In this theoretical paper, I use an empirically based example to illustrate particular design features of the Learning Through Activity (LTA) design framework and examine the impact of particular design principles. The LTA design framework is based on our elaboration of Piaget's construct of reflective abstraction. The example discussed here,…

Teachers are key users of classroom assessment data; however, their needs and preferences are often overlooked in the design and development of the assessments themselves. We used principles of Human-Centered Design (HCD) to systematically solicit, study, and integrate teachers' needs in the design and development of a classroom-based early…

The aim of this article is to present a pedagogical approach for history education. This approach is called Meaningful History and it outlines the process by which upper-level secondary history students can cultivate historical consciousness. Based on the notion of learning as meaning making and historical consciousness as a disposition to engage…

How instructional sequences guide learning processes are often regarded as a neutral act. However, does designing instruction carry a politics? This investigation explores how instruction is made as a pedagogical object. The purpose is to explore the epistemological principles and conceptual framework that produce instruction's formalized…

In 2020, two teachers and seven students participated in an action research project that sought to improve the teaching and learning of fractions in a New Zealand primary school. This research revealed that the collaborative creation of hypothetical learning trajectories was beneficial to the teachers' practice, content knowledge, and confidence,…

Background and Context: Since the surge of grounded cognition (GC) theories in cognitive psychology, many studies have focused on demonstrating the importance of embodiment and sensorimotor activities on students' conceptual development. In computing education, however, there is not yet a conceptual framework for developing age-appropriate.…

We discuss the importance of bringing teaching to the forefront of instructional design. We do so by describing the process of developing an instructional sequence for early number, using design research. The instructional sequence was developed with the specific aim of supporting teaching, conceived as a complex and demanding job, not reducible…

This study aims to establish a knowledge base on how to support students in learning. We develop an initial hypothetical learning trajectory by formulating learning activities and predicting the development of students' thinking and understanding. The methodological framework employed in this study is design research, which seeks to generate…

The Association of Mathematics Teacher Educators recommends that well-prepared beginning mathematics teachers apply their understanding of mathematics, curriculum, pedagogy, student learners, and social constructions to facilitate mathematics learning for all students. Using the context of a secondary methods course, where prospective mathematics…

This research report describes a Learning Trajectory-based Curricular Design project that engaged teachers and coaches in the design and implementation process. As the project team, we focused on deepening teacher designers' understanding of the learning trajectory (LT) while situating student learning along a continuum to advance student…

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…

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…

In this paper, we present the development of an investigation on the promotion of covariational reasoning in high school students (14-15 years old) in Mexico. The study consists of designing and applying a sequence of didactic activities that simulate a real situation virtually. The activities are organized through a Hypothetical Learning…

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…

Learning the content of entrepreneurship arithmetic is an extension of social arithmetic that focuses on mathematical calculations in business or creative economy. Most teachers do not link students' daily activities to classroom teaching and learning on traditional markets around the environment. This significantly affects the interest in…