We designed a student-centered cultural awareness unit as a resource for mathematics teacher educators (MTEs) who want to explore the issues of culture, equity, and diversity with their preservice teachers (PSTs) but are not sure how and where to start. This unit is an introductory step toward beginning to listen to PSTs' views about culture and diversity in mathematics education. In this article, we report on three cohorts of PSTs who participated in the unit, which consisted of an article critique, class discussion, and postdiscussion reflection. We describe the methods courses, the unit, the impact of the unit on PSTs' cultural awareness, our reflections as MTEs, and suggested modifications to the unit.

### Dorothy Y. White, Kanita K. DuCloux, Ángel M. Carreras-Jusino, Darío A. González and Kirsten Keels

### Ji-Yeong I and Jasmine Stanford

Using visuals is a well-known strategy to teach emergent bilinguals (EBs). This study examined how preservice teachers (PSTs) implemented visuals to help EBs understand mathematical problems and how an innovative intervention cultivated PSTs' capability of using visuals for EBs. Four middle school mathematics PSTs were engaged in a _ eld experience with EBs to work on mathematical problems; during the _ eld experience, the PSTs received interventions. In one intervention session, the PSTs were asked to make sense of a word problem written in an unknown language with different visuals. After this intervention, they changed their use of visuals when modifying tasks for EBs. The results suggest that immersive experiences where PSTs can experience learning from the perspective of EBs helps PSTs implement mathematically meaningful visuals in a way that makes mathematical problems accessible to EBs.

### Andrew Tyminski, Corey Drake and Tonia Land

Despite the prevalence of mathematics curriculum materials in elementary classrooms, most current mathematics methods texts provide little or no support for preservice teachers (PSTs) learning to use curriculum materials. To meet this need, we have designed and studied several modules intended to provide PSTs with opportunities to learn about and from the use of curriculum materials. This article describes our research related to 1 of these modules–Addition Starter Sentences. Our results examine the nature of PSTs' developing content knowledge and pedagogical content knowledge, evidenced through their interactions with and reflections on *Standards*-based curriculum materials. We conclude with implications for mathematics teacher education research and practice.

### Julie M. Amador, Anne Estapa, Zandra de Araujo, Karl W. Kosko and Tracy L. Weston

In an effort to elicit elementary preservice teachers' mathematical noticing, mathematics teacher educators at 6 universities designed and implemented a 3-step task that used video, writing, and animation. The intent of the task was to elicit preservice teachers' mathematical noticing–that is, noticing specific to mathematics content and how students reason about content. Preservice teachers communicated their noticing through both written accounts and selfcreated animations. Findings showed that the specific city of mathematical noticing differed with the medium used and that preservice teachers focused on different mathematical content across the methods sections, illuminating the importance for mathematics teacher educators understanding of the noticing practices of the preservice teachers with whom they work. This report includes implications for using the task in methods courses and modifying course instruction to develop noticing following task implementation.

### Stephanie Casey and Joel Amidon

Dr. Stacey, a mathematics teacher educator (MTE), and Erica, a preservice teacher (PST), are observing a secondary mathematics class. As part of the task setup, the class instructor presents the students with data, collected by travelers on the

### Linda M. Simonsen and Anne R. Teppo

During their undergraduate program, preservice elementary teachers are expected not only to become generalists across a wide range of school subjects but also to develop pedagogical knowledge of the developmental and social needs of children. We have developed a twosemester freshman-level mathematics-content course that attempts to address multiple needs of preservice teachers. The goals of this course are to help preservice teachers (a) deepen their understanding of mathematical concepts; (b) restructure their attitudes toward, and beliefs about, the nature of mathematics and how it is learned; (c) investigate pedagogical issues; and (d) experience mathematics learning within a reformbased environment. These goals are interrelated and reflect the complexity of the nature of the knowledge and disposition, both mathematical and pedagogical, that preservice teachers are expected to develop.

### Andrew Izsák and Erik Jacobson

Past studies have documented students' and teachers' persistent difficulties in determining whether 2 quantities covary in a direct proportion, especially when presented missing-value word problems. In the current study, we combine a mathematical analysis with a psychological perspective to offer a new explanation for such difficulties. The mathematical analysis highlights numbers of equal-sized groups and places reasoning about proportional relationships in the context of reasoning about multiplicative relationships more generally. The psychological perspective is rooted in diSessa's (diSessa, 1993, 2006; diSessa, Sherin, & Levin, 2016) knowledge-in-pieces epistemology and highlights diverse, fine-grained knowledge resources that can support inferring and reasoning with equal-sized groups. We illustrate how the combination of mathematical analysis and psychological perspective may be applied to data using empirical examples drawn from interviews during which preservice middlegrades teachers reasoned with varying degrees of success about relationships presented in word problems that were and were not proportional.

### Corey Webel and Kimberly Anne Conner

In this article, we report on efforts to develop a set of Web-based teaching simulations within the Lesson*Sketch* platform to support shifts in how preservice elementary teachers (PSTs) enact and evaluate their questioning practices in response to specific examples of students' mathematical thinking. The simulations included storyboard depictions of classroom situations, along with prompts for the PSTs to first analyze mathematical thinking and then construct, select, and analyze the effects of possible teacher questions. Participants included 54 PSTs across 5 sections of a mathematics content/methods class. Data were analyzed to document how PSTs enacted and reflected on their questioning practices in the context of these Lesson*Sketch* simulations. In this article, we focus on 2 storyboard depictions of classroom situations and describe how each appeared to provide different opportunities for PSTs to revise their ideas about questioning.

### Jean M. Shaw and Debby A. Chessin

In preparing preservice teachers for classroom work, some of our goals include getting to know our students hotter and helping them to build confidence in their ability to learn mathematics and communicate it effectively to others.

### Dina Tirosh and Anna O. Graeber

This study investigated conflict teaching as a means of probing the misconception held by many preservice elementary teachers that in a division problem the quotient must be less than the dividend. Individual interviews were held with 21 preservice teachers who were able to correctly compute quotients for division problems with decimal divisors less than one, but who agreed with an explicit statement that the quotient must be less than the dividend and who selected operations to solve word problems that reflected this misconception. The interviews illustrated how preservice teachers' reliance on information about the domain of whole numbers and their instrumental understanding of the division algorithm support their misconception. The authors also noted preservice teachers' lack of access to the measurement interpretation of division and their willingness to change procedural rules to preserve their misconception.