We discuss the importance of bringing teaching to the forefront of instructional design. We do so by describing the process of developing an instructional sequence for early number, using design research. The instructional sequence was developed with the specific aim of supporting teaching, conceived as a complex and demanding job, not reducible…

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students' understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real…

It is not yet understood how children acquire the meaning of numerical symbols and most existing research has focused on the role of approximate non-symbolic representations of number in this process (see Piazza, ("Trends in Cognitive" 14(12):542-551, 2010). However, numerical symbols necessitate an understanding of both order and…

Adult proficiency in numeracy in the United States lags that of other developed nations, and the nonselective institutions that dominate the higher education sector struggle to address the learning needs of the sizeable proportion of students who enroll in their institutions and are deemed academically underprepared in mathematics. Research on…

As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

This article describes a comprehensive and novel approach to assessment in early numeracy. Topics include the significance of early numeracy, developing a nomenclature for early numeracy, and describing the context for the development of this approach to assessment. The largely unrealised importance of numerals and numeral sequences in early…

Short term memory is famously limited in capacity to Miller's (1956) magic number 7 plus or minus 2--or, in many more recent studies, about 4 plus or minus 1 "chunks" of information. But the definition of "chunk" in this context has never been clear, referring only to a set of items that are treated collectively as a single unit. We propose a new…

A GROUP OF REPRESENTATIVES FROM FIVE SCHOOLS MET FOR TWO WEEKS TO DISCUSS MEANS OF IMPROVING ARITHMETIC TEACHING. THE CONTENT OF EACH GRADE WAS EXAMINED. THE PURPOSE WAS TO DETERMINE VARIOUS APPROACHES TO MOTIVATE BETTER LEARNING. NOTES OF THESE MEETINGS HAVE BEEN REPRODUCED AND SUGGESTIONS FOR TEACHERS OFFERED. TEACHERS SHOULD PROVIDE MANY…

This study compared effectiveness of either a concrete-representational-abstract (CRA) or a representational-abstract (RA) instructional sequence in teaching fraction concepts to 50 middle school students with mathematics disabilities. On all achievement measures, students in the CRA group had overall higher mean scores than did students in the RA…

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…