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Visual representations and manipulatives are a highly advocated mathematical tool for the teaching and learning of multiplication and division. Although there is some prior research on elementary teachers' general use of manipulatives and visual representations, there is little to no specific focus on use of such representations on a specific mathematical concept. The present study examined third grade teachers' reported use of visual representations for teaching multiplication and division. Findings indicate prevalent use of discrete models and infrequent use of continuous models. Length models and number lines are rarely used across all Common Core standards focusing on multiplication/division, with numeric‐only representations being reported frequently across all standards. Groups‐of and array models were the most prevalent visual model reported by third grade teachers. Although teachers report higher degrees of access to certain materials than previous reports on manipulative use, interview data suggests this may have more to do with purchase agreements between school districts and textbook companies than pedagogical preferences of classroom teachers. Supporting findings in prior decades, teachers in the present study report prevalent use of flashcards, charts and grid paper, and variations of counters. [ABSTRACT FROM AUTHOR]

In theory, STEM (interdisciplinary science, technology, engineering and mathematics) is cross‐disciplinary and situated in real‐world problem‐solving contexts. In practice, STEM disciplines are often implemented separately using contrived contexts. This paper examines theoretical and empirical aspects of Montessori middle school science in the United States, and its alignment with the conceptual framework of integrated STEM. We selected Montessori adolescent environments because the Montessori philosophy involves interdisciplinary application contextualized in purposeful work and learning. Our research sought to investigate how Montessori middle schools have designed their science programs, and to situate these findings within the current landscape of STEM education and reform‐based science. Based on the results of our survey of 96 U.S. Montessori middle schools, we argue Montessori offers an integrated educational approach that meaningfully situates academic disciplines to mirror local and global challenges, well supported by theory and literature on STEM and situated learning theories. We assert that integrated STEM happens organically in many Montessori middle schools, and takes place through authentic work in communities of practice. Our research communicates the value of looking outside traditional school settings to examine alternative formal education spaces, like Montessori classrooms where integrated STEM happens organically. [ABSTRACT FROM AUTHOR]

Despite agreement among teacher educators, scholars, and policymakers on the importance of teachers' subject matter knowledge (SMK), existing models provide limited information about the nature of this foundational component of teacher knowledge. The common assumption is that teachers need to know more about the science subject matter than their students are expected to learn, but what and how much more is underspecified. In order to more characterize science teachers' SMK, we present the science knowledge for teaching (SKT) model, which has been adapted from the mathematics education literature to apply to science education. The SKT model includes three domains: core content knowledge, specialized content knowledge, and linked content knowledge. We used this model to explore the SMK new secondary chemistry teachers in South Africa and the United States drew on when they explained the conservation of mass and analyzed a related teaching scenario, two important tasks of teaching. Findings indicated these new teachers drew on knowledge from all three SKT domains in order to engage in these tasks of teaching. This result suggests the potential of the SKT model to characterize the nature of science teachers' SMK and thereby better inform teacher preparation and professional development programs. [ABSTRACT FROM AUTHOR]

This paper examines the implementation of an instructional module on preservice elementary teachers' professional noticing of children's mathematical thinking. The module focuses on professional noticing skills through the content focus of early algebraic reasoning and uses complex video vignettes from whole class instruction in authentic elementary mathematics classrooms. Findings indicated that two of the three components of professional noticing (attending and interpreting) showed statistically significant increases in a treatment group that did not occur in a comparison group. The deciding component remains a challenge that warrants further research. [ABSTRACT FROM AUTHOR]

This paper presents qualitative and quantitative approaches to exploring teachers' experiences of mathematics anxiety (for learning and doing mathematics) and mathematics teaching anxiety (for instructing others in mathematics), the relationship between these types of anxiety and test/evaluation anxiety, and the impacts of anxiety on experiences in teacher education. Findings indicate that mathematics anxiety and mathematics teaching anxiety may be similar (i.e., that preservice teachers perceive a logical continuity and cumulative effect of their experiences of mathematics anxiety as learners in K–12 classrooms that impacts their work as teachers in future K–12 classrooms). Further, anxiety is not limited to occurring in evaluative settings, but when anxiety is triggered by thoughts of evaluation, preservice teachers may be affected by worrying about their own as well as their students' performances. The implications for preservice experiences within a teacher education program and for impacting future students are discussed. [ABSTRACT FROM AUTHOR]

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and their applications to solving problems arising in real-world situation. Clearly, it is assumed that the teachers themselves are able to make such connections. On the other hand, research shows that mathematics teachers find it difficult to make those connections. In this paper, we present the results of the study that investigated the ways in which exploring mathematics in informal sites, and in particular science museum, assist teachers with making connections between school mathematics and its applications in real world. [ABSTRACT FROM AUTHOR]

The integration of science, technology, engineering, and mathematics (STEM) education has received increased attention in the last decade. This is in part because of the need for students to increase in their STEM knowledge and competencies. Research is still needed to determine effective implementation models and curriculum for integrated STEM. Mathematics in particular has not received the focus it deserves with STEM integration. This paper discusses integration of STEM subjects that has a focus on mathematics (integrated steM); including summarizing and analyzing research done in the last ten years. A s.t.e.m. (Support, Topics, Emphasis, and Mathematical content) model for integrated steM research is presented to guide future research. [ABSTRACT FROM AUTHOR]

This paper presents the results of a Q‐sort activity in which 38 grades 4–10 mathematics teachers reflected on their classroom teaching and ranked a set of teaching actions that support high‐leverage mathematics teaching from most to least characteristic of their classroom teaching. Data analysis included examining the overall ranking of each teacher action as well as the overall ranking of the associated high‐leverage teaching practice. Examination of the rankings indicated that teachers identified actions associated with the practices of supporting productive struggle in students' learning of mathematics and posing purposeful questions as most characteristic of their teaching. Teachers identified actions associated with the practices of eliciting and using evidence of student thinking and establishing mathematics goals to focus learning as least characteristic of their teaching. Thematic networks were created to represent the teachers' rationales for their priorities regarding implementation of high‐leverage teaching practices. We share the implications of our findings for the mathematics education field and professional development leaders. [ABSTRACT FROM AUTHOR]

There is a compelling need to develop an algebra teacher self‐efficacy instrument (ATSEI) as algebra continues to be considered a gatekeeper course for postsecondary educational and career opportunities, which is seen as a crucial piece in closing the achievement gap. This paper reports on the development and validation of the ATSEI, an instrument that measures two domains, Efficacy To Do School Algebra (Knowledge Efficacy, KE‐A) and Efficacy to Teach Algebra (Personal Teaching Efficacy, PTE‐A) along six categories. Four of the categories represented content standards (variables, functions, patterns, and modeling) and two of the categories represented process standards (technology and concrete models, and multiple representations). Through conducting an exploratory factor analysis across two phases, the instrument was reduced and refined from an initial 118 items developed from a curriculum analysis to 36 items that reflected two significant categories, Functions and Technology. The ATSEI measure is validated for in‐service mathematics teachers and thus provides an instrument to examine need and impact in professional development venues. The specificity of the ATSEI allows those working with teachers to be better able to support them in the field and in return positively influence the learning outcomes of the students they teach. [ABSTRACT FROM AUTHOR]

The article reports on the use of handheld computers for data collection. It mentions that handheld computers or personal digital assistants (PDAs) are seen as more affordable and effective than laptop and desktop computers. The article also discusses the factors affecting the effectiveness of PDAs including interoperability and accuracy.

The Going Green! Middle Schoolers Out to Save the World project aims to direct middle school students' enthusiasm for hands‐on activities toward interest in science and other STEM areas while guiding them to solve real‐world problems. Students in this project are taught by their teachers to use energy monitoring equipment to audit standby power consumed by electronic devices in their homes and communities. Major findings were: (a) Beliefs in climate change increased more for students in the treatment than comparison group, pre to post; and (b) For girls there was a larger positive impact on climate change beliefs than for boys. These and additional findings presented in this paper provide evidence that a hands‐on engaged‐learning curriculum can have a positive influence on climate change beliefs and intentions and strengthen the association between the two constructs. [ABSTRACT FROM AUTHOR]

This study examined how Black students responded to the utilization of culturally responsive stories in their mathematics class. All students in the two classes participated in mathematics lessons that began with an African American story (culturally responsive to this population), followed by mathematical discussion and concluded with solving problems that correlated to the story. The researcher observed and recorded responses by students during each part of these lessons with protocols. Students independently reflected weekly by answering five questions to share their perspective on the African American stories. The teacher reflected on each lesson as well, describing thoughts on how these students responded to the story in each lesson. This paper examines the analyzed data from the target audience: Black students. Results revealed that Black students responded to the use of African American stories with high self-rated levels of engagement and enjoyment and that the stories helped them think about mathematics to varying degrees. Since students who are engaged and are thinking about mathematics are more likely to achieve mathematical understanding, the researcher concludes that this strategy should continue to be tested in diverse classrooms with an emphasis on student reflection to determine if the outcomes are transferable and generalizable. [ABSTRACT FROM AUTHOR]