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 paper describes the conceptions about complex numbers that a group of university students has, these were built from the application of an activity sequence centered on these numbers. This sequence is based on the APOS theory, some aspects of semiotic representation theory, and the use of digital technology. Particularly, both the general…

In recent studies, test-score increases have been shown in rule-based intelligence test tasks, such as number series, after watching a corresponding video tutorial. An open question remains regarding the mechanisms involved. Specifically, taking notes to describe the relations between numbers might be linked to test scores, and is hypothesized to…

The understandings prospective mathematics teachers develop by focusing on quantities and quantitative relationships within real numbers have the potential for enhancing their future students' understanding of real numbers. In this article, we propose an instructional sequence that addresses quantitative relationships for the construction of real…

We introduce a methodology for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We studied 12 pre-service teachers as they solved a set of fractions tasks, ranked by cognitive demand. We present the unit transformation graphs for one of those pre-service teachers, to illustrate how she experienced and met…

Adult proficiency in numeracy in the United States lags that of other developed nations, and the nonselective institutions that dominate the higher education sector struggle to address the learning needs of the sizeable proportion of students who enroll in their institutions and are deemed academically underprepared in mathematics. Research on…