Informative tools for characterizing individual differences in learning: Latent class, latent profile, and latent transition analysis

This article gives an introduction to latent class, latent profile, and latent transition models for researchers interested in investigating individual differences in learning and development. The models allow analyzing how the observed heterogeneity in a group (e.g., individual differences in conceptual knowledge) can be traced back to underlying homogeneous subgroups (e.g., learners differing systematically in their developmental phases). The estimated parameters include a characteristic response pattern for each subgroup, and, in the case of longitudinal data, the probabilities of transitioning from one subgroup to another over time. This article describes the steps involved in using the models, gives practical examples, and discusses limitations and extensions. Overall, the models help to characterize heterogeneous learner populations, multidimensional learning outcomes, non-linear learning pathways, and changing relations between learning processes. The application of these models can therefore make a substantial contribution to our understanding of learning and individual differences.</p

Individual differences and change relationships between algebraic ability, working memory, and worry

© 2015 Dr. Kelly TreziseThe effects of emotion on cognition and of cognition on emotion are commonly examined separately. Anxiety-performance theorists, for example, claim that anxiety reduces available working memory (WM) capacity, and emotion regulation theorists claim that good working memory capacity allows emotions (e.g., anxiety) to be controlled. Since WM and anxiety have been implicated in math problem solving abilities, an explicit understanding of the reciprocal relationship between WM and anxiety would be beneficial for theories of math cognition. Currently, little is known whether the reciprocal interactions between WM and anxiety remain stable over time, are similar or different across individuals, are affected by contextual goals (studying for an exam), or different patterns of stability and/or change affect complex math problem solving differentially. To investigate these issues three studies examined the impact of WM-worry interactions on 14 year-olds’ algebraic problem solving. In Study 1, 80 students completed algebraic worry, algebraic WM, algebraic problem solving, non-verbal IQ and general math ability tasks. Worry level and WM capacity were subjected a latent profile analysis; four subgroups that differed in worry level and WM capacity were identified. Subgroup membership predicted algebraic problem solving accuracy: High WM/Low Worry > Moderate WM/Low Worry = Moderate WM/High Worry > Low WM/High Worry. The findings suggest a non-linear relationship between WM and worry relationship, and that WM-worry relationships predict algebraic problem solving abilities. The study suggests that individual differences in WM and worry interact, but indicate a different approach is required to separate the effects of WM and worry to identify their effects on each other, and their respective effects on algebraic problem solving. In Study 2, 137 students completed WM and algebraic worry tasks several times in a single day. A latent change model analysis examined the reciprocal influences of WM and worry over time, as well as their conjoint effects on an algebraic problem solving performance test. The findings showed WM decreased when worry was high, and worry increased when WM was low and WM and worry conjointly independently affected algebraic problem solving ability. The findings suggest that worry reduces WM capacity, and a good WM capacity helps to regulate worry, and that WM supports problem solving, while worry impairs problem solving ability. In Study 3, 126 students’ algebraic WM and algebraic worry were assessed twice in a single day. Latent transition analysis identified different patterns of WM/worry relationships. Subgroups differed in the degree to which WM and worry remained stable and/or changed across the two assessment occasions. For some subgroups, WM and worry remained stable across occasions and, for others, WM/worry relations changed. Moreover, subgroup membership predicted algebraic problem solving accuracy and response times. Overall, the findings show that individual differences in the stability/change patterns of WM/worry relationships are important predictors of math problem solving abilities. The pattern of findings suggests contemporary anxiety-cognition theories need to be amended to better account for individual differences in WM and anxiety. It is proposed that future research examine profiles of cognition-emotion relationships and their transitions over time, in order to characterise the cumulative effects of individual differences

Patterns of anxiety in algebraic problem solving in Australian adolescents: Athree-step latent variable analysis

Adolescents math anxiety is commonly assessed using questionnaires that identified the anxiety experienced solving arith-metic problems. A more nuanced understanding of math anxiety would be gained by investigating anxiety associated withmath problems encountered in school at the time they are encountered. To this end, we investigated the anxiety associ-ated with algebraic problem solving ability relationships in 129 14-year-olds. We varied problem difficulty and the timeallowed to solve problems, and assessed students anxiety concurrently as they solved problems. Latent variable mixturemodelling revealed meaningfully different patterns of algebra ability and anxiety relationships that changed as a functionof problem difficulty and time pressure. A second study, examining 257 13- to 15-year-olds, successfully replicated theStudy 1 findings. The results highlight the value of using latent variable analysis to identify subgroup patterns of abilitiesand caution against making overly general claims about the role of anxiety in math problem solving

Finding the subitizing in groupitizing: Evidence for parallel subitizing of dots and groups in grouped arrays

‘Groupitizing’ refers to the observation that visually grouped arrays can be accurately enumerated much faster than can unstructured arrays. Previous research suggests that visual grouping allows participants to draw on arithmetic abilities and possibly use mental calculations to enumerate grouped arrays quickly and accurately. Here, we address how subitizing might be involved in finding the operands for mental calculations in grouped dot arrays. We investigated whether participants can use multiple subitizing processes to enumerate both the number of dots and the number of groups in a grouped array. We found that these multiple subitizing processes can take place within 150 ms and that dots and groups seem to be subitized in parallel and with equal priority. Implications for research on mechanisms of groupitizing are discussed.<br

Characterizing Mathematics Anxiety and Its Relation to Performance in Routine and Adaptive Tasks

Mathematics anxiety hinders students' mathematical achievement already in primary school, but research on its effects beyond whole number knowledge is limited. The main aim of the current study is to examine how state and trait mathematics anxiety relate to performance across five tasks that are relevant for the development of mathematics in primary school, including a measure of adaptive expertise with school mathematics. These include mathematical tasks with non-symbolic quantities, whole numbers, and rational numbers. The participants were 406 primary school students attending the 5th grade (N = 188) and 6th grade (N = 218). Our results showed that state anxiety varies across task type. Furthermore, students' self-evaluated state and trait mathematics anxiety had varying negative relations with performance depending on the task type. In particular, we found that mathematics anxiety may limit students' adaptive expertise with rational numbers, even after controlling for other relevant mathematical skills. Overall, our results indicate that existing accounts on the role mathematics anxiety plays in school mathematics should expand to consider differences across task type and measures of anxiety

Procedural and conceptual confusion in a discovery-based digital learning environment

Confusion has been found beneficial to learning in specific conditions. However, the roles of procedural and conceptual confusion in such conditions are still unknown. This paper presents a preliminary study investigating the relationship between procedural and conceptual confusion and their impact on learning processes and outcomes in a non-challenging online task. Participants completed an online predict-observe-explain task on star lifecycles, which included a star simulation. One group watched a video tutorial on how to use the simulation prior to the task (n=22), while the control group did not (n=22). The tutorial group reported higher confidence and lower challenge in using the simulation compared to the control group. The tutorial group also reported higher confidence towards the concept being learnt than the control group, although no differences were found on concept challenge. However, these differences on conceptual and procedural confidence and challenge did not impact time spent on the simulation, use of self-regulatory skills or learning outcomes. Implications for future studies are discussed

Informative tools for characterizing individual differences in learning: latent class, latent profile, and latent transition analysis

This article gives an introduction to latent class, latent profile, and latent transition models for researchers interested in investigating individual differences in learning and development. The models allow analyzing how the observed heterogeneity in a group (e.g., individual differences in conceptual knowledge) can be traced back to underlying homogeneous subgroups (e.g., learners differing systematically in their developmental phases). The estimated parameters include a characteristic response pattern for each subgroup, and, in the case of longitudinal data, the probabilities of transitioning from one subgroup to another over time. This article describes the steps involved in using the models, gives practical examples, and discusses limitations and extensions. Overall, the models help to characterize heterogeneous learner populations, multidimensional learning outcomes, non-linear learning pathways, and changing relations between learning processes. The application of these models can therefore make a substantial contribution to our understanding of learning and individual differences

Writing analytics across essay tasks with different cognitive load demands

Essay tasks are a widely used form of assessment in higher education. Writing analytics can assist with challenges related to using essay tasks at scale and to identifying different issues in academic integrity. In this paper, we combined two techniques to investigate how students’ writing analytics varied across essay tasks with different cognitive load, considering both their typing behavior (i.e., writing process) and writing style (i.e., writing product). We also examined their relationship across these essay tasks. Findings showed that writing processes change across tasks with different cognitive load: when cognitive load increases, the interword intervals (indicator of planning and/or reviewing processes) increased, the burst length (indicator of translation processes) decreased, and the number of revisions per minute (indicator of reviewing processes) decreased. In contrast to the relation between the writing process and cognitive load, the relation between the writing product and cognitive load was found less clear. The results showed small and mixed effects of the tasks differing in cognitive load on the different writing product metrics. Hence, although the writing product follows from the writing process, the relation between cognitive load and the writing product and process appears to be less straightforward