Thoughtful implementation of the Common Core State Standards for Mathematics (CCSSM) (CCSSI 2010) presents an opportunity for increased emphasis on the development of mathematical understanding among students. Granted, ascertaining the mathematical understanding of an individual student is highly complex work and often exceedingly difficult.…

Teachers typically teach subjects separately, but integrated science, technology, engineering, and mathematics (STEM) curriculums that focus on real-world practices are gaining momentum (NAE and NRC 2009). Before release of the "Next Generation of Science Standards" ("NGSS") (NGSS Lead States 2013), 36 states already had a…

From the early nineties, most reformed curricula at upper secondary level choose to give functions a major position and a priority over rational expressions and equations of traditional algebra. The goal of this paper is to introduce key challenges resulting from this choice and to discuss the contribution that software environments associating…

The perception of what a teacher says s/he does in the classroom may or may not match the reality of their actual teaching practice. This case study considers one second-grade teacher's instructional methods and pedagogical decisions when teaching number sense and her perception of what informed her teaching practice. This teacher supported…

This study investigated the relationship among working memory, processing speed, math performance, and reactivity to stress in 83 Grade 1 children. Specifically, 39 children with math disability (MD) were compared to 44 children who are typically achieving (TA) in mathematics. It is the first study to use a physiological index of stress (salivary…

How can the key concept of equivalent expressions be addressed so that students strengthen their representational fluency with symbols, graphs, and numbers? How can research inform the synergistic use of both paper-and-pencil analysis and computer algebra systems (CAS) in a classroom learning environment? These and other related questions have…

Educational systems throughout the world serve students from diverse populations. Often students from minority populations (i.e. racial, ethnic, linguistic, cultural, economic) face unique challenges when learning in contexts based on the cultural traditions and learning theories of the majority population. These challenges often leave minority…

Increasing pressure is mounting from all areas of society to maximise technology use within educational domains. Whilst curriculum documents call for the utilisation of technology as a teaching tool in the mathematics classroom, the benefits of exploring forms of dynamic mathematical software, such as GeoGebra, are often introduced in the senior…

From 2011-2013 the VCAA conducted a trial aligning the use of computers in curriculum, pedagogy and assessment culminating in a group of 62 volunteer students sitting their end of Year 12 technology-active Mathematical Methods (CAS) Examination 2 as a computer-based examination. This paper reports on statistical modelling undertaken to compare the…

The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

This case study examines the salient features of two individuals' reasoning when confronted with a task concerning the cardinality and associated cardinal number of equinumerous infinite sets. The APOS Theory was used as a framework to interpret their efforts to resolve the "infinite balls paradox" and one of its variants. These cases…

To support university students' understanding of mathematical proofs, pictures accompanying text are frequently used in textbooks as well as in lectures. However, it is unclear if such pictures influence the individual's reading behaviour. By recording the eye movements of eight mathematicians, we investigated whether and how adults with high…

A fundamental issue facing mathematics educators is developing rich, deep mathematical understanding in teacher candidates. Research suggests teachers need more than just a basic knowledge of the math they teach. They need mathematical knowledge for teaching (MKT): the ability to unpack mathematical ideas, to interpret student errors, and to…

D. Elkonin's thesis that thinking is much more closely related to writing than to oral speech formed the basis of our three-year formative experiment at the elementary school level. In order to test this idea, second-graders through fourth-graders were given a few assignments in which they were asked to exchange thoughts in writing with their…

Many teacher education programs are criticized for their failure to prepare pre-service teachers to utilize and transfer their knowledge of content and educational principles into authentic classroom teaching. Studies also consistently report that pre-service teachers' ability to identify what is noteworthy about a mathematics classroom situation…