A model of instruction is a set of strategies that guide teachers in their instructional practice. The purpose of this paper is to dispel the myth that mathematics teaching in Singapore schools is all about drill and practice, as perceived of many Asian systems. This paper draws on data of a large project that examined the enactment of school…

This paper uses the commognitive framework to analyse how a group of four primary school students classify odd and even numbers. The findings show how students' reasoning is grounded in their personal uses of "odd" and "even". The students attend to different features of "oddness" and "evenness" and agree on…

This paper describes the development and efficacy of an online tool for assessing the numeracy of undergraduate students. The tool was designed to be easy to administer, provide immediate feedback to students on whether they had the required level of numeracy, and to be consistent with other measures of adult numeracy. When used with students…

Pedagogical Content Knowledge (PCK) is a powerful construct for examining the complexity of teacher knowledge. Together with teachers' moment-by-moment choices of action, it provides insight into teachers' knowledge and its influence on student learning. This paper investigates the PCK experienced by a senior secondary mathematics class during a…

A significant number of students who enroll in community colleges are placed in remedial courses for which the credits do not count toward degree attainment. These remedial courses cost the same as first-year, credit-bearing college courses, and research indicates that students who enroll in these courses are less likely to finish their degree…

This quantitative, causal-comparative ex-post-facto study primarily examined differences in mathematics achievement between Latinx English Learner (EL) fourth-grade students instructed in English and Spanish within one-way dual/developmental additive elementary bilingual language programs but tested in English. Additional analyses examined the…

The aim of this research was to study and investigate first year university calculus students' misconceptions about how to use the definition of limit to find the first derivative of functions and then remediate these misconceptions by using APOS theory (Action, Process, Object, and Schema). Students (n = 82 female and male) were selected based on…

This qualitative semi-structured interview study investigated how the opportunity to learn with productive struggle emerges in a teacher's beliefs, anticipation, planning, teaching, and response to struggle in learning mathematics. In this study, the experiences of student struggle in the teaching and learning of fractions was investigated through…

Mathematics scores on the 2019 National Assessment of Education Progress increased by only two points for both fourth and eighth grade students since 2007, indicating that students continue to struggle in mathematics (National Center for Educational Statistics, 2007; U.S. Department of Education, 2019). The development of both conceptual and…

We apply an advanced data visualization technique, "Sankey diagram," to explore how middle-school students (N = 343) solved problems in a game-based algebraic notation tool. The results indicate that there is a large variation in the types of students' strategies to solve the problems, with some approaches being more efficient than…

Students with a learning disability (LD) are experts in their lived experiences within the classroom. Yet, little is known about the ways in which students with LD perceive their instruction in mathematics and whether this instruction meets their learning needs. Similarly, the mathematical thinking and content knowledge of students with LD is…

Measures of teacher mathematical knowledge are notoriously difficult to develop (e.g., Orrill et al., 2015). This is in part because of the multidimensional nature of teacher knowledge. As part of two separate projects being undertaken by this research team, we have attempted to write assessments of teacher pedagogical content knowledge (PCK) in…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

Mathematics education is important for students with developmental disabilities. Additional research is needed that examines interventions to teach grade-level mathematics content to these students. In this single-case multiple probe across participants study, researchers explored the functional relation for four middle school students with…

Mathematics education is constantly changing due to the growing use of computers worldwide, and these global changes greatly affect mathematics education. In a computerized and changing society, it is paramount schools prepare students to acquire both procedural knowledge and conceptual knowledge in mathematics. In the state of Georgia, fourth…