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Curriculum materials have a substantial influence on mathematics instruction and, consequently, students’ learning opportunities. Many curriculum programs provide instructional notes for teachers and tasks for students as a means of accommodating particular student groups, such as those identified for English language learners. The presence of such materials communicates a narrative about the students they seek to accommodate. In particular, this narrative entails what English language learners need to learn mathematics. We examined the curriculum materials in four commercially available curriculum programs to understand the learning opportunities they provide for the target group and their assumed needs inferred from analyzing those opportunities. We found the curriculum materials implied a homogenous view of English language learners as a group who requires mathematical remediation and additional vocabulary practice. The curriculum materials provided a narrow set of learning opportunities, in terms of both mathematics and language, and may reinforce teachers’ existing deficit perspectives.

Teachers are implementing flipped instruction in an increasing number of mathematics classes but the research base is not yet well developed on this topic. Many studies of flipped instruction in ma...

In this study we examined three preservice elementary teachers’ (PSTs) use of mathematics tasks with English learners (ELs) during a field experience. For each of the first three weeks of the field experience, the PSTs were provided tasks for which to plan a lesson for a one-on-one session with an EL. Drawing on Brown’s (2009) notion of Pedagogical Design Capacity, we analyzed the PSTs’ lesson plans, weekly interviews, and written reflections to identify the ways in which the PSTs’ beliefs about, goals for, and experiences with the ELs impacted their use of the tasks. We were particularly interested in how the PSTs attended to the linguistic aspects of the tasks. We found that the PSTs’ overarching beliefs about teaching drove their desire to remove potential barriers and that they attempted to reduce students’ struggles by modifying the tasks that they were provided. The PSTs utilized a range of modifications, including replacing potentially unfamiliar words, changing contexts, and increasing the white space in the tasks. Though some of these strategies were successful in removing barriers, they did not always facilitate students’ linguistic development. Implications include the need for teacher educators to disrupt PSTs’ notions of effective teaching in the hopes their goals transition from removing barriers to providing scaffolds.

Encourage student collaboration in problem solving by altering the who, when, and what of the homework videos you use in flipped lessons.

There is growing recognition of the prevalence of “within school churn”, a phenomenon in which teachers remain within a school but are assigned a new grade level or course. In this study we examine...

Teachers who are flipping instruction face the challenging task of selecting or creating high-quality videos for their students. This article presents a framework for evaluating videos and describes the benefits of including interactive features and considering options beyond lecture videos.

In this paper we discuss different ways teachers can integrate science and mathematics into their curriculum. In particular, we focus on science and mathematics integration via the disciplinary practices.

In this growing problem solvers article, readers explore their impact on the environment with their use of straws through measurement and geometry. The sequence of tasks spans grades P-12 and we invite readers to explore real world contexts with mathematics.

Implementing challenging mathematics tasks with multilingual students who are not yet fluent in the instructional language is difficult for monolingual teachers because of the linguistic and cultur...

Alongside the increased presence of students classified as English learners (ELs) in mathematics classrooms exists a persistent pattern of the marginalization of ELs. Educators have sought research to identify how to provide ELs with high-quality mathematics education. Over the past two decades, education researchers have responded with increased attention to issues related to the teaching and learning of mathematics with ELs. In this review we analyzed literature published between 2000 and 2015 on mathematics teaching and learning with K–12 ELs. We identified 75 peer-reviewed, empirical studies related to the teaching and learning of mathematics with ELs in Grades K–12 and categorized the studies by focus (Learning, Teaching, and Teacher Education). We synthesize the results of these studies through the lens of a sociocultural perspective on language in mathematics. We then discuss avenues for future research and calls to action based on the extant body of literature.

While there is considerable scholarship describing principles for effective professional development, there have been few attempts to examine these principles in practice. In this paper, we identify and examine the particular design features of a mathematics professional development experience provided for middle grades teachers over 14 weeks. The professional development was grounded in a set of mathematical tasks that each had one right answer, but multiple solution paths. The facilitator engaged participants in problem solving and encouraged participants to work collaboratively to explore different solution paths. Through analysis of this collaborative learning environment, we identified five design features for supporting teacher learning of important mathematics and pedagogy in a problem-solving setting. We discuss these design features in depth and illustrate them by presenting an elaborated example from the professional development. This study extends the existing guidance for the design of...

The tasks teachers select impact students’ opportunities to learn mathematics and teachers’ beliefs influence their choice of tasks. Through the qualitative analysis of surveys, interviews ...

The rise of digital resources has had profound effects on mathematics curricula and there has been a concurrent increase in teachers flipping their instruction—that is, assigning instructional videos or multimedia for students to watch as homework and completing problem or exercise sets in class rather than vice versa. These changes have created a need to better understand not only the features and learning affordances of these videos but also the phenomena of instructional videos taking the place of textbooks altogether. Drawing on an enacted mathematics curriculum framework, this article reports on a study of a mathematics teacher who implemented flipped instruction and created her own instructional videos and multimedia resources as replacements of printed textbooks. We examined the relationship between the teacher’s printed textbook and the digital curriculum materials she used with her flipped mathematics classroom. We also explored her role in creating the digital curriculum materials and the ways in which those materials were used in-class. The case reveals similarities between the new material design and conventional textbooks and it also illustrates the teacher’s simultaneous work designing and enacting digital curriculum materials. The broad issue of considering videos as curriculum materials rather than only as instructional representations is discussed.

Elementary preservice teachers at six universities engaged in a task that provided them opportunities to articulate their professional noticing within video representations, written decompositions, and animated approximations of practice. The preservice teachers’ written accounts indicated that a majority attended to students or student thinking; however, when asked to illustrate their noticing through animation, focus shifted to the classroom teacher. Findings indicate the extent to which preservice teachers articulated specific mathematics concepts within and across pedagogies of practice and highlight the critical importance for selecting and utilizing multiple types of tasks to better understand preservice teacher noticing. Implications for eliciting and supporting preservice teacher noticing are discussed.

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.

Educational research communities bear responsibility for establishing a substantial body of evidence to support claims that drive the field. For example, one commonly accepted claim is that there is a relationship between the cognitive demand of mathematical task enactments and students’ learning. One study that is often cited in association with this claim is Stein and Lane (1996), and in 44% of those citations, Stein and Lane (1996) is the sole reference. Citation analysis reveals that many of these claims go beyond the warrants provided by the Stein and Lane study, either by granting more confidence in the relationship than the study design allows or by phrasing the claim as a causal relationship between cognitive demand and student learning. A few other studies are occasionally cited in conjunction with Stein and Lane (1996) and are summarized in this article, but there remains a need for replication studies to provide better empirical support for claims about cognitive demand and student learning and to refine our shared understanding.

The ‘conceptual storyline’ of a lesson refers to the flow and sequencing of learning activities such that science concepts align and progress in ways that are instructionally meaningful to student learning of the concepts. Research demonstrates that when teachers apply lesson design strategies to create a coherent science content storyline, student learning is positively impacted (Roth et al., 2011). Because the conceptual storyline is often implicit within a lesson, and teachers often have difficulty articulating this aspect of lesson design (Lo et al., 2014), our professional development program engages elementary teachers in analyzing and developing graphic representations of a lesson’s conceptual storyline to make that element explicit. In this exploratory study, we present typologies that represent two primary challenges teachers faced in developing coherent conceptual storylines in their lesson design, and examine the extent to which professional development enhanced their capacity to develop a coherent conceptual storyline.

This department accepts articles that examine mathematics education issues with the potential to stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education. This editorial analyzes and responds to viral Web posts that claimed to reveal the absurdity of math problems inspired by the Common Core.

Although English learners (ELs) are one of the fastest growing groups of students in the United States, many teacher preparation programs have yet to require preservice teachers (PSTs) to receive training in effective practices for teaching ELs. We examined four elementary PSTs’ instructional practices when implementing cognitively demanding mathematics tasks with ELs during a 4-week field experience. Through interviews, observations, and written reflections, we found that the PSTs tried to support the ELs, with varying degrees of success, by allowing for multiple modes of communication, including visual supports, pressing for explanations, and checking for understanding. The PSTs’ use of these strategies during the field experience was largely in response to the ELs’ use of language rather than mathematics. Furthermore, although the PSTs’ attention to linguistic supports was well intentioned, it often resulted in the PSTs taking on much of the mathematical thinking or failing to consider different student mathematical conceptions. We conclude that explicit instruction in and reflection on effective instructional strategies with ELs, set in authentic experiences, could help PSTs to more effectively develop the knowledge and skills necessary to meet the needs of ELs in the mathematics classroom.

In this qualitative research study, we sought to understand teachers' conceptions of integrated mathematics. The participants were teachers in the first year of implementation of a state-mandated, high school integrated mathematics curriculum. The primary data sources for this study included focus group and individual interviews. Through our analysis, we found that the teachers had varied conceptions of what the term integrated meant in reference to mathematics curricula. These varied conceptions led to the development of the Conceptions of Integrated Mathematics Curricula Framework describing the different conceptions of integrated mathematics held by the teachers. The four conceptions—integration by strands, integration by topics, interdisciplinary integration, and contextual integration—refer to the different ideas teachers connect as well as the time frame over which these connections are emphasized. The results indicate that even when teachers use the same integrated mathematics curriculum, they may have varying conceptions of which ideas they are supposed to connect and how these connections can be emphasized. These varied conceptions of integration among teachers may lead students to experience the same adopted curriculum in very different ways.

Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsák, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study investigated the utility of an alternative called themixture Rasch modelthat allows for subgroups. The model was applied to middle-grades teachers' performance on pretests and posttests bracketing a 42-hour professional development course focused on drawn models for fraction arithmetic. Results from psychometric modeling and evidence from video-recorded interviews and professional development sessions suggested that there were 2 subgroups of middle-grades teachers, 1 better able to reason with 3-level unit structures and 1 constrained to 2-level unit structures. Some teachers, however, were easier to classify than others.

The Guess My Number game gets students out of their seats as they engage in questioning and numerical reasoning while using academic language. To begin, each student writes a secret number on a sticky note and tapes it onto another student's back. Students then meet with others in the classroom. For each meeting, they show one another the numbers on their backs and then ask one yes-no question to try to determine their number.

Large cacti called saguaros (pronounced so-WAH-ros) have astounding growth rates and long life spans. Kelly took a picture of Zandra standing next to a saguaro. They then wondered about the height and the age of the cactus in the photograph. Use the following information to help them satisfy their curiosity.