Every business leader is, in a sense, a teacher.

“Not in the sense that their job description says “Teacher”; not in the sense that they stand up in front of a lecture hall,” says Mitchell Petersen. “But their job will entail communicating ideas to others, convincing them the ideas are right—convincing them that this is the right way to think about a problem.”

As a professor of finance at the Kellogg School and an expert in empirical corporate finance, Petersen spends a lot of his time trying to convince people about how to think about problems.

He offers up these six tools to help you communicate complicated ideas to audiences—whether you are sitting down for a one-on-one, leading a company all-hands meeting, or just trying to make sense of something yourself.

1. DATA. Data provide a detailed, and dispassionate, characterization of what has occurred previously. As such, data serve as the foundation for predictions about the future. Before financial experts began collecting daily data on stock prices, returns, and dividends, for example, nobody had a sense of how typical stocks performed over time—and thus how they might be expected to perform going forward.

“The beauty of data is it tells us what happened in the past,” says Petersen. “It’s descriptive.”

“Now, the disadvantage of data is it doesn’t necessarily tell you how variables are related. It is just the landscape without any underlying structure.”

In other words, all the raw data points in the world are not going to automatically provide you with a solid case for favoring one decision or prediction over another—which can be where logic comes in.

2. LOGIC. Sometimes, casual observation or even simple intuition can offer the initial structure you need to wrestle with a complex problem. Just as you have a mental model of how gravity operates on objects, you may over time develop a notion about why some stocks are riskier than others, or why certain firms ought to employ more or less leverage.

“Quite often you have an idea of how two variables are related,” says Petersen. “That’s logic.”

Logic is valuable in its own right—after all, if your audience struggles to follow the thread of your argument, it will be tough to convince them that the argument is sound. But logic also serves as a fruitful breeding ground for more rigorous analysis.

“Equations are a way to boil complex relationships down into a small number of important levers.”

3. EQUATIONS. Equations allow you to make your case with precision and accuracy. Equations capture relationships between variables mathematically, so that those relationships can be mapped to actual data.

How exactly do two variables move in relation to one another? “It’s one thing to say the more debt a firm has, the higher its expected return on equity—but is that a small change or a big change?” asks Petersen.

It is rare for an equation to capture every relationship among a complicated set of variables, so good equations also make a statement about the most important relationships. They offer “a way to boil complex relationships down into a small number of important levers,” Petersen says.

“The equations are always a simplification of reality, so they never fit perfectly. The question is: Is the fit sort of close, or is it way off?”

4. PICTURES. Pictures or visuals offer your audience an invaluable way of remembering the relationships between different variables. Consider how easy it is to picture the trajectory of a rock rolling down a hill or the ripples it creates as it splashes into a pond. Likewise, the right visual offers an easy way to see, internalize, and later recall even complicated informational trends.

When presenting complex information to an audience, “I’ll put up the data in a table, because I want them to see the details,” says Petersen. “I also put up the picture, because it makes the concept much more persistent.”

5. STORIES. Stories that summarize certain logics or relationships between variables are perhaps stickiest of all. “There are no cultures that I know of that don’t tell stories,” says Petersen. “It’s fundamentally part of what it means to be human.”

These stories can become memorable, almost tangible shorthand for even very abstract concepts. An elaborate story about a Coca-Cola investor swapping shares with first a Pepsi investor, then an orange juice investor, next a peanut butter investor, and finally a tractor investor, might vividly encapsulate the benefits of an otherwise nebulous concept like diversification.

When thinking up stories, do not be afraid to channel the ridiculous. “The dopier the story, the more people may groan—but years later they remember it,” says Petersen. “I will meet people 5, 10, 15 years after and they do not remember the specific data, but that stupid story I told them years ago has rooted itself in their brain.”

It helps also to keep in mind that stories are not just for your audience. “By telling that story to ourselves, it’s a way for us to understand the world and cement it in our memory.”

6. PARTICIPATION. Tools like data or equations or even stories are of limited value if an audience feels they can’t push back, disagree, or ask for clarification. The more senior your audience is, says Petersen, the more important it is to actively create pauses or other spaces where misunderstandings can be voiced.

Want to know whether your audience is with you? Consider a straightforward approach. “I’ll just stop and say, ‘Somebody please ask me a question,’” he says.

And as you answer, use your body language to communicate that you genuinely welcome the opportunity to clarify. “Do you lean forward? Do you lean backwards? Do you nod? Do you shake your head?” he asks.

Above all, do not assume that the brave questioner is the only one confused.

“Watch the expressions of the three people sitting behind them. Their bodies all of a sudden relax. What effectively they’re saying is: ‘I was lost but I didn’t want to ask,’ or ‘I was lost and I couldn’t articulate the question. Amanda’s question actually sorted it out. Now I understand what I don’t understand.’”