Addition and subtraction: A cognitive perspective

  • [Show abstract] [Hide abstract]
    ABSTRACT: This paper describes the structure and contents of EC301, a standardized testing battery for the evaluation of brain- damaged adults in the area of calculation and number processing. The battery was administered to 180 normal subjects stratified by education(3 levels), age (3) and gender. EC301 is composed of a large variety of tasks dealing with basic arithmetic skills, and their linguistic, spatial, and mnesic dimensions. The three main notational systems for numbers - Arabic digits, written verbal, and spoken verbal number forms - are explored. Analysis of error rates indicated the effect of some demographic factors (principally, education; incidentally, gender) on normal performance in some tasks.
    Journal of Clinical and Experimental Neuropsychology 01/1994; 16(2):195-208. · 2.16 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Abstract Twenty 4th-grade children were matched according to performance on a whole-number calculation and concepts pretest and assigned at random to one of two groups: wooden,base-ten blocks and computerized microworld. Instruction in each group was designed to orient students toward relationships between notation and meaning. Instruction given the two groups was based upon a single script that extended whole number numeration to decimal numeration, and emphasized solving problems in concrete settings while inventing notational schemes to represent steps in solutions. Neither group changed in regard to whole-number notational methods. Blocks children understood decimal numerals as if they were funny whole numbers; Microworld children attempted to give meaning,to decimal notational methods, but were largely in a state of disequilibrium at the end of the study. Notations, Conventions, and Constraints 1 The use of concrete materials in elementary mathematics instruction has been widely advocated. Textbooks on methods for teaching elementary school mathematics and college textbooks on mathematics for elementary school teachers promote liberal use of concrete materials. Yet, the research literature on effectivenessof instruction involving uses of concrete materials is equivocal at best (Fennema, 1972; Labinowicz, 1985; Resnick, 1982; Resnick & Omanson, 1987; Sowell, 1989; Suydam & Higgins, 1977; Wearne & Hiebert,
    Journal for Research in Mathematics Education 03/1992; 23(2). · 1.27 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: This article examines mathematics instruction and its intersection with culturally relevant teaching in an elementary/middle school in a Mexican American community. The findings are based on a collaborative-research and school-change project involving university researchers, teachers, and the school's principal. On the basis of ethnographic data and an interdisciplinary theoretical framework, we propose a three-part model of culturally relevant mathematics instruction. The 3 components are (a) building on students' informal mathematical knowledge and building on students' cultural and experiential knowledge, (b) developing tools of critical mathematical thinking and critical thinking about knowledge in general, and (c) orientations to students' culture and experience. I was 15 (when I came to the U.S.) The first thing I learned was that I was different. Even with my Latino peers. There are levels of being Mexican. I didn't know how bad it was to be who I was. There were so many pressures from name calling, insults in the street, said aloud because I was so Mexican … I had a lot of anger. It was this anger, and anger at the experiences of my brother in school. We all did not do as well because of the school experiences. That made me want to be a teacher. —Ms. Salinas, a sixth-grade teacher in the school In this article, we hope to contribute to a theory of culturally relevant teaching (Ladson-Billings, 1995) of mathematics in a Mexican immigrant community. Our analysis is based on the ideas and practices of five teachers. The teachers are par- ticipating in a school-change project in a public school located in a low-income Mexican American community in a large midwestern U.S. city. The purpose of the project is to help teachers use what they know about their students' culture to improve stu- dents' learning of mathematics, and of other subjects as well, and to help students develop critical approaches to knowledge and the tools they will need to be agents
    Journal for Research in Mathematics Education 12/1997; 28(6). · 1.27 Impact Factor