Isomorphism and homomorphism are topics central to abstract algebra, but research on mathematicians' views of these topics, especially with respect to sameness, remains limited. This study examines 197 mathematicians' views of how sameness could be helpful or harmful when studying isomorphism and homomorphism. Instructors saw benefits to…

We believe that professional mathematicians who teach undergraduate mathematics courses to prospective teachers play an important role in the education of secondary school mathematics teachers. Thus, we explored the views of research mathematicians on the mathematics that should be taught to prospective mathematics teachers, on how the courses…

This quantitative descriptive study aims to describe the Mathematical Literacy of Grade 5 of Primary Students regarding their mathematical problem-solving abilities. The samples of this study were 35 5th-gradestudents at Muhammadiyah Condongcatur Elementary School in academic year 2017/2018. The data were collected through observations and tests…

This study explored the trends in students' achievement in Senior School Certificate Examination (SSCE) in Further Mathematics in Kwara State, Nigeria. The study adopted descriptive research design of ex-post factor type. The sample comprised all Further Mathematics students in 79 public senior secondary schools with 3 Local Government Areas in…

Project-based learning supports unique and authentic problems in differential equations courses. An intuitive, interesting and deep differential equations project is described. The description illustrates a case study of guiding students through a complex project and the technical and personal rewards gained from it. Valuable advice is provided to…

Background: In the US, there is significant interest from policy boards and funding agencies to change students' experiences in undergraduate mathematics classes. Even with these reform initiatives, researchers continue to document that lecture remains the dominant mode of instruction in US undergraduate mathematics courses. However, we have…

This article provides an overview of a modeling sequence that culminates in student reinvention of a bifurcation diagram. The sequence is the result of years of classroom-based research and curriculum development grounded in the instructional design theory of Realistic Mathematics Education. The sequence of modeling tasks and examples of student…

Translating a mathematics lesson from curriculum materials into instruction is not straightforward, and launching, or beginning, a lesson such that students will become productively engaged in the target mathematics is nontrivial. The purpose of the study was to investigate preservice teachers' curricular noticing as they draw upon curriculum…

Research Findings: This study examined the interrelations between fine motor skills, executive functions, and basic numerical skills in kindergarten as well as their predictive value for mathematics achievement in 2nd grade in a sample of 136 children. Structural equation modeling techniques were used to uncover the unique predictive value and…

There has been a lack of research into conceptually teaching the structure of contextual problems to kindergarten students. This is despite the popularity of contextual problems and the difficulties that students have with them. This study focuses on creating a textless, image-based application that uses the Triplet Structure Model to teach about…

Should proof by induction be reserved for higher levels of mathematical instruction? How can teachers show students the nature of mathematics without first requiring that they master algebra and calculus? Proof by induction is one of the more difficult types of proof to teach, to learn, and to understand. Thus, this article delves deeper into…

The structure sense is a part that must be learned in order to help understand and construct connection in abstract algebra. This study aimed at building the pattern of a structure sense as a profile of the structure sense in group property. Using a qualitative study, the structure sense of group property was explored through lecturing activity of…

It is of critical importance, in particular, for mathematics teachers who will teach future generations to understand and do mathematical proofs. It is important to determine future teachers' beliefs about and difficulties with proofs because their knowledge of this issue affects their teaching. This study aims to determine and compare the proof…

A phenomenographic study at a research university identified five categories of description for how STEM (science, technology, engineering, and mathematics) instructors conceptualize the design and redesign of undergraduate courses. These categories form a hierarchical outcomes space with increasing complexity of awareness of the phenomenon. The…

Students' beliefs that mathematical abilities are fixed can cause long-standing problems with motivation and learning. Hence, teachers should notice such problematic beliefs about identity among their students and handle them adequately. We used written descriptions of classroom situations to determine whether preservice mathematics teachers (n =…