Creativity research often relies on human raters to judge the novelty of participants’ responses on open-ended tasks, such as the Alternate Uses Task (AUT). Albeit useful, manual ratings are subjective and labor intensive. To address these limitations, researchers increasingly use automatic scoring methods based on a natural language processing technique for quantifying the semantic distance between words. However, many methodological choices remain open on how to obtain semantic distance scores for ideas, which can significantly impact reliability and validity. In this project, we propose a new semantic distance-based method, maximum associative distance (MAD), for assessing response novelty in AUT. Within a response, MAD uses the semantic distance of the word that is maximally remote from the prompt word to reflect response novelty. We compare the results from MAD with other competing semantic distance-based methods, including element-wise-multiplication—a commonly used compositional model—across three published datasets including a total of 447 participants. We found MAD to be more strongly correlated with human creativity ratings than the competing methods. In addition, MAD scores reliably predict external measures such as openness to experience. We further explored how idea elaboration affects the performance of various scoring methods and found that MAD is closely aligned with human raters in processing multi-word responses. The MAD method thus improves the psychometrics of semantic distance for automatic creativity assessment, and it provides clues about what human raters find creative about ideas.

Creative thinking is important for success in the fields of science, technology, engineering, and mathematics (STEM). Yet creativity in STEM is perhaps the most under-researched question in the creativity literature, with little known about the neurocognitive mechanisms supporting scientific creative thinking abilities, such as hypothesis generation. In the present functional magnetic resonance imaging study, undergraduate STEM majors (n = 47) completed a scientific hypothesis generation task (thinking of novel/plausible explanations for hypothetical scenarios) and a control task (thinking of synonyms to replace a word in a hypothetical scenario). Multivariate pattern analysis identified a whole-brain network supporting hypothesis generation, including hubs of the default (posterior cingulate cortex [PCC]), salience (right anterior insula [AI]), and semantic control (left inferior frontal gyrus [IFG]) networks. Using these network hubs as seed regions, we found increased between-network functional connectivity during hypothesis generation, including stronger coupling between semantic control (IFG) and posterior default regions (PCC and bilateral angular gyrus) and stronger coupling between salience (AI) and default regions, alongside weaker within-network functional connectivity. Our results indicate that scientific creative thinking involves increased cooperation among the default, salience, and control networks-similar to creative thinking in other domains-potentially reflecting a coordination of spontaneous/generative and controlled/evaluative processes to construct original explanations for scientific phenomena.

Women remain underrepresented in most math- intensive fields. [Breda and Napp, Proc. Natl. Acad. Sci. U.S.A. 116, 15435 (2019)] reported that girls' comparative advantage in reading over math (i.e., the intraindividual differences between girls' reading vs. math performance, compared to such differences for boys) could explain up to 80% of the gender gap in students' intentions to pursue math- intensive studies and careers, in conflict with findings from previous research. We conducted a conceptual replication and expanded upon Breda and Napp's study by using new global data (PISA2018, N = 466,165) and a recent US nationally representative longitudinal study (High School Longitudinal Study of 2009, N = 6,560). We coded students' intended majors and careers and their actual college majors. The difference between a student's math vs. reading performance explained only small proportions of the gender gap in students' intentions to pursue math- intensive fields (0.4 to 10.2%) and in their enrollment in math- intensive college majors (12.3%). Consistent with previous studies, our findings suggest girls' comparative advantage in reading explains a minority of the gender gap in math- related majors and occupational intentions and choices. Potential reasons for differences in the estimated effect sizes include differences in the operationalization of math- related choices, the operationalization of math and reading performance, and possibly the timing of measuring intentions and choices. Therefore, it seems premature to conclude that girls' comparative advantage in reading, rather than the cumulative effects of other structural and/or psychological factors, can largely explain the persistent gender gap in math- intensive educational and career choices.

The feelings of difficulty and familiarity (FOD and FOF) are two types of metacognitive experiences. Both may influence student engagement and the application of metacognitive strategies, but these relationships are not well understood, in part because many studies have relied on self-report measures of behaviors that may not accurately reflect students' actual behaviors. In this study, FOD and FOF were related to objective measures of off-task behaviors and metacognitive strategies. These measures were extracted from 88 sixth graders' action logs within a computer-based learning environment known as Betty's Brain. Pre- and post-tests were administered to assess learning. Results reveal that high-FOD students showed more off-task behaviors and fewer strategic behaviors than low-FOD students, particularly when this difference was measured in terms of the frequency (as opposed to proportion) of strategic behaviors. FOF was not associated with off-task behaviors and metacognitive strategies but emerged as a moderator in the relationship between FOD and learning gains. Low-FOD students learned more than high-FOD students in the low-FOF group, but such a difference was not found in the high-FOF group.

It is widely recognized that debugging is challenging for novice programmers and, as such, computing educators and researchers have called for explicit debugging instruction. Debugging requires various knowledge and skills, and different students may show different strengths and weaknesses. An understanding of such individual differences is important as it may guide personalized instruction. The current study investigated individual differences in debugging in an undergraduate introductory computer science course. We extracted variables related to debugging from students' submission traces to programming problems in the first month of the course. We applied latent profile analysis to these variables and identified three distinctive profiles. Profile A showed higher debugging accuracy and speed. Profile B showed lower debugging performance in runtime and logic errors, while profile C had lower performance in syntactic errors and tended to make large code edit every submission. Students' gender and self-rated programming ability predicted profile membership. Moreover, profile A got higher scores than the others in the first exam, and this difference persisted in the second and third exam, even controlling for background variables and score on the first exam. We investigated how students transitioned across debugging profiles over the duration of the course. From the beginning to the end of the course, a large part of students stayed in lower performance profiles. Overall, these findings support the call that debugging should be taught at an early stage and suggest that different groups may need different debugging instructions or support.

Although designed to prepare students for future coursework or to fulfill basic degree requirements, introductory math courses often serve as barriers to student success. In two double-blind randomized field experiments, we tested the efficacy of a utility-value intervention on improving community college students' perceived math relevance and achievement in introductory math courses. Building upon prior research, we examined whether the intervention particularly benefited first-generation and racially marginalized students. Study 1 (N = 696) was conducted before the COVID-19 pandemic and within in-person classrooms, whereas Study 2 (N = 1,318) was conducted during the pandemic and within virtual learning environments. Across Studies 1 and 2, students in the utility-value condition benefited more in terms of their perceived relevance compared to their peers in the control condition. Additionally, in both studies, math relevance mediated the effects of the intervention on math grades. In Study 2, with a larger sample, the positive effect of the intervention on math relevance was more pronounced for first-generation students. Our findings imply that community colleges could significantly improve students' academic experiences by investing in motivation-enhancing activities such as utility-value interventions in introductory math courses. This strategy could especially help first-generation students' academic achievement and retention rates.

Productive learning of algebra is supported when students reflect on multiple strategies, compare them and discuss the rationale behind and relative merits of particular strategies. Comparison and Discussion of Multiple Strategies (CDMS) is an instructional approach designed to support these processes in math classrooms. In the current study, 16 Algebra I teachers received professional development and supplemental materials to support CDMS when teaching a unit on linear equation solving and 475 of their students completed assessments of their linear equation solving knowledge before and after the unit. Thirteen Algebra I teachers and their 359 students were the business-as-usual control group. CDMS increased how often teachers engaged their students in comparison of multiple strategies, sustained small group work, and sustained mathematical discussions. Students in CDMS classrooms also had higher knowledge of linear equations on the posttest, particularly procedural flexibility, even after controlling for pretest knowledge and school demographic differences. Thus, encouraging teachers to regularly compare and discuss multiple strategies increases students' algebra learning. Findings highlight the need to expand theories of algebra learning to include attention to procedural flexibility, illustrate an instructional theory and method to promote broader learning about algebra, and provide evidence for effective instructional practices.

There is a need for a more robust conceptualization of engagement in mathematics education research. Investigating how teachers describe engagement can provide insight into relationships between purposes of engagement and dimensions of engagement. In this exploratory study, we examined how 28 secondary mathematics teachers in two states in the USA talked about their students' engagement. During interviews, we asked teachers to provide their definitions for engagement, describe their teaching strategies for engaging students, and describe their observations of engagement during a video clip from their own classroom. We interpreted teachers' talk to identify how they described the nature of mathematics engagement (dimensions such as behavioral, cognitive, affective, and/or social engagement) and purposes of engagement (engagement in learning or in schooling [Harris, 2011]). When teachers described the purpose of engagement as engagement in learning, they also tended to describe the nature of engagement with cognitive and social dimensions and with multiple dimensions of engagement.

Human languages can express an infinite number of thoughts despite having a finite set of words and rules. This is due, in part, to recursive structures, which allow us to embed one instance of a rule inside another. We investigated the origins of recursion by studying the development of Nicaraguan Sign Language (LSN), which emerged in the last 40 years and is not derived from any existing language. Before this, deaf individuals in Nicaragua lacked access to language models and each individual created their own gestural system, called homesign. We tested four groups: homesigners, who represent the point of origin, and the first three generations of LSN signers, who represent consecutive stages in the language's development. We used a task that was designed to elicit sentences with relative clauses, a device that allows for the recursive embedding of sentences inside of sentences (e.g., [the girl [who was drawing] removed the picture]). Signers in all three LSN cohorts consistently produced utterances that appeared to have embedded predicates (girl draw remove picture) which served the function of a relative clause (picking out the correct member of a set, based on previously mentioned information). Furthermore, in these utterances, the first verb was shorter than the second and shorter than the same verb in parallel unembedded structures. In contrast, homesigners produced similar utterances in embedded and unembedded contexts. They did not reintroduce previously mentioned information or produce reduced verb forms in the embedded context. These results demonstrate that syntactic embedding that is potentially recursive can emerge very early in a language. These embedded predicates, however, may not be widespread, or sys-tematically marked, in homesign systems. This raises the possibility that the emergence of recursive linguistic structure is a consequence of interaction within a language community. These findings pave the way for future work which investigates the syntactic form of these embedded predicates and explores whether multiple levels of embedding are possible.

Teachers' mathematical knowledge has important consequences for the quality of the learning environment they create for their students to learn mathematics. Yet relatively little is known about how teachers reason proportionally, despite the fact that proportional reasoning is foundational for several mathematics concepts and that ratios and proportional relationships constitute a major component of the middle school mathematics curriculum. In this study, we investigated how teachers reasoned proportionally on a nonroutine ratio task and the extent to which their proportional reasoning was able to predict their overall understanding of the relevant concepts: ratios and proportional relationships. Using data collected from 238 US mathematics teachers, we found that teachers' proportional reasoning could be grouped into four categories: incorrect, additive, relative, and proportional reasoning. Our results also indicated that teachers' overall knowledge of ratios and proportional relationships aligned with the way they reasoned proportionally, meaning that teachers who used incorrect reasoning on a separate task received the lowest scores on average on the ratios and proportional relationships measure, whereas those who reasoned proportionally had the highest mean scores on average. Implications of the study include the need to shift attention to the way teachers reason in relation to the two elements of proportional reasoning (covariance and invariance) to capture the nuances in their understanding of ratios and proportional relationships.