This qualitative research study uses middle-grades students' numerical reasoning to model their symbolic representations of the relationship between two multiplicatively related unknowns on an algebra task. Students in sixth grade through ninth grade participated in clinical interviews that assessed their numerical reasoning using the Number…

Quantitative reasoning takes on different meanings based on experience and background. Across the curriculum students have various needs for their quantitative reasoning experience. As a result, at our university students have a range of choices that more closely fit their future needs. Seven different departments across campus offer quantitative…

Understanding the magnitudes represented by numerals is a core component of early mathematical development and is often assessed by accuracy in situating numerals and fractions on a number line. Performance on these measures is consistently related to performance in other mathematics domains, but the strength of these relations may be…

Preparing graduates for employment is the goal of postsecondary education. In response to the national quantitative reasoning deficiency, institutions have joined nationwide to align college math content and learning outcomes to meet the needs of common careers and everyday life. The problem addressed in this study is that traditional college math…

Problem solving and reasoning are two key components of becoming numerate. Reports obtained from international assessments show that Australian students' problem solving ability is in a long-term decline. There is little evidence that teachers are embracing problem solving as part of the classroom routine. In this study, we analyse 598 Year 7 to…

This study investigated the role of tools in supporting students to reason about even and odd numbers. Participants included Kindergarten, Grade 1, and Grade 2 students (ages 5-8) at two schools in the USA. Students took part in a cross-sectional early algebra intervention in which they were asked to generalize, represent, justify, and reason with…

Issues within college algebra are well-documented. Over the past two decades, reform has brought about significant modifications in the course, yet to date there has been no synthesis of the efficacy of these efforts. This paper situates college algebra within a historical context, and synthesizes research on reform. I argue that, notwithstanding…

Adults with learning disabilities (LD) face educational and employment challenges and may also have other disabilities and health conditions. Little is known about these adults' numeracy skills and how they use numeracy at work or home. The article's objective was to investigate numeracy skills and skill use for U.S. adults with LD. The author…

Federal legislation requires every student receive access to and make progress in the general curriculum. Teachers have reported difficulties in meeting this requirement for students with extensive support needs (ESN) who do not yet demonstrate foundational academic skills, such as in the areas of literacy and numeracy. Once students enter high…

Numerical magnitude knowledge is related to current math abilities and predictive of future math learning. However, this relationship has previously been shown only for knowledge of positive magnitudes; the present study is the first, to our knowledge, to examine the connection between magnitude knowledge and math ability with negative integers.…

South African Mathematical Literacy (ML) learners are unlikely to have mastered the mathematical skills essential for undergraduate degree studies in Business Science and are most likely to commence tertiary studies in a foundation programme (FP). One such FP at one private higher education institution included an algebra course and provided an…

We investigated how the opportunity to learn (OTL) with different types of mathematics tasks are related to mathematical literacy and the role of perceived control in the relationship between OTL and mathematical literacy. The structural equation modeling was applied to the data of 1,649 Korean students from the PISA 2012 database. OTL with the…

The capacity to recognise, represent, and reason about relationships between different quantities, that is, to think multiplicatively, has long been recognised as critical to success in school mathematics in the middle years and beyond. Building on recent research that found a strong link between multiplicative thinking and algebraic, geometrical,…

Background: Key to optimizing Computational Thinking (CT) instruction is a precise understanding of the underlying cognitive skills. Román-González et al. (2017) reported unique contributions of spatial abilities and reasoning, whereas arithmetic was not significantly related to CT. Disentangling the influence of spatial and numerical skills on CT…

Low passing rates in developmental mathematics have been a serious concern for community colleges for many years. A course in Quantitative Literacy (QL) offers non-STEM students an alternative option to introductory algebra as a path to a degree. This paper describes the implementation and evolution of QL at the Borough of Manhattan Community…