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In the post-pandemic world, UNESCO advocates the development of open educational resources (OER) to remedy the financial pressures of students and their families. We thus conducted a dual-cycle action research study aiming to develop a sustainable model with minimal cost for creating OER for secondary school mathematics teachers and students. Our theoretical foundations drew upon existing sustainable models of OER development and experiential learning theory to enhance the efficacy of OER. Formative evaluation techniques were employed in both action research cycles, where pre-service teachers developed the OER and in-service teachers provided suggestions for improvement. In the second cycle, we tested the use of our OER with 35 Grade 11 students to examine both student achievement and retention. The test results showed a significant learning gain (pre-test: Mdn = 2.00; post-test: Mdn = 10.00), which was retained over 2 weeks (delayed post-test: Mdn = 11.00). However, the students' performance on more advanced questions was not satisfactory. Based on an overall reflection on the study, we proposed a sustainable model of OER development, which leveraged the manpower of pre-service and in-service teachers and incorporated formative evaluation techniques. Furthermore, we provided recommendations for enhancing the future development of OER in mathematics education. [ABSTRACT FROM AUTHOR]

In this paper we describe learners being asked to generate examples of new mathematical concepts, thus developing and exploring example spaces. First we elaborate the theoretical background for learner generated examples (LGEs) in learning new concepts. The data we then present provides evidence of the possibility of learning new concepts through a symbiosis of induction and abduction from experience and deduction from the relationships generated in exemplification. In other words, experience can be organised in such a way that shifts of understanding take place as a result of learners’ own actions. Actions, in this context, include mental acts of organisational reflection. [ABSTRACT FROM AUTHOR]

In this paper we examine the possibility of differentiating between two types of nonexamples. The first type, intuitive nonexamples, consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples. The second type, non-intuitive nonexamples, consists of nonexamples that bear a significant similarity to valid examples of the concept, and consequently are more often mistakenly identified as examples. We describe and discuss these notions and present a study regarding kindergarten children’s grasp of nonexamples of triangles. [ABSTRACT FROM AUTHOR]

The CAME1 project was inaugurated in 1993 as an intervention delivered in the context of mathematics with the intention of accelerating the cognitive development of students in the first two years of secondary education. This paper reports substantial post-test and long-term National examination effects of the intervention, yet, by discussing the methodology used, questions the assumptions implicit in the original intention. It is now suggested that a better view is to regard CAME as a constructive criticism of normal instructional teaching, with implications for the role of mathematics teachers and university staff in future professional development. [ABSTRACT FROM AUTHOR]

My purpose in this paper is to present a didactic tool – a set of specially designed problems and questions for discussion – that can help making students better aware of the various aspects of the formal notion of limit of a sequence. The didactic tool will be justified using results from my own and other authors' research on students' naïve or erroneous conceptions of limit of a sequence. [ABSTRACT FROM AUTHOR]

Introduction: Reading and math proficiency are assumed to be crucial for the development of other academic skills. Further, different studies found reading and math development to be related. We contribute to the literature by looking at the relationship between reading and math using continuous time models. In contrast to previous studies, this allows us to (a) report estimates for autoregressive and cross-lagged effects for a range of possible time intervals while still only estimating one set of continuous time parameters and (b) identify peak effects for the relationship between the two. Using data from Starting Cohort 3 of the National Educational Panel Study, we find, in line with previous evidence, a larger effect of reading on math than the other way around. Furthermore, we identify peak standardized cross-lagged effects ( , ) for a time interval of approximately 6 months. [ABSTRACT FROM AUTHOR]

Photovoice is a participatory action research tool that is grounded in the literature for critical consciousness (Wang & Burris, ). Four creative high school girls who reported struggles with mathematics were given cameras and asked to take photographs to answer the following questions: (1) What is mathematics? (2) What is your ideal learning environment? (3) What things impede your learning of mathematics? Within-case and cross-case analyses of the photographs and interview responses were conducted. Each individual case was analyzed using the work of Belenky, Clinchy, Goldberger, and Tarule ( Women's Ways of Knowing, ) who investigated women's epistemological perspectives. The girls were either silenced (disconnected from the mathematical knowledge of the teacher), received (lacked confidence to do mathematics independently), or 'fragily' subjective (viewed mathematical knowledge as personal rather than imparted by the teacher) knowers of mathematics. The use of photovoice has the power to facilitate the nurturing of silence as it moves toward the 'roar which is on the other side of silence' (Belenky et al., , p. 4). [ABSTRACT FROM AUTHOR]

The general background of this study is an interest in how digital tools contribute to structuring learning activities. The specific interest is to explore how such tools co-determine students’ reasoning when solving word problems in mathematics, and what kind of learning that follows. Theoretically the research takes its point of departure in a sociocultural perspective on the role of cultural tools in thinking, and in a complementary interest in the role of the communicative framing of cognitive activities. Data have been collected through video documentation of classroom activities in secondary schools where multimedia tools are integrated into mathematics teaching. The focus of the analysis is on cases where the students encounter some kind of difficulty. The results show how the tool to a significant degree co-determines the meaning making practices of students. Thus, it is not a passive element in the situation; rather it invites certain types of activities, for instance iterative computations that do not necessarily rely on an analysis of the problems to be solved. For long periods of time the students’ activities are framed within the context of the tool, and they do not engage in discussing mathematics at all when solving the problems. It is argued that both from a practical and theoretical point of view it is important to scrutinize what competences students develop when using tools of this kind. [ABSTRACT FROM AUTHOR]

Interspersing easy problems among challenging problems has been shown to both increase students’ preference for completing math worksheets and the fluency with which they complete challenging problems. Although early research examining the interspersal procedure in mathematics was conducted with college-age students, there are a growing number of studies utilizing the interspersal procedure in elementary and secondary school settings. A particular concern with existing research however is whether the beneficial effects are maintained across multiple sessions and whether effects generalize when implemented with large groups of students. The current study addressed this concern by administering both control and interspersal math worksheets consisting of instructionally relevant problems to 75 fourth grade students across four sessions. Because students’ instructional levels differed, analyses were conducted separately for students identified as fluent and less fluent based upon student performance on the control worksheet administered during session 1. Dependent measures included digits correct and problems correct as well as students’ responses to four preference questions following each session. Although results differ from previous research in that students completed significantly more digits correct on control worksheets, explanations of these differences are examined and implications are discussed. [ABSTRACT FROM AUTHOR]

To reflect academic challenges and enrollment patterns of today’s freshmen, this study measures the impact of high school preparation, first-year academic performance, multi-institution enrollment, and financial aid support on second-year persistence. Using multi-year cohorts at a public research university, results confirm the importance of including first-year math experience, math intensity of the declared major, simultaneous enrollment at another college/university, and second-year financial aid offers when measuring freshmen retention. The positive impact of a large-scale, state-funded scholarship program in widening access to college must be balanced against findings that show academic performance and readiness to take on and pass first-year math to be more important than aid in explaining freshmen dropout and transfer-out during both first and second semesters. Middle-income students with greater levels of unmet need face an elevated departure risk, while academically well-prepared freshmen with unmet need are more likely to transfer to other institutions. [ABSTRACT FROM AUTHOR]

This study examined changes in 26 fourth-grade students' early conceptions of rational number representations as a function of receiving one of two curricular interventions. The first group of 12 students received a curriculum that emphasized constructing knowledge through extended problem solving with a single perspective of the rational number domain based on part-whole relations. A second group of 14 students received a curriculum that emphasized a more conceptually diverse multiple perspective view of the domain through problem solving with operator and ratio relations. Analyses of the students' rational number knowledge before and after the interventions indicated that students in the single perspective group produced organizations of knowledge that more frequently diverged from a formal domain analysis than those produced by students in the multiple perspective group. Further, students in the single perspective group increased their focus on superficial surface features. Alternatively, students in the multiple perspective group demonstrated an increased focus on operations that more frequently reflected the underlying mathematical relation conveyed by the representation. The findings indicate that an early exposure to more diverse perspectives of rational numbers assists students in developing more interconnected and viable representation knowledge for rational numbers. [ABSTRACT FROM AUTHOR]