Although we cannot see or touch time, across many cultures, we use spatial representations to think about this abstract concept. Spatial representations of time are thought to support temporal concepts that might otherwise be difficult to represent and reason about, such as the temporal component of episodic memory. One common form of spatially representing time is the mental timeline, which is a linear projection of time onto space. Adults and older children from many cultures spontaneously activate the mental timeline when remembering the order of events. However, the mental timeline develops slowly throughout early childhood as children gain increasing experience with formal schooling and cultural artifacts. Here, we explored how individual differences in the development of American children's mental timelines relate to their memory for temporal order (N = 96, Mage = 6.22 years). We first tested children's memory for the order and location of events through a memory task involving short videos. We then tested children's spontaneous spatial representations of temporal order using an open-ended timeline construction task. The linearity of children's timeline arrangements predicted their memory for temporal order but not memory for locations: children who spontaneously represented time linearly had significantly better temporal memory performance than children who represented time nonlinearly, but there was no difference in location memory performance. These data provide preliminary evidence that the development of the mental timeline may support the development of temporal memory.

Promoting equitable classrooms is a goal of postsecondary mathematics education, but there is still limited research on how faculty learn to teach more equitably. Despite the variety of techniques developed in primary and secondary education, there has been less use in higher education. This manuscript focuses on the 'assigning competence' technique from Complex Instruction, and how it can disrupt gender inequities in postsecondary mathematics. This manuscript draws on video data, coded classroom observations, recorded debrief sessions, and faculty interviews to illustrate faculty learning and the impact on student participation.

Motivating girls to enroll in computer science (CS) courses is critically important. Stereotypes that girls are less interested than boys in CS may deter girls. Three preregistered experimental studies (N = 1,053) examined causal links between gender-interest stereotypes and middle school students' CS motivation. Experiment 1 showed that stereotypes reduced girls' motivation to enroll, mediated by a lower sense of belonging. Experiment 2 showed that underrepresentation is a cue to stereotypes. Experiment 3 demonstrated that providing information about other girls' interest countered stereotypes and promoted motivation. Directly addressing stereotypes may be instrumental in promoting equity for all in CS.

Users of forced-choice questionnaires (FCQs) to measure personality commonly assume statement parameter invariance across contexts – between Likert and forced-choice (FC) items and between different FC items that share a common statement. In this paper, an empirical study was designed to check these two assumptions for an FCQ assessment measuring interpersonal and intrapersonal skills. We compared parameters of common statements between two Likert forms and two FCQ forms with a block size of two (statement pairs) and among five FCQ pair forms. In three of the five FCQ forms, statements were paired only with a statement they had appeared with in a triplet block. In the other two FCQ forms, statements were paired with statements they had not been paired with in a triplet block. This design allows us to evaluate statement parameter changes due to changes in context. The results do not support the statement parameter invariance assumption between Likert and FC items or the assumption between FC items when recombining statements form new items. However, the assumption between FC items was generally held for pairs formed by dropping a statement from a triplet item. There were some suggestions for sources of context effects, but the analyses were not definitive. Implications of the findings for test practice are discussed.

One reason mathematical modeling remains highly challenging for students is because it requires knowledge about both mathematics and the real-world. Recent work suggests promoting the learning of mathematical modeling as conceiving quantities and establishing relationships among quantities could help students overcome the challenges they experience. While promising, this approach may be oversimplistic in its claims. Through analyzing data collected via a teaching experiment methodology, we present one student’s (Szeth’s) work on two tasks to illustrate how Szeth’s reasoning with quantities was limited during his model construction process in the following ways: Szeth (i) used already constructed mathematical expressions to reason about how quantities vary, and (ii) did not construct a mathematically correct expression despite having reasoned with quantities. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

In this chapter, we address the problem of why blockages occur during mathematization by introducing a method for studying mathematizing based in quantitative reasoning. We report on interview data with six tertiary STEM majors as they developed models of the population dynamics of cats and birds in a backyard habitat. Our analysis focused on real-world relationships participants tried to express when using a given arithmetic operation in a predator–prey modeling task. Our results reveal the conceptions of × participants used to justify their models when constructing an expression for the decrease in the bird population. We conclude by discussing the method’s utility for studying mathematization and with conjectures on how instructors might leverage participants’ justifications to scaffold their emergent models toward a conventionally correct model. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

Self-regulated learning (SRL), or the ability for a learner to monitor and change their cognitive, affective, metacognitive, and motivational processes, is a critical skill to enact, especially while learning about difficult topics within an intelligent tutoring system (ITS). Learners' enactment of SRL behaviors during learning with ITSs has been extensively studied within the human-computer interaction field but few studies have examined the extent to which learners' SRL behaviors quantitatively demonstrate a functional system (i.e., equilibrium of repetitive and novel behaviors). However, current analytical approaches do not evaluate how the functionality of learners' SRL behaviors unfolds as time on task progresses. This paper reviews two analytical approaches, both based within categorical auto-recurrence quantification analysis (aRQA), for examining how learners' SRL complex behaviors emerge during learning with an ITS. The first approach, binned categorical aRQA, segments learners' SRL behaviors into bins and performs categorical aRQA on the SRL behaviors enacted within those bins to produce metrics of complexity that demonstrate how learners' functionality of their SRL systems change over time. The second approach, cumulative categorical aRQA, continuously calculates complexity metrics as learners enact SRL behaviors to identify the evolution of learners' functional SRL. These two approaches allow researchers to identify how the functionality of SRL behaviors change over time in relationship to the occurrences within the ITS environment. From this discussion, we provide actionable implications for contributing to how learners' SRL functionality can be visualized and scaffolded during learning with an ITS.

A key aim for science education is the improvement of scientific reasoning through inquiry-based learning which asks students to think and act like scientists. This requires the regulation of specific skills and abilities such as identifying problems, generating hypotheses and evidence, and drawing conclusions. Goal setting and planning can help learners regulate their learning as they engage with scientific inquiry, especially within investigative exploration. Contemporary work on scaffolds for science inquiry-learning requires we (1) understand how students set goals and plans, (2) measure the quality of goals and plans, and (3) develop adaptive intelligent goal and planning scaffolds. This paper presents the development of a new planning scaffold used by 101 middle school students during interactions with CRYSTAL ISLAND, a game-based learning environment designed to teach students about microbiology and through scientific inquiry. We map student goals and plans from the scaffold to a series of epistemic scientific reasoning activities to use in conjunction with online trace data of student behaviors to analyze student goal setting and planning constructed throughout the game. This study describes the development of an analytical mapping approach between (sub)goals and (sub)activities to measure student plan quality build using a planning scaffold. We report on the use of the scaffold as well as implications for future development of an adaptive and intelligent version of the tool. This work highlights that online-trace data should be contextualized to (sub)goals, and the design of intelligent and adaptive goal and planning tools should be dynamic to account for open-ended exploration that differs across learners.

This work investigates how tutoring discourse interacts with students' proximal knowledge to explain and predict students' learning outcomes. Our work is conducted in the context of high-dosage human tutoring where 9th-grade students (N = 1080) attended small group tutorials and individually practiced problems on an Intelligent Tutoring System (ITS). We analyzed whether tutors' talk moves and students' performance on the ITS predicted scores on math learning assessments. We trained Random Forest Classifiers (RFCs) to distinguish high and low assessment scores based on tutor talk moves, student's ITS performance metrics, and their combination. A decision tree was extracted from each RFC to yield an interpretable model. We found AUCs of 0.63 for talk moves, 0.66 for ITS, and 0.77 for their combination, suggesting interactivity among the two feature sources. Specifically, the best decision tree emerged from combining the tutor talk moves that encouraged rigorous thinking and students' ITS mastery. In essence, tutor talk that encouraged mathematical reasoning predicted achievement for students who demonstrated high mastery on the ITS, whereas tutors' revoicing of students' mathematical ideas and contributions was predictive for students with low ITS mastery. Implications for practice are discussed.

We conducted a 2 x 2 study comparing the digital learning game Decimal Point to a comparable non-game tutor with or without self-explanation prompting. We expected to replicate previous studies showing the game improved learning compared to the non-game tutor, and that self-explanation prompting would enhance learning across platforms. Additionally, prior research with Decimal Point suggested that self-explanation was driving gender differences in which girls learned more than boys. To better understand these effects, we manipulated the presence of self-explanation prompts and incorporated a multidimensional gender measure. We hypothesized that girls and students with stronger feminine-typed characteristics would learn more than boys and students with stronger masculine-typed characteristics in the game with self-explanation condition, but not in the game without self-explanation or in the non-game conditions. Results showed no advantage for the game over the non-game or for including self-explanation, but an analysis of hint usage indicated that students in the game conditions used (and abused) hints more than in the non-game conditions, which in turn was associated with worse learning outcomes. When we controlled for hint use, students in the game conditions learned more than students in the non-game tutor. We replicated a gender effect favoring boys and students with masculine-typed characteristics on the pretest, but there were no gender differences on the posttests. Finally, results indicated that the multidimensional framework explained variance in pretest performance better than a binary gender measure, adding further evidence that this framework may be a more effective, inclusive approach to understanding gender effects in game-based learning.