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The purpose of this paper is to demonstrate the mathematical understanding of Latino immigrant parents in curricular and pedagogical practices in elementary school. The paper seeks to counter widely spread deficit discourses about the parental involvement of Latinos in education. Using data from the Agency and Young Children project, a video-cued ethnographic study (Tobin, Wu, & Davidson, 1989; Tobin, Hsueh, Karasawa, 2009; Tobin, Arzubiaga, & Adair, 2013), we highlight aspects from home that schools can use as resources to build a bridge that supports children's mathematical understanding. [ABSTRACT FROM AUTHOR]

This paper describes seven in-service teachers' interpretations of student statements about slope. The teachers interpreted sample student work, conjectured about student contributions, assessed the students' understanding, and positioned the students' statements in the mathematics curriculum. The teachers' responses provide insight into their Knowledge of Content and Students (KCS) and Knowledge of Content and Curriculum (KCC). Results suggest these teachers value academic terminology related to slope, have limited perspectives on slope in real world contexts, and struggle to describe the extension of slope to precalculus. [ABSTRACT FROM AUTHOR]

Parents' growing concerns about the "new math" are drawing public attention. Rather than dismiss such concerns, understanding parent perceptions and garnering their support is essential to ongoing curriculum transformation and children's success. In this paper, we present the preliminary findings of a phenomenographic study examining parent perceptions of children's mathematics learning. We focus specifically on the sources of curriculum related communication identified by parents: (a) homework, learning tasks, and other products the children brought home, (b) direct reports from teachers and schools, (c) the child's problem solving demonstrated outside of school, and (d) public media coverage (e.g., newspaper). [ABSTRACT FROM AUTHOR]

This paper describes two researchers engagement with two teachers as they taught a middle grades mathematics course, Current Events Math, in a large urban school district. The researchers share bits of data and their ethical entanglements as they entered into the site to find the truth about what works in middle grades mathematics classrooms only to realize that truth cannot be found through research. They then grappled with the question of the purpose of research and their roles as researchers in the school and the academy. [ABSTRACT FROM AUTHOR]

This paper investigates how the selected three East Asian countries--Japan, Korea, and Taiwan-- introduce and develop ideas related to fractions and fraction addition and subtraction compared to the Common Core State Standards of Mathematics and EngageNY. Looking at curricular approaches used across countries can provide a better picture of what is of importance in instruction aimed at developing students' mathematical proficiency. Understanding how the aforementioned three Eastern Asian materials treat fractions will offer both mathematics teachers and teacher educators some concrete images of the visions of the Common Core State Standards of Mathematics and specific ideas on teaching and learning of fractions. [ABSTRACT FROM AUTHOR]

This paper explores the construct of curricular noticing, defined as the act of teachers making sense of the complexity of content and pedagogical opportunities in written or digital curricular materials (Dietiker, Amador, Earnest, Males, & Stohlmann, 2014), and reports the results of four exploratory studies aimed to examine the Curricular Noticing framework. Taken together, these studies capture work done with 62 PSTs in elementary and secondary mathematics methods courses at four universities. Findings illuminate what PSTs attend to in curriculum materials and how they interpret and respond to these materials. Irrespective of level (i.e., elementary, secondary) and materials, PSTs can learn to notice aspects of curriculum materials in order to make decisions about what to do and how to do it, and activities within methods courses can facilitate this development. [ABSTRACT FROM AUTHOR]

The paper examined the uses of visual representations in Japanese and U.S. elementary mathematics textbook series and investigated how they support student learning. U.S. series used representations to narrow student thinking to help them solve problems in the manner students previously learned only using numerals; Japanese series used representations to create space for students to analyze contexts using mathematics. The purpose of the contextual problems in U.S. textbooks is for application, while Japanese textbooks used them for mathematical analysis. ..PAT.-Unpublished Manuscript [ABSTRACT FROM AUTHOR]

More than 50% of PK-12 students in the United States are students of color and/or from historically underrepresented populations (NCES, 2020). Yet for so long, mathematics curriculum has not been representative of diverse student populations or inclusive of their backgrounds and their identities (AMTE, 2015; D'Ambrosio, 2017; TODOS, 2020). Through a focus on the intersections of mathematical modeling, ethnomathematics and cultural and historical practices, this ethnomodeling research study intentionally connects ways to engage and value each and every students' culture and identity while emphasizing essential geometry content. During this presentation, we share results from a study examining how a sequence of geometry-focused ethnomodeling tasks informed secondary mathematics prospective teachers' perceptions of valuing their own as well as their future students' cultures and identities. [ABSTRACT FROM AUTHOR]

We describe results of a long-term design experiment focused on promoting mathematics learning among multilingual ninth graders classified as English Learners. The intervention at a linguistically diverse public high school in the US focused on a unit introducing concepts related to linear rates of change. We analyze results from a curriculum-aligned pre- and post-unit assessment used to document student learning across each design cycle. The main result is that students in both the Pre-Intervention and Redesigned classrooms made gains on the pre- and post-unit assessments. However, student gains on the assessments were higher in the Redesigned classrooms than in the Pre-Intervention classrooms. Additionally, on the assessment in the Redesigned classes, students classified as English Learners made larger gains than their non-EL peers, and the majority of the gains occurred on conceptually-focused items. [ABSTRACT FROM AUTHOR]

Despite of the significance of visual fraction models for teaching and learning fraction multiplication, how students are supported to learn fraction multiplication through representations remains unknown. By examining the presentation of visual representations in the contexts of word problems and computational processes in representative Korean and U.S mathematics textbook series, this study explores how the Korean and U.S. mathematics textbooks may facilitate student learning of fraction multiplication. Analyses showed that the selected U.S. mathematics textbooks provide more instances of fraction multiplication with various types of word problems and computational procedures in developing fraction multiplication. However, Korean textbooks use representations with different purposes, which in turn leads to students’ explicit and meaningful understanding of fraction multiplication concepts and procedures. [ABSTRACT FROM AUTHOR]

Most existing measures of mathematical knowledge for teaching (MKT) assume a unidimensional structure and report scores that reflect the "amount" of MKT possessed by each examinee. These measures aggregate scores on MKT items that each tap different kinds of teacher work (e.g., explaining concepts, using representations) and different curricular topics. Although this approach is useful for some purposes, the author argues that a new way of conceptualizing measures of MKT will be more useful for gathering data to address open questions about MKT. A review of existing measures is used to argue that conceptualizing measures of MKT in terms of underlying components has promise for building MKT theory. [ABSTRACT FROM AUTHOR]

This report shares the initial results from research of a model designed to support Precalculus adjunct instructors. The model is based on the organization and coordination of Precalculus along with sustained professional development in the form of a professional learning community. The initial results for instructional practices and job satisfaction show that instructors found access to a course-coordinator and participation in a PLC beneficial. [ABSTRACT FROM AUTHOR]

Multiple representations, multiple modalities, and technology can be helpful in the understanding of mathematical concepts when used in an appropriate manner (Shah & Freedman, 2003; Goldman, 2003), but this alone does not account for the student benefits of creating and using dynamic models over teacher generated graphs to construct connections between representations. By uncovering the dynamic nature of mathematics, calculus becomes more transparent as relationships and patterns emerge. The struggle to understand becomes worthwhile and rewarding for students as they create and observe the action of a dynamic mathematical object. This study shows an improvement in attitude, and academic achievement when students develop dynamic mathematical object to understand calculus and poses new questions to explore. [ABSTRACT FROM AUTHOR]

Although an increasing number of teachers report flipping a lesson or their entire class, little is known about what leads teachers to this decision or how they implement flipped instruction. Understanding these factors is important because it can allow teacher educators and researchers to investigate ways to support teachers in enacting practices that can achieve their goals and improve student learning. In this study we examine two teachers' motivations for and conceptualizations of flipped instruction. We discuss the ways in which these motivations aligned, or not, with their enactments and suggest implications for research and practice. [ABSTRACT FROM AUTHOR]

Evidenced by the lack of research considering queer students, mathematics education researchers are continuing to marginalize the experiences of queer youth and the only resolution is to center the queer student experience in the mathematics context. To accomplish this, I choose to dwell in the borderlands between queer theory and mathematics not only to challenge the border between them, but also to push on the borders of mathematics education research. In order to do so, I offer ways in which mathematics education researchers can take a queer turn in mathematics education research by generating queer curriculum, engaging in queer pedagogy, and queering mathematics content. [ABSTRACT FROM AUTHOR]

This goal of this study is to investigate how preservice elementary teachers describe equity and equitable mathematics teaching on a brief survey before and after taking an equity focused elementary mathematics methods course. At the beginning and end of this course, the preservice teachers completed a brief survey of questions that asked them to define equity and equitable teaching and give examples of how they would teach in equitable ways. Results indicate that students' pre and post responses changed in meaningful ways before and after the course. The definitions and examples were coded into three different categories: equity as academic success, equity as management of the classroom, and equity as teachers' relationships with students. Findings from this study support the hypothesis that more sophisticated or advanced ways of thinking can be developed through an equity focused methods course. [ABSTRACT FROM AUTHOR]

This study describes efforts at two institutions to integrate critical pedagogy within the context of two mathematics content and pedagogy courses for K-8 pre-service teachers (PSTs). The purpose of the curriculum within these courses was to focus PSTs' attention on how issues pertaining to social justice may be taught within mathematics contexts. The desired goals were for PSTs to: 1) come to appreciate individuals within their own communities as valid practitioners of mathematics; and 2) come to understand the responsibility that they, their school districts, curriculum developers, and others bear to ensure that all students have equitable opportunities to learn mathematics. [ABSTRACT FROM AUTHOR]

Research indicates that U.S. students have misunderstandings in measurement, and one reason is the highly procedural focus of elementary curricula. Because the definitions of quantities are basic conceptual content, we examined definitional-type expressions (related to formal mathematical definitions) for spatial quantities (length, area and volume) within and across elementary curricula with special attention to the inclusion of units, quantification, and exhausting space. We found inconsistencies in the ways these conceptual aspects were presented. In some cases, the inclusion of particular conceptual content depended on the type of quantity, (e.g. "exhausting space" was strongly emphasized in area measure, but less so in length and volume). [ABSTRACT FROM AUTHOR]

We describe two metaphors that we hope can be used to better understand the contemporary mathematics curriculum context in U.S. middle schools, to see how this new context is both similar to and different from prior curriculum contexts. We explain the role and positioning of middle school mathematics curriculum materials over the last century or more and build from learning theory to develop the metaphors. The first metaphor, curriculum as delivery mechanism, builds from technical rational or scientific discourses and encompasses perspectives that are so pervasive they are often unstated and unquestioned. The second metaphor, curriculum as epistemic device, posits that role of curriculum is to provoke interactions that generate understanding. In this metaphor, the role of tasks in curriculum materials is to provoke and progressively refine student thinking, individually and collectively. [ABSTRACT FROM AUTHOR]

The interaction between types of communication and socio-mathematical norms on students' learning autonomy in five curriculum programs was investigated. Uni-directional, contributive, reflective, and instructive types of communications were present in curriculum programs studied. Investigations in Number Data and Space and Math Trailblazers provided opportunities for students to explain, justify, and compare solution strategies. Math in Focus and Scott Foresman Addison Wesley-Mathematics required explanations, justifications, and comparisons of solution strategies, but those were mainly provided by the teacher. The former and latter programs potentially foster intellectual autonomous and intellectual heteronomous learning in students, respectively, while Everyday Mathematics almost equally supports both. [ABSTRACT FROM AUTHOR]

Reform-based mathematics curricula in the United States place new demands on both teachers and students for mathematizing situations that need to be interpreted through talk, texts, stories, pictures, charts, and diagrams. In urban middle schools, where many students are struggling with reading and writing, meeting these demands is especially urgent. In this study, we examine how teachers learned to recognize and to address the literacy demands in conceptually rich, but contextually complex curricular materials. The teachers' perspectives on the materials have implications for the design of curricula materials. This study also has implications for theorizing about teachers' learning in practice. ..PAT.-Conference Proceeding [ABSTRACT FROM AUTHOR]

The article discusses a study on the cultural diversity knowledge base (CDKB) of mathematics pre-service teachers (PSTs) in the U.S. The study examined how PSTs can use their knowledge of culture to identify and create culturally responsive curriculum for African American and Latin American students. It also investigated the teachers' attempt to use culturally responsive mathematics instructional materials and algebraic word problems.

The article discusses a study on the role of mathematics teacher educators (MTEs) in the development of awareness and agency regarding issues of equity for pre-service teachers (PSTs) in elementary education the U.S. The study examined the use of a social justice mathematics methods learning module by 100 PSTs. It analyzed quantitative and qualitative data from the engagement of teachers in the module.

The article presents ways to improve the quality of mathematical teaching in the U.S. The article suggests to enhance curriculum decisions of teachers at varying scales and their need to analyze the curriculum beyond just attention to individual tasks and directions. The experiences of mathematics teachers who participated in a professional development in Summer 2015 are also given.

The article discusses a study on the impact of a graduate program on mathematics leadership actions pursued by elementary and middle school teachers in their schools in the U.S. The study examined mathematical knowledge for teaching, teaching practices of the participants and their coaching and facilitation skills. It also analyzed course assignment, online discussions, and verbal and email conversations concerning the program.

The article discusses a study on the understanding of role and influence of the Common Core State Standards (CCSS)-focused curriculum materials on middle grade teacher instruction. The study examined the teachers' perception on the curriculum on their teaching practices and student learning. It also identified the stance of teachers on the use of a unified form of mathematics standards.

The article discusses a study on the accessibility of the high school curriculum under the Core-Plus Mathematics Project (CPMP) funded by the U.S. National Science Foundation (NSF). The study applied a framework that was used in the evaluation of textbooks across different disciplines. It analyzed the potential of the framework's dimensions to affect the accessibility of problems from the perspectives of students.

The article discusses a study which investigated the relationship between new curriculum, teacher beliefs and teaching practices in elementary mathematics education in the U.S. The study examined the conceptual understanding of students through their engagement in mathematical processes such as reasoning, problem solving and communication. It used a survey, interviews and classroom observation in a case study with three elementary teachers.

The article discusses a study on an educative guideline for children's mathematical thinking in terms of elementary mathematics curriculum in the U.S. The study identified lesson features indicative of an educative guideline and their modification to address the guideline's other aspects in three lessons. It also stated the implications of the guideline for curriculum materials and prospective teachers's reading of curriculum.

The article discusses a study which examined the learning experiences of highly mobile, marginalized youth in the U.S. who received direct instruction. The study utilized an analytic framework to determine the mathematical empowerment of students. It highlighted a Mexican American high school student's experiences of curricular structures in her classrooms.

The article discusses a study which investigated the alignment of mathematical tasks in Common Core textbooks to Learning trajectories (LT) in geometry in the U.S. The study used the Surveys of Enacted Curriculum (SEC) to examine this alignment. Area and volume lessons were selected since geometry topics are connected to other areas of mathematics.

The article discusses a study which differentiated quantitative reasoning (QR) skills in liberal arts students taking a QR course and STEM students taking an algebra sequence course in the U.S. The study analyzed how the course can explain QR skills of students. It used the Quantitative Literacy & Reasoning Assessment (QLRA) to measure quantitative literacy of students from a college in Florida.

The article presents an overview of the result of a study which identified and described gender differences found in third grade students' work on a written mathematics curriculum using "Investigation in Number, Data, and Space," a reform-minded mathematics curriculum whose development has been funded by the National Science Foundation. Third grade school students from an urban school district in the Midwestern U.S. participated in the study. Methods used and conclusion are discussed.

The Common Core State Standards for Mathematics (CCSSM) have now become law in most all of the United States. "Mathematics teachers will direct and determine the extent to which any curriculum changes in mathematics affect student learning." (Reys, 2011) In addition, teachers of rural, poor students face added difficulties in providing an equitable education for their students. (Harmon and Smith, 2012) Much research goes into the big picture changes in curriculum, assessment, and instruction; however, what is known of the specific experiences of teachers in adjusting to change? This research is an attempt to understand the effects of implementation through the unique lens of three rural Appalachian mathematics teachers. [ABSTRACT FROM AUTHOR]