Provide Evaluative Meaning and Direct Attention

This chapter, “Provide Evaluative Meaning and Direct Attention,” links earlier chapters about the habits of the highly numerate to evidence-based communication solutions that especially help the less objectively numerate. In particular, Chapter 17 provides techniques to assist decision makers when they are unable to evaluate the good or bad meaning of numeric information. These techniques range from providing numeric comparisons to carefully using evaluative labels and symbols, more imaginable data formats, and emotion. Evidence exists that emotional communications also facilitate communication by grabbing and holding attention. Other methods that allow the less numerate access into these attentional habits of the highly numerate include ordering information based on its importance, highlighting the meaning of only the most important information, and increasing the visual salience of key numbers. The chapter concludes with a brief summary of some of the challenges that communicators face to presenting information well.

Provide Numbers but Reduce Cognitive Effort

This chapter, “Provide Numbers but Reduce Cognitive Effort,” challenges the notion that numbers mislead people and should be avoided. This chapter recommends instead that communicators provide numeric information but reduce how much effort is required from consumers and patients to use it. In particular, the chapter discusses five ways that providing numeric information is useful for decision makers. Then it summarizes evidence-based methods to present such numeric data to decrease effort and increase numeric comprehension and use. The methods include providing fewer options and less information, presenting absolute risks, keeping denominators constant, doing any needed math operations for them, and using appropriate visual displays. Concrete examples are explained in plain language.

Reflections on Numeracy and the Power of Reasoning Numerically

This chapter, “Reflections on Numeracy and the Power of Reasoning Numerically,” looks back at what you have learned in this book. Innumeracy presents major challenges to people due to the ubiquity of numbers in daily decisions and the less objectively numerate’s inability to understand and use them appropriately. However, the less numerate can become better decision makers by learning the habits of the highly numerate, receiving information in evidence-based communication formats, or becoming more numerate themselves. This chapter also introduces the idea that some heuristic use may be “friendlier” to the less numerate. Researchers need to understand better the ecology of numeracy, heuristic use, and their interactions. We also need to understand more, both theoretically and practically, about how and when the persistence of subjective numeracy and the intuitive power of the approximate number system (ANS) help versus hurt decisions and decision outcomes. Overall, understanding and building numeracy should allow us to produce better opportunities and a healthier and wealthier nation of individuals.

Evidence-Based Information Presentation Matters

This chapter, “Evidence-Based Information Presentation Matters,” introduces the problem: poorly presented numbers, widespread innumeracy, and barriers introduced by the communicators themselves. These issues combine to produce negative consequences for health and financial well-being and for shared decisions about public resources. Because risk and other numbers can be confusing and overwhelming, the challenge is not merely to provide them accurately. Instead, the communication challenge includes presenting them so that consumers can comprehend and use them and thus increase control over their experiences and outcomes. Chapter 15 links earlier chapters on the psychology of how decision makers process information to five evidence-based strategies for how to present numbers to increase how well people comprehend and use them in judgments and decisions. Strategically choosing information-formatting techniques allows abstract and impotent data to become useable information that facilitates informed decisions that concord with what people value.

The Highly Numerate Understand the Feel of Numbers

This chapter, “The Highly Numerate Understand the Feel of Numbers,” discusses the critical importance to decision making of good and bad feelings derived from numeric information. Decisions are hard to make sometimes because we don’t have a feel for what an important number means. The highly numerate, however, appear to compare numbers more, derive more number-related affect, and use those feelings to guide their decision making. This process is believed to underlie part of the highly numerate’s ability to be more sensitive to numeric data in judgments and decisions. This same process, however, can result in the highly numerate overusing or making faulty interpretations of numbers. This chapter continues to explain the rules and principles followed by the highly numerate.

Thinking Harder with Numbers

This chapter “Thinking Harder with Numbers,” is the first of four chapters focusing on how more objectively numerate people think harder and, as a result, judge and decide better when numeric information is involved. First, they attend to and search for numeric information more than the less numerate do. Second, they think more with numbers by (1) thinking longer in numeric decisions; (2) performing more numeric operations, for example by transforming numeric information from one format to another; and (3) understanding better what they know and do not know. These processes generally result in the highly numerate making better decisions. The highly numerate not only understand numbers better, but they also have better habits for dealing with numeric and non-numeric information in judgment and choice.

The Types and Extent of Innumeracy

This chapter, “The Types and Extent of Innumeracy,” briefly describes three kinds of numeric competency. First, people can score high or low on tests of their understanding and use of mathematical concepts (called objective numeracy). Objective innumeracy occurs across levels of education and is not the same as intelligence; very smart people can be quite poor with numbers in critical ways. Second, people can be good or bad at persisting in numeric tasks because of their subjective numeric confidence. Despite existing objective innumeracy, 63% of Americans nonetheless say that understanding medical statistics is easy. Finally, people differ in an intuitive number sense that appears to underlie childhood development of objective numeracy and to compensate for adults’ low objective numeracy abilities. The Appendix for this chapter introduces measures of objective numeracy and subjective numeracy.

Subjective Numeracy and Knowing What You Know

This chapter, “Subjective Numeracy and Knowing What You Know,” reviews what is known about the role of subjective numeracy in decision making, independent of objective numeracy. In particular, it examines how numeric self-efficacy (confidence in one’s math ability) and math anxiety propel how much people understand and persist with numeric information and, ultimately, how they judge and decide. Even when an individual with low subjective numeracy has adequate objective ability with numbers, they appear to understand less and make worse decisions nonetheless because they enjoy the process less, give up more easily, and ultimately perform less well. Having lower subjective numeracy (operationalized in this book as having lower numeric confidence, aka self-efficacy, or higher math anxiety) may hold us back as individuals and as a society from realizing our numeric potential and its positive effects.

Discriminating Numbers Allows for Better Decisions

This chapter, “Discriminating Numbers Allows for Better Decisions,” focuses on the role of our intuitive sense of numbers in decision making. Humans have evolved beyond these intuitions about quantities to know modern numeric abstractions. However, the evolutionarily old approximate number system (ANS) nonetheless remains pivotal to human decisions. Just as non-human animals use the proportional reasoning and estimation skills that come from the ANS, so do humans. The chapter introduces three systematic properties of the ANS that can explain differences in how people make decisions. These numeric intuitions, independent of objective ability, relate to having superior numeric memory and (usually) more accurate perceptions of value. Sometimes, however, the ANS’s reliance on proportional reasoning can produce what looks like worse decisions. The Appendix to this chapter describes ANS measures.

The Approximate Number System (ANS) and Discriminating Magnitudes

This chapter, “The Approximate Number System (ANS) and Discriminating Magnitudes,” discusses our intuitive, rather than deliberative, understanding of numbers. Humans are born with an innate sense of number and an ability to perform simple arithmetic operations with sets of objects without counting. We share this intuitive sense of numeric magnitude (how big one quantity is relative to another) with other species. Non-human animals cannot count as humans do. However, they have a keen sense of quantity that allows them to tell quickly and efficiently which quantity is bigger so that they can make better choices about food, mates, and safety. In humans, this intuitive sense of numbers develops from infancy to adulthood, and it appears to underlie the emergence of symbolic math ability (objective numeracy) in children.