This study compares the relative influence of syntax, semantics, and pragmatics in university students' interpretation of multiply quantified statements in mathematics, both before and after instruction. Like previous studies, results show that semantics plays a heavy role in student interpretation, especially before instruction. Unlike previous…

We describe how we supported middle-school students developing meanings for quadratic growth by bringing together three theoretical framings and designing a task sequence grounded in that framework. Specifically, this framework was assembled from the research on students' quantitative and covariational reasoning, Realistic Mathematics Education,…

Reflection on the theme of the paper makes one to remember Sir Snow's 1959 lecture on The Two Cultures in which Snow had advanced the thesis that the sciences and the humanities had become split into two cultures and had argued that this division had become a major handicap to solving the world's problems. Mathematics education itself has always…

Do you sometimes start to teach a mathematics concept and feel like you are staring at a sea of bewildered faces? What happens when you discover that students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to…

Do you sometimes start to teach a mathematics concept and feel like you are staring at a sea of bewildered faces? What happens when you discover that students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to…

Do you sometimes start to teach a mathematics concept and feel like you are staring at a sea of bewildered faces? What happens when you discover that students previously learned a calculation trick or a mnemonic that has muddied their long-term understanding? When "rules" seem to change from year to year, teacher to teacher, or school to…

Research on middle-level schools and student achievement revealed a drop in academic performance when students transitioned from elementary school to a traditional middle school. In the United States, the middle school years have historically seen a decline in student achievement following a transition from elementary school. According to the…

In this paper, we explore how students' algebraic noticing's and explanations changed across a two-year period with the introduction of designed instructional material. The data in this report is drawn from n=53 Year 7-8 students' responses to a free-response assessment task across two different years. Analysis focused on how students noticed and…

Background: Previous research examined the relationship between teaching characteristics and constructs of attitudes towards mathematics (ATM) from the student perspective in isolation. Aims: This study aims to survey the relationship between instructional clarity and classroom management and ATM constructs (i.e., mathematics self-concept,…

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate a series of six mathematical arguments, purportedly produced either by fellow mathematicians or undergraduate students. In this paper, we attend to the role of context in mathematicians' responses, leading to four themes in expectations when…

Curriculum-based measurement (CBM) has conventionally included accuracy criteria with recommended fluency thresholds for instructional decision-making. Some scholars have argued for the use of accuracy to directly determine instructional need (e.g., Szadokierski et al., 2017). However, accuracy and fluency have not been directly examined to…

Objective: In Spring 2020 when COVID-19 hit, community colleges moved almost all classes online. This disruption impacts recent math reforms, including contextualization, raising concerns about sustained faculty and institutional leadership commitment. This study investigated how community college faculty teaching contextualized math courses…

In this paper we consider how the integration of mobile technology apps into classroom practice can form an alternative pedagogical medium that influences the learning process in mathematics. We give an account of one aspect of a research project that examined the use of tablets and apps in primary school mathematics programmes and report teacher…

The purpose of this study was to determine the extent to which professional development on assessment for learning improves pre-service teachers' self-regulated learning. Helping students develop self-regulation abilities in learning and assessment remains difficult due to the widespread culture of summative assessment in teacher education. A…

This paper investigates how to reduce the theory-practice gap by making research the object of discussion for researchers and practitioners. The study is situated in the wicked problem of using digital technology in mathematics education. To investigate this problem a workshop of the format data-sprint is conducted, investigating the challenges…