Students in most fields will need to write with numbers, but the ways that quantitative data are used vary across courses and curricula. In experimental and scientific courses, students may be taking measurements and recording outcomes of tests. In social science courses, students will interpret statistical data to describe populations and to draw inferences. Even in arts and humanities courses, numbers pervade disciplinary processes of description and analysis.

Although the old adage suggests that “numbers speak for themselves,” the ways in which we present quantitative data and the ways we select that data for our purposes and audience make a huge difference in the success of documents. Unfortunately, students often learn the algorithmic processes of deriving, reporting, and analyzing numbers without considering the contexts, purposes, and audiences that turn numbers into insight. Providing students the opportunity to write with and about data will allow them to use their computational and analytic skills to inform and persuade. On this page, we identify strategies for helping students develop effective habits for writing with data.

## Preparing Your Students to Write with Data

Numerous statisticians, economists, mathematicians, and psychologists have independently reached the conclusion that humans are relatively weak intuitive statisticians. We have a very difficult time understanding probability in context, especially when we consider risks or consider outcomes in which we have an interest. We are often very poor at understanding the differences between normal variation, biases, and statistical noise. We suffer from recency effects, halos, and horns. Perhaps worst of all, we will often abandon the successful and accurate conclusions of statistical data if doing so allows us to retain our previously held beliefs.

#### Consider an ungraded pretest activity

If your course requires a familiarity with statistics, assess your students’ statistical knowledge early in the semester. A low-stakes quiz or an informal writing activity on relevant statistical terms and concepts will help you to understand the extent of students’ background knowledge. If you find that students lack understanding of some foundational concepts, you might either consider a brief review in class or recommend supplemental instruction on statistics online. Otherwise, misunderstandings of statistical models and tests may only appear in final graded work when it is too late to revise.

Frequent, low-stakes opportunities to test students’ familiarity with concepts and methods offer multiple advantages to students, for both demonstrating and building confidence. In Make it Stick: The Science of Successful Learning, Brown, Roediger and McDaniel emphasize the value of self-testing for retrieval practice:

#### Help students understand that computational familiarity isn’t the same as selection and application

Students may be familiar with mathematical and statistical concepts from their previous coursework, but they may not have a sense of how or why particular measures or numbers may be relevant in context. For example, most students know the difference between mean, median, and mode, but they may not understand when a median statistic is more representative than a mean, or why a mode may be of interest with a particular data set. Students may be able to describe a correlation mathematically, but they may not know whether a correlation is meaningful or if an effect size is large enough to matter. Providing students with cases and context-rich opportunities for application can help them keep the big picture in mind.

#### Be on the lookout for common statistical misconceptions (especially counterintuitive conceptions)

Even though students may be familiar with positive and negative correlations, they may still misapply their knowledge of positive and negative numbers to assume that variables that rise together are positively correlated and variables that are negatively correlated fall together (rather than diverge).

Perhaps the most common statistical errors emerge when statistical terms with technical meaning are misunderstood by their conventional definitions. For example, students may confuse significance (mathematical evidence of a non-random effect) with significance (something meaningful or important). Students may inadvertently associate positive correlations with preferred outcomes and negative correlations as bad news. In their analysis of specialized vocabulary in statistics, Kaplan, Fisher, and Rogness noted that ambiguity around key statistical terms (‘average’, ‘confidence’, ‘random’, and ‘spread’) created challenges for students in their early statistics learning. Providing students with opportunities to write with these terms in their specialized statistical context can help them master important statistical concepts.

## Selecting the Best Tools: Describing and Representing Data

Although quantitative reasoning is common across the curriculum, the means by which disciplines gather, report, synthesize, and attach significance to data can differ dramatically. In the previous section, we looked at ways to use writing to address potential conceptual problems, in this section, we emphasize teaching disciplinary practices of reporting and representing data.

#### Identify the common reporting practices of your field

When addressing course readings or looking at examples, it can be valuable to reinforce which measures and tests are included and why those measures are considered important to the field. In addition to describing the quantitative techniques involved, students will benefit from descriptions of how and why the technique involved applies to the context. Ideally, students will not only build technical skills with the tools of the field, but they will also have a system for organizing and selecting the appropriate tool for their data tasks. Further, identifying the “why” of a particular mathematical or statistical technique will help students to distinguish between merely describing a process and using that process to generate conclusions. Using pedagogical techniques like metateaching or even merely being more explicit about why certain reporting practices are the best tools can help students to understand the sometimes implicit values of disciplines.

#### Provide context-rich problems and questions

Conversely, when students are turned over to their own quantitative analyses, providing opportunities to draw meaningful conclusions will reinforce how and why a particular quantitative technique is useful or applicable. In many fields, small case studies from professional or laboratory contexts can give students more opportunities to connect their quantitative analyses to meaningful conclusions. Similarly, scaffolding larger assignments can provide opportunities for meaningful student learning and effective feedback on writing.

#### Insist on consistent, careful attention to units of measurement

A common error students make in their writing with quantitative data is omitting units of measure. When students are preparing writing for assessment by an instructor or teaching assistant, they may (correctly) assume that their reader already knows the context, problem, and answer and is merely interested in “the number” that provides the answer. Asking students to consistently include units of measure (even with problem sets and homework) reminds them that in most real-world instances, analyses are provided to audiences who may need to be supplied with elements of context in order to draw appropriate conclusions.

#### Ask students to express their answers in a sentence

One of the simplest strategies for assisting students in writing about numbers is to give them practice. Requiring students to write their answers in a complete, *meaningful *sentence can be a valuable habit. For example:

The best answers to questions requiring data should include relevant context (who, what, when, where) and ascribe significance (why and how it matters).

## Data Analysis and Synthesis: Drawing Conclusions to Inform and Persuade

The terms “data analysis” and “data synthesis” are often used interchangeably, but they might be usefully distinguished by the purposes for which data are collected and used. Data *analysis *typically involves the application of statistical tests or formulae to draw conclusions based on data. Most efforts to draw generalizations, conclusions, or predictions involve computational work. Data *synthesis *occurs when someone brings together data from multiple sources for the purpose of aggregation or presentation. Systematic literature reviews or observational studies will often involve data synthesis. Again, our common understanding of these terms can be confusing, especially if one of these terms is used simply to mean “make meaning from numbers.”

#### First, help your students differentiate data collection from data analysis

When presenting their data, students sometimes merely describe their processes for collecting data in a sequence of steps rather than providing analysis and synthesis of results. Students may misunderstand the process of describing methods to mean offering an account of what they did, rather than as a description of methodology and its value and limitations. If students' data collection is to be assessed, be clear about why raw data is necessary. If only students' conclusions are most important, remind them that displaying raw data may not be necessary. Providing students with annotated examples can help them to recognize which information is relevant to different audiences.

#### Identify examples of successful data analysis in course readings and literature

When students interact with their course readings, they may be tempted to focus on the what—what is described?—rather than the how--how do authors use evidence to make their case? By connecting the organization of written material in your course to the purposes and audiences they serve, instructors can advise students to keep audience needs and genre expectations in mind.** **Simple, authentic examples that connect claims to data can be especially useful in helping students understand synthesis. For especially complex readings or foundational texts, the use of tools like social annotation can assist students in recognizing the features of successful writing with data.

#### Provide systematic reviews and meta-analyses to illustrate data synthesis

Some research genres depend primarily on aggregating previously recorded data to explain the state of knowledge on a topic or to illustrate broader claims about previous research. These explicitly synthetic forms of writing can be meaningfully contrasted with other types of quantitative research, whether they involve collecting data or querying existing data sets. Some disciplines may even be quite explicit about the relative value of different methods of data collection for supporting evidence-based practice.