The goal of this paper is to express necessary conditions for arithmetic in ways that are compatible with the unity of being and knowing understood within first-person experience. In psychological literature, this experience of unity is discussed as flow, but the epistemological and ontological unity is prior to the observer's position from which…

This chapter considers psychological and neuroscience research on how people understand the integers, and how educators can foster this understanding. The core proposal is that new, abstract mathematical concepts are built upon known, concrete mathematical concepts. For the integers, the relevant foundation is the natural numbers, which are…

Mistakes are at the crux of daily classroom learning. This is the case even in the earliest grades. While the instructional value of mistakes is wellknown among educators, little research documents how young children experience mistakes in real-world school settings. In the present study, I conducted semi-structured interviews with 25 Kindergarten…

We examined the associations of cognitive skills, math-related emotions and beliefs, and gender with responses to an arithmetic fluency intervention. Elementary school children with dysfluent arithmetic skills (N=69) participated in an arithmetic fluency intervention (with and without self-efficacy support) implemented in small groups in schools…

Objective: Cardiovascular reactivity to laboratory stressors was investigated as (a) a moderator of associations of partner aggression with affective functioning, alcohol problems, and parenting; and (b) a consequence of partner aggression. Method: Cohabiting adult couples (N = 453) with 3- to 7-year-old children were recruited by random digit…

This paper reports on an investigation into managing cognitive conflict in the context of student learning about decimal magnitude. The influence of prior constructs is examined through a brief review of the literature. A micro-genetic approach was used to capture detail of the teaching intervention used to facilitate development in student…

In a previous article of the same journal, we have discussed the interrelations of students' beliefs and self-efficacy beliefs for the use of representations and their respective cognitive performance on the learning of fraction addition. In the present paper, we confirm a similar structure of cognitive and affective factors on using…

We examine the role of tasks that have the intended effect of teachers re-conceiving the mathematics they teach as comprising a coherent body of meaningful ideas. We ground our discussion in ideas of trigonometry and modular functions and draw from a professional development research project to illustrate our approach. In this project, many…

Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the…

Objective: To test if visual focusing and mimic display as features of self-regulation in ADHD children show a curvilinear relation to rising methylphenidate (MPH) doses. To test if small dose steps of 2.5mg MPH cause significant changes in behavior. And to test the relation of these features to intellectual performance, parents' ratings, and…

The first of five articles in this journal reports on a project aimed at studying the influence of the way in which problems of arithmetic are worded. Some variables in the wording were found to affect the performance of children, and terms were isolated which increased the percentage of failure. The second article describes a technique for…

This study on psychological traits examines three hypotheses: (1) there is a similarity between parents and their children unexplained by a similarity between the parents, (2) this similarity may be explained by hereditary components, and (3) these hereditary components are of the discrete or segregated type of inheritance. There were 104 families…