THE EFFECT OF TOKEN REWARDS ON “INTRINSIC” MOTIVATION FOR DOING MATH

This study used a multielement baseline design to analyze the effects of token rewards delivered contingent upon completion of math problems by 2 middle-school boys. Time spent on math and number of work pages completed increased (with high accuracy) during reward conditions and were maintained during fading and withdrawal. At follow-up, time spent and work pages completed remained well above baseline for 1 boy and fell below for the other, while accuracy remained high and ratings of liking math were the highest possible for both boys. Overall, the results are inconsistent with warnings about use of token rewards to motivate children.     

Relationship Between Academic Motivation and Mathematics Achievement Among Indian Adolescents in Canada and India

This study examined the relationships between academic motivation—intrinsic motivation, extrinsic motivation, amotivation—and mathematics achievement among 363 Indian adolescents in India and 355 Indian immigrant adolescents in Canada. Results of hierarchical multiple regression analyses showed that intrinsic motivation, extrinsic motivation, and amotivation were not statistically significantly related to mathematics achievement among Indian adolescents in India. In contrast, both intrinsic motivation and extrinsic motivation were statistically significantly related to mathematics achievement among Indian immigrant adolescents in Canada. While intrinsic motivation was a statistically significant positive predictor of mathematics achievement among Indian immigrant adolescents in Canada, extrinsic motivation was a statistically significant negative predictor of mathematics achievement among Indian immigrant adolescents in Canada. Amotivation was not statistically significantly related to mathematics achievement among Indian immigrant adolescents in Canada. Implications of the findings for pedagogy and practice are discussed.     

Empiricism,probability, and knowledge of arithmetic: A preliminary defense

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgments of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity (Section 2.1), while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic (Section 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (Section 3.1) or to the non-computability and non-continuity of probability assignments (Section 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments (Appendix A–Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated (Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar.     

Spatial numerical associations in preschoolers

ABSTRACT

Three-to-five-year-old French children were asked to add or remove objects to or from linear displays. The hypothesis of a universal tendency to represent increasing number magnitudes from left to right led to predict a majority of manipulations at the right end of the rows, whatever children's hand laterality. Conversely, if numbers are not inherently associated with space, children were expected to favour laterality-consistent manipulations. The results showed a strong tendency to operate on the right end of the rows in right-handers, but no preference in left-handers. These findings suggest that the task elicited a left-to-right oriented representation of magnitudes that counteracted laterality-related responses in left-handed children. The young age of children and the lack of a developmental trend towards right preference weaken the hypothesis of a cultural origin of this oriented representation. The possibility that our results are due to weaker brain lateralisation in left-handers compared to right-handers is addressed in Discussion section.     

Developing a Learning Progression for Curriculum,Instruction, and Student Learning: An Example from Mathematics Education

Learning progressions have been demarcated by some for science education, or only concerned with levels of sophistication in student thinking as determined by logical analyses of the discipline. We take the stance that learning progressions can be leveraged in mathematics education as a form of curriculum research that advances a linked understanding of students learning over time through careful articulation of a curricular framework and progression, instructional sequence, assessments, and levels of sophistication in student learning. Under this broadened conceptualization, we advance a methodology for developing and validating learning progressions, and advance several design considerations that can guide research concerned with engendering forms of mathematics learning, and curricular and instructional support for that learning. We advance a two-phase methodology of (a) research and development, and (b) testing and revision. Each phase involves iterative cycles of design and experimentation with the aim of developing a validated learning progression. In particular, we gathered empirical data to revise our hypothesized curricular framework and progression and to measure change in students. thinking over time as a means to validate both the effectiveness of our instructional sequence and of the assessments designed to capture learning. We use the context of early algebra to exemplify our approach to learning progressions in mathematics education with a focus on the concept of mathematical equivalence across Grades 3-5. The domain of work on research on learning over time is evolving; our work contributes a broadened role for learning progressions work in mathematics education research and practice.     

Student-produced representations as a means for interrupting the flow of an interview / Representaciones producidas por una alumna para interrumpir el flujo de una entrevista

Abstract

This work provides evidence that children as young as six years old successfully leverage written representations to their own purposes. During a modified clinical interview, Maggie created an idiosyncratic written representation to negotiate understanding of the interview task. In this move, Maggie shifted her role in the interview from sharing her own thinking to understanding the interviewer’s thinking. Her representations were not strictly for communication but also for control. This fleeting but illuminating episode points to young children’s intuitive perspective on written representations as a cultural tool.     

A Bizarre Property Equivalent to the -Fan Theorem

It is shown, with intuitionistic logic, that if every locallyconstant function from to has a property akinto constancy, then the fan theorem for -bars holds, and conversely.     

Investigations of the Behavior of Paramecium Aurelia: III. The Effect of the Presence and Absence of Light on the Occurrence of a Response

This study was designed to evaluate how a series of measures made on 77 infants at ages 3, 6, 9, 12, 18, and 24 months could be used to predict measures made at about 5 years of age. The analytical procedures were selected to be sensitive to differences among individuals in the function that relates test performance to age. Neither evidence for such heterogeneity nor incremental validity of the measures made at 18 months and earlier was obtained. It is concluded that the Gesell Developmental Schedule, the Cattell Infant intelligence Scale, and the California Infant Scale of Motor Development, administered at 18 months and earlier, are invalid both as static indicators of later performance and as dynamic indicators of development.     

Ethics in process perspective

Embedded in the thought of Whitehead is an extremely interesting but relatively neglected ethic which has relevance to current attempts to reflect creatively on the ethical dimension of human existence both in South Africa and the wider world. This paper notes the main features of the context in which such reflection is taking place, and then proceeds to give an account of process ethics. Thereafter it offers a critical discussion whose main conclusion is that process ethics has more to commend it than other approaches to ethics.