The goal of this paper is twofold. First, the paper clarifies and elaborates on an important theoretical construct called orientation with respect to understanding in mathematics, which denotes the degree to which students exhibit an inclination towards and demonstrate an earnest concern for understanding in mathematical learning. Second, the…

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, proposes that…

Measures of teacher mathematical knowledge are notoriously difficult to develop (e.g., Orrill et al., 2015). This is in part because of the multidimensional nature of teacher knowledge. As part of two separate projects being undertaken by this research team, we have attempted to write assessments of teacher pedagogical content knowledge (PCK) in…

In this paper, we extend our previous work on challenges teachers face when engaging with proportional reasoning contexts to investigate two contexts that included four problems for middle grades teachers to solve as well as eight student solutions. Analysis included coding for correct solving of the problem as well as making sense of and…

This study explores show students' secondary history classroom experiences related to their learning new knowledge and skills. Findings indicate that all students improved on pre-test and post-test scores. In think-alouds of the test students could often reference class activities that helped them learn. However, their ability to correctly answer…

Most studies which investigate mathematics teacher noticing cast perception into a passive role. This study develops an ecological analysis of mathematics teachers' noticing in order to investigate how teachers actively look for information in classroom environments. This method of analysis is applied to data collected as an experienced primary…

Despite the importance placed on how children come to solve single-digit addition problems, many children count on to solve these problems when they are expected to use accurate retrieval-based strategies. In this study, we assessed if a subitising intervention improved the rate at which problem-solving practice promoted retrieval, using a…

This study examines a teacher's questioning strategies in mathematics classrooms in China when implementing reform-based mathematics curriculum. It explores teacher's strategies to deal with the tensions involved in the creation of opportunities for students to express and communicate mathematics ideas while ensuring the productivity of…

While collaborative Intelligent Tutoring Systems (ITSs) have been designed for older students and have been shown to support sense-making behaviors, there has not been as much work on creating systems to support collaboration between elementary school students. We have developed and tested, with 84 students, individual and collaborative versions…

This article is a report on the findings of three case studies that focused on elementary teachers' in-the-moment noticing across a month of instruction. Extending Jacobs and her colleagues' framework (Jacobs, Lamb, and Philipp, 2010), this articles categorizes the mediums (i.e., written accounts, verbal interactions, physical strategies) by which…

The authors present an analysis of facilitation across three cohorts of a phase-two professional development project. Four types of discourse are introduced and defined (correcting, eliciting, probing, and responsive). The analysis attends to implementation fidelity and facilitator moves in light of these four types of discourse. Conjectures about…

The goal of this study was to explore the educational potential of Minecraft. This project was conducted with 118 elementary-school students from Canada during the 2016-2017 school year. To explore the educational potential of Minecraft on the students, we designed a "Minecraft challenge" for students. 10 game levels of ascending…

The World Bank 2007 TIMSS Video Study provided a distinctive insight into the practices of the Indonesian classroom and identified key strengths and weaknesses of current teaching. This investigation considered this evidence in the development of a structured lesson design that specifically addressed the instructional practices of the teaching and…

This paper examines the role of scaffolding in the process of abstraction. An activity-theoretic approach to abstraction in context is taken. This examination is carried out with reference to verbal protocols of two 17 year-old students working together on a task connected to sketching the graph of |f|x|)|. Examination of the data suggests that…

A study examined the relative merits of characteristics of general modeling when applied to cognitive modeling of reading comprehension processes and whether the characteristics of modeling, when applied to cognitive modeling of reading processes, influence comprehension and comprehension monitoring. Subjects, 100 eighth grade students who could…