The aim in the current study is to examine the conceptualizations of zero in arithmetic operations among students with learning disabilities (LD) and no learning disabilities (N-LD). The similarities and differences in the understandings of students with LD and N-LD of zero in arithmetical operations will be discussed. The study is a multiple case…

Teachers' understanding of the concepts they teach affects the quality of instruction and students' learning. This study used a sample of 303 teachers from across the USA to examine elementary school mathematics teachers' knowledge of key concepts underlying fraction arithmetic. Teachers' explanations were coded based on the accuracy of their…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

Children learn to find answers when multiplying two whole numbers (e.g., 3 × 7 = 21). To this end, they may repeatedly add one number (e.g., 7 + 7 + 7 = 21). But what meanings do they have for multiplication? The authors address this issue while sharing an innovative, playful task called Please Go and Bring for Me (PGBM). Drawing on the…

Provides an alternative to traditional instruction in multiplication and division to develop computational fluency in students. (Author/NB)

Limitations in children's understanding of the symbols of arithmetic may inhibit choice of appropriate solution procedures. The teacher's role involves negotiation of new meanings for words and symbols to match extensions to solution procedures. (MKR)

Fourteen third graders were given numerical computation and division-with-remainder (DWR) problems both before and after they were taught the division algorithm in classrooms. Their solutions were examined. The results show that students' initial acquisition of the division algorithm did improve their performance in numerical division computations…

Supports teachers in resolving problems of teaching long division. Discusses an approach focusing first on modeling the partition process with base-10 blocks and having students come to a conceptual understanding of the standard long division algorithm. Evaluation of the approach concluded that it helped students conquer the division concept. (ASK)

Discusses the development of multiplicative and divisional schemes within a constructivist framework. Illustrates child thinking and child methods relative to the meanings of these operations using interviews with children. Compares the constructivist perspective on the development of meanings of multiplication and division to what is found in…

Discusses mathematics education research on multiplication and division which implies that instruction should emphasize development of a sound conceptual basis for multiplication and division rather than memorization of tables and rules. Presents action research ideas. (10 references) (MKR)

Introduces a toy, the Educated Monkey, developed to help students learn multiplication tables and associated division, factoring, and addition tables and associated subtraction. Explains why the monkey works and reviews geometric, algebraic, and arithmetic concepts. (KHR)

This paper reports on a study of seventh grade students (N=4) who attend a rural K-12 school. Students participated in a 5-week teaching experiment designed to build on their existing knowledge of the unit concept and extend it to the rational number operations of multiplication and division. Data collected comes in the form of videotapes,…

Discusses three methods to teach the order of operations to middle school students: (1) asking students to fill in operations in a statement to obtain a given answer; (2) using mnemonics to remember operation order; and (3) having students discover the logic system used by their calculators. (MDH)

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

This paper describes the BUD project which surveyed childrens' conceptions of division, and of fractions and decimals. The lack of connection between counting skills and conceptual understanding is discussed. The expectations for new algorithms and the basic idea in planning the BUD project are summarized. Some previous studies on counting, the…