Understanding equivalence is fundamental to STEM disciplines, but many students struggle with the concept. We present a novel method for students to explore ideas of equivalence where students dynamically transform expressions from initial states to goal states in the web-based app Graspable Math. The structure of the goal state activities implies…

The current study investigated how prior knowledge moderated the effects of three educational technologies ("From Here to There," "DragonBox 12+," and problem sets in "ASSISTments") on seventh-grade students' later algebraic knowledge. Pretest scores only moderated effects of "From Here to There," with…

This paper examines the mathematics content knowledge of graduate entry middle school mathematics pre-service teachers at the beginning (n=105; 80%) and end of a mathematics curriculum course. It was found that mathematics content knowledge at the commencement of the course was not strong. An intervention was designed to take account of content…

We share results of a study on the analytic stances of coaches' and teachers' as they annotated key moments from classroom video of the teacher's lessons. In the analysis, emphasis was on the analytic stances of the coaches and how their annotations related to trends in teachers' annotations. Findings indicate differences in how coaches and…

Homeland is generally the land where one person was born and grew up and also it is a broad concept that includes language, history, culture and family ties as well as being the land that a nation freely lives on. Homeland is not only a physical space, but a strong association of cultures, arts assets, and language, religion and common past…

Open-ended questions in mathematics are commonly used by teachers to monitor and assess students' deeper conceptual understanding of content. Student answers to these types of questions often exhibit a combination of language, drawn diagrams and tables, and mathematical formulas and expressions that supply teachers with insight into the processes…

The overall project "Denken lernen - Probleme lösen" has been expanded in recent years after an initial sub-project in elementary school to include one for the lower secondary level. Schools throughout Austria were provided with the micro:bit and related materials. A training initiative for teachers was rolled out. In this article I…

Learning experience designers consistently balance the trade-off between open and close-ended activities. The growth and scalability of Computer Based Learning Platforms (CBLPs) have only magnified the importance of these design trade-offs. CBLPs often utilize close-ended activities (i.e. Multiple-Choice Questions [MCQs]) due to feasibility…

Understanding fraction as a quantity has been identified as a key developmental understanding. In this study, students in Grades 5, 8, and 11 were asked to compare the areas of two halves of the same square--a rectangle and a right triangle. Findings from this study suggest that students who understand fraction as a quantity use reasoning related…

"Papel y lápiz" (Paper and pencil) is the result of a qualitative research project carried out using the Participatory Action Research (PAR) as a model. "Papel y lapiz" seeks to teach young people and children, who are identified as being at high social risk, in 35 different public educational institutions (PEIs) from Cartagena…

Covariational reasoning and the creation and interpretation of graphs of covariational situations are important skills in math and science. Unfortunately, research shows that students often struggle to make meaningful connections between graphs and the covariational situations they represent. Educational activities designed to help students…

This paper draws on numerous data sources to better understand the shift from additive to multiplicative thinking in years 4 to 9. Research studies that have used the Scaffolding Numeracy in the Middle Years assessment tasks have found that while students can be supported to move through the early and upper zones of the Learning and Assessment…

In this paper, we explore student solutions to a free response mathematical assessment task which had opportunities for students to notice structural properties in the context of number systems. In total, 308 students aged between 10 years to 13 years participated in the study. Their responses were analysed to determine whether they noticed…

One pedagogical technique that promotes conceptual understanding in mathematics learners is self-explanation integrated with worked examples (e.g., Rittle-Johnson et al., 2017). In this work, we implemented self-explanations with worked examples (correct and erroneous) in a software-based Intelligent Tutoring System (ITS) for learning algebra. We…

In this study, based on the analysis of a teaching experiment with middle school students, we propose a framework for describing meanings of a point represented on a plane in terms of multiplicative objects in the context of graphing. We classify those meanings as representing: (1) non-multiplicative objects; (2) quantitative multiplicative…