In the context of an analytical geometry, this study considers the mathematical understanding and activity of seven students analyzed simultaneously through two knowledge frameworks: (1) the Van Hiele levels (Van Hiele, 1986, 1999) and register and domain knowledge (Hibert, 1988); and (2) three action frameworks: the SOLO taxonomy (Biggs, 1999;…

In this paper, we present a novel approach to defining, teaching, and assessing creativity by examining its origins and delineating the processes involved. The rationale for introducing this framework developed from studying existing thinking and questioning the current metrics for measuring creativity, which we posit are unfit for purpose. We…

The present study determined the effects of instructional models and spatial intelligence on students' mathematics learning outcomes after controlling for their initial competence. The study was conducted at Senior High School (SHS) 6 Kendari, Indonesia using a quasi-experimental method designed by level 2×2. Samples consisted of 40 students…

This qualitative case study examined similarities and differences between circle geometric proof development tasks set up in the Malawian Grade 11 mathematics textbook, and those that are set up and implemented by teachers in the classroom. Data generation included analysing the content of circle geometry proof tasks from the mathematics textbook…

The study investigated the difficulties encountered by Grade 11 teachers in teaching Senior High School General Mathematics, the reasons for the problems, and the strategies employed by teachers in overcoming the challenges with an end view of developing training design. The sequential explanatory mixed methods design was used in the study with…

In this study, we explored the critical thinking of 47 eleventh-grade students in a mathematics problem-based learning (PBL) classroom in November 2016. A critical thinking test was used along with classroom observations to gather the critical thinking data in five dimensions according to the Association of American Colleges & Universities…

The purpose of this article is to report on a newly funded research project in which we will investigate how secondary students apply mathematical modelling to effectively address real world situations. Through this study, we will identify factors, mathematical, cognitive, social and environmental that "enable" year 10/11 students to…

In recent years, researchers have become more interested in quadratic equations. This study explores the conceptions high school students have concerning quadratic equations with one unknown, while using concept definition and images as theoretical framework. The data was gathered through semi-structured interviews with 14 eleventh grade high…

A mathematical client-driven task known as Model-Eliciting Activities was implemented with students of different levels of achievement (i.e., low, average, and high) at the high-school level. The study strived to prove that Model-Eliciting Activities can be solved by students at any achievement level and be used as an assessment tool. Students…

This purpose of this paper is to deepen the understanding for a problem of practice in the mathematics educators' classroom of low retention of information thus leading to poor mathematics achievement. The identification of the problem of practice led to a development of a research focus examining the effects of using intelligent tutoring software…

Despite proof being fundamental to the mathematics discipline and its role as a means to convey mathematical content, little is known about the effect of resources on influencing students' proof construction ability. The purpose of this study was to compare two didactic environments, one regarded as resourced (favored) and the other…

In this paper I analyze students' conceptual understanding of the quality of polynomial approximation. In particular, I analyze to what extent the interactive play with various methods of interpolation enables the students to build visual pictures that help understanding the formal mathematical statements. The role of the Mathematica software in…

In a cross-sectional study, 160 students in Grades 2, 4, 7, and 11 were interviewed about their reasoning when solving integer addition and subtraction open-number-sentence problems. We applied our previously developed framework for 5 Ways of Reasoning (WoRs) to our data set to describe patterns within and across participant groups. Our analysis…

Integration of history of mathematics (HOM) in mathematics education is emerging as frontier endowed with utility to stem decline in uptake, enhance performance and alter the negative perceptions about the subject. This case study sought to explore the influence of history of mathematics on grade eleven girls' perceptions of the Theorem of…

A classroom activity for high-school students, aiming at introducing space geometry from plane geometry has been introduced back in 2009 by Mammana, Margarone, Micale, Pennisi and Pluchino (2009a). The activity was based on the use of a Dynamic Geometry System and of the analogy between figures. Several aspects of the activity have been studied in…