In a pre-service mathematics methods class I taught, in which we mathematized political districting (first horizontally, then vertically), student questions led to engaging mathematics, in particular, the development of a new number sequence.

Inquiry is the essence of social studies, and inquiry "looping" in social studies curricula means offering students opportunities to engage in inquiry in regular intervals and in a coherent fashion within and across grade levels. This can benefit the youngest students since they are filled with hope and want to make a difference in the…

We propose an algorithm that allows calculating the remainder and the quotient of division between polynomials over commutative coefficient rings, without polynomial long division. We use the previous results to determine the quadratic factors of polynomials over commutative coefficient rings and, in particular, to completely factorize in Z[x] any…

In this student analysis, Ryan Brown examines two critical themes from the global migration literature found throughout Leila Abdelrazaq's graphic novel "Baddawi," including the "geographical lens" and "citizenship and belonging." The author intertwines these themes throughout her story by depicting her father Ahmad's…

For nearly three years, a task force with diverse professional backgrounds convened to update the National Physical Education Standards with consideration of the various stakeholders who will be impacted by these changes--most especially students. The previous iteration of the National Standards has been the foundation for the implementation of…

The majority of states with a weighted, student-based K-12 funding formula include weights that allocate additional funding based on the enrollment of students in poverty, students with special education needs, and English learners (ELs). Research shows that all three of these student groups need additional support and resources to succeed. Many…

Visuospatial representations of numbers and their relationships are widely used in mathematics education. These include drawn images, models constructed with concrete manipulatives, enactive/embodied forms, computer graphics, and more. This paper addresses the analytical limitations and ethical implications of methodologies that use broad…

This technical report describes the entire development process for all mathematics items and tests used in CBMSkills. A brief introduction highlights the purpose of the assessment system, noting their important relationship with easyCBM. Given the items are designed to provide teachers diagnostic information on students' specific skills within…

A test method is described for determining the divisibility of non-negative integers by a prime number. The test uses an integer multiplying factor that is defined for each prime, designated as [beta], to reduce the non-negative integer that is being tested by an order of magnitude in each of a sequence of steps to obtain a series of new numbers.…

For several decades, digital formative assessment tools and platforms have been promoted as promising for supporting adaptive teaching. For learning goals such as procedural fluency, this promise has been held across a range of subject-matter topics. For conceptual learning goals, however, the available digital formative assessment tools are much…

Teachers have long struggled with the tension between ensuring a rigorous education for all their students and the reality that students arrive at the start of a school year with vastly different skills and conceptual understandings. The tension can be even more acute in math, which relies heavily on students mastering foundational concepts in…

We propose some generalizations of the classical Division Algorithm for polynomials over coefficient rings (possibly non-commutative). These results provide a generalization of the Remainder Theorem that allows calculating the remainder without using the long division method, even if the divisor has degree greater than one. As a consequence we…

This report provides information on the structure of mainstream European education systems, from pre-primary to tertiary level for the 2022/2023 school and academic year. It includes national schematic diagrams and a guide to reading the diagrams. It also contains a map visually showing the main organisational models of primary and lower secondary…

During the 2021-22 school year, the Mathematics Standards Review Committee reviewed the 2007 Minnesota K-12 Academic Standards in Mathematics, other states' recently revised standards, current academic research, K-12 instructional best practices and public feedback. This review process followed the guidelines in Minnesota Statutes 2023, section…

Within a study of student reasoning in abstract algebra, we encountered the claim "division and multiplication are the same operation." What might prompt a student to make this claim? What kind of influence might believing it have on their mathematical development? We explored the philosophical roots of "sameness" claims to…