Relational Reasoning

The Ability to Reason Relationally Is Foundational and Pervasive

As we (Alexander & DRLRL, 2012) and others (James, 1890; Spearman, 1927) have argued, the ability to discern patterns within any information stream is foundational to learning and performance. For example, in his classic volume, Principles of Psychology (1890), William James described the mental ability used to uncover relations of differences and similarity between mental representations. James argued that without such ability, humans would be trapped in a world filled with isolated stimuli, unable to connect objects perceived across time and space. Similarly, the research on perception by Gestalt psychologists demonstrated humans’ tendency to impose some order or structure on otherwise unrelated information (Köhler, 1929; Wertheimer, 1900).

Moreover, contemporary advances in cognitive and neuroscience research further establish relational reasoning’s foundational nature (Bazargani, Hillebrandt, Christoff, & Dumontheil, 2014; Krawczyk, 2012). For example, functional brain imaging enabled neuroscientists to examine relational reasoning. As such, a growing literature studies higher order processes, such as deductive reasoning (Monti, Osherson, Martinez, & Parsons, 2007) and complex problem solving (Campitelli, Gobet, Williams, & Parker, 2007; Goel & Grafman, 1995). The prefrontal cortex is activated when one reasons relationally (Robin & Holyoak, 1995).

More specifically, the prefrontal cortex has been implicated in the performance of higher level cognitive functions (Duncan, Burgess, & Emslie, 1995; Smith, Patalano, & Jonides, 1998). Neuroscientists hypothesize that given its increase in size over human evolution (Benson, 1993), the prefrontal cortex may be the locus for the system of relational reasoning. Furthermore, these researchers conjecture that its growth may reflect the increasing cognitive demands humans encounter daily (Lenhart, 2005; Purcell, Weigand, & Schall, 2012; Robin & Holyoak, 1995). In effect, these emerging findings in cognition and neuroscience give credence to our claim that relational reason ability is foundational to living and learning in contemporary society.

Relational reasoning is not only foundational but also pervasive, permeating all manner of human thought. More specifically, relational reasoning has been empirically linked to academic achievement in a variety of domains, such as reading (Ehri, Satlow, & Gaskins, 2009), chemistry (Bellocchi & Ritchie, 2011), mathematics (Richland & McDonough, 2010), technological literacy (Jablansky et al., 2015), and nursing education (Fountain, 2015). Beyond academic domains, the pervasiveness of relational reasoning has been repeatedly demonstrated in the words and actions of professionals engaged in critical and creative problem solving (Dumas et al., 2014; Paletz, Schunn, & Kim, 2013).

For example, a study exploring relational reasoning in medical education found all four forms of relational reasoning during discussions between an attending clinical neurologist and his team of residents making diagnostic and therapeutic decisions about their patients in a hospital setting (Dumas et al., 2014). Another example of the ubiquity of relational reasoning in real-world contexts (Dumas & Schmidt, 2015) examined relational reasoning as a predictor of the quantity and quality of engineering designs; relational reasoning was an underlying ability that supported the innovative processes required for the production of creative solutions to mechanical problems. Based on these examples, relational reasoning is a cognitive capacity required in the execution of complex tasks—whether in schools or in professional venues.

Relational Reasoning Varies by Age, Domain, and Context

Internal and external factors ultimately determine the quality and quantity of relational reasoning. These factors include reasoners’ age, knowledge of, and familiarity with the domain and task at hand, as well as the reasoning context.

Clearly, relational reasoning operates across the life span, observed in children as young as four (Gentner, 1977; White & Alexander, 1986) and adults older than 80 (Fischer, Norberg, & Lundman, 2008). Although most research on young children centers on analogical reasoning (e.g., Gentner, Loewenstein, & Hung, 2007), a cross-sectional study of kindergarten through 11th-grade students found analogy, anomaly, antinomy, and antithesis in their discourse at all grade levels (Jablansky et al., 2015). The relative prevalence for each form, however, differed by age. Specifically, analogical and anomalous reasoning prevailed in the talk of children between kindergarten and fourth grade, while children in sixth to 11th grade demonstrated more antinomous and antithetical reasoning (Jablansky et al., 2015).

These results suggest differentiating between “typical” and “maximal” performance (Dubois, Sackett, Zedeck, & Fogli, 1993). Although children can reason relationally, their “default” forms of relational reasoning differ from those that can be prompted under certain circumstances. Contextual factors, such as the person or object that elicits the reasoning, are therefore key in determining the occasions and forms that are ultimately expressed. For example (Jablansky et al., 2015), students’ verbalized forms of relational reasoning appeared to be shaped, in part, by support offered by the researcher whose questions and comments scaffolded students’ thinking. When such supports are minimal, the relational reasoning manifested might well be constrained (e.g., Taverna & Peralta, 2013). Moreover, the familiarity with the object or topic, along with prior learning opportunities (Klahr & Dunbar, 1988), may influence the occasions of relational reasoning (Defeyter, Hearing, & German, 2009; Jablansky et al., 2015). In this way, age necessarily interacts with environmental supports and individuals’ prior experiences with the objects of reasoning.

Beyond age, the domain per se can affect the forms of relational reasoning. For instance, medicine demands anomalous reasoning to identify abnormalities in a patient’s symptoms (Dumas et al., 2014). In contrast, writing can call for antithetical reasoning when synthesizing across multiple sources (Diakidoy, Mouskounti, & Ioannides, 2011). However, a domain does not elicit only one type of relational reasoning. As a case in point, a reasoning sequence emerged, as doctors analyzed patients’ symptoms and worked toward diagnoses. While doctors generally began by identifying a case’s anomalies, they often followed with antinomies, and then analogical references to previous cases, before making a preliminary diagnosis (Dumas et al., 2014).

Tasks themselves contribute to relational reasoning’s manifestations. When the task involves classifying or differentiating among categories of objects, antinomous reasoning is most prevalent, be the domain physics (Schneider & Hardy, 2013), technology (Jablansky et al., 2015), or engineering (Dumas & Schmidt, 2015). By contrast, when the task involves reconciling conflicting sources of information, antithetical reasoning may prove most useful (Hynd & Alvermann, 1986; van den Broek & Kendeou, 2008). Relational reasoning is a multifaceted construct whose manifestations are multiply determined. Verbalizations of each form are influenced by age and domain, with the contexts of task, environment, and experience contributing.

Relational Reasoning Can Be Observed and Measured in Diverse Ways

Given that relational reasoning manifests differently as a function of individual and environmental factors, the construct itself can be measured in a variety of ways. Educational and psychological researchers interested in complex thinking and learning use diverse measures and methodologies for tapping into relational reasoning ability. That variety includes psychometric measures and tasks (e.g., Alexander, Dumas, et al., 2015; Richland, Chan, Morrison, & Au, 2010), naturalistic observations (e.g., Chan & Schunn, 2015; Dumas et al., 2014), and cognitive interview techniques (Jablansky et al., 2015).

Of the possible methods for assessing relational reasoning, one in particular has stood out: four-term analogies (Alexander, White, Haensly, & Crimmins-Jeanes, 1987; Goswami & Bryant, 1992; Maguire, McClelland, Donovan, Tillman, & Krawczyk, 2012; Sternberg, 1977). Four-term analogies follow the form A:B::C:D, where the A and B term are linked to the C and D term by a higher order relation of similarity. For example, the four-term verbal analogy wolf:pack::lion:pride allows for the identification of the lower order relation of “is a member of” between wolf and pack as well as lion and pride. A higher order relation of similarity links the two lower order relations, forming an analogy. Four-term analogies do not necessarily need to be verbal in nature, but can be presented pictorially (e.g., Krawczyk et al., 2008; Richland et al., 2010) or figurally (e.g., Tunteler & Resing, 2010).

One commonly used expansion of classic analogy problems is matrix analogies (Alexander et al., 2015; Naglieri & Insko, 1986; Raven, 1941). Today, the matrix format remains the gold standard for assessing visuospatial analogical reasoning and fluid ability (Krawczyk, McClelland, & Donovan, 2011). Matrix analogies are also the measure of choice for many neuroscientists working in relational reasoning, perhaps because their complex visuospatial nature suit them for neuroimaging brain activation (see Krawczyk, 2012, for a review). Recently, Alexander and colleagues (2012) have built on the matrix format to assess other forms of relational reasoning (e.g., antinomy). Together, these figural arrays constitute the Test of Relational Reasoning (TORR; Alexander, 2012; Dumas & Alexander, in press).

While the previously described measures utilize a selected-response (closed-ended) format, open-ended and naturalistic observations have also tapped relational reasoning. For example, text-based studies, especially those incorporating refutational texts, challenge participants to identify and describe higher order relations while reading (Kendeou & O’Brien, 2015; Sinatra & Broughton, 2011). Moreover, cognitive interviews can capture students’ relational reasoning about particular objects or processes (e.g., Jablansky et al., 2015; Rush & Roy, 2001). Semistructured interviews, in which the researcher prompts or supports participants’ relational reasoning, may be especially useful for young respondents (e.g., Jablansky et al., 2015). Furthermore, naturalistic, or in vivo methodologies, have repeatedly captured relational reasoning on complex problems (e.g., Chan & Schunn, 2015; Dumas et al., 2014; Trickett, Trafton, & Schunn, 2009). These methods, which tap relational reasoning as it occurs within a domain-specific problem-solving context, may be necessary to uncover differences related to domains (e.g., engineering or medicine) or levels of expertise (e.g., teacher or student; attending or resident physician), or to model how various reasoning forms work in concert in educational or professional contexts.

Based on extant investigations, the relational reasoning construct still has much remaining to be learned. For greater insights, the entire gamut of measurement tools must be used: from selected-response assessments and neuroimaging methods to semistructured interviews and naturalistic observations. In this way, the nature of relational reasoning may be more fully uncovered, and those engaged in complex reasoning in school and the workplace may be systematically supported.

Relational Reasoning Is Malleable and Teachable

Relational reasoning capability should not be viewed as a predetermined or fixed entity (Blackwell, Trzesniewski, & Dweck, 2007; Dweck & Bempechat, 1983; Mangels, Butterfield, Lamb, Good, & Dweck, 2006). Rather, an individual’s ability to discern meaningful patterns and to utilize that capacity strategically can be shaped through relevant experiences. Drawing analogously on the empirical work in intelligence, the simple understanding that relational reasoning can transform to some degree can motivate and catalyze cognitive and metacognitive action (Burke & Williams, 2012; Cornoldi, 2010; Miele, Son, & Metcalfe, 2013).

The events that might shape relational reasoning can be both direct and indirect. For instance (Murphy et al., 2016), a brief compare–contrast writing intervention affected students’ relational reasoning in a fifth-grade classroom: students’ ability to engage in relational reasoning and generate, compare, and reconcile arguments developed in line with the writing intervention. Similarly, high-school physics and chemistry students’ relational reasoning and scientific understanding gained through an intervention that focused on evidence-based discussions (Greene et al., 2016).

In an example of the impact of a more indirect intervention on relational reasoning ability (Dumas & Schmidt, 2015), graduate students in mechanical engineering received inventive problem-solving instruction (i.e., TRIZ) to improve solutions to design problems. While relational reasoning predicted ideation generation success prior to the TRIZ, the association between TRIZ and relational reasoning strengthened after the intervention. In sum, if relational reasoning were a fixed construct, none of the changes in relational reasoning ability described herein would manifest.

In the aforementioned cases, relational reasoning was broadly targeted through various experiences such as compare–contrast lessons (Murphy et al., 2016) or a creative problem-solving methodology (Dumas & Schmidt, 2015). Component-based analogy training studies, grounded in the processes underlying thinking (i.e., encoding, inferring, mapping, and applying; Sternberg, 1982), offer additional credence to the claim that relational reasoning is malleable and teachable. For instance, explicit instruction of the component processes (e.g., inferring and mapping) facilitate elementary, middle, and secondary school students’ ability to solve analogy problems in linguistic and nonlinguistic forms and in the domains of history and biology (Alexander, Pate, Kulikowich, Farrell, & Wright, 1989; Alexander, White, & Mangano, 1983). Furthermore, late adolescents and young adults provide evidence of successful analogy performance following component-based training (Sternberg & Ketron, 1982).

The role of the same components to the processing of anomalous, antinomous, and antithetical forms of relational reasoning has also been empirically established (Grossnickle, Dumas, Alexander, & Baggetta, 2015). Thus, as the prior studies suggest, the component processes underlying relational reasoning are ripe for direct intervention. Specifically, this ability to discern meaningful patterns within any information stream seemingly relies on basic cognitive processes that already have a place within learning environments across grades and academic domains (Ward, Suss, & Basevitch, 2009). The goal should be to make these component processes more transparent and to demonstrate how they uniquely combine to give each form of relational reasoning its defining character. Of course, much is still to be learned about the best time, place, and contexts to enhance relational reasoning. Yet, if relational reasoning is demonstrably malleable and teachable, then to ignore those educational opportunities seems unconscionable.

Think Critically and Analytically About Higher Order Thinking

The contemporary focus on critical, analytical, and higher order thinking in educational policies and curricular initiatives is laudable. Yet, these policies and initiatives demand deeper reflection on the processes and components that ultimately fuel these alternatives to superficial thinking (Stanovich et al., 2011). Relational reasoning can serve that goal. It can help promote the systematic attention to similarities and dissimilarities in what is seen, heard, or sensed. Relational reasoning promotes examining not just analogical or similarity associations but also associations of discrepancy, exclusion, and opposition. It can be the mechanism by which ideas, objects, or situations are perceived in conjunction rather than as isolated phenomena. Relational reasoning can, therefore, become a means to those worthwhile ends of critical, analytical, and higher order thought.

Unearth the Potential of Relational Reasoning

It is not enough to recognize the foundational character of relational reasoning or acknowledge its central role in all forms of “higher” thinking. What is also essential is to devise measures and techniques that would allow researchers and practitioners to make the internal mechanisms of relational reasoning more transparent. Until students’ relational reasoning can be made visible, there will be no way to document its role in academic achievement or to permit students to bear witness to the power of thinking analogically, anomalously, antinomously, or antithetically. Toward that end, we have been laboring to devise psychometrically sound measures of relational reasoning that be used with elementary and middle school students (i.e., TORRjr; Jablansky, Alexander, & Singer, 2016). We have also developed and calibrated a figural measure of relational reasoning for older students and adults (TORR; Alexander, 2012; Alexander et al., 2015), as well as a verbal form for this same population (vTORR; Alexander, Singer, Jablansky, & Hattan, 2015).

These formal measures assess students’ capacity to reason relationally in a manner not previously available. These formal measures complement with creative techniques for documenting relational reasoning within the flow of naturally occurring problem solving, including among medical professionals and children engaged in technical literacy tasks (Dumas et al., 2014; Jablansky et al., 2015). Collectively these in vivo techniques, combined with more formal assessment tools, can afford researchers and practitioners the means of excavating the reasoning processes of individuals at all ages in diverse contexts.

Be Models of the Processes of Relational Reasoning

It would seem unjust to expect students to demonstrate the depth of thinking fueled by relational reasoning, without populating classrooms with teachers model these valued mental processes. Yet, given that relational reasoning is apt to be a novel, unfamiliar notion within teacher education, we cannot presume that those guiding the learning of others are prepared to assume the role of reasoning model. That is not to say that teachers are incapable of rising to that task if they are provided with the professional development required. These professional development initiatives should not attempt simply to lay relational reasoning on top of all other agendas and mandates that fall on teachers’ shoulders. Rather, professional development should strive to demonstrate how relational reasoning could be woven into the existing fabric of the educational experience. Teachers and administrators can see that relational reasoning could empower the agendas and mandates already in place—not simply add to them.

Arm Students With the Language and Knowledge of Relational Reasoning

Finally, our concluding principle sought to make clear that relational reasoning is by no means a fixed capacity. Rather, relational reasoning is susceptible to experiences that stimulate students’ perceptiveness, demand the integration of ideas, and necessitate the resolution of contrasting evidence. If relational reasoning is both foundational and teachable, then we have no choice but to make such transformational experiences available to students. An initial step in these experiences would be to equip students with the language of relational reasoning. Teach them what analogy, anomaly, antinomy, and antithesis mean, and encourage students to use those terms when engaged in the analysis of ideas, objects, and situations.

Beyond labeling relational reasoning forms (e.g., antinomy and antithesis) and underlying component processes (i.e., mapping and applying; Sternberg, 1977), students need to witness firsthand the power of relational reasoning across academic domains and tasks. In effect, as students study reading, history, mathematics, or science, they should be given the opportunity to craft analogies, identify anomalies, point out antinomies, and forge antitheses. Furthermore, students should be helped to realize how these reasoning processes are central to all academic domains and to see how successful readers, historians, mathematicians, and scientists are ultimately successful relational reasoners. Moreover, the assessment of learning within these academic domains should require manifesting these foundational reasoning processes. Aligning foundational capacities with effective instructional initiatives and innovative assessment practices will help make the praiseworthy goal of an informed citizenry a reality.

Clearly, these four recommendations are modest actions that should be undertaken within the educational enterprise. Specifically, teachers and administrators can (a) use relational reasoning theory and research to help refine current notions of “higher” thinking, (b) utilize measures and methods to bring students’ relational reasoning to the surface for inspection and reshaping, (c) model the forms and processes of relational reasoning within the learning environment, (d) teach the forms and component processes of relational reasoning, and (e) make those processes central to assessment practices. To do otherwise would be to let the instructional power of relational reasoning wither; to do otherwise would be to watch students’ reasoning potential remain unfulfilled; and to do otherwise would be to miss the opportunity to strengthen existing policies that address critical, analytical, and higher order thinking.