Standards-based Mathematics Research Articles

An Anti-deficit Counter-story of a Black Girl’s Forms of Resilience in a Standards-based Mathematics Classroom

An Anti-deficit Counter-story of a Black Girl’s Forms of Resilience in a Standards-based Mathematics Classroom

\u201cThe Wall Now Between Us\u201d: Teaching Math to Students with Disabilities During the COVID Spring of 2020

This paper presents a case study of the experiences of a special educator named Ms. Montes (pseudonym) teaching standards-based mathematics during Emergency Remote Teaching (ERT) during spring 2020. Ms. Montes was interviewed twice during this period; data were analyzed through inductive thematic analysis. Pre-COVID, Ms. Montes provided her students daily opportunities to tackle challenging mathematical problems and taught self-regulation strategies for students to better understand themselves as learners. After the shift to ERT, Ms. Montes described “the wall between us” as various barriers that made teaching mathematics online far more challenging. Challenges included supporting students with productive struggle when not physically present with them and supporting student self-regulation during mathematical problem-solving. Supporting students with disabilities to learn mathematics during ERT and distance learning will require considering emotional and affective dimensions of learning. Coaching students and families in self-regulation strategies could support student engagement in mathematical problem-solving in online learning.

Examining the Validity Argument of A Survey Measuring Elementary Teachers’ Implementation of Standards-Based Mathematics Teaching: An Argument-Based Approach

ABSTRACT In this paper the authors review the validity claims of a survey published in 2003, A Survey Measuring Elementary Teachers’ Implementation of Standards-Based Mathematics Teaching. Though the original survey received widespread attention and use, little formal review had been performed beyond the original estimates of reliability and validity. A content analysis was performed as well as exploratory and confirmatory factor analyses in order to understand the continued validity of the interpretations and uses of the instrument results. Although the content the survey measures aligns with contemporary conceptualizations of high-quality teaching practices and was originally published with a reliability estimate and evidence of its overall validity, its use should be modified to some degree in order to align with the further validity analyses described in this paper.

Utilizing the M-Scan to measure standards-based mathematics teaching practices: affordances and limitations

The Mathematics Scan (M-Scan), a content-specific observational measure, was utilized to examine the extent to which standards-based mathematics teaching practices were present in three focal lessons. While previous studies have provided evidence of validity of the inferences drawn from M-Scan data, no prior work has investigated the affordances and limitations of the M-Scan in capturing standards-based mathematics teaching. We organize the affordances and limitations into three categories: the operationalization of the M-Scan, the organization of the M-Scan, and the M-Scan within the larger ecology of instruction. Our analysis indicates the M-Scan differentiates among lessons in their use of standards-based mathematics teaching practices by operationalizing the M-Scan dimensions at the lesson level, sometimes at the expense of capturing the peaks and valleys within a single lesson. Simultaneously, the analysis revealed how the application of the rubrics may be impacted by lesson transcripts. We discuss the theoretical organization of the M-Scan and its implications for researchers and practitioners applying the rubrics. Finally, we point to the affordances and limitations of the M-Scan within the larger ecology of instruction by considering curricular issues and two dimensions of instruction not highlighted by the M-Scan.

Standards-based mathematics instruction and sociomathematical norms: Facilitating change in an undergraduate classroom

ABSTRACTResearch indicates that standards-based mathematics instruction positively supports students’ academic development. Although standards documents identify accepted best practices, they do not speak to the impact that students’ expectations of the mathematics classroom has on the successful implementation of standards-based instruction at the university level. Using a mixed-methods approach, this study investigates those challenges with an iterative self-study of one undergraduate mathematics classroom that seeks to answer the question: How can postsecondary teachers change the expected classroom culture of lecture and practice to new sociomathematical norms that (a) support a community of learners and (b) help students develop a productive disposition toward mathematics within these new norms? An analysis of classroom interactions, students’ work, and researcher reflections reveals the need for these changes to be (a) executed over time with attention to students’ thoughts and needs and (b) supported with learning tools that provide structure to sometimes seemingly chaotic lessons. The study also highlights the need for teacher support in the form of collaboration, teacher professional development, and reflection.

Equity-Directed Instructional Practices: Beyond the Dominant Perspective

In this article, the author synthesizes four equity-directed instructional practices: standards-based mathematics instruction, complex instruction, culturally relevant pedagogy (CRP), and teaching mathematics for social justice (TMfSJ). The author organizes these practices according to the dominant and critical axes in Gutiérrez's (2007a) equity framework. Among 12 teachers from 11 schools in a large urban school district, the author presents case studies of 3 teachers who excelled with the aforementioned dominant equity-directed practices but struggled with the critical practices of connecting to students' experiences called for in CRP and critical mathematics called for in TMfSJ. The analysis explicitly explores the role of whiteness in these struggles. The author presents implications and recommendations for mathematics teacher education on how to better support teachers for equitable teaching that includes these critical equity-directed practices.

Factors Associated with Alignment between Teacher Survey Reports and Classroom Observation Ratings of Mathematics Instruction

AbstractWe investigated the alignment between a teacher survey self-report measure and classroom observation measure of ambitious mathematics instructional practice among teachers in two urban school districts using two different standards-based mathematics curricula. Survey reports suggested mild differences in teachers’ instructional practices between the two districts, whereas observation ratings indicated starker differences. That said, teachers’ survey and observer ratings were significantly correlated in both districts. Factors significantly predicting the extent of survey-observation alignment included teachers’ grade level, Mathematical Knowledge for Teaching, cognitive demand, and—for one district—teachers’ adherence to the surface-level aspects of their curriculum. Qualitative analyses suggested that teachers’ survey-observation alignment could be a function of their interaction with colleagues who provided instructional models against which they could gauge the extent of their standards-based i...

Standards-based mathematics curricula and the promotion of quantitative literacy in elementary school

Background: Prior research has shown that students taught using Standards-based mathematics curricula tend to outperform students on measures of mathematics achievement. However, little research has focused particularly on the promotion of student quantitative literacy (QLT). In this study, the potential influence of the Investigations in Number, Data, and Space curriculum on student quantitative literacy is investigated. Quantitative literacy is conceptualized as a hierarchical three-factor model comprising the interrelationship among a student’s mathematical beliefs, disposition, and cognition. This theoretical model is validated with elementary-aged students and used to investigate whether students’ quantitative literacy is related to the use of the Investigations curriculum. Results: The hierarchical three-factor QLT model was found to have relatively good fit for the sample of elementaryaged students, and all inter-factor relationships were found to be consistent with the proposed theoretical model of the quantitative literacy construct. On average, students in the school district using a Standards-based mathematics curriculum had increased levels of quantitative literacy when compared to students in the district not using the curriculum or using it for less time. Conclusions: Based on the findings of this study, the Investigations mathematics curriculum has potential to promote students’ development of quantitative literacy in elementary school. Furthermore, the results of the study provide additional validation for the theoretical quantitative literacy construct modeled as a second-order factor comprising the interrelationship among a student’s mathematical beliefs, mathematical disposition, and mathematical cognition.

The Impact of a Standards-based Mathematics Curriculum on Students’ Mathematics Achievement: The case of Investigations in Number, Data, and Space

Background:The purpose of this research is to examine the impact of a Standards-based elementary mathematics curriculum on third grade students’ mathematics performance.Materials and methods:A total of 707 students participated in this study. Of this total, 368 students were from eight schools located within the same school district in a racially and ethnically diverse large city in the Midwest. Another 339 of the students were from four schools located in two different school districts in a middle- to high-SES, largely white, suburban area in the Northeast.Results:Third grade students using Investigations curriculum outperformed in most cases and performed the same in the other cases matched comparison groups who were using a range of conventional curricula on the mathematics assessment. The Investigations groups did the same or better on the decontextualized, contextualized, and algebraic-reasoning constellations compared with their counterparts.Conclusions:In conlusion, the revised Investigations curriculum is not as effective with the low SES African-American students as it is for middle to high SES, white students.The curriculum fidelity measures did not differentiate achievement differences.

Mathematical Knowledge for Teaching, Standards-Based Mathematics Teaching Practices, and Student Achievement in the Context of the Responsive Classroom Approach

This study investigates the effectiveness of the Responsive Classroom ( RC) approach, a social and emotional learning intervention, on changing the relations between mathematics teacher and classroom inputs (mathematical knowledge for teaching [MKT] and standards-based mathematics teaching practices) and student mathematics achievement. Work was conducted in the context of a randomized controlled trial. Participants were 88 third-grade teachers and their 1,533 students. A multigroup path analysis accounting for fidelity of implementation revealed no direct or indirect effects linking MKT to student achievement in the RC or control condition. The same analysis revealed different findings for the RC versus control teachers. In the RC group only: (a) Teachers trained in RC who used more RC practices showed higher use of standards-based mathematics teaching practices, and (b) higher use of standards-based mathematics teaching practices related to greater improvements in math achievement. No comparable findings were evident in the control condition. Results demonstrate the importance of building social and emotional capacity in teachers by helping create a supportive classroom that helps teachers provide stronger mathematics teaching practices that lead to improved student learning.

Examining the Influence of a Curriculum-Based Elementary Mathematics Professional Development Program

This study presents findings from the first cohort of teachers in a U.S. Department of Education Mathematics Science Partnership (MSP) grant designed to support the use of a standards-based elementary school mathematics curriculum, Investigations in Number, Data, and Space (Investigations). In line with the goals of the MSP program, the 84-hour professional development program focused on building teachers’ knowledge of mathematics content, examining how the mathematics content is embedded into curriculum, and supporting teachers’ enactment of reform-based pedagogies. Teacher participants had a positive gain in their content knowledge, but this increase did not have any statistically significant impact on student gains in the assessment of mathematics proficiency. Results about teacher beliefs were inconclusive, as more time is needed to change teacher beliefs. Teachers who changed their practices from teacher centered to student centered found their students with statistically more gains in their performance in curriculum-based mathematics assessments. Discussions and implications of these findings were also presented.

Alignment of game design features and state mathematics standards: Do results reflect intentions?

This paper describes the results of a randomized control trial of a standards-based mathematics software on elementary school students' (3rd–5th graders; N = 10,860) mathematics achievement. Spatial Temporal Mathematics (ST Math) engages students by presenting them with a series of game-like activities that are directly tied to the California State Standards for mathematics. We report the effects of the program on students' specific mathematics skills, as well as uncover which elements of the design of the games could be responsible for gains in achievement. We pay particular attention to the alignment of design features of the games, the standards to which developers intended to align their games, and assessments of specific mathematics skills. Results indicate a statistically significant effect of the program on students' basic number sense skills as measured by a standardized measure of mathematics achievement (effect size of 0.14). Subsequent coding of the games for elements that are related to number sense, such as the occurrence of number lines and objects that represent numbers, revealed that these design elements occur throughout the software. We discuss these findings as they relate to the development and design of standards-based mathematics curricula as well as how these features relate to their assessment.

School-Based Communities of Practice as Mechanisms for Standards-Based Mathematics Curriculum Implementation

In this article, we draw upon Remillard and Bryans’ (2004) categorization of curriculum use in observations of two middle-grade teachers’ integration of Standards-based curriculum materials (National Council of Teachers of Mathematics, 1989, 2000). Each teacher participated in a two-year professional development program focused on increasing content knowledge and pedagogical content knowledge, as well as fostering the development of communities of practice within each school site. We introduce the design of the professional development program to explain how the design supported each teacher's use of Standards-based curriculum materials. Results indicated that the existence of site-based communities of practice established during the professional development program afforded one teacher continued opportunities to reflect upon and critique her instructional decisions, whereas the lack of a community of practice at another school site served to limit the integration of Standards-based materials.

Curriculum-Based Measurement and Standards-Based Mathematics

This purpose of this study was to examine the reliability and validity of a curriculum-based measure of word problem solving (CBM-WPS) as an indicator of performance and progress in a sample of 136 third-grade students at risk for mathematics difficulties (MDs) instructed in a standards-based mathematics curriculum. Students completed the CBM-WPS measure every 2 weeks across 12 school weeks. Results indicated that the CBM-WPS measure was reliable and significantly correlated with measures of arithmetic WPS, number combinations fluency, and a standardized test of mathematics achievement. Results of growth modeling indicated that students showed significant growth on the CBM-WPS measure, with an average increase of 0.33 problems correct per week. Additional analyses revealed that students identified as high at-risk demonstrated similar growth as students identified as low at-risk. Furthermore, the CBM-WPS growth slopes were a significant predictor of students’ spring performance on a standardized test of mathematics achievement, demonstrating their predictive validity. Implications for practice and future research for assessing mathematics skill development are discussed.

Setting Instructional Expectations: Patterns of Principal Leadership for Middle School Mathematics

Principal instructional leadership has been found to support improved instruction. However, the methods through which principal leadership influences classroom instruction are less clear. This study investigates how principals’ leadership may predict the expectations that mathematics teachers perceive for classroom practice. Results from a hierarchical generalized linear (HGLM) model, using data from four urban school districts, show that the principal's work to frame instructional vision, and the principal's own vision, both predict perceived instructional expectations. However, other conventional leadership activities are not predictive. Finally, principals appear to provide a baseline of expectations for standards-based mathematics instruction rather than comprehensive expectations.

Introducing an observational measure of standards-based mathematics teaching practices: Evidence of validity and score reliability

The purpose of this study is to introduce a measure of standards-based mathematics teaching practices, the Mathematics Scan (M-Scan), and to examine its validity and score reliability. First, we define standards-based mathematics teaching practices based on eight dimensions that have emerged in recent conceptualizations by researchers and in the context of existing observational measures. Second, we present three sources of validity evidence: content review by experts, analysis of response processes of coders, and convergent and discriminant patterns with existing observational measures. Third, we provide evidence of inter-coder (or inter-rater) reliability through analyses of variance components and calculation of reliability coefficients, using the framework of generalizability theory. Results show the M-Scan holds promise as a useful tool in mathematics education research, measuring indicators of standards-based teaching practices unique to the subject of mathematics.

Does the Responsive Classroom Approach Affect the Use of Standards-Based Mathematics Teaching Practices?

This study highlights the connections between two facets of teachers' skills—those supporting teachers' mathematical instructional interactions and those underlying social interactions within the classroom. The impact of the Responsive Classroom (RC) approach and use of RC practices on the use of standards-based mathematics teaching practices was investigated in third-grade classrooms. Eighty-eight third-grade teachers from 24 elementary schools in a large suburban district were selected from a sample of teachers participating in a larger randomized-control study. Results showed that teachers at schools assigned randomly to receive training in the RC approach showed higher use of standards-based mathematics teaching practices than teachers in control schools. These findings were supported by analyses using fidelity of implementation: greater adherence to the intervention predicted the use of more standards-based mathematics teaching practices. Findings support the use of the RC approach for creating classroom social environments that facilitate standards-based mathematical practices.

Understanding and Accessing Standards-Based Mathematics for Students With Mathematics Difficulties

In this introduction to the special issue, the author provides a brief overview of (a) standards-based mathematics and implications for students with learning disabilities and those at risk for mathematics difficulties and (b) research on mathematics interventions/instructional practices and student outcomes. Furthermore, the author highlights how the articles in this special issue address these areas. The article concludes with a description of the purposes of this special issue.

Teacher Learning and Perceptions Across the Professional Continuum

Learning occurs throughout a teacher's career and as the result of engagement with a multitude of experiences, both within and outside of formal teacher education venues. This volume of Journal of Education contains seven articles that inform the teacher education community about teacher learning across the professional continuum. Within these pages, readers will consider three studies about effective professional development for inservice teachers (Slavit, Nelson, & Deuel; Wager & Foote; Shultz & Ravitch), one study about alternative field placements for preservice teachers (Brayko), two studies about teacher perceptions of their preparation for teaching (Smith, Corkery, Buckley, & Calvert; Eckert), and one study about teacher learning whose participants span the professional continuum (Kleickmann, Richter, Kunter, Elsner, Besser, Krauss, & Baumert). Also of note with regard to this collection of studies is the inclusion of two studies conducted outside the United States--one conducted in Germany and the other in New Engaging teacher teams in the process of collecting, analyzing, and acting on the interpretation of student data has become a widespread professional development activity in American schools; however, to date, very little empirical research has focused on that domain. In their article titled Teacher Groups' Conceptions and Uses of Student-Learning Data, David Slavit, Tamara Holmlund Nelson, and Angie Deuel make an important contribution to the literature by examining how teacher groups spend time when working with student data as well as the types of inquiry activities in which they engage. The conceptual underpinnings for the study come from a two-dimensional framework that depicts the inquiry orientation of the group as a whole as well as the dialogic interactions that occur among group members. In the second article, Locating Praxis for Equity in Mathematics: Lessons from and for Professional Development, Anita Wager and Mary Foote contribute to an emerging line of inquiry in mathematics education that considers the role of teacher education and professional development in equitable mathematics pedagogy. Using the constructs of figured worlds and praxis, the authors analyzed teachers' participation in professional development focused on both mathematics and issues of equity and diversity. The article offers compelling case studies of three teachers, selected from a larger set of teachers in the year-long professional development, to illustrate a variety of experiences and how these teachers developed identities within the figured worlds of standards-based mathematics, multicultural education, and equitable mathematics pedagogy. Particularly noteworthy is how the teachers located praxis--potential sites for transformative action--in different spaces: their own classrooms, their schools or districts, and the society at large. Investigations of preservice teachers' perceptions continue to enhance our understandings of the types of experiences that impact their learning. In the third article, Lisa Smith, Gaynor Corkery, Judy Buckley, and Amanda Calvert present findings from a study of the relationship between preservice teachers' concerns and teaching efficacy in Changes in Secondary School Preservice Concerns About Teaching in New Zealand. Through analyzing data from two survey instruments and follow-up focus group interviews, these authors contribute to the teacher education community's understandings of preservice teachers' perceptions of themselves as teachers--useful information that has implications for teacher education programs around the world. Although content knowledge (CK) and pedagogical content knowledge (PCK) have been linked with teachers' instructional practice and student outcomes in previous studies, little is known about the impact of teacher education on CK and PCK. The article by Thilo Kleichmann, Dirk Richter, Mareike Kunter, Jurgen Eisner, Michael Besser, Stefan Kraus, and Jurgen Baumont, Teachers' Content Knowledge and Pedagogical Content Knowledge: The Role of Structural Differences in Education, contributes to our understanding of how differences in three phases of teacher education (university studies, induction, and inservice) impact these two aspects of teacher knowledge in mathematics. …

Assessing Instructional Quality in Mathematics

AbstractAssessments of instructional quality based on classroom observations and artifacts have the potential to measure and improve mathematics instruction and learning. This article describes the Instructional Quality Assessment (IQA) Mathematics Toolkit and examines its ability to identify the nature and quality of classroom instruction. The IQA assesses elements of ambitious instruction in mathematics; specifically, the level of instructional tasks and task implementation, opportunities for mathematical discourse, and teachers' expectations. Results are reported from a study of 13 middle school teachers in a mid-sized urban district, following a professional development initiative and the adoption of standards-based mathematics curricula. The IQA identified high-quality assignments and student work, and that teachers who utilized cognitively challenging tasks could maintain the cognitive demands in lesson observations. The IQA also identified that observed instruction lacked high-quality whole-group d...