Sarah Quebec Fuentes

Unifying the Algebra for All Movement.

There exists an increased focus on school mathematics, especially first-year algebra, due to recent efforts for all students to be college and career ready. In addition, there are calls, policies, and legislation advocating for all students to study algebra epitomized by four rationales of the Algebra for All movement. In light of this movement, there must be a clear consensus about what is taught in the name of algebra. Yet, researchers documented this is not the case. The present research proposes to unify the leading algebra standards and assessment framework documents to identify the key ideas of algebra. The analysis resulted in six key ideas: (a) Variables, (b) Functions, (c) Patterns, (d) Modeling, (e) Technology, and (f) Multiple Representations. Outlined is the research process and resulting unification of existing algebra framework documents, and consideration is given for its uses in educational policy regarding algebra and potential directions for future research.

Reframing a problem: identifying the sources of conflict in a teacher education course

Abstract This article exemplifies the critical initial phase of action research, problem identification, in the context of a teacher education course. After frustration arose between preservice elementary teachers (PSTs) and their instructor over classwork quality, the instructor employed reflective journaling and discussions to examine the source of the conflict. Qualitative analysis of class reports, journal entries, and discussions revealed that PSTs’ perceptions of their role in a teacher education course did not align with those of their instructor; goal orientation is used as a conceptual framework to contrast the perspectives. Implications of purposeful and methodical collection and analysis of data (in the initial stage of action research) include reframing a problem using data representing PSTs’ perspectives; allowing instructors to carefully consider possible solution strategies; providing a democratic setting for learning by giving voice to PSTs; and modeling reflective practice as a mode of conflict resolution in an authentic classroom setting.

Using Self-Study to Evaluate a Pedagogical Approach for Navigating Conflict in a Science Content Course for Preservice Teachers

This self-study describes a conflict that occurred between a teacher educator (TE) and a class of preservice elementary teachers (PSTs) in a science content course. The conflict centered on the widely disparate views of the quality of classwork produced by the PSTs. While the TE initially evaluated the classwork in a way that was highly critical of the PSTs, he chose to halt the course progression and use reflection activities (e.g., journaling) to better understand the perspectives of the PSTs as well as consider how his pedagogical approach was contributing to the conflict. Through careful analysis of journal responses, in conjunction with a critical friend, insight into the particular needs of the PSTs was achieved. The TE was then able to design and implement targeted instructional activities to navigate the conflict and support the PSTs’ professional identity development.

Navigating the Environmental Politics of Energy Production: Using Mathematical Modeling as a Tool for Educating Science Teachers for Sustainability

This chapter describes the results of a professional development (PD) workshop conducted for inservice science teachers. The PD focused on local energy sources and the environmental politics that must be navigated in order to make decisions about which energy sources are most environmentally friendly and/or most sustainable. The teacher participants were taken on numerous field trips to energy extraction and production sites including coalmines, hydroelectric dams, wind farms, and nuclear power plants. At each site, the participants were exposed to differing perspectives on the environmental costs and benefits of the source of energy. These perspectives ranged from positive views expressed by representatives of the energy sector, mixed reviews by environmental biologists who exposed the impacts to wildlife, and negative views expressed by groups who opposed the energy source. Additionally, timely representations of some energy sources in the mainstream news media (e.g., Deepwater Horizon oil spill, fracking for natural gas, Fukishima nuclear power plant meltdown) were also explored. Group discussions allowed for sharing of participants’ thoughts on each perspective and mathematical modeling was used as a tool for evaluating the various sources of energy to determine the relative environmental costs and benefits of each. This chapter closes with challenges that participants faced in using mathematical modeling to evaluate energy sources and their shifting perspectives on various sources of energy over the course of the PD.

Catching Up to the CCSS A Principal Navigates Out-of-Subject Instructional Leadership

This case provides principals and principal licensure candidates an opportunity to delve into the nuances of supervising teachers in content areas, which may be unfamiliar, and to explore strategies for increasing knowledge about the structures and emphases of the Common Core State Standards (CCSS). The case presents issues related to curriculum, instructional leadership strategies, professional learning networks, and supervision and evaluation of teachers. It can also be a springboard for connecting principals and licensure candidates with resources to deepen familiarity with best practice research in mathematics instruction.

Small-Group Discourse: Establishing a Communication-Rich Classroom

Abstract Establishing a communication-rich classroom can be difficult. This article describes the process and findings of a practitioner action research study addressing the question of how teachers can interact with their students while they are working in groups to encourage and enhance student-to-student communication. Recommended research-based teacher interventions that foster small-group discourse are provided as well as suggestions for practitioners who are interested in conducting practitioner action research to improve their practice.Abstract Establishing a communication-rich classroom can be difficult. This article describes the process and findings of a practitioner action research study addressing the question of how teachers can interact with their students while they are working in groups to encourage and enhance student-to-student communication. Recommended research-based teacher interventions that foster small-group discourse are provided as well as suggestions for practitioners who are interested in conducting practitioner action research to improve their practice.

Evaluating Quantitative Reasoning Strategies for Comparing Fractions: A Tool for Teachers

Meaningful inclusion of quantitative reasoning into mathematics instruction requires meaningful ways to evaluate it. Few formative assessments exist to evaluate the strategies students use when reasoning mathematically. The Framework for Evaluating Quantitative Reasoning Strategies presented in this article provides teachers with categories for evaluating types of quantitative reasoning strategies students use for problems in the mathematical domain of number and operations. Numerous examples of the types of strategies students use for comparing fractions and how to evaluate the complexity of these strategies are provided. Included are research-based instructional recommendations for moving students toward a deeper conceptual understanding of fractions as numbers.

An Examination of the Implementation of Mathematics Lessons in a Chinese Kindergarten Classroom in the Setting of Standards Reform.

ABSTRACT In China, the 2001 Kindergarten Education Guidelines (Trial), or New Outline, delineates what constitutes high-quality, developmentally appropriate practices in all early childhood education curriculum domains, including mathematics. The New Outline is known for advocating a child-centered, play-based approach to teaching and learning, a significant change from teacher-directed instruction. Research highlights a gap between the intended practices set forth in the New Outline and the enacted practices in Chinese kindergarten classrooms. This descriptive study examines the implementation of 10 mathematics lessons, delivered over a 6-month period, from one Chinese kindergarten classroom in light of the New Outline. The analysis revealed that the lessons reflected aspects of the New Outline. However, overall, the lessons lacked critical components to provide students with opportunities to construct an understanding of the mathematics and become independent learners in five areas: (1) opportunities to inspire autonomous and life-long learning, (2) strategies for differentiated instruction, (3) use of resources to represent mathematics concepts, (4) student-centered instructional approaches, and (5) ways to foster communication.