The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Ngā mihi aroha ki ngā tangata katoa and warm greetings to you all. Welcome to Herenga Delta 2021, the Thirteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. It has been ten years since the Volcanic Delta Conference in Rotorua, and we are excited to have the Delta community return to Aotearoa New Zealand, if not in person, then by virtual means. Although the limits imposed by the pandemic mean that most of this year’s 2021 participants are unable to set foot in Tāmaki Makaurau Auckland, this has certainly not stopped interest in this event. Participants have been invited to draw on the concept of herenga, in Te Reo Māori usually a mooring place where people from afar come to share their knowledge and experiences. Although many of the participants are still some distance away, the submissions that have been sent in will continue to stimulate discussion on mathematics and statistics undergraduate education in the Delta tradition. The conference invited papers, abstracts and posters, working within the initial themes of Values and Variables. The range of submissions is diverse, and will provide participants with many opportunities to engage, discuss, and network with colleagues across the Delta community. The publications for this thirteenth Delta Conference include publications in the International Journal of Mathematical Education in Science and Technology, iJMEST, (available at https://www.tandfonline.com/journals/tmes20/collections/Herenga-Delta-2021), the Conference Proceedings, and the Programme (which has created some interesting challenges around time-zones), by the Local Organizing Committee. Papers in the iJMEST issue and the Proceedings were peer reviewed by at least two reviewers per paper. Of the ten submissions to the Proceedings, three were accepted. We are pleased to now be at the business end of the conference and hope that this event will carry on the special atmosphere of the many Deltas which have preceded this one. We hope that you will enjoy this conference, the virtual and social experiences that accompany it, and take the opportunity to contribute to further enhancing mathematics and statistics undergraduate education. Ngā manaakitanga, Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local Organising Committ

An investigation of prospective elementary teachers' use of mathematical representation as exhibited in their lesson plans

The purpose of this study was to investigate how the notion of representation occurs within the context of prospective teachers' thinking about planning for instruction in mathematics. This study was designed to seek out patterns within the types of mathematical representations that preservice teachers use in designing lesson plans. Major goals of this study were to uncover aspects of how prospective teachers' knowledge develops in the area of mathematics instruction, with respect to representation. Specifically, this study sought to (1) determine the types and frequency of mathematical representations used by prospective teachers when designing lesson plans regarding various topics in K--8 mathematics and (2) ascertain any changes that occurred over the course of a semester with respect to the uses of representations as revealed in prospective teachers' lesson plans. The study involved thirty-two elementary education majors enrolled in a 15-week field-based mathematics methods course at a large southwestern university. The findings were reported by representation type, namely, concrete , linguistic, symbolic, semi-concrete, and contextual. From the initial to the final interval, the overall percentages of the: (a) concrete manipulative representation increased; (b) linguistic representation increased; (c) symbolic representation decreased; (d) semi-concrete pictorial and the contextual representations both remained more or less the same. Overall, the linguistic representation was the most used representation; specifically, the informational and/or procedural subcategory of the linguistic representation was used the most, and in contrast, the discourse subcategory of the linguistic representation was used the least. Five cases were developed to illustrate the preservice teachers' thinking individually and as a group with respect to the uses of mathematical representations on given topics in individual lesson plans and group lesson plans. The process of moving from individual planning to group planning indicated some degree of malleability with respect to the uses of mathematical representations. Ten individual cases were analyzed with respect to the initial and final intervals. Seven of the 10 cases showed results in which the preservice teachers' preconceptions regarding the use of mathematical representations evolved. These findings are discussed relative to their implications for research, practice, and teacher education

Lesson Study: Collaboration among Middle School Mathematics Teachers of Latino Students

This lesson study experience occurred within a partnership between mathematics educators and four middle school mathematics teachers of ELLs. The lesson focus was addition of fractions of unlike denominators. The students were given opportunities to think individually and then work with a partner using fraction bars to explain and justify their solutions

Engaging Teachers in the Powerful Combination of Mathematical Modeling and Social Justice: The Flint Water Task - National Council of Teachers of Mathematics

Two major challenges in mathematics teacher education are developing teacher understanding of (a) culturally responsive, social justice–oriented mathematics pedagogies and (b) mathematical modeling as a content and practice standard of mathematics. Although these challenges may seem disparate, the innovation described in this article is designed to address both challenges in synergistic ways. The innovation focuses on a mathematical modeling task related to the ongoing water crisis in Flint, Michigan. Through qualitative analysis of instructor field notes, teachergenerated mathematical models, and teacher survey responses, we found that teachers who participated in the Flint Water Task (FWT) engaged in mathematical modeling and critical discussions about social and environmental justice. The evidence suggests that integrating these 2 foci—by using mathematical modeling to investigate and analyze important social justice issues—can be a high-leverage practice for mathematics teacher educators committed to equity-based mathematics education. Implications for integrating social justice and mathematical modeling in preservice and in-service mathematics teacher education are discussed

Exploring the Nature of Mathematical Modeling in the Early Grades

This working group will engage PMENA members to better understanding the nature of mathematical modeling in the early grades while considering the student perspective and recognizing the importance of teachers knowing their students and the contexts that are meaningful to their students. We will investigate how PK-6 teachers demonstrate the interdisciplinary nature of mathematical modeling, the diversity of mathematical approaches taken by student modelers, and the multiple pathways the teacher can use to elicit students' mathematical thinking. We will explore how mathematical modeling bridges equity and social community in teaching and learning mathematics for all students. Exemplar tasks that emphasized local contexts and tapped into students' funds of knowledge and student artifacts will be shared to illustrate the child's perspective and the developmental progression. These topics will facilitate group discussions exploring the learning progression for mathematical modeling thinking and habits of mind that can develop for emergent mathematical modelers from an early grade. Finally, based on the interests of the participants, we will devote work time to finding synergistic collaborative topics to pursue for future research and practice. [For the complete proceedings, see ED606556.]Elementary Educatio