On Guåhan (Guam), the large percentages of students enrolling in non-credit-bearing courses at Kulehon Kumunidåt Guåhan (Guam Community College) and Unibetsedåt Guåhan (University of Guam) have raised concerns about college readiness and early college success. Without adequate research on predictors of college readiness and early success among…

These are the appendixes for the study, "Using High School Data to Predict College Readiness and Early College Success on Guåhan (Guam)." On Guåhan (Guam), the large percentages of students enrolling in non-credit-bearing courses at Kulehon Kumunidåt Guåhan (Guam Community College) and Unibetsedåt Guåhan (University of Guam) have raised…

On Guåhan (Guam), the large percentages of students enrolling in non-credit-bearing courses at Kulehon Kumunidåt Guåhan (Guam Community College) and Unibetsedåt Guåhan (University of Guam) have raised concerns about college readiness and early college success. Without adequate research on predictors of college readiness and early success among…

High school calculus has become indispensable for students seeking a college degree in a STEM field. However, in the present study, we argue that the mathematics opportunities that students seize (when afforded) in middle grades are the key to earning calculus credit in high school. To take calculus in high school, students usually need to take…

The field of mathematics education research has seen a resurgence of interest in understanding collaborative learning because students in K-12 classrooms are increasingly expected to make sense of mathematics problems together. This Research Commentary argues for the importance of understanding student authority relations in collaborative…

This study presents a methodology for investigating teacher learning in and from practice based on "discourses" that are in constant flux and transformation. Conceptualizing teacher learning as a frame of meaning based on "knowing" and "doing" discourses, the ideas are illustrated through data collected from a…

To make progress toward ambitious and equitable goals for students' mathematical development, teachers need opportunities to develop specialized ways of knowing mathematics such as mathematical knowledge for teaching (MKT) for their work with students in the classroom. Professional learning communities (PLCs) are a common model used to support…

The Common Core State Standards for Mathematics (CCSSM) states that high school students should be able to recognize patterns of growth in linear, quadratic, and exponential functions and construct such functions from tables of data (CCSSI 2010). In their work with practicing secondary teachers, the authors found that teachers may make some tacit…

"The root of 18 is closer to 4 than it is to 5 because 18 is closer to 16 than it is to 25". Is this statement, voiced in an 8th grade class, valid? We suggest hypothetical arguments upon which this statement might be based, and analyze them from two complementary perspectives--epistemic and pedagogical--drawing on Toulmin's notion of…

During their middle and early high school years, students generally finalise their attitude towards mathematics and their perception of themselves as students of mathematics, in terms of aptitude, motivation, interest, and competence. Therefore, giving them varied opportunities to foster a positive and successful approach to the study of…

In this paper, an investment problem is investigated in terms of elementary algebra, recurrence relations, functions, and calculus at high school level. The problem comes down to understanding the behaviour of a function associated with the problem and, in particular, to finding the zero of the function. A wider purpose is not only to formulate…

Effectiveness of mathematical education as non-linear, composite and open system, formation and development of cognitive abilities of the trainee are wholly defined in the solution of complex tasks by means of modern achievements in science to high school practice adaptation. The possibility of complex tasks solution arises at identification of…

The purpose of this research was to reveal how the construction process of symbolic representation and verbal representation made by students in problem solving. The construction process in this study referred to the problem-solving stage by Polya covering; 1) understanding the problem, 2) devising a plan, 3) carrying out the plan, and 4) looking…

In this article, we consider the potential influences of the study of proofs in advanced mathematics on secondary mathematics teaching. Thus far, the literature has highlighted the benefits of applying the conclusions of particular proofs to secondary content and of developing a more general sense of disciplinary practices in mathematics in…

A first-year algebra student's curiosity about factorials of negative numbers became a starting point for an extended discovery lesson into territory not usually explored in secondary school mathematics. In this article, the authors, math teachers in Massachusetts, examine how to solve for factorials of negative numbers and discuss how they taught…