The purpose of the study is to evaluate how prospective mathematics teachers (PMTs) modify tasks to facilitate students' learning of pattern generalization through the use of their mathematical knowledge for teaching. Case study, which is a type of qualitative research method, was used to determine the mathematical characteristics that PMTs use…

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.…

The objective of this article is to describe types of mathematical reasoning evidenced by a middle school mathematics teacher, when answering two generalization questions in a figural pattern generalization task, related to quadratic sequences. Reasoning is delimited from teacher's arguments, reconstructed from a theoretical-methodological…

Despite the call for an argument-based approach to validity over 25 years ago, few examples exist in the published literature. One possible explanation for this outcome is that the complexity of the argument-based approach makes implementation difficult. To counter this claim, we propose that the Assessment Triangle can serve as the overarching…

Self-regulated learning (SRL) is a critical component of mathematics problem-solving. Students skilled in SRL are more likely to effectively set goals, search for information, and direct their attention and cognitive process so that they align their efforts with their objectives. An influential framework for SRL, the SMART model (Winne, 2017),…

Recent work in predictive modeling has called for increased scrutiny of how models generalize between different populations within the training data. Using interaction data from 69,174 students who used an online mathematics platform over an entire school year, we trained a sensor-free affect detection model and studied its generalizability to…

Recent work in predictive modeling has called for increased scrutiny of how models generalize between different populations within the training data. Using interaction data from 69,174 students who used an online mathematics platform over an entire school year, we trained a sensor-free affect detection model and studied its generalizability to…

Research has shown that social anxiety generalises to sporting and athletic situations. The present study explored the applicability of the Clark and Wells model of social anxiety--and its metacognitive extension--to sport anxiety. Participants were 290 students aged 11-13 years, who completed measures of sport anxiety, social anxiety, depression…

In this article we examine how secondary school students think about functional relationships. More specifically, we examined seven students' intuitive knowledge in regards to representing two real-world situations with functions. We found students do not tend to represent functional relationships with coordinate graphs even though they are able…

Intervention studies in school systems are sometimes aimed not at changing curriculum or classroom technique, but rather at changing the way that teachers, teaching coaches, and administrators in schools work with one another--in short, changing the professional social networks of educators. Current methods of social network analysis are…

Information and communication technology (ICT)-enhanced research methods such as educational data mining (EDM) have allowed researchers to effectively model a broad range of constructs pertaining to the student, moving from traditional assessments of knowledge to assessment of engagement, meta-cognition, strategy and affect. The automated…

In the current educational climate of IDEA 2004 and No Child Left Behind, teachers are required to find methods to give all students, including students with mild intellectual disability, access to the general education curriculum. The purpose of this study was to investigate the effects of instruction integrating the…

The internal/external frame of reference (I/E) model and dimensional comparison theory posit paradoxical relations between achievement (ACH) and self-concept (SC) in mathematics (M) and verbal (V) domains; ACH in each domain positively affects SC in the matching domain (e.g., MACH to MSC) but negatively in the nonmatching domain (e.g., MACH to…

Intervention models based on data use can be effective in raising student achievement. This article presents 3 studies of one such model which had reported improved reading comprehension levels in 7 poor urban multicultural schools serving indigenous and ethnic minority communities. The intervention (the Learning Schools Model) used a process…

The reciprocal internal/external frame of reference model (RI/EM) combines the internal/external frame of reference model and the reciprocal effects model. The RI/EM predicts positive effects of mathematics and verbal achievement and academic self-concepts (ASC) on subsequent mathematics and verbal achievements and ASCs within domains and negative…