This paper is concerned with developing a new class of generalized numbers. The main advantage of this class is that it generalizes the two classes of generalized Fibonacci numbers and generalized Pell numbers. Some new identities involving these generalized numbers are obtained. In addition, the two well-known identities of Sury and Marques which…

This study reports findings of a systematic replication and as such sought to evaluate effects of an early numeracy curriculum on early number sense attainment for Kindergarten students with autism. Through daily 15-min story-based math lessons with embedded systematic instruction delivered by their classroom teacher, participants learned to…

The importance of understanding the various uses of the literal symbol in algebra, and in particular the idea of generalised number, is well documented in the literature. Many research findings have also reported student difficulties with this vital and central concept. This research study examines the use of a combination of historical and…

The paper describes evolution of an approach to teaching mathematically disabled and slow learning students through a Piagetian framework. It is explained that a step-by-step procedure is used to internalize material actions into mental actions via perception and verbalization. Formulae are introduced early, and emphasis is placed on promoting…

Eight students with Down's syndrome, aged 11 through 13, were taught to add by counting-on in a 5-day teaching program. Teaching included instruction in component skills and use of precision teaching techniques. All students continued to use the technique six months later and generalized the technique to other materials. (Author/DB)

Describes a method of teaching the order of mathematical operations based upon the psychological theory of conceptual generalization. (MDH)

Stimulus control technology was used to instruct seven students in grades five and six who demonstrated difficulty with fraction ratio and decimal relations. Students were trained to match pictorial representations of fractions to printed counterpart fraction ratios and to match printed decimals to pictorial representations of counterpart…

This study addressed the problem of promoting generalization of knowledge in people with mental handicaps, by presenting an approach based on the idea that certain cognitive representations of strategies and related concepts are common to solving a wide variety of problems. The surface context of these problems may vary considerably, but all will…

The teacher of mathematics or science must be aware of the concepts, facts, and generalizations of his field, of psychological principles of learning, and of teaching methods. Methods appropriate to the teaching of concepts differ from methods for teaching generalizations. (SD)

A multisensory program using a counting technique was effective in teaching math skills to three elementary students with mild disabilities. Results showed significant gains in acquisition of target skills as well as maintenance and generalization to novel math problems. (Author/DB)

The study examined the effectiveness of a program to improve the cognitive skills of 91 hearing impaired college students. Experimental students received systematic cognitive instruction focusing on specific generalizable skills during the experimental period, several times per week, in the contexts of their regular college classes. Instructors of…

This issue of the newsletter focuses on the teaching of mathematics to mildly handicapped students. The feature article reviews the theory of generalization and its application to specific practices in teaching arithmetic. A set of six-step guidelines is offered for the teacher to follow in ensuring that generalization of arithmetic skills takes…

This study compared the acquisition of an initial place value skill when presented in a concrete, semiconcrete, abstract teaching sequence to acquisition of the same skill when presented at the abstract level only. The 24 subjects were elementary and middle school students (ages 8-13) with learning disabilities who were randomly assigned to…

This volume of the 27th International Group for the Psychology of Mathematics Education Conference includes the following research reports: (1) Improving Decimal Number Conception by Transfer from Fractions to Decimals (Irita Peled and Juhaina Awawdy Shahbari); (2) The Development of Student Teachers' Efficacy Beliefs in Mathematics during…

This volume of the 30th annual proceedings of the International Group for the Psychology of Mathematics Education conference presents: plenary panel papers; research forum papers; short oral communication papers; and poster presentation papers from the meeting. Information relating to discussion groups and working sessions is also provided.…