The second volume of this proceedings contains the papers presented at the 21st annual meeting of the Mathematics Education Research Group of Australasia. Full papers include: (1) "Teachers Interpreting Algebra: Teachers' Views about the Nature of Algebra" (Brenda Menzel and David Clarke); (2) "Long Odds: Longitudinal Development of…

This profile is designed as a recording sheet for monitoring an individual student's progress throughout the school year. Kindergarten assessment materials and the "Strategies for Instruction in Mathematics" suggests tasks and questions that can be used for on-going and summative assessment. Directions for use and descriptions of levels of…

This profile is designed as a recording sheet for monitoring an individual student's progress throughout the school year. Sixth grade assessment materials and the "Strategies for Instruction in Mathematics" suggest tasks and questions that can be used for on-going and summative assessment. Directions for use and descriptions of levels of…

This profile is designed as a recording sheet for monitoring an individual student's progress throughout the school year. Eighth grade assessment materials and the "Strategies for Instruction in Mathematics" suggests tasks and questions that can be used for on-going and summative assessment. Directions for use and descriptions of levels of…

Discusses a framework for assessing middle school students' thinking in conditional probability and independence. Establishes four levels of thinking from subjective to numerical reasoning for both constructs. Students (n=15) from grades 4-8 were interviewed. Profiles reveal that levels of probabilistic thinking were stable across the two…

The performance of sixth and seventh graders on a variety of tasks involving estimation and reasonableness of results were studied. Also examined was the effect of a short unit of activities on these two topics. Correct answers approximately doubled after instruction. (MNS)

Presents an instructional approach that utilizes paper-folding activities to help students understand the concept of fractions. Utilizes an area model of multiplication to extend the concept of multiplication of whole numbers to multiplication of fractions. (MDH)

This article presents the "concrete semiconcrete abstract" (CSA) teaching sequence for teaching basic math skills to students with and without learning disabilities. Guidelines include providing a minimum of nine instructional lessons (three at each level), each with four lesson steps. Validation of the CSA sequence and lesson format with 15…

Presents a series of hands-on activities for grades K-2, 3-4, 5-6, and 6-8 using the common theme of kites to develop number sense in basic operations and fractions. Teachers' guides and worksheets are provided. (MDH)

Presents teaching methods to rectify the tendency of students and even teachers to divide the smaller number into the larger in problem situations requiring division, while recognizing the impossibility of the answer in the situation. (MDH)

Presents activities developed for teacher training courses for the middle school level that integrate mathematics history with the selected topics of number systems, fractions, and geometry. The activities seek to give relevance to history and to motivate and deepen students' understanding of the evolution of mathematical concepts. (MDH)

Discusses duality between process and concept in mathematics, ambiguity of symbolic notation, and flexibility in thought processes of successful students. Content analysis and empirical evidence suggest a qualitatively different kind of mathematical thought in more able compared to less able elementary students (n=72) in arithmetic. (Contains 42…

Described are three activities and variations that can help students to understand the concept of place value. Allowing students to use concrete materials and helping them to bridge the gap between manipulatives and paper-and-pencil tasks are emphasized. (KR)

The influence that number naming grammar has on the understandings of two-digit numbers and place value of kindergarten children of European and Asian background was examined. Results indicate that Asian verbal/numerical representation patterns naming tens and units in order may be associated with distinctive place value concepts that support…

Research on cognitive representation of numbers and understanding of place value of U.S. and Japanese first graders was extended to France, Sweden, and Korea (118 subjects; approximately 24 from each of the 5 countries). Basic differences in children's cognitive representations of number are influenced by characteristics of their languages. (SLD)