This project describes a way to help students recognise that the expressions on both sides of the equals sign are the same. It was developed to support teachers in disadvantaged communities to help their students make sense of mathematics.

Algebraic reasoning is foundational to all mathematical thinking. This is no less the case in the early years of school, where the capacity to recognise the structure of mathematical processes enables students to acquire deep conceptual understanding. It is through algebra, therefore, that students are able to explore and express mathematical…

We build on research connecting teaching assignments to teacher effectiveness by examining the characteristics of secondary grades mathematics teachers with more course preparations--both the unique number of courses taught and courses never taught before--and by assessing whether additional course preparations predict teacher value-added.…

Remedial/developmental and introductory university mathematics courses have a long history of high attrition rates. Recently, university administration and mathematics departments have been considering technological solutions, and one such solution is computer-adaptive-instruction (CAI). In fact, CAI has been touted as a "silver bullet"…

Enrollment in eighth-grade algebra doubled from the 1990s to 2012 (National Center for Education Statistics, 2013) as research demonstrated that Algebra I operates as a "gateway" to advanced mathematics courses in high school (Adelman, 2006), and that students who succeed in Algebra I in middle school have more success in mathematics…

The mathematics test is the most difficult test in the GED (General Education Development) Test battery, largely due to the presence of story problems. Raising performance levels of story problem-solving would have a significant effect on GED Test passage rates. The subject of this formative research study is Ms. Stephens' Categorization Practice…

In this study, I examined links between College Algebra students' covariational reasoning and their conception of general function notation (y = f(x)). I investigated the following research questions: How might students' conceptions of function impact their conceptions of function notation? How might covariational reasoning related to function…

Previous research has found that different presentations of the same concept can result in different patterns of transfer to isomorphic instances of the same concept. Much of this work has framed these effects in terms of advantages and disadvantages of concreteness or abstractness. We note that mathematics is a richly structured field, with…

Binary operation is one of the main topics of undergraduate mathematics. A binary operation is also used as a foundation for other disciplines such as physics, chemistry and biology. This study aims to describe the conceptual knowledge level of pre-service mathematics teachers regarding binary operation. In order to achieve this, a test consisting…

The importance of students being acquainted with algebraic ideas before secondary education has been revealed in the research literature. It is therefore essential that prospective elementary teachers (PTs) be prepared to instill an early algebra perspective in their teaching. However, PTs often show difficulties in algebra content knowledge,…

The purpose of this study was to investigate the possibility of a relationship between second-order change leadership behaviors of high school administrators and changes in student achievement on the Florida Standards Assessment English Language Arts/Reading component and the Algebra 1 End of Course examination in two large urban school districts.…

Data science has maintained its popularity for about 20 years. This study adopts a bottom-up approach to understand what data science is by analyzing the descriptions of courses offered by the data science programs in the United States. Through topic modeling, 14 topics are identified from the current curricula of 56 data science programs. These…

The purpose of this non-experimental, correlational, explanatory, cross-sectional design with quantitative methods was to examine the relationship between the length of the school day and the percentage of students who achieved Met Expectations and Exceeded Expectations scores on the 2018 Partnership for Assessment of Readiness for College and…

In this study, I examined how 34 Spanish-speaking English language learners (ELLs) used their linguistic resources (English and Spanish) and language modes (oral and written language) to demonstrate their knowledge of proportional reasoning in a dual language mathematics assessment task. The assessment allows students to see the item in both…

One of the challenges of understanding the complexity of so-called reform mathematics instruction lies in the observational tools used to capture it. This article introduces a unique tool, drawing from commognitive theory, for describing classroom discussions. The Realization Tree Assessment tool provides an image of a classroom discussion,…