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

Early number and arithmetic performance of Ecuadorian 4-5-year-olds

This study aimed at (a) constructing a reliable and valid test to assess Ecuadorian 4–5-year olds’ number and arithmetic skills; (b) providing empirical data on Ecuadorian 4–5-year olds’ number and arithmetic skills; and (c) confronting these children’s actual performances with the performances expected by national experts in this domain. We administered the Test of Early Number and Arithmetic (TENA), developed on the basis of the Ecuadorian mathematics standards to 86 Preschoolers and 127 Kindergartners and asked 10 experts to evaluate TENA’s validity and predict children’s performances on it. Results supported the overall reliability and validity of the TENA. Furthermore, we observed differences in number and arithmetic competencies between and within Preschoolers and Kindergartners, but not between boys and girls. Finally, experts overestimated children’s performances on the test. The scientific and practical implications of these results are discussed

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

Efficacy of a Learning Trajectory Approach Compared to a Teach-to-target Approach for Addition and Subtraction

Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a “LT approach”—that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child’s present level of thinking. The present report serves to address the question: Is it necessary to teach each contiguous level of a LT or can instruction be similarly or more effective when skipping levels, provided the necessary exemplars are made? In a multimethod research study that included individual teaching experiments embedded inside of a quasi-experimental research design, one group of 13 kindergartners received instruction based on an empirically-validated LT for addition and subtraction (the “LT” treatment). The counterfactual, “skip” treatment (n = 12), received instruction focused mainly on levels at least two levels above their present level for the same amount of time as the LT treatment. More children in the LT treatment exhibited greater addition and subtraction learning during sessions and from pretest to posttest than children in the skip treatment. Implications for future study are discussed

Lean methods applied above floor

Thesis (M.B.A.)--Massachusetts Institute of Technology, Sloan School of Management, 1999.Includes bibliographical references (leaf 55).Investigate the feasibility of implementing productivity improvement processes such as lean methods to the product development phase of major military aircraft programs. The study concentrated on the understanding of the current state of the industry from the point of view of the customer as well as the contractor team The primary source of information was a number of interviews with executives from the Aerospace Industry. The major obstacles to the implementation of lean methods were discussed and the current industry implementation status was described. Using the acquired knowledge, two system dynamics casual loop models were developed to enhance the understanding of the extremely complex product development process as well as a framework designing the process of incorporation of lean principles to a major program development. The first model described the macro view of a program and identified external forces acting on the product development process. The second model described a micro view of the product development cycle concentrating on activities internal to a program Utilizing the models and the framework, possible intervention points were identified which could enhance the successful implementation and sustain of leanflean methods. The focus of the thesis was to concentrate on managing the product development cycle time as the key indicator of the overall performance of the program The current st.ate of the industry appears to experience longer and longer development cycles, which leads to financial and political strain. Results show that application of lean methods to activities off the manufacturing floor is feasible with the premise that understanding of the overall system dynamics is essential to the implementation of successful measures.by Jorge F Gonzalez and Thomas J Sarama.M.B.A

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