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Background. This article describes the redesign, implementation, and students' experiences with an elementary mathematics teaching methods course in the Pacific Northwest of the United States that was forced online due to COVID-19 restrictions. We share course design principles, changes to reflect online teaching, and students' experiences of relational equity, "the care and consideration students and teachers must take with each other to establish and maintain a culture of equitable learning." Methods: This study took place online. 50 out of a cohort of 54 pre-service elementary teacher candidates participated. Our methods included analysis of course documents, analytic memoing, and analysis of students' responses to online open response surveys. We qualitatively analyzed the responses from the surveys, coding for a priori and emergent themes (Charmaz, 1995; Emerson et al., 2011; Miles et al., 2019). Findings: The results share the ways the instructors modified the course for online instruction and indicate that our participants experienced successes or challenges to enacting relational equity in the following: (i) curriculum and assessments, (ii) instructors, (iii) generic reference to the course, (iv) technology limits, and (v) future teaching. Contribution: This work sheds light on how two mathematics teacher educators redesigned their course for online instruction while centering and modeling relational equity teaching practices.

Background: This article describes teachers' equity concerns related to teaching mathematics online as a result of the COVID-19 pivot to online/distance-based instruction. COVID-19 restrictions forced the creation of virtual education contexts that magnified existing equity issues related to access to technology and the challenges of providing inquiry-based, student-centered instruction. Methods: This study took place under conditions promulgated by the COVID-19 pandemic. Nine teachers agreed to share their observations and experiences with the sudden switch to teaching mathematics online. Our methods included two online open response surveys. We qualitatively analyzed the responses from the surveys, coding for a priori, and emergent themes (Charmaz, 1995; Emerson et al., 2011). Findings: The results indicate that our participants experienced concerns for students and families struggling to effectively engage with and access online education, and shared the practices and online tools they found most and least helpful in enacting equitable instruction. Contribution: This work sheds light on how skilled and caring teachers leveraged prior experiences, collegial support, and technological tools to meet the challenges brought by the sudden transition to online mathematics pedagogy.

There is a growing need for teacher preparation courses that support teacher candidates (TCs) in meeting requirements to obtain a supplemental teaching credential. In particular, given the demands for secondary mathematics teachers, developing effective cross-disciplinary coursework within preparation programs is timely and important work. Our study examines the development and evolution of TCs' experiences in a mathematics teaching methods course designed for TCs seeking a supplemental credential. We describe the design principles and practices used to create, and modify, a course to meet (a) state licensure requirements, (b) the goals of the teacher education program, and (c) the individual needs of the TCs. Using survey and interview data, we report on TCs' experiences with the course and their future plans for obtaining a supplemental teaching credential in mathematics. Our study contributes to discussions on teacher preparation for interdisciplinary teaching, licensure requirements, conceptual and practical tools for teaching, and effective course design.

As institutions strive to improve teaching and learning for all, educators must consider equitable instruction. This includes equitable distributions of authority and agency among students. The authors define distribution of authority as shared opportunities for decision-making in enacting mathematical tasks and agency as the power to carry out these self-made decisions. Equitable distributions of authority and agency can be enhanced in mathematics public sensemaking classrooms where students participate in discourse as active members of the classroom. In public sensemaking classrooms, students understand and acknowledge one another's ideas, present and revise arguments, and take risks by sharing ideas. This study investigates one group of students and how they positioned one another during mathematical groupwork in a public sensemaking classroom as well as how the positioning impacted the distribution of agency and authority. At the time of data collection, the students attended a school for grades 6-12 situated in an urban public school that focuses largely on preparing students for careers in the health sciences and other health-related fields. Data was collected as video footage and analyzed using a priori codes. Analyses indicate that one student replicates the role of teacher by redistributing authority and agency back to other students through self-removal. This is contrasted with other motivations for self-removal while doing mathematics in a team. The findings inform researchers and classroom teachers of potential metacognitive awareness of equity between students, positioning patterns that may occur during collaborative groupwork, and the effectiveness of public sensemaking classrooms on distributing authority and agency equitably during groupwork.

What does it mean to be "good-at-math," and how is it determined? Cobb et al. (2009) defined the normative identity of mathematics classrooms as the obligations that students must meet to be considered good-at-math. Obligations are negotiated between teachers and students through series of bids. Normative identities reveal distributions of agency and authority within classrooms, which affect learning opportunities for students. Traditionally, mathematics teachers held the predominance of agency and authority in classrooms. Research supports shifting toward more equitable teaching and learning (e.g., National Council of Teachers of Mathematics, 2018). Clear examples of enacting and supporting changes are helpful. This article shares how sixth-grade students and their teacher co-constructed good-at-math to invite and obligate students to become active agents in mathematical argumentation.

As members of a research group taking initial steps for creating mathematics curriculum in an Indigenous language (Yakama Ichishkíin), we engaged with an unanticipated outcome: the ways Indigenous identities and homelands are fractionated, as part of ongoing colonizing harm. Our work centers on how mathematics instruction can help heal, by recognizing, valuing, and inviting learners to wholly engage in mathematics in ways that honor and reflect Indigenous ways of being and knowing.

The beginning of the school year is a time of intense work for students and teachers, especially if it means learning mathematics in new ways (Ruef 2016). Students need guidance and support if they are shifting beliefs about what it means to do mathematics. This article shows how Torres and her students co-created new ways to be good at mathematics. It describes an extended lesson and concludes with a menu of scaffolds to support risk taking.

This article describes the initial work and next steps for the development of a mathematics curriculum in Ichishkíin, an Indigenous Yakama language. Framed by the Ichishkíin concept of pinak'inut'áwaas (mirror/window), our work seeks to answer the following questions: How are mathematical concepts represented in Yakama culture, and how is Yakama culture reflected in mathematical concepts? How can we respectfully and reflectively craft new Ichishkíin words to express mathematical concepts not reflected in Yakama culture? This is decolonizing work, and joins a growing body of Culturally Sustaining and Culturally Reviving Pedagogies, which center teaching and learning on the lived experiences of students while critiquing culture for the ways it both sustains and diminishes. Given the dominant nature of mathematical culture, a key tenet of our project is privileging Yakama culture and the development of Ichishkíin language. We discuss the values and respect that are foundational to our ongoing collaboration to craft curriculum.

Mathematics Teacher Educators (MTEs) help preservice teachers in transitioning from students to teachers of mathematics. They support PSTs in shifting what they notice and envision to align with the collective vision encoded in the AMTE and NCTM standards. This study analyzes drawings and descriptions completed at the beginning and end of a one-year teacher education program--snapshots depicting optimized visions of teaching and learning mathematics. This study analyzed drawings-and-descriptions by cohort and by participants. The findings suggest that the task can be used as formative assessment to inform supports for specific PSTs such as choosing a cooperating teacher or coursework that challenges problematic beliefs. It can also be used as summative assessment to inform revision of coursework for the next cohort.

As the diagnoses of autism in young children continually increase, the need for families to have access to research-based treatment models that are effective and efficient has become clear. Current research demonstrates the demand for parent-delivered behavioral interventions. The aim of this single-case study, conducted as part of an integrated Masters in Education/Special Education Credential Program, was to examine the relationship between one parent trained in pivotal response treatment (PRT), her implementation of PRT techniques, and the correlated gains of behavioral compliance in her 6-year-old boy with high-functioning autism (HFA). Visual analysis of collected data as well as calculation of nonoverlapping data points suggest that a parent, when effectively trained, can utilize PRT to increase the rate of behavioral compliance of his or her own children.

With the large number of students with autism entering the educational system, the need for empirically supported treatment (EST) in the classroom and special education teachers with training in autism and ESTs is necessary now more than ever. This paper describes a collaborative model between 2 universities aimed at providing teacher-candidate graduate students training and community-based practice in an EST, pivotal response treatment (PRT). Three components of the model are described: (1) the community-based service delivery system, (2) the Masters/special education credential program and (3) training in PRT. Additionally, issues around student and family participation are discussed along with possible solutions and future directions. Finally, model benefits are described with regard to graduate students, children with autism, families and the community. (Contains 2 tables.)

With the large number of students with autism entering the educational system, the need for empirically supported treatment (EST) in the classroom and special education teachers with training in autism and ESTs is necessary now more than ever. This paper describes a collaborative model between 2 universities aimed at providing teacher-candidate graduate students training and community-based practice in an EST, pivotal response treatment (PRT). Three components of the model are described: (1) the community-based service delivery system, (2) the Masters/special education credential program and (3) training in PRT. Additionally, issues around student and family participation are discussed along with possible solutions and future directions. Finally, model benefits are described with regard to graduate students, children with autism, families and the community. (Contains 2 tables.)

Under conditions of uncertainty, we predict that development will be tied to the idiosyncrasy of organizational forms represented within local regions. Our investigation applies this theory to data on 342 counties and 43,352 businesses in the U.S. South during Reconstruction, finding support for the thesis that organizational idiosyncrasy generally dampens growth and challenges taken-for-granted norms of community structure. The causal effect varies somewhat depending on whether the underlying mechanisms entail increases in the production of local goods, the accumulation of fixed capital, or the attraction of new residents and retention of existing ones. We conclude by considering if the theory may generalize to other settings, including locales that depart markedly from the close-knit agrarian culture of the postbellum South. (Contains 7 notes, 7 tables, and 3 figures.)

This study explored perceptions of nine adults with cognitive disabilities and/or autism regarding barriers and solutions experienced due to problem behavior and elicited suggestions for improving quality of life while reducing problem behavior. Emergent themes included communication difficulties, need for privacy and personal decision making, and the importance of recreation, employment, choice of living settings, and relationships with friends and family. (Contains references.) (Author/PB)

A study explored the perceptions of 12 administrators and policy makers, 13 family members, 12 friends, and 9 adults with challenging behavior and mental retardation and/or autism, 7 researchers, and 13 teachers regarding current behavioral information and dissemination. Results indicate a continued gap between research and practice. (Contains references.) (CR)

Interviews conducted with 17 families of children, youth, and adults with problem behavior investigated inclusive lifestyle issues that are important to families. Issues surrounding family life, friendship, school, community inclusion, and supported living/supported employment are discussed. Results indicate the families want more collaborative help from professionals and the community. (CR)

Interviews were conducted with 17 families having a member with mental retardation and problem behavior, to investigate the families' definition of problem behavior, challenges the family faces, and successful approaches to changing the behavior. The needs of families were identified, such as the need for more information on the problem behavior. (CR)

Reports on the effects of computer-assisted instruction on student achievement in U.S. history classes. Studies two groups of students: those who used the computer to learn the material and those who did not. Reports no difference in the two groups. Outlines recommendations for computer use in the classroom. (RW)

Describes 11 World Wide Web sites which provide information for teachers on behavior management. Sites were recommended by a panel of teachers, family members, researchers, and communication specialists. (DB)