# Principles for Teaching QR

Initial Publication Date: October 22, 2013
"Quantitative literacy involves sophisticated reasoning with elementary mathematics more than elementary reasoning with sophisticated mathematics." Lynn Arthur Steen in Achieving Quantitative Literacy

There are several principles for teaching QR that will help you and students remain on track to learn the kinds of skills you are interested in teaching them without getting buried in complicated calculations or endlessly long tasks.

## 1. Emphasize accuracy relative to precision

The real-world data which quantitative reasoning (QR) routinely takes as a starting point for analysis often contain significant measurement error either because what is measured isn't quite "right" or because the methodology inherently includes measurement error. And sometimes QR asks us to form back-of-the-envelope estimates without access to any specific data whatsoever! One important aspect of QR is working through this lack of precision to arrive at accurate solutions nonetheless. For example, in a discussion of all-day kindergarten initiatives you may ask students to estimate the cost of implementation in your own state. Students would need to combine a guesstimate of the number of 5-year-olds with a guesstimate of the cost of the additional half day of schooling to arrive at a reasonable figure without any precise inputs.

Encourage your students to embrace this reality and be prepared for some resistance. Many students immediately associate quantitative work with their experience in traditional math courses in which problems often have only two types of answers: exactly right and wrong. (Of course, in advanced mathematics the reality is far more complex, but that is not the typical student's experience.) As a result, they may initially stumble when asked to make rough estimates or to analyze the quality of someone else's back-of-the-envelope calculation.

Of course, data can be so imprecise that it effectively fails to answer our questions. For example, if the data only shows if a family's income is above or below \$75,000 then a student will not be able to answer many important questions about class. Recognizing these limitations is certainly part of the QR discipline. But the point here is that there are many times when being "approximately accurate" is more valuable than being precisely wrong.

Require students to make rough estimates. Give them problems for which you intentionally withhold some information which they have to "guesstimate." Give assignments in which students collect samples of data, and then show them how to present their findings with appropriate recognition of the limitations implied by their data gathering.

## 2. Consider the social construction of numbers--and then help students get past it

In his book More Damned Lies and Statistics Joel Best explores the social process that determines what we count (or don't) and how. While Best does acknowledge that some numbers are intentionally slanted or cherry-picked, his focus is on the more mundane realities--that all variables have to be defined by someone, that our minds are pre-disposed to look for causal connections even though often a correlation is not causal, that numbers carry with them an authority that may be greater than the strength of the data.

When first encountering these facts students can easily slip into Twain's unconstructive cynicism referred to in Best's book title, concluding that numbers are always the worst of lies. If we leave them in this half-baked QR state of mind we have done them a great disservice. By engaging them in active learning, we can move through this early stage of learning to a better and more balanced perspective in which they take a critical perspective that questions numerical evidence while remaining open to its power. Force students to make data-based arguments of their own (whether in essays, spreadsheets or charts & graphs). In the process they will come to learn that social construction is inevitable; it is literally impossible to say anything quantitative without making many important choices. But they will also learn that there are better and less sound ways of making those choices.