular:

Of course, one of the best suggestions for assignment redesign is simple: borrow and steal!

1. Keep your eye on your course goals and align QR activities accordingly

When was the last time you got toward the end of the term and thought, "Gee, I have no idea how I will fill the last days of the class. I have completely achieved all I had hoped to for this term!"? The reality is that time is scarce. We never cover everything we had hoped to cover in our courses. We struggle to teach everything that is presumed by courses that list our own courses as pre-reqs. And now we are being asked to take on general education learning goals like QR.

The solution to this tension is not to speed up the class to squeeze in 10% more content. And it isn't to jettison the disciplinary content expectations of our colleagues. Instead, we need to think hard about how QR naturally fits in the context of our course. We need to make the introduction of QR a means for doing better what we already are trying to achieve rather than a competitive threat to our primary priorities. Otherwise it is a safe bet you will drop QR altogether.

So, start by articulating the goals you have for students in your course. Then look for where QR is relevant and important to meeting fully those objectives.

In some fields it is obvious how teaching QR complements traditional course goals. In other fields it may take a little more thought. To jumpstart that process, look through the collection of Quantitative Reasoning in Writing assignments from disciplines close to your own. Even if you don't intend to give writing assignments, these existing assignments can spark ideas of how QR can be connected to your discipline.

2. Backward-design your course and assignments

It is generally best practice to start course planning at the end. Broadly speaking, start with the course goals, then move back to how you will know if those goals are met (i.e. assessments), and finally consider how you will bring students to a successful outcome (activities). You might think about answering the following questions: What do I want my students to learn by the end of the term? How will I know if they achieve those goals? In order to get to that point, what will students need to learn first? How can the assignments and activities in early stages of the course support later learning. Similarly, complex assignments may benefit from backward-design. What class activities must happen first to arm students with the tools to complete the assignment? Should the assignment be broken into sub-parts so that later sub-assignments can build on previous activity?

These same general principles apply to teaching QR. It is worth thinking a little, though, about the specific way these principles play out in the QL context.

Course design: QR involves application of mathematical concepts. These methods may be very basic, such as computing an arithmetic mean, or relatively involved (e.g. formal statistical estimation). Either way, be sure students are armed with the skills they will need before they are asked to apply them. The trap to avoid is assuming that students know more than they do. For example, it might seem obvious that a graph should include a title and axis labels and should employ a color scheme that provides enough contrast to be easily read. But to students who have never been asked to create a graph of their own, these things are not obvious. Design your QR course content and assignments to build from basic to more advanced activity. Don't forget: We can't reasonably expect students to perform what we don't teach.

Assignment design: QR assignments are inherently complex for students because they ask students to combine math skills with the context of a problem and (often) craft an argument about it. That's a lot of moving parts. You can ease this burden by scaffolding early assignments. For example, give students feedback on the data they propose to use before they try to embed it in the argument. This practice can also make grading easier. (It can be very difficult to assign a grade when a student writes a nice argument around a fundamentally mixed-up interpretation of the data!) As the course progresses, you will need to do less and less of this assignment scaffolding.

3. Be very clear on your goals for including real-world data in your activities

There are many lessons for students to learn by using real data in their assignments. How do you find relevant data? How do you interpret the variables available and choose the best items to use and which to avoid? How do you clean data, with an eye toward both practicality and ethics? How do you analyze raw data? How do you present data in text, charts, and tables? Any one of these would be worth the time of an assignment. As you design your assignment, ask yourself which of these are the goals you have for your students. Then focus the assignment on those aspects. For example, if finding and cleaning data isn't critical to your course goals, consider offering students a clean version of the data they need with the assignment so that they don't spend time on the data gathering process.

Once you decide on your goals for the assignment, be sure to share your intentions with reference library staff. If you really want students to struggle through the process of finding data, you don't want reference librarians resolving that struggle too early in the process!

4. Set assignments in an explicit, real-world context

John Bean suggests a helpful acronym–"Give your students a RAFT"–when creating context-rich assignments in general:

For example, you might provide the following prompt:
"You are an aide to a US Senator (role and audience) who must vote on guest worker immigration reform legislation. She has asked you to prepare a white paper to help inform her thinking (format). She would like to understand what the model of supply and demand suggests concerning the effects of this bill on the labor market (task part a). She doesn't want pure theory, however. She reminds you that she is an elected official and so in addition to knowing the directions of the predicted changes to employment and wages she also could use help finding data that suggests the magnitudes of those effects (task part b). Because she is busy, the white paper can be no longer than five pages in length."

In addition to these generic context principles, remember that QR includes sifting through conflicting data and weighing source credibility. Consider providing more information than is needed for the assignment and requiring students to make reasoned judgements about what information to use.

5. Plan your assessments and assignments for the course from the start

QR assignments inevitably involve multiple facets. At very least, the assignment includes disciplinary content in addition to QR components. It is very likely that some students will succeed in one dimension while struggling in another. To avoid difficult grading dilemmas at the end of the assignment, decide in advance how you will grade the work.

One way to do this is to create a rubric that identifies the criteria to be evaluated and describes varying levels of student success for each. Such rubrics can include numerical scores which are added up to arrive at a final score. Or they can be qualitative. Whatever the choice, making these decisions up front and communicating the criteria to students in advance will save trouble in the long run. (Also, check out the discussion of designing assessments to aid this decision process.)

6. Tell students what you are up to

For many students, the introduction of QR in your course may seem foreign. Not surprisingly, in their first encounter with QR practices students will bump into many challenges. You can minimize their sense of frustration with this learning process by using the suggestions above to support them along the way. But it is also very helpful to tell your students what you are trying to achieve.

In your syllabus and at the top of your assignments, explicitly articulate your QR objectives. After students turn in their assignments, devote 5 or 10 minutes of class time to talking about their experience with the assignment. What did they find interesting? What was challenging? What was frustrating? What was rewarding? Not only will this conversation give you ideas about how better to teach the material next time around, these conversations also give you an opportunity to articulate how QR assignments give students a deeper understanding of the course material and its applications. While nothing can guarantee student good will, open communication about course objectives and your reasons for setting those objectives can earn you the benefit of the doubt.



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