This paper aims to reveal the potential of inferentialism, an emerging philosophy in mathematics education, to extend contemporary constructivist research regarding conceptual development. Going against the traditional view of a notion as the name of a corresponding concept and a constructivist way of naming second-order models, we provide a new…

Children develop and learn within dynamic contexts, yet the simplifying assumptions of common statistical methods often relegate such complexity to unexplained error. This chapter discusses ideas from the dynamic systems literature, which focuses on the interplay within and between components of complex systems, such as individuals and their…

In acquiring number words, children exhibit a qualitative leap in which they transition from understanding a few number words, to possessing a rich system of interrelated numerical concepts. We present a computational framework for understanding this inductive leap as the consequence of statistical inference over a sufficiently powerful…

We present a hierarchical Bayesian framework for modeling the acquisition of verb argument constructions. It embodies a domain-general approach to learning higher-level knowledge in the form of inductive constraints (or overhypotheses), and has been used to explain other aspects of language development such as the shape bias in learning object…

In this article, the authors describe a lesson that uses the 5E Learning Cycle to help students not only understand the atomic model but also how Ernest Rutherford helped develop it. The lesson uses Rutherford's gold foil experiment to focus on three aspects of the nature of science: the empirical nature of science, the tentativeness of scientific…

Beginning with a reference to living in a time of both uncertainty and opportunity, this article presents a discussion of key areas where shared understanding is needed if we are to successfully realize the design and use of high quality, valid assessments of science. The key areas discussed are: (1) assessment purpose and use, (2) the nature of…

According to one theory about how children learn the meaning of the words for the positive integers, they first learn that "one," "two," and "three" stand for appropriately sized sets. They then conclude by inductive inference that the next numeral in the count sequence denotes the size of sets containing one more object than the size denoted by…

Informal inferential reasoning has shown some promise in developing students' deeper understanding of statistical processes. This paper presents a framework to think about three key principles of informal inference--generalizations "beyond the data," probabilistic language, and data as evidence. The authors use primary school classroom…

There is often confusion about distinctions between growth models and value-added models. The first half of this paper attempts to dispel some of these confusions by clarifying terminology and illustrating by example how the results from a large-scale assessment can and will be used to make inferences about student growth and the value-added…

Four bonobos, seven gorillas, and six orangutans were presented with two small rectangular boards on a platform. One of the boards had a piece of food under it so that it acquired an inclined orientation whereas the other remained flat on the platform. Subjects preferentially selected the inclined board. In another experiment, subjects were…

Students can imitate scientists at work by conducting inquiry investigations in the classroom, thereby exhibiting a multitude of skills and competencies. As stated by Bransford and Donovan (2005), learning science as a process of inquiry involves students in observation, imagination, and reasoning about the phenomena under investigation. Rather…

The authors use proven cognitive and learning principles and recent developments in the field of educational psychology to teach the concept of the sampling distribution of the mean, which is arguably one of the most central concepts in inferential statistics. The proposed pedagogical approach relies on cognitive load, contiguity, and experiential…

Users of educational hypertext are faced with the challenge of creating meaning both within and between texts. Cohesion is an important factor contributing to whether a reader is able to capture meaning and comprehend text. When readers are required to fill in conceptual gaps in text, comprehension can fail if they do not have sufficient…

Many students find it difficult to learn the kinds of knowledge and thinking required by college or high school courses in mathematics, science, or other complex domains. Thus they often emerge with significant misconceptions, fragmented knowledge, and inadequate problem-solving skills. Most instructors or textbook authors approach their teaching…

Describes the Higher Order Thinking Skills (HOTS) Program, which replaces drill and practice with thinking skills activities for grades three through six. The HOTS curriculum, which is built around commercially available software, is reviewed; special teaching techniques that emphasize teacher-student dialog are presented; and benefits for at-risk…