*Leitung: Maartje Raijmakers*

Individual differences in developmental and educational context are considered to be of great importance at multiple levels of the educational system from policy makers to teachers. Teachers might want to adapt education to individual differences (Hattie, 2009), policy makers might want to create a school context that avoids large individual differences (Unicef, 2018).

There are different methodologies to better understand individual differences in learning and development. One approach towards understanding the origin of these individual differences is to relate them to meaningful individual characteristics, such as IQ or SES. This group level approach does not necessarily tell us a lot about what individual children are actually doing, such that interventions can be adapted to it. At the other end of the spectrum, n = 1 models can describe the dynamics of individual learning and developmental processes on the basis of, usually high-density time series (e.g., Hamaker & Wichers, 2017). This, relatively new approach does not necessarily show us general mechanisms of learning and development of the whole sample. In the symposium we will focus on a methodology in between these two ends of the spectrum: modeling latent subgroups of individuals that show similar behavior.

The application of latent variable mixture models (e.g., McMullen & Hickendorff, 2018) reveals latent solution strategies that apply to a limited number of subgroups in the sample. These solution strategies do not necessarily need to be fully specified a priori. In this way, strategies of different achievement levels can be inferred from a sample of children showing important individual differences. In this way, meaningful variation (in terms of different solution strategies) is separated from noise. In addition, these techniques allow to separate unsystematic behavior, such as guessing due to limited understanding of the task, from more systematic behavior.

In the symposium several examples will be presented, with latent variable mixture models describe different solution strategies within a sample of children. Different types of models will pass in review aiming to present inspiring examples for different learning and developmental contexts.

- • Maartje Raijmakers
^{1,2}& Linde Lichtenberg^{1}(^{1}Dept. of Psychology, University of Amsterdam;^{2}Vrije UniversiteitAmsterdam) - Johanna van Schaik, Tessa Slim, Rooske Franse, & MaartjeRaijmakers (
^{1}Dept. of Psychology, University of Amsterdam;^{2}Vrije Universiteit Amsterdam). - Christopher Osterhaus
^{1}, Erika Stauss^{2}, & Martha W. Alibali^{2 }(^{1}Ludwig-Maximilians-Universität München,^{2}University of Wisconsin-Madison) - Peter Edelsbrunner
^{1}, Hanna Grimm^{2}, Kornelia Möller^{3}(^{1}ETH Zurich,^{2}University of Münster,^{3}University of Münster).

**Modeling feedback learning in preschoolers with hidden Markov models**

**Maartje Raijmakers ^{1,2} & Linde Lichtenberg^{1}**

^{1}Dept. of Psychology, University of Amsterdam; ^{2}Educational Sciences, Vrije Universiteit Amsterdam

Learning form feedback is an important ability in daily life, but develops at least until late childhood (e.g., van Duijvenvoorde et al., 2006; Minda, Desroches & Church, 2008; Schmittmann et al., 2012). However, very little is known about the underlying abilities that are related to feedback learning in preschoolers, especially the youngest children. For example, cognitive flexibility seems crucial to test hypotheses, but also inhibitory control and short-term memory might also be important (Zelazo, 2006). Another important aspect might be the way feedback is provided (Bohlman & Fenson, 2005; Espinet, Anderson & Zelazo, 2013; van Bers et al., 2014). In the current research we tested several hypotheses regarding preschoolers’ difficulty in hypothesis testing. To this end, we designed very easy hypothesis-testing tasks, such that performance differences of 3- and 4 years old children would consist of their solution efficiency. Solution strategies are modeled with latent variable models that account for both intra- and inter-individual differences. To this end, we developed latent markov models with individual characteristics as covariates on the learning (and perseveration) parameters. These models can account for changes of responses within a learning process (e.g., pre-solution and solution phase) and individual differences in learning paths between individuals. Modeling the data allows to test hypotheses concerning the specific relation between subprocesses of hypothesis testing and individual levels of executive functioning.

Two specific experiments will be discussed with newly developed hypothesis testing tasks, based on the format of computerized Dimensional Change Card Sorting task (DCCS; Zelazo, 2006; van Bers et al., 2011; under review). With the outcomes of Experiment 1 we preregistered models and hypotheses for Experiment 2.

The hypotheses were that 1) Type of feedback is related to task difficulty; 2) Even in 3-year old preschoolers different learning paths will be found: efficient hypothesis testing, inefficient hypothesis testing, and continued random responding; 3) executive functions are specifically related to learning parameters of both the efficient and inefficient learning mode.

**Latent class analyses of children’s learning about buoyancy: The effect of object variability on children’s predictions and explanations of floating and sinking **

**J.E. van Schaik ^{2}, T. Slim^{2}, R.K. Franse^{1}, & M.E.J. Raijmakers^{1}**

^{1} Educational Sciences, Vrije Universiteit Amsterdam, ^{2}Dept. of Psychology, University of Amsterdam

**Introduction**

This study investigates how the type of objects used during hands-on exploration of buoyancy influences children’s learning.We employ latent regression analyses to determine whether different learning patterns exist and to identify how these patterns differently incorporate object dimensions to predict and explain buoyancy.

**Methods**

Four- to nine-year-olds (n=191) were given either a set of systematically varied cubes (i.e. systematic condition) or a set of common objects (i.e. not systematic condition) to test in a water basin. The water basin and objects were subsequently removed, and children were asked to predict whether each of a test set of ten new objects (i.e. five cubes, five common objects; random order) would float or sink. Then, children were asked to explain their predictions.

**Results**

With respect to the predictions, children in the systematic condition were more accurate in their predictions of the cubes than children in the not systematic condition, while the conditions did not differ significantly in their performance on the common objects. To better understand which features children used to make their predictions, the data are being analyzed with Latent Class Regression Analyses. Preliminary results indicate that three classes can be detected and that children in the systematic condition are more likely to belong to a class in which mass and volume of cubes are both considered, while children in the not systematic condition are more likely to belong to a class in which mass is given more predictive load than volume. With respect to the explanations, these were coded for the occurrence of five types (i.e. irrelevant, facts, mass or volume, material, mass and volume), such that multiple codes could be allocated to one explanation. Whereas the conditions do not differ in how many types of explanations children gave, preliminary results from Latent Class Analyses suggest there are classes of explanation patterns of the cubes that differ in the extent to which both mass and volume are mentioned.

**Conclusion**

Thus far, the findings indicate that latent analyses provide a mechanistic insight into how children understand buoyancy that goes beyond the findings of typical statistical analyses. Letting children experiment with systematically varied cubes instead of common objects seems to lead to a better integration of mass and volume in their subsequent predictions, and to a lesser extent explanations, of novel cubes’ buoyancy.

**Discovering data-interpretation strategies through latent class analysis**

*Christopher Osterhaus ^{1}, Erika Stauss^{2}, & Martha W. Alibali^{2}*

^{1 }Ludwig-Maximilians-Universität München, ^{2}University of Wisconsin-Madison

Data-interpretation skills are an important ability in modern knowledge societies. This aspect of scientific reasoning, however, is difficult: Children and adults struggle with the interpretation of covariation evidence. The present study investigates the strategies that reasoners use when they interpret data that is presented in contingency tables, and it examines the factorsthat contribute to adequate strategy use. Altogether 233 participants (50 sixth and seventh graders, 183 undergraduates) interpreted 13 contingency tables, and, in addition, they were assessed for their mathematics skills, their metaconceptual understanding of the nature of science (what is science about?), and their experimentation skills (what makes a good experiment?). General information-processing skills (inhibition, working memory, and language skills) were measured as control variables. The middle-schoolers interpreted on average 9 of the 13 contingency tables correctly (*SD* = 3), the adults 10 (*SD *= 3). A latent class analysis confirmed earlier findings from a study with adults (Osterhaus, Magee, Saffran, & Alibali, 2019, Quarterly Journal of Experimental Psychology) and it revealed three distinct strategies: *compare two* (middle-schoolers: 24%, adults: 13%); *anchor and compare* (middle-schoolers: 46%, adults: 39%); and *compare conditional probabilities *(middle-schoolers: 30%, adults: 48%). Compare two and compare conditional probabilities are strategies that have previously been reported in the literature; anchor and compare emerged as a novel strategy in our studies that used the latent class approach. There was a significant partial correlation between the number of correct contingency interpretations and participants’ experimentation skills that was independent of the influences of the cognitive control variables. For the subsample of middle-schoolers, there were significant relations between correct strategy use (compare conditional probabilities) andmathematics and experimentation skills. Our results confirm earlier findings on diverse strategy use in the interpretation of contingency tables andthey suggest that children’s ability to interpret such data depends on their mathematics and experimentation skills. Our study highlights the usefulness of latent variables mixture models for describing distinct strategy use in scientific reasoning and it shows how this approach can help to better understand the mechanisms that are involved in learning and development.

**Application of a Latent Transition Analysis to Model the Interaction of Instructional Scaffolding with Prior Knowledge and Inhibition in Third-Graders’ Acquisition of Hypothesis-Based Reasoning**

*Peter Edelsbrunner, ETH Zurich, peter.edelsbrunner@ifv.gess.ethz.ch*

*Hanna Grimm, University of Münster, hanna.grimm@uni-muenster.de*

*Kornelia Möller, University of Münster, kornelia.moeller@uni-muenster.de*

Inquiry skills such as hypothesis-based reasoning have become an integral part of modern elementary school curricula in many countries. The teaching of these skills at this early stage of education, however, is demanding, particularly in groups of students with heterogeneous learning preconditions. One promising approach for meeting heterogeneous student preconditions is instructional scaffolding. In the present study, a mixture model, specifically a latent transition analysis, is applied to examine the interaction of instructional scaffolding with student preconditions in the learning of hypothesis-based reasoning. Within an inquiry-based learning setting, *N* = 143 third graders underwent either an experimental condition in which they received explicit scaffolds to foster hypothesis-reasoning, or a control condition in which they did not receive those additional scaffolds. Employing the latent transition analysis, supported by a non-linear regression model, it is examined how the additional scaffolds interacted with students’ prior knowledge and inhibition ability. The latent transition analysis shows how students in both conditions switch between different learning states that are characterized by their levels of expertise in reasoning based on evidence that either supports, rejects, or is irrelevant for a hypothesis. It is found that the additional scaffolds manage to meet the needs of students with little prior knowledge; under the control condition, students with little prior knowledge showed decreased learning achievement, while under the experimental condition, students with differing prior knowledge learned to a similar extent and on a higher level. The scaffolds also supported students with high inhibition ability in mastering the most difficult aspect of reasoning based on hypothesis-irrelevant evidence. These analyses shed new light on theories about how to accommodate heterogeneity in groups of learners, and prior findings about expertise reversal effects. It is discussed to which degree the latent transition analysis worked out within this experimental sample of typical size, and what more common alternative statistical analyses such us multiple regression and regular structural equation modeling (do not) show about students’ learning.