This mixed methods study explores secondary students' math identities. The primary purpose of this dissertation is to examine the relationships among students' math identities, their perceived problem solving practices, and their perceived self-regulated learning strategies. This study holds implications for teachers, school administrators,…

The strategy choice model (SCM) is a highly influential theory of human problem-solving. One strength of this theory is the allowance for both item and person variance to contribute to problem-solving outcomes, but this central tenet of the model has not been empirically tested. Explanatory item response theory (EIRT) provides an ideal approach to…

This paper reports the results of an investigation into the ways pre-service teachers engaged in structured problem solving as part of their first-year mathematics education course. The purpose of this study was to determine the preferred problem solving strategies of pre-service teachers and the types of difficulties they experienced. The written…

Today, beginning algebra in the high school setting is associated more with remediation than pride. Students enroll by mandate and attend under duress. Class rosters in this "graveyard" course, as it is often referred to, include sophomores and juniors who are attempting the course for the second or third time. Even the ninth graders…

Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

The simple question of how much paper is left on my toilet roll is studied from a mathematical modelling perspective. As is typical with applied mathematics, models of increasing complexity are introduced and solved. Solutions produced at each step are compared with the solution from the previous step. This process exposes students to the typical…

Rhetoric about the importance of students being equipped to apply mathematics to relevant problems arising in their lives, individually, as citizens, and in the workplace has never been matched by serious policy or curricular support. This paper identifies and elaborates authenticity implications for addressing this issue, and describes aspects of…

The problem-posing process represents one of the forms of authentic mathematical inquiry which, if suitably implemented in classroom activities, could move well beyond the limitations of word problems, at least as they are typically utilized. The two exploratory studies presented sought to investigate the impact of "problem-posing" activities when…

Interesting and engaging mathematics problems can come from anywhere. Sometimes great problems arise from interesting contexts. At other times, interesting problems arise from asking "what if" questions while appreciating the structure and beauty of mathematics. The intriguing problem described in this article resulted from the second…

Background: In the last decades, children's understanding of mathematical principles has become an important research topic. Different from the commutativity and inversion principles, only few studies have focused on children's understanding of the addition/subtraction complement principle (if a - b = c, then c + b = a), mainly relying on verbal…

Writing in mathematics provides students with the opportunity to think critically about and reflect on their experiences while solving problems. While many studies have documented the benefit of writing in math, it is not clear which instructional methods should be used to help students learn how to use writing to support learning. In this study,…

The purpose of this investigation was to identify strategies used by effective instructors of developmental mathematics, and to discover the perceptions developmental mathematics students have about these strategies. While there are research projects focusing solely on developmental mathematics achievement, this study fills a need by incorporating…

Homework is transforming at a rapid rate with continuous advances in educational technology. Computer-based homework, in particular, is gaining popularity across a range of schools, with little empirical evidence on how to optimize student learning. The current aim was to test the effects of different types of feedback on computer-based homework.…

The concept of multiple representations of functions and the ability to make translations among representations are important topics in secondary school mathematics curricula (Moschkovich, Schoenfeld, & Arcavi, 1993; NCTM, 2000). Research related to students in this domain is fruitful, while research related to teachers is underdeveloped. This…

This study investigates interactions between calculus learning and problem-solving in the context of two first-semester undergraduate calculus courses in the USA. We assessed students' problem-solving abilities in a common US calculus course design that included traditional lecture and assessment with problem-solving-oriented labs. We investigate…