A retrospective account of the evolution of the Beginning Teacher Support and Assessment (BTSA) program shows how English learners and students of diverse cultural backgrounds were marginally considered throughout the development of the "California Standards for the Teaching Profession" and BTSA induction development, implementation, and…

In this article I present an activity introducing statistical concepts to engineering students to help them develop inductive reasoning and problem-solving skills.

In this article we derive all salient properties of analytic functions, including the analytic version of the inverse function theorem, using only the most elementary convergence properties of series. Not even the notion of differentiability is required to do so. Instead, analytical arguments are replaced by combinatorial arguments exhibiting…

Evaluating whether a limited sample of evidence provides a good basis for induction is a critical cognitive task. We hypothesized that whereas adults evaluate the inductive strength of samples containing multiple pieces of evidence by attending to the relations among the exemplars (e.g., sample diversity), six-year-olds would attend to the degree…

Teaching students to doubt, that is, to "test," theological arguments as one might test any other kind of knowledge is challenging in that the warrant for such testing is not immediately clear. Stephen Toulmin, Richard Rieke, and Allan Janik's model of reasoning provides a conceptual framework that demonstrates the logical relationships between a…

In this article, I argue the proposition that educators ought to be including a serious consideration of intelligent design as a counterexample to the scientific explanations of human origins. The article first distinguishes between three different ways people ask "why": the Scientific Why, the Ultimate Why, and the Teleological Why. Although…

The spacing effect describes the robust phenomenon whereby memory is enhanced when learning events are distributed, instead of being presented in succession. We investigated the effect of spacing on children's memory and category induction. Three-year-old children were presented with two tasks, a memory task and a category induction task. In the…

Different intuitive theories constrain and guide inferences in different contexts. Formalizing simple intuitive theories as probabilistic processes operating over structured representations, we present a new computational model of category-based induction about causally transmitted properties. A first experiment demonstrates undergraduates'…

Many students experience considerable difficulties when they learn and then attempt to construct and communicate proofs of conjectures using the principle of mathematical induction. Although research on the pedagogy of mathematical induction has gained only occasional attention since the 1970s, there has been an increasing interest in this field…

The author reflects on Piaget's 1972 article, "Intellectual evolution from adolescence to adulthood," addressed to questions regarding what he alleged to be the final, most advanced level of cognition in his developmental stage theory--formal operations, as described in his 1958 volume coauthored with Inhelder, "The growth of logical thinking from…

There are currently increased efforts to make proof central to school mathematics throughout the grades. Yet, realizing this goal is challenging because it requires that students master several abilities. In this article we focus on one such ability, namely, the ability for "deductive reasoning," and we review psychological research to enhance…

The study deals with the development of an analogy-integrated e-learning module on Cellular Respiration, which is intended to facilitate conceptual understanding of students with different brain hemisphere dominance and learning styles. The module includes eight analogies originally conceptualized following the specific steps used to prepare…

In 2004, the Transition Mathematics Project (TMP), funded by the state of Washington and The Bill and Melinda Gates Foundation, was established to create projects to help high school students gain the necessary skills to become college and work-ready. Aligned to TMP's College Readiness Mathematics Standards, a fourth-year capstone mathematics…

The Inviting School Survey-Revised (ISS-R) was adapted and translated into Traditional Chinese (ISS-RC), using a five-step process, based on international test administration guidelines, involving judgmental, logical, and empirical methods. Both versions were administered to a convenience sample of Chinese-English fluent Hong Kong school community…

Changes in the kinds of technology used in modern society are changing the ways in which people think. Russian students, like those elsewhere, are increasingly thinking in terms of short, unconnected forms of knowledge and are losing the ability to see connections, to think holistically. This presents a special challenge to education in Russia.