The Klein bottle and hairy ball theorem are important concepts in advanced mathematics and they are both examples of the Poincaré-Hopf theorem. Complex theories such as these usually remain unrealized in the minds of mathematicians. In this collaborative work between a mathematician and a designer, we introduce the concept of the hairy Klein…

Textbooks on Dynamical Systems Theory usually present only three types of codimension-one bifurcations occurring in autonomous first-order nonlinear differential equations. These three types are called saddle-node, transcritical, and pitchfork. However, the number of bifurcations is virtually infinite. In this didactic work, the bifurcation…

It's often useful extending students beyond the limiting geometry of triangles and quadrilaterals to regularly consider generalizations of results for triangles and quadrilaterals to higher order polygons. A brief heuristic description is given here of the author applying this strategy, and which led to an interesting result related to the…

Fractions are a very important but difficult topic in elementary and secondary mathematics curricula around the world. The difficulty in teaching and learning fractions is usually caused by their various subconstructs. To facilitate learning of fractions, a test consisting of 20 items was developed to examine 310 sixth graders' hierarchical…

In this survey paper we aim to provide an overview of research on mathematics textbooks and, more broadly, curriculum resources as instruments for change related to mathematical content, instructional goals and practices, and student learning of mathematics. In particular, we elaborate on the following themes: (1) The role of curriculum resources…

In the article 'How Long Is My Toilet Roll--A Simple Exercise in Mathematical Modelling' several models of increasing complexity are introduced and solved to calculate indirectly the length of paper on a toilet-roll. All these results are presented without errors. The authors of this comment believe the error analysis of measurements made in a…

The COVID-19 global pandemic has required everyone to make sense of data about community spread, levels of risk, and vaccine efficacy. Yet research shows that students are underprepared in data literacy. Tanya LaMar and Jo Boaler argue that data science education provides an opportunity to address this problem while providing much needed updates…

This study aimed to investigate the mathematical proficiency level of the Hashemite University female students in teaching mathematics during practicum program. The study sample consisted of (41) female classroom teacher students at the second semester of the academic year 2019/2020. The study adopted the descriptive approach. The data were…

Although raised in the early days of research on teacher noticing, the question of context specificity has remained largely unanswered to this day. In this study, we build on our prior research on a specific aspect of noticing, namely teachers' analysis of how representations are dealt with in mathematics classroom situations. For the purpose of…

Numerous studies have reported positive outcomes of noticing interventions on the development of prospective mathematics teachers' (PMTs) noticing of a range of important aspects of classroom instruction. Less is known, however, about whether noticing skills that are developed during an intervention transfer to support PMTs' in-the-moment noticing…

Brief experimental analysis (BEA) is a quick method used to identify the function of student learning difficulties and match effective interventions to students' needs. Extensive work has been done to explore the use of this methodology to determine effective reading interventions; however, a smaller number of published studies have examined the…

Evidence for associations between spatial skills and mathematics has led to the argument that spatial visualization plays a role in mathematical calculation. However, there is no single accepted definition of what spatial visualization encompasses. Here, we investigated spatial visualization in the context of a mental imagery framework. We applied…

Decades of research have established that solving geometry proof problems is a challenging endeavor for many students. Consequently, researchers have called for investigations that explore which aspects of proving in geometry are difficult and why this is the case. Here, results from a set of 20 interviews with students who were taught proof in…

Representing and recording student thinking in public spaces during mathematics discussions is challenging work. In this article, the authors articulate why skillfully recording and representing during discussions matters. The authors share principles for recording student thinking in the moment and share an activity structure to use with…

This article presents reflections on a research that investigated processes operationalized by mathematical thoughts and practices which sought explanations for the ways of being of mathematical objects in their correlations in the socio-cultural context throughout our human history and how these ways of being they were captured, and still are, by…