Children's understanding of the quantities represented by number words (i.e., cardinality) is a surprisingly protracted but foundational step in their learning of formal mathematics. The development of cardinal knowledge is related to one or two core, inherent systems--the approximate number system (ANS) and the object tracking system (OTS)--but…

Numerical comparison is a primary measure of the acuity of children's approximate number system. Approximate number system acuity is associated with key developmental outcomes such as symbolic number skill, standardized test scores, and even employment outcomes (Halberda, Mazzocco, & Feigenson, 2008; Parsons & Bynner, 1997). We examined…

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the…

We present a self-organizing approach to sentence processing that sheds new light on notional plurality effects in agreement attraction, using pseudopartitive subject noun phrases (e.g., "a bottle of pills"). We first show that notional plurality ratings (numerosity judgments for subject noun phrases) predict verb agreement choices in…

Young children can quickly and intuitively represent the number of objects in a visual scene through the Approximate Number System (ANS). The precision of the ANS--indexed as the most difficult ratio of two numbers that children can reliably discriminate--is well known to improve with development: whereas infants require relatively large ratios to…

It is important for students to connect with real life in mathematics courses. The aim of this study is to investigate the activities which are written by prospective primary school teachers in the context of Realistic Mathematics Education. This research is a case study of which data were collected by qualitative methods. The participants of the…

Pre-service mathematics teachers' content knowledge is an important issue. Therefore, detailed studies are needed to be conducted on mathematical topics. The study examines preservice elementary mathematics teachers' (PEMTs) special content knowledge (SCK) of integer addition and subtraction in the context of using multiple representations,…

This chapter identifies the ways in which 15 prospective teachers engage the strands of mathematical proficiency as they solve word problems involving integer addition and subtraction. The prospective teachers, through think-aloud interviews, demonstrated a strong focus on solving problems using procedures, which some did not explain and others…

In this dissertation, I address two outstanding questions regarding how linguistic and extra-linguistic information are brought together in the interpretation of language situated within a discourse. The first part of this dissertation experimentally addresses how alternatives invoked by sentences containing the focus-sensitive operator 'only' are…

It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, ("Trends in Cognitive" 14(12):542-551, 2010). However, numerical symbols necessitate an understanding of both order and…

A 1 h classroom activity is presented, aimed at consolidating the concepts of microstates and Russell-Saunders energy terms in transition metal atoms and coordination complexes. The unconventional approach, based on logic and intuition rather than rigorous mathematics, is designed to stimulate discussion and enhance familiarity with quantum…

Multiplicative thinking is a critical stage in mathematical learning and underpins much of the mathematics learned beyond middle primary years. Its components are complex and an inability to understand them conceptually is likely to undermine students' capacity to develop beyond additive thinking. Of particular importance are the ten times…

Connecting theory and practice in teaching is sometimes difficult, as it requires expensive or delicate equipment, thus limiting the teacher to giving demonstrations in which students are passive participants. Numerical mathematics, as an applied discipline, should be taught on real world examples. By using inexpensive Arduino hardware, we can…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

In the entertainment world, people usually like, and find memorable, novels, short stories, and movies with surprise endings. This suggests that classroom teachers might want to present to their students examples of surprising facts associated with principles of physics. Possible benefits of finding surprising facts about principles of physics are…