Throughout my career, I have collaborated with dedicated and hard-working teachers who have opened their classrooms so that others could learn from them. Yet, one teacher, Sara, stood out from all the others. From the first time I visited Sara's classroom in 1992, I knew she was extraordinary--a teacher who could inspire a Hollywood production. Sara taught Latino English language learners (ELLs) in a low-income urban neighborhood in ways that I had not observed or read about in the literature. She did not reduce the curriculum's level of complexity, especially its language, even though the students were ELLs. Instead, Sara engineered a mathematics learning environment where students actively engaged in collaborative problem solving, oral and written communication and justification, and independent thinking. To give other practitioners insight into how Sara facilitated the participation of ELLs during mathematics, I share my experiences of researching Sara's fifth-grade classroom and provide images of her teaching.

This article provides a cultural-historical (CHAT) analysis of the practices used by an effective teacher of Latino/a children previously classified as “underachieving” and “beginning/novice” English Language Learners. Although the teacher would not describe her practices in strict CHAT, or sociocultural theory (SCT) terms, our analysis shows that teaching practices in this classroom are better understood using a SCT model rather than more prevalent second language acquisition (SLA) models that dominate the field of bilingual/English as a Second Language education. We describe the fundamental limitations of SLA assumptions about learners vis-à-vis a SCT perspective and use classroom and case study data to illustrate how a CHAT perspective illuminates this teacher’s practices. From a CHAT perspective, teaching and learning are socially reorganized around the mediation of dynamic learner identities and include shifts in expert–novice status, dialogic interactions, and the use of innovative mediational tools (e.g., keystrokes on a calculator) to promote academic writing and oral communication. The mediational reorganization described in the classroom opened up access to students who might have been dismissed by a SLA model as “incapable” of engaging in such tasks. We draw on classroom-level data (i.e., standardized scores in reading and math) as well as the work of selected focal students to illustrate our case.

A middle school mathematics teacher taught native English speakers for the first fifteen years of her career. As immigrants from other countries moved into the community and student demographics began to change, she realized that she was not prepared to teach mathematics to students who were English language learners (ELLs).
The demands that she faced are not unique. The recent growth of the ELL population in the United States has challenged teachers to identify effective strategies to meet the needs of ELL students and their families.

Equity in mathematics education should be one of the most important concerns of
teachers, administrators, policy makers, mathematicians, and mathematics educators. In fact, the Association of Mathematics Teacher Educator (AMTE), the National Council of Supervisors of Mathematics (NCSM), and the National Council of Teachers of Mathematics NCTM), three national organizations that support teacher educators, mathematics teachers, and teacher leaders, have made equity a priority for their organizations (Gutierrez et al. 2008). Position statements, standards documents, and various books identify key equity issues and recommend directions compelling all involved in the mathematics education of students to become aware of equity issues and to take steps toward eliminating the inequities that plague K-16 education.

Research in student knowledge and learning of science has typically focused on explaining conceptual change. Recent research, however, documents the great degree to which student thinking is dynamic and context-sensitive, implicitly calling for explanations not only of change but also of stability. In other words, when a pattern of student reasoning is sustained in specific moments and settings, what mechanisms contribute to sustaining it? We characterize student understanding and behavior in terms of multiple local coherences in that they may be variable yet still exhibit local stabilities. We attribute stability in local conceptual coherences to real-time activities that sustain these coherences. For example, particular conceptual understandings may be stabilized by the linguistic features of a worksheet question or by feedback from the students’ spatial arrangement and orientation. We document a group of university students who engage in multiple local conceptual coherences while thinking about motion during a collaborative learning activity. As the students shift their thinking several times, we describe mechanisms that may contribute to local stability of their reasoning and behavior.

The second law of thermodynamics is typically not a central focus either in introductory university physics textbooks or in national standards for secondary education. However, the second law is a key part of a strong conceptual model of energy, especially for connecting energy conservation to energy degradation and the irreversibility of processes. We are developing a conceptual model of the second law as it relates to energy, with the goal of creating models and representations that link energy, the second law, and entropy in a meaningful way for learners analyzing real-life energy scenarios. We expect this model to help learners better understand how their everyday experiences relate to formal physics analyses. Our goal is to develop tools for use with elementary and secondary teachers and secondary and university students.

The Energy Project at Seattle Pacific University has developed representations that embody the substance metaphor and support learners in conserving and tracking energy as it flows from object to object and changes form. Such representations enable detailed modeling of energy dynamics in complex physical processes. We assess student learning by means of representations that learners invent to explain energy dynamics in specific real-world scenarios. Refined versions of these learner-generated representations have proven valuable for our own teaching, physics understanding, and research.

The nature of energy is not typically an explicit topic of physics instruction. Nonetheless, verbal and graphical representations of energy articulate models in which energy is conceptualized as a quasimaterial substance, a stimulus, or a vertical location. We argue that a substance ontology for energy is particularly productive in developing understanding of energy transfers and transformations. We analyze classic representations of energy—bar charts, pie charts, and others—to determine the energy ontologies that are implicit in those representations, and thus their affordances for energy learning. We find that while existing representations partially support a substance ontology for energy and thus the learning goal of energy conservation, they have limited utility for tracking the flow of energy among objects.

In this paper, we present an overview of the National Science Foundation (NSF) funded Knowledge for Algebra Teaching for Equity (KATE) Project and experiences from preservice teachers who are preparing for teaching middle grades mathematics. We highlight findings from a preliminary analysis of the effectiveness of virtual simulations of problem-based teaching of algebra concepts in enhancing preservice teachers' knowledge and skill in teaching diverse students.

This article presents our plans and initial work to explore how mathematics teacher education programs can prepare teachers for diverse middle grades classrooms. It describes the start-up of a five-year National Science Foundation project to design, develop, and test technology-enriched teacher preparation strategies to address equity in algebra learning. The participants in this pilot group demonstrated a need to develop their mathematical problem-solving skills, but they also exhibited strong beliefs about their own potential to be successful in the mathematics classroom. Preliminary results appear to indicate that Second Life (software) simulations can provide rich settings for teacher development on specific mathematics teaching skills and challenge them to apply their ideas about diversity. (Contains 5 tables and 4 figures.)