Leveraging Student Identities to Develop Pedagogical Fluency

Mathematics education can be positioned as fertile ground for societal change. This article deconstructs the complex work of supporting students’ positive mathematical identities by introducing pedagogical fluency to embody equitable beliefs and practices.

An exploration of the mathematical learner identities of high school learners who participated in after school mathematics clubs in primary school

This study focuses on understanding mathematics learner identities of high school learners who participated in the South African Numeracy Chair Project after school mathematics clubs, an environment that afforded different mathematics identities from the traditional South African classroom. Mathematics learner identities feature prominently in current research on mathematics education because they affect whether and how learners engage in mathematics. They play a critical role in enhancing (or detracting from) learners’ attitudes, dispositions, emotional development, and general sense of self as they learn mathematics. Development of positive learner mathematical identity is therefore useful in making learners commit to their mathematics work. South African primary mathematics education is described as being in a state of crisis, and various programmes are being implemented to develop intervention models to improve quality and ensure the effective teaching and learning of primary mathematics. The South African Numeracy Chair Project initiative at Rhodes University provides for longitudinal research and development programmes with primary mathematics teachers and learners from previously disadvantaged schools, in order to find ways of mitigating the crisis. The after school mathematics clubs provide extra-curricular activities focused on developing a supportive learning community where learners’ active mathematical participation, engagement, enjoyment, and sense making are the focus. The clubs provide a supportive learning environment that is different to the traditional classroom and in which learners can participate actively and freely in mathematical activities. The study explores the nature of mathematics learner identities as learning trajectories that connect the past and future in negotiation of the present. It also seeks to discover how primary school club participation and experiences feature in the learners’ mathematical identities. The study employs two theoretical frameworks to analyse qualitative data that was gathered in the form of spoken and written stories, by 14 learners who participated in the after school mathematics clubs in primary school. The stories covered learners’ engagement in mathematics in different landscapes of practice that promoted the construction of different learner mathematical identities. A close analysis of the qualitative data revealed that learners’ mathematical identities are heavily influenced by the values that were foregrounded in the after school mathematics clubs. The clubs valued hard work and encouraged learners to ask for assistance when in doubt. In line with the club ethos, the learners storied resilience and hard work in their narratives. In addition, although many learners storied Mathematics as difficult in high school, they chose to continue taking the subject.

Mathematics Heritage Project: An Exploration Empowering Students' Mathematical Identities

The International Study Group on Ethnomathematics (ISGEm) supports incorporating cultural diversity of mathematical practices to promote the teaching and learning of school mathematics. Through The Mathematics Heritage Project, students at a middle school in the southeastern United States developed unique creations to connect with the mathematics connected to their identities and self-identified cultural group. Upon reflection, students reported an increased awareness of the relevance of mathematics in their lives and a sense of ownership that is both meaningful and modern.

Mathematical Engagement through Family Communication

This article examines action research findings within a fourth-grade mathematics classroom. The researcher explores the effects of positive communication to family members on the engagement of learners receiving Tier 2 behavioral support, as well as potential considerations for building young learners’ mathematical identities.

Identities for droplets with circular footprint on tilted surfaces

Exact mathematical identities are presented between the relevant parameters of droplets displaying circular contact boundary based on flat tilted surfaces. Two of the identities are derived from the force balance, and one from the torque balance. The tilt surfaces cover the full range of inclinations for sessile or pendant drops, including the intermediate case of droplets on a wall (vertical surface). The identities are put under test both by the available solutions of a linear response approximation at small Bond numbers as well as the ones obtained from numerical solutions, making use of the Surface Evolver software. The subtleties to obtain certain angle-averages appearing in identities by the numerical solutions are discussed in detail. It is argued how the identities are useful in two respects. First is to replace some unknown values in the Young–Laplace equation by their expressions obtained from the identities. Second is to use the identities to estimate the error for approximate analytical or numerical solutions without any reference to an exact solution.

Conformal Field Theory of Free Bosonic and Fermionic Fields

Free theories are usually regarded as trivial examples of quantum systems. This chapter proves that this is not the case of the conformal field theories associated to the free bosonic and fermionic fields. The subject is not only full of beautiful mathematical identities but is also the source of deep physical concepts with far reaching applications. Chapter 12 also covers quantization of the bosonic field, vertex operators, the free bosonic field on a torus, modular transformations, the quantization of the free Majorana fermion, the Neveu–Schwarz and Ramond sectors, fermions on a torus, calculus for anti-commuting quantities and partition functions.