Candace Walkington

Motivating Students by “Personalizing” Learning Around Individual Interests: A Consideration of Theory, Design and Implementation Issues

Abstract Purpose As educators seek ways to enhance student motivation and improve achievement, promising advances are being made in adaptive approaches to instruction. Learning technologies are emerging that promote a high level of personalization of the learning experience. One type of personalization is context personalization, in which instruction is presented in the context of learners’ individual interests in areas like sports, music, and video games. Personalized contexts may elicit situational interest, which can in turn spur motivational and metacognitive states like positive affect and focused attention. Personalized contexts may also allow for concepts to become grounded in prior knowledge by fostering connections to everyday activity. In this Chapter, we discuss the theoretical, design, and implementation issues to consider when creating interventions that utilize context personalization to enhance motivation. Design/methodology/approach First, we provide an overview of context personalization as an instructional principle and outline the emerging evidence that personalization can enhance motivation and improve achievement. We then discuss the theory hypothesized to account for the effectiveness of context personalization and discuss the approaches to personalization interventions. We close by discussing some of the practical issues to consider when bridging the design and implementation of personalization interventions. Throughout the paper, we anchor our discussion to our own research which focuses on the use of context personalization in middle and high school mathematics. Findings The theoretical mechanisms through which context personalization enhances learning may include (1) eliciting positive affective reactions to the instruction, (2) fostering feelings of value for the instructional content through connections to valued personal interests, or (3) drawing upon prior funds of knowledge of the topic. We provide hypotheses for the relatedness of context personalization to triggering and maintaining situational interest, and explore potential drawbacks of personalization, considering research on seductive details, desirable difficulties, and authenticity of connections to prior knowledge. We further examine four approaches to personalized learning – “fill-in-the-blank” personalization, matching instruction to individual topic interests, group-level personalization, and utility-value interventions. These approaches vary in terms of the depth of the personalization – whether simple, shallow connections are made to interest topics, or deep, meaningful connections are made to learners’ actual experiences. The consideration of depth also interacts with grain size – whether content is personalized based on the broader interests of a group, or the individual experiences of a particular learner. And finally, personalization interventions can have different levels of ownership – an instructor can generate the personalized connections, the connections can be made by the curriculum designers, or learners can take an active role in personalizing their own learning. Finally, we discuss the practical implementation issues when bringing context personalization interventions into K-12 classrooms. Personalization can be logistically difficult to implement, given that learners hold a diverse array of interests, and may experience each of those interests differently. In addition, particular types of instructional content may show greater sensitivity when personalization is implemented, and personalization may be most helpful for learners with certain background characteristics. Originality/value Realizing the promise of personalized learning is an unsolved problem in education whose solution becomes ever more critical as we confront a new digital age. Context personalization has the potential to bring together several well-established strands of research on improving student learning – research on the development of interest, funds of knowledge, and utility value – into one powerful intervention.

Expanding Notions of “Learning Trajectories” in Mathematics Education

Over the past 20 years learning trajectories and learning progressions have gained prominence in mathematics and science education research. However, use of these representations ranges widely in breadth and depth, often depending on from what discipline they emerge and the type of learning they intend to characterize. Learning trajectories research has spanned from studies of individual student learning of a single concept to trajectories covering a full set of content standards across grade bands. In this article, we discuss important theoretical assumptions that implicitly guide the development and use of learning trajectories and progressions in mathematics education. We argue that diverse theoretical conceptualizations of what it means for a student to “learn” mathematics necessarily both constrains and amplifies what a particular learning trajectory can capture about the development of students’ knowledge.

The Role of Situational Interest in Personalized Learning

Context personalization—the incorporation of students’ out-of-school interests into learning tasks—has recently been shown to positively affect students’ situational interest and their performance and learning in mathematics. However, few studies have shown effects on both interest and achievement, drawing into question whether context personalization interventions can achieve both ends. The effects of personalization are theorized to result from activation of students’ prior knowledge of personal interests and generation of situational interest in math tasks, though theorists have begun to question whether situational interest serves as a mechanism by which learning outcomes are achieved. This experimental study examines whether personalizing 4 units of algebra problems that high school students (N = 150) solve in an intelligent tutoring system could improve their performance in units (i.e., accuracy and learning efficiency) and on classroom exams, whether adolescents who solved personalized problems would report greater situational interest in units (and later, individual interest in math) than peers who solved standard problems, and whether paths through situational interest would contribute to effects of personalization on outcomes. High school students in the personalization condition reported greater triggered situational interest in experimental units, and triggered interest predicted in-tutor outcomes (accuracy, learning efficiency). A total effect of personalization was also observed on classroom exam performance and individual interest in mathematics. Implications for theories of interest and context personalization are discussed, as are implications for math instruction and design of personalized learning environments.

Threading mathematics through symbols, sketches, software, silicon, and wood: Teachers produce and maintain cohesion to support STEM integration

ABSTRACT This classroom-based investigation sought to document how, in real time, STEM teachers and students attempt to locate the invariant mathematical relations that are threaded through the range of activities and representations in these classes, and how highlighting this common thread influences student participation and learning. The authors conducted multimodal discourse analyses of teacher–student interactions during multiday observations in 3 urban high school STEM classes. The focal lessons were in electrical engineering and mechanical engineering (within Project Lead the Way), and precollege geometry. Across 3 cases, teachers and students actively built and maintained cohesion of invariant mathematical relations across activities and representations. Pre- and postlesson interviews revealed that teachers intentionally managed cohesion to provide the continuity across the curricular activities that teachers believed would promote student understanding. The findings contribute to ways of fostering STEM integration and ways of grounding abstractions to promote meaning making and transfer.

Grounded and embodied mathematical cognition: Promoting mathematical insight and proof using action and language

We develop a theory of grounded and embodied mathematical cognition (GEMC) that draws on action-cognition transduction for advancing understanding of how the body can support mathematical reasoning. GEMC proposes that participants’ actions serve as inputs capable of driving the cognition-action system toward associated cognitive states. This occurs through a process of transduction that promotes valuable mathematical insights by eliciting dynamic depictive gestures that enact spatio-temporal properties of mathematical entities. Our focus here is on pre-college geometry proof production. GEMC suggests that action alone can foster insight but is insufficient for valid proof production if action is not coordinated with language systems for propositionalizing general properties of objects and space. GEMC guides the design of a video game-based learning environment intended to promote students’ mathematical insights and informal proofs by eliciting dynamic gestures through in-game directed actions.GEMC generates several hypotheses that contribute to theories of embodied cognition and to the design of science, technology, engineering, and mathematics (STEM) education interventions. Pilot study results with a prototype video game tentatively support theory-based predictions regarding the role of dynamic gestures for fostering insight and proof-with-insight, and for the role of action coupled with language to promote proof-with-insight. But the pilot yields mixed results for deriving in-game interventions intended to elicit dynamic gesture production. Although our central purpose is an explication of GEMC theory and the role of action-cognition transduction, the theory-based video game design reveals the potential of GEMC to improve STEM education, and highlights the complex challenges of connecting embodiment research to education practices and learning environment design.

Middle School Students' and Mathematicians' Judgments of Mathematical Typicality

K-12 students often rely on testing examples to explore and determine the truth of mathematical conjectures. However, little is known about how K-12 students choose examples and what elements are important when considering example choice. In other domains, experts give explicit consideration to the typicality of examples – how representative a given item is of a general class. In a pilot study, we interviewed 20 middle school students who classified examples as typical or unusual and justified their classification. We then gave middle school students and mathematicians a survey where they rated the typicality of mathematical objects in two contexts – an everyday context (commonness in everyday life) and a mathematical context (how likely conjectures that hold for the object are to hold for other objects). Mathematicians had distinct notions of everyday and mathematical typicality – they recognized that the objects often seen in everyday life can have mathematical properties that can limit inductive generalization. Middle school students largely did not differentiate between everyday and mathematical typicality – they did not view special mathematical properties as limiting generalization, and rated items similarly regardless of context. These results suggest directions for learning mathematical argumentation and represent an important step towards understanding the nature of typicality in math.

Personalizing Algebra to Students’ Individual Interests in an Intelligent Tutoring System: Moderators of Impact

Students experience mathematics in their day-to-day lives as they pursue their individual interests in areas like sports or video games. The present study explores how connecting to students’ individual interests can be used to personalize learning using an Intelligent Tutoring System (ITS) for algebra. We examine the idea that the effects of personalization may be moderated by students’ depth of quantitative engagement with their out-of-school interests. We also examine whether math problems designed to draw upon students’ knowledge of their individual interests at a deep level (i.e., actual quantitative experiences) or surface level (i.e., superficial changes to problem topic) have differential effects. Results suggest that connecting math instruction to students’ out-of-school interests can be beneficial for learning in an ITS and reduces gaming the system. However, benefits may only be realized when students’ degree of quantitative engagement with their out-of-school interests matches the depth at which the personalized problems are written. Students whose quantitative engagement with their interests is minimal may benefit most when problems draw upon superficial aspects of their interest areas. Students who report significant quantitative engagement with their interests may benefit most when individual interests are deeply incorporated into the quantitative structure of math problems. We also find that problems with deeper personalization may spur positive affective states and ward off negative ones for all students. Findings suggest depth is a critical feature of personalized learning with implications for theory and AI instructional design.