Background: Early patterning competence has recently been identified as an important precursor of mathematical development. Whereas the focus of this research has been on children's ability regarding repeating patterns, children might also differ in their spontaneous attention to patterns. Aims: The present study aimed to explore 4- to 5-year…

Secondary students with persistent mathematics difficulties need the most intensive intervention in order to improve their mathematics outcomes. One approach to intensifying and individualizing intervention is through data-based individualization (DBI). The present study used a single-subject, multiple-baseline-across-participants,…

For many of my students, Real Analysis I is the first, and only, analysis course they will ever take, and these students tend to be overwhelmed by epsilon-delta proofs. To help them I reordered Real Analysis I to start with an "Analysis Boot Camp" in the first 2 weeks of class, which focuses on working with inequalities, absolute value,…

The paper firstly clarified the characteristic of competencies being discussed in African countries by comparing them with competencies being discussed in developed countries. It has become clear that both countries are very similar. In other words, against the background of rapidly increasing internationalization and globalization, the…

The importance of reasoning quantitatively is reflected in both mathematics education research and mathematical standards for K-12 students. In this article, we detail how a quantitative reasoning framework can be used to help differentiate two quantities we have found students often struggle with: arc length and the measure of a central angle. We…

Most of the research examining the relation between instructional quality (INQUA) and mathematics teachers' competence was restricted to a limited set of competence facets. Furthermore, mostly variable-oriented approaches were applied that assume homogeneity of teacher competence. In our study, teacher competence is conceptualized as a…

Mathematical argumentation, justification, and proof are practices at the heart of mathematics. Yet mathematics teachers generally operate without clear definitions of these practices making it difficult to communicate expectations, decide what to accept or expect from students at different grade levels, and distinguish these activities from…

Can a school or district improve student achievement simply by switching to a higher quality textbook or curriculum? We conducted the first multi-textbook, multi-state effort to estimate textbook efficacy following widespread adoption of the Common Core State Standards (CCSS) and associated changes in the textbook market. Pooling textbook adoption…

Mathematical proof is a logically formed argument based on students' thinking process. A mathematical proof is a formal process which needs the ability of analytical thinking to solve. However, researchers still find students who complete the mathematical proof process through intuitive thinking. Students who have studied mathematical proof in the…

In educational research, the cognitive activity of problem posing is recognized as an important component of mathematics teaching and learning. Compared to the prevailing educational paradigm of problem solving, problem posing features less commonly in classroom instruction. During the past 20 years, numerous studies examining the use of problem…

Ongoing policy discussions emphasize the need for more STEM professionals to keep the United States internationally competitive in scientific fields and industry. From a K-16 perspective, it is important to note that students' trajectories into STEM professions are often shaped by their high school experiences--especially in mathematics.…

The research literature on middle grades mathematics teachers' mathematical literacy indicates that mathematical problem solving and problem posing are essential skills for mathematics instruction, and that teachers must be skilled in mathematical problem solving and mathematical problem posing. However, it is not well known how these two skills…

An increasing number of high school students are enrolling in statistics courses. Hence, an increasing number of teachers are needed to plan and implement these courses. Yet, many teachers report feeling unprepared to teach statistics. When planning and implementing these courses, teachers draw upon their knowledge and beliefs when making…

Community colleges began as a way to offer higher education to those that wanted it but could not leave home to further their degree. As they evolved, they began allowing students to be admitted with very little admission requirements. The lack of admission requirements led to students being admitted into community colleges that were not prepared…

While teacher evaluation policies have been central to efforts to enhance teaching quality over the past decade, little is known about how teachers change their instructional practices in response to such policies. To address this question, this paper drew on classroom observation and survey data to examine how early career teachers' (ECTs')…