This study aims to analyse teachers' understanding of realistic mathematics education (RME) through a blended workshop on designing an RME-based learning trajectory. Data was collected via online pre-test and post-test, involving mathematics teachers of junior high schools in Banda Aceh, Indonesia. The tests were accompanied by interviews, chats…

Children's informal and formal learning experiences with geometric shapes currently result in misconceptions that persist into adulthood. Here, we combine research from mathematics education as well as cognitive science pertaining to concepts, categories, and learning strategies to propose a more optimal progression that is better specified and…

In our data-driven society, it is essential for students to become statistically literate. A core domain within Statistical Literacy is Statistical Inference, the ability to draw inferences from sample data. Acquiring and applying inferences is difficult for students and, therefore, usually not included in the pre-10th-grade curriculum. However,…

Research on LTs remains a central topic in mathematics education. In this plenary paper, I argue that LT-based research needs a hard re-set if it is to play a role in creating more equitable and anti-oppressive experiences for historically marginalized students. I begin with an overview of LT-based research presented during PME-NA plenary…

Learning progressions have become increasingly prevalent in mathematics education as they offer a fine-grain map of possible learning pathways a child may take within a particular domain. However, there is an opportunity to build upon this research in ways that consider learning from multiple perspectives. Many current forms of learning…

The evolution of U.S. secondary school mathematics requirements throughout the 20th century included a significant shift towards more rigorous standards by the end of the century. Initially, many states required minimal or no mathematics for high school graduation. However, reforms led most states to adopt a 3-year mathematics requirement, with…

There is little empirical research related to how elementary students develop computational thinking (CT) and how they apply CT in problem-solving. To address this gap in knowledge, this study made use of learning trajectories (LTs; hypothesized learning goals, progressions, and activities) in CT concept areas such as sequence, repetition,…

This paper provides a case study account of a preservice secondary mathematics teacher's thinking while engaging in slope tasks using dynagraphs. The data included audio recordings and screen captures of a small group of preservice teachers engaging with these tasks, with our analysis focusing on the case of Robin. Despite familiarity using slope…

Background: With the increasing interdisciplinarity between computer science (CS) and other fields, a growing number of non-CS students are embracing programming. However, there is a gap in research concerning differences in programming learning between CS and non-CS students. Previous studies predominantly relied on outcome-based assessments,…

This research aimed to generate a learning trajectory in an introduction to early mathematics, precisely to measure learning using educational games and Realistic Mathematics Education (RME) and to describe young children's curiosity in learning early mathematics. Children need to have an understanding to take a measurement and use a learning…

Designers of critical mathematics instruction have documented difficulties in simultaneously fostering the development of critical consciousness while supporting students in developing understandings of new mathematics. However, confining justice-oriented tasks to applications of previously learned mathematics limits the degree to which these…

This paper explores how student performance across the full set of multiple modular assessments of individual standards, which we refer to as mini-assessments, from a large scale, operational program of interim assessment can be summarized using Bayesian networks. We follow a completely data-driven approach in which no constraints are imposed to…

Learning progressions have become an important construct in educational research, in part because of their ability to inform the design of coherent standards, curricula, assessments, and instruction. In this paper, I discuss how a learning progressions approach has guided our development of an early algebra innovation for the elementary grades and…

This study explores a spatial reasoning learning trajectory of a student with difficulty in mathematics. Using a teaching experiment methodology across 15 instructional sessions, we observed how the student responded to instruction based on an established 2D shape composition learning trajectory (Sarama & Clements, 2009). A narrative…

One challenge facing the fields of mathematics education and special education is how to design instruction on fraction concepts that can meet the needs of diverse learners. An innovation that shows promise is to base instructional design upon well-established trajectories of students' fraction learning. However, little research has been done to…