This study investigated how 155 pre-service teachers solved three pattern generalization problems in a two-part written test and sequenced them for teaching purposes to demonstrate their curricular noticing. Participants' solutions were analyzed using inductive content analysis, which showed that only 8.4% of PSTs produced correct answers to all…

Large scale international assessments depend on invariance of measurement across countries. An important consideration when observing cross-national differential item functioning (DIF) is whether the DIF actually reflects a source of bias, or might instead be a methodological artifact reflecting item response theory (IRT) model misspecification.…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

Generalizing patterns is an important feature of algebraic reasoning that is accessible to students across grade-levels because it connects their numerical reasoning to algebraic reasoning. In this article, the authors describe how teachers can use the game Crack the Code to introduce generalizing to their students or can extend students'…

Due to their abstract nature, representation of mathematical concepts through different registers favors their understanding. In the case of ''sequences and regularities'', it becomes propitious the exploration of different registers of representation in the institution of topics, such as term, order, formation law, and generating expression.…

The importance of students being acquainted with algebraic ideas before secondary education has been revealed in the research literature. It is therefore essential that prospective elementary teachers (PTs) be prepared to instill an early algebra perspective in their teaching. However, PTs often show difficulties in algebra content knowledge,…

This paper explores how a group of pre-service elementary school teachers training to become mathematics teachers for elementary schools arrived at generalizations based on patterns. Two representative problems were investigated with these preservice teachers. The focus of this study was how these preservice teachers analyze and symbolize…

The ability to categorize concepts is an essential capability for human thinking and action. On the one hand, the investigation of such abilities is the purview of psychology; on the other hand, subject-specific educational research is also of interest, as a number of research works in the field of science education show. For computer science…

The authors who are mathematics teacher educators, have found that classifying, composing, and transforming shapes (in particular, rotations and reflections) are areas of difficulty for adults as well as for children. However, these are also some of the most important geometric ideas. They are fundamental topics in the K-8 Geometry and Measurement…

In this article we advance characterizations of and supports for elementary students' progress in generalizing and representing functional relationships as part of a comprehensive approach to early algebra. Our learning progressions approach to early algebra research involves the coordination of a curricular framework and progression, an…

Fluent word reading is hypothesized to facilitate reading comprehension by improving automatic word reading, thus releasing a reader's cognitive resources to focus on meaning. Many students with learning disabilities (LD) struggle to develop reading fluency, which affects reading comprehension. This synthesis extends Chard, Vaughn, and Tyler's…

TIMSS (Trends in International Mathematics and Science Study) is an international assessment of mathematics and science at the fourth and eighth grades that has been conducted every four years since 1995, with the most recent assessment in 2011. PIRLS (Progress in International Reading Literacy Study) is an international assessment of reading…

The technology of brief experimental analysis is just beginning to be used for identification of effective treatments for individual students who experience difficulty with oral reading fluency. In this study, the effect of a reading fluency treatment package was examined on easy and hard passages, and generalization was assessed on passages with…