This case study explores how 12-13-year-old students encounter proportional reasoning
while working with geometric patterning tasks using concrete materials. The focus is on the …

This study is a case study within a three-year-long design research study. The purposes of
this study are twofold. The first purpose includes investigating whether there is a significant …

This article presents a study of 8th grade students working in groups to solve a task about
generalizing patterns. The study aimed to openly explore how progress in mathematical …

While it has been suggested that patterning activities support early algebra learning, it is
widely acknowledged that the shift from perceiving patterns to understanding algebraic …

Proportional reasoning, the ability to use ratios in situations involving comparison of
quantities, is essential for mathematical competence, especially in the middle school years …

This paper examines young students' development and use of justification strategies when
engaged in numeric patterning activities. Drawing on findings from a three-month teaching …

This paper reports the results of two interventions involving the integrated study of
mathematics and technology practice to girls in Years 6 and 7. The focus of the study was to …

The way to teach proportion by giving a ready used-formula remains meaningless for the
students. They may just memorize the procedure of cross multiplication without understand …

In this paper, we analyze and compare two didactical designs for introducing primary school
pupils to proportional reasoning in the context of plane polygons. One of them is well …

While patterning was commonly seen as evidence of mathematical thinking, interdisciplinary
interest has recently increased due to pattern-recognition applications in artificial …