Intuitive and Informal Knowledge in Preschoolers’ Development of Probabilistic Thinking

Preschoolers develop a wide range of mathematical informal knowledge and intuitive thinking before they enter formal, goal-oriented education. In their everyday activities young children get engaged with situations that enhance them to develop skills, concepts, strategies, representations, attitudes, constructs and operations concerning a wide range of mathematical notions. Recently there is scientific interest in linking children’s informal and formal knowledge in order to provide them with opportunities to avoid biases aiming at formulating, perceiving, reflecting on and exercising probabilistic notions. The current study investigates preschoolers’ (N=90) intuitive understanding of the likelihood of events in a probabilistic task with spinners. Participants, at the age of 4 to 6, are tested on their predictions of the most probable outcome prior to and after an instructive session of reasoning. The probabilistic task, based on constructivist principles, includes methodological alterations concerning the sample space and the themes of the stimuli. Educational implications are further discussed under the general point of view that in order to link informal to formal mathematical learning in preschool classroom, the subject content and the cognitive capacity of children are important to match

Foundations of academic knowledge

This chapter assesses the acquisition of academic knowledge and skills in domains including literacy, numeracy, sciences, arts and physical education. It examines how learning trajectories arise from complex interactions between individual brain development and sociocultural environments. Teaching literacy and numeracy to all students is a goal of most school systems. While there are some fundamental skills children should grasp to succeed in these domains, the best way to support each student’s learning varies depending on their individual development, language, culture and prior knowledge. Here we explore considerations for instruction and assessment in different academic domains. To accommodate the flourishing of all children, flexibility must be built into education systems, which need to acknowledge the diverse ways in which children can progress through learning trajectories and demonstrate their knowledge

Expression of the transcription factor Hes3 in the mouse and human ocular surface, and in pterygium

Purpose: In this work we examined the presence of the neural stem cell biomarker Hairy and Enhancer of Split 3 (Hes3) in the anterior eye segment and in the aberrant growth condition of the conjunctiva pterygium. Further, we studied the response of Hes3 to irradiation. Materials and methods: Adult mouse and human corneoscleral junction and conjunctiva, as well as human pterygium were prepared for immunohistochemical detection of Hes3 and other markers. Total body irradiation was used to study the changes in the pattern of Hes3 expression. Results: The adult rodent and human eye as well as pterygium, contain a population of cells expressing Hes3. In the human eye, Hes3-expressing (Hes3+) cells are found predominantly in the subconjunctival space spanning over the limbus where they physically associate with blood vessels. The cytoarchitecture of Hes3 + cells is similar to those previously observed in the adult central nervous system. Furthermore, irradiation reduces the number of Hes3 + cells in the subconjunctival space. In contrast, irradiation strongly promotes the nuclear localization of Hes3 in the ciliary body epithelium. Conclusions: Our results suggest that a recently identified signal transduction pathway that regulates neural stem cells and glioblastoma cancer stem cells also operates in the ocular surface, ciliary body, and in pterygium

Lessons Learned from 10 Experiments That Tested the Efficacy and Assumptions of Hypothetical Learning Trajectories

Although reformers have embraced learning trajectories (LT, also called learning progressions) as an important tool for improving mathematics education, the efficacy and assumptions of LT-based instruction are largely unproven. The aim of a recently completed research project was to fill this void. Fulfilling this aim was more challenging than many supporters of LT-based instruction might imagine. A total of 10 experiments were untaken, of which 5 demonstrated that LT-based instruction was significantly more efficacious than a counterfactual involving either a Teach-to-Target/Skip-Level approach (Assumption 1) or the same unordered activities (Assumption 2). The results of the remaining studies were non-significant either for theoretical (2) or methodological (3) reasons. In the five indicating LTs’ efficacy, we found that some LTs consists of levels that are facilitative conditions for the next higher level and, thus, may be helpful but perhaps not necessary for the subsequent level

What Is the Long-Run Impact of Learning Mathematics During Preschool?

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention‐produced change at age 4 is associated with a 0.24‐SD gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly controlled ordinary least squares (OLS) regression models (Claessens et al., 2009; Watts et al., 2014) using national data sets. Implications for developmental theory and practice are discussed

Risky business: Correlation and causation in longitudinal studies of skill development.

Developmental theories often posit that changes in children's early psychological characteristics will affect much later psychological, social, and economic outcomes. However, tests of these theories frequently yield results that are consistent with plausible alternative theories that posit a much smaller causal role for earlier levels of these psychological characteristics. Our article explores this issue with empirical tests of skill-building theories, which predict that early boosts to simpler skills (e.g., numeracy or literacy) or behaviors (e.g., antisocial behavior or executive functions) support the long-term development of more sophisticated skills or behaviors. Substantial longitudinal associations between academic or socioemotional skills measured early and then later in childhood or adolescence are often taken as support of these skill-building processes. Using the example of skill-building in mathematics, we argue that longitudinal correlations, even if adjusted for an extensive set of baseline covariates, constitute an insufficiently risky test of skill-building theories. We first show that experimental manipulation of early math skills generates much smaller effects on later math achievement than the nonexperimental literature has suggested. We then conduct falsification tests that show puzzlingly high cross-domain associations between early math and later literacy achievement. Finally, we show that a skill-building model positing a combination of unmeasured stable factors and skill-building processes can reproduce the pattern of experimental impacts on children's mathematics achievement. Implications for developmental theories, methods, and practice are discussed. (PsycINFO Database Recor

Risky Business: Correlation and Causation in Longitudinal Studies of Skill Development.

Developmental theories often posit that changes in children’s early psychological characteristics will affect much later psychological, social, and economic outcomes. However, tests of these theories frequently yield results that are consistent with plausible alternative theories that posit a much smaller causal role for earlier levels of these psychological characteristics. Our article explores this issue with empirical tests of skill-building theories, which predict that early boosts to simpler skills (e.g., numeracy or literacy) or behaviors (e.g., antisocial behavior or executive functions) support the long-term development of more sophisticated skills or behaviors. Substantial longitudinal associations between academic or socioemotional skills measured early and then later in childhood or adolescence are often taken as support of these skill-building processes. Using the example of skill-building in mathematics, we argue that longitudinal correlations, even if adjusted for an extensive set of baseline covariates, constitute an insufficiently risky test of skill-building theories. We first show that experimental manipulation of early math skills generates much smaller effects on later math achievement than the nonexperimental literature has suggested. We then conduct falsification tests that show puzzlingly high cross-domain associations between early math and later literacy achievement. Finally, we show that a skill-building model positing a combination of unmeasured stable factors and skill-building processes can reproduce the pattern of experimental impacts on children’s mathematics achievement. Implications for developmental theories, methods, and practice are discussed