Logical Thinking Research Papers - Academia.edu (original) (raw)

Inductive learning is impossible without overhypotheses, or constraints on the hypotheses considered by the learner. Some of these overhypotheses must be innate, but we suggest that hierarchical Bayesian models can help to explain how the... more

Inductive learning is impossible without overhypotheses, or constraints on the hypotheses considered by the learner. Some of these overhypotheses must be innate, but we suggest that hierarchical Bayesian models can help to explain how the rest are acquired. To illustrate this claim, we develop models that acquire two kinds of overhypotheses – overhypotheses about feature variability (e.g. the shape bias in word learning) and overhypotheses about the grouping of categories into ontological kinds like objects and substances.

The problem of how to distribute available resources among members of a group is a central aspect of social life. Adults react negatively to inequitable distributions and several studies have reported negative reactions to inequity also... more

The problem of how to distribute available resources among members of a group is a central aspect of social life. Adults react negatively to inequitable distributions and several studies have reported negative reactions to inequity also in non-human primates and dogs. We report ...

We tested whether individual differences in a component of early conscience mediated relations between parental discipline and externalizing behavior problems in 238 3.5-year-olds. Parents contributed assessments of discipline practices... more

We tested whether individual differences in a component of early conscience mediated relations between parental discipline and externalizing behavior problems in 238 3.5-year-olds. Parents contributed assessments of discipline practices and child moral regulation. Observations of children's behavioral restraint supplemented parental reports. Parents and teachers reported on child externalizing symptoms. Parental induction, warm responsiveness, and less frequent use of physical punishment generally were associated with higher levels of moral regulation and fewer externalizing problems. Moreover, moral regulation partially mediated relationships between discipline and externalizing symptoms, with the clearest case of mediation involving induction. However, relationships were found for boys only. Results support a mediation model wherein inductive and physical discipline may influence the expression of boys' externalizing behavior through effects on conscience. Finally, results suggest that different developmental processes may be associated with early externalizing problems in boys and girls, and confirm that fathers' reports contribute to our understanding of the origins of child externalizing problems.

Abstract: This Research & Policy Brief addresses the aspect of the teacher support system that is perhaps the most important and often the most weakly implemented: teacher learning and development. This brief includes the following to... more

Abstract: This Research & Policy Brief addresses the aspect of the teacher support system that is perhaps the most important and often the most weakly implemented: teacher learning and development. This brief includes the following to help state and district leaders select ...

Dynamic geometry software provides tools for students to construct and experiment with geometrical objects and relationships. On the basis of their experimentation, students make conjectures that can be tested with the tools available. In... more

Dynamic geometry software provides tools for students to construct and experiment with geometrical objects and relationships. On the basis of their experimentation, students make conjectures that can be tested with the tools available. In this paper, we explore the role of software tools in geometry problem solving and how these tools, in interaction with activities that embed the goals of teachers and students, mediate the problem solving process. Through analysis of successful student responses, we show how dynamic software tools can not only scaffold the solution process but also help students move from argumentation to logical deduction. However, by reference to the work of less successful students, we illustrate how software tools that cannot be programmed to fit the goals of the students may prevent them from expressing their (correct) mathematical ideas and thus impede their problem solution.

Across four studies, we directly compared children’s essentialist reasoning about the stability of race and language throughout an individual’s lifespan. Monolingual English-speaking children were presented with a series of images of... more

Across four studies, we directly compared children’s essentialist reasoning about the stability of race and language throughout an individual’s lifespan. Monolingual English-speaking children were presented with a series of images of children who were either White or Black; each face was paired with a voice clip in either English or French. Participants were asked which of two adults each target child would grow up to be – one who was a ‘match’ to the target child in race but not language, and the other a ‘match’ in language but not race. Nine- to 10-year-old European American children chose the race-match, rather than the language-match. In contrast, 5–6-year-old European American children in both urban, racially diverse, and rural, racially homogeneous environments chose the language-match, even though this necessarily meant that the target child would transform racial categories. Although surprising in light of adult reasoning, these young children demonstrated an intuition about the relative stability of an individual’s language compared to her racial group membership. Yet, 5–6-year-old African American children, similar to the older European American children, chose the race-match, suggesting that membership in a racial minority group may highlight children’s reasoning about race as a stable category. Theoretical implications for our understanding of children’s categorization of human kinds are discussed.

There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge of proof, but limited research has examined this knowledge. This paper... more

There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating preservice elementary and secondary school mathematics teachers’ knowledge of proof by mathematical induction. This research can inform the knowledge about preservice teachers that mathematics teacher educators need in order to effectively teach proof to preservice teachers. Our analysis is based on written responses of 95 participants to specially developed tasks and on semi-structured interviews with 11 of them. The findings show that preservice teachers from both groups have difficulties that center around: (1) the essence of the base step of the induction method; (2) the meaning associated with the inductive step in proving the implication P(k) ⇒ P(k + 1) for an arbitrary k in the domain of discourse of P(n); and (3) the possibility of the truth set of a sentence in a statement proved by mathematical induction to include values outside its domain of discourse. The difficulties about the base and inductive steps are more salient among preservice elementary than secondary school teachers, but the difficulties about whether proofs by induction should be as encompassing as they could be are equally important for both groups. Implications for mathematics teacher education and future research are discussed in light of these findings.

Previous studies have suggested that children as young as 9 years old have developed an understanding of non-linear growth processes prior to formal education. The present experiment aimed at investigating this competency in even younger... more

Previous studies have suggested that children as young as 9 years old have developed an understanding of non-linear growth processes prior to formal education. The present experiment aimed at investigating this competency in even younger samples (i.e., in kindergartners, first, and third graders, ages 6, 7 and 9, respectively). Children (N = 90) solved non-verbal inductive reasoning tasks by forecasting linear and exponential growth. While children of all ages forecasted linear growth adequately, exponential growth was also estimated remarkably well. Surprisingly, kindergartners and third graders showed similar high achievement concerning the magnitude and curve shape of forecasts, whereas first graders performed significantly worse. We concluded that primary knowledge of both linearity and non-linearity exists even in kindergartners. However, children's understanding is quite fragile, as their performance was strongly affected by task sequence: Children underestimated exponential growth when the previous task required a forecast of linear growth, and overestimated linear growth when the previous task required forecasting of exponential growth.