Middle Grades Mathematics Teachers Research Articles

Connections Between Prospective Middle-Grades Mathematics Teachers’ Technology-Enhanced Specialized Content Knowledge and Beliefs

The authors explore the influence of instructional technologies on teachers’ subject-matter knowledge as well as how this knowledge is mediated by context, experience, and beliefs about teaching, mathematics, and technology. This study examined how four pre-service middle grades mathematics teachers’ (PSTs) beliefs about teaching, mathematics, and technology influenced their subject matter knowledge specific to the teaching profession (i.e, specialized content knowledge [SCK]). Embedded-unit single case study analysis revealed that PSTs’ different beliefs about teaching, mathematics, and technology indicated various impacts of the use of dynamic geometry software on their SCK. PSTs who viewed teaching mathematics with technology as an effective pedagogical decision to support students’ understanding and self-discovery of their subject matter knowledge demonstrated more dynamic SCK with dynamic geometry software. The authors discuss interconnections between PSTs’ beliefs and knowledge and share implications for technology-enhanced teacher education of middle grades mathematics teachers.

A Curriculum-Based Approach to Learning Trajectories in Middle School Algebra

Our aim is to contribute to the body of research on learning trajectories (LTs) in mathematics by making visible a process for articulating a hypothetical learning trajectory implicit in a widely adopted, reform-based, middle-grades mathematics curriculum. In doing so, we highlight considerations, decisions, and challenges we faced as part of this work. By describing our LT articulation process, our aim is to highlight ways in which curriculum-specific LTs can be articulated to serve as a more proximal and instrumental tool for teachers’ instructional practice. Furthermore, to illustrate we describe how the products of the work were used in practice-based professional learning experiences with middle-grades mathematics teachers.

Investigation of Middle Grade Mathematics Teachers’ Suggestions for Eliminating Student Misconceptions According to Different Variables

Bu araştırmanın amacı, ortaokul matematik öğretmenlerinin matematik derslerinde karşılaştıkları kavram yanılgılarının gidermeye yönelik sundukları çözüm önerilerini ve bu çözüm önerilerini etkileyen faktörleri incelenmektir. Bu çalışmada tarama modeli kullanılmıştır. Araştırma 2015- 2016 eğitim-öğretim yılında Ankara il Milli Eğitim Müdürlüğü’ne bağlı ortaokullarda, görev yapan 129 matematik öğretmeni ile gerçekleştirilmiştir. Araştırmanın verileri 6 sorudan oluşan Kavram Yanılgıları Çözüm Anketi (KYÇA)’nden elde edilmiştir. Öğretmenlerin KYÇA’ da sundukları çözüm önerileri puanlandırılarak elde edilen nicel verileri analiz etmek için Mann- Whitney U ve Kruskal Wallis Testleri kullanılmıştır. Elde edilen bulgulara göre ortaokul matematik öğretmenlerinin kavram yanılgılarını gidermeye yönelik ürettikleri çözüm önerilerinin sayısında cinsiyet, öğrenim durumu, lisans akademik başarı düzeyi, mesleki kıdem, meslektaşlarla iletişim, eğitim yaklaşımı ve sınıf mevcudu değişkenlerine göre anlamlı bir fark gözlenmemiştir (p>0.05). Nitel verilerin analizinde ise içerik analizi yöntemi kullanılmıştır. Analiz sonuçlarına göre öğretmenlerin kavram yanılgılarının giderilmesine yönelik sundukları çözüm önerileri öğretim bilgisi, öğretim için teknoloji bilgisi, öğrenci bilgisi ve diğer olmak üzere dört temada ele alınmıştır. Öğretmenlerin bu temalar altında kritik noktaları vurgulama, matematiksel şekil ve modelleme, konu tekrarı, somut öğretim materyali kullanma, kavram yanılgılarına hitap etme vb. gibi çeşitli çözüm önerileri sundukları görülmüştür.

Helpful and Hindering Features of GeoGebra: Understanding What Affords Conceptual Understandings of Definite Integrals Among Pre-Service Middle Grades Mathematics Teachers

This paper introduces the Affording Understanding Conceptual Framework as a way for mathematics teacher educators to analyze student’s perceptions of a digital math tool’s helpfulness (e.g., GeoGebra) versus the instructor’s perceptions when seeking insights into how a lesson design could be improved. An example of this action research process is provided using GeoGebra to help pre-service middle grades mathematics teachers (MGMTs) develop their conceptual understandings of definite integrals. Findings showed that the pre-service MGMTs noticed four categories of what they considered to be primarily helpful features: “Ease of Use,” “Pictorial Representation,” “Colored,” and “Slider/Dynamic Movement” types. While the pre-service MGMTs all described these as helpful, the content of their comments showed that there was a material difference in how they viewed the “Ease of Use” type from the other three suggesting ways in which the lesson could be revised to be more effective.

Middle Grades Mathematics Teachers’ Mixed Perceptions of Content-Focused Professional Development

The purpose of this study was to understand how and why middle grades mathematics teachers did or did not fully participate in sustained, content-focused professional development. Qualitative data were collected from middle grades teachers who demonstrated varying levels of participation. The teachers identified opportunities to engage in novel ways with mathematics content as effective in improving their own mathematics understanding and, consequently, their own instruction. Participants who were more critical of the professional development felt the mathematics content was often beyond their specific grade-level. Factors identified as affecting teachers’ participation in the training included administrative support and school-related responsibilities. Offering content-focused professional development designed to reflect the structures and characteristics established in research to most effectively provide teachers with needed knowledge and skills was not enough to ensure teacher participation.

Surveying Middle-Grades Teachers' Reasoning About Fraction Arithmetic in Terms of Measured Quantities

We report a novel survey that narrows the gap between information about teachers' knowledge of fraction arithmetic provided, on the one hand, by measures practical to administer at scale and, on the other, by close analysis of moment-to-moment cognition. In particular, the survey measured components that would support reasoning directly with measured quantities, not by executing computational algorithms, to solve problems. These components—each of which was grounded in past research—were attention to referent units, partitioning and iterating, appropriateness, and reversibility. A second part of the survey asked about teachers' professional preparation and history. We administered the survey to a national sample of in-service middle-grades mathematics teachers in the United States and received responses from 990 of those teachers. We analyzed responses to items in the first part of the survey using the log-linear diagnostic classification model to estimate each teacher's profile of strengths and weaknesses with respect to the four components of reasoning. We report on the diversity of profiles that we found and on relationships between those profiles and various aspects of teachers' professional preparation and history. Our results provide insight into teachers' knowledge resources for enacting standards-based instruction in fraction arithmetic and an example of new possibilities for mathematics education research afforded by recent advances in psychometric modeling.

Metacognition and Middle Grade Mathematics Teachers: Supporting Productive Struggle

Communicating mathematical ideas through writing, listening, and verbalizing allows students to think about how they “think” about mathematics. By focusing this communication on a reflection of how one thinks about mathematics, metacognitive writing engages students as mathematicians and learners. In this article we describe a professional development that we implemented with middle grade mathematics teachers focused on metacognitive writing as a tool to support productive struggle in the mathematics classroom. Thus, this practitioner article adds to the knowledge base on how to develop middle grade teachers metacognitive writing through engagement in productive struggle. Recommendations for practice are included.

Supporting Middle Grades Mathematics Teachers and Students: A Curricular Activity System Used in an Urban School District

The exploration of proportional relationships is foundational to the mathematics studied in the middle grades and beyond. Research has shown that an early emphasis on procedures often leaves students with a shallow understanding of the important underlying mathematical concepts of proportional relationships. One approach that addresses the needs of both teachers and students when it comes to mathematics that middle grades students find challenging (e.g., ratios and proportions) is a unified curricular activity system (i.e., a system of curricular materials, technology, and teacher professional development). The mixed-method study presented in this article outlines a curricular activity system that was designed to underpin middle grades mathematics teachers’ implementation of a learning module addressing proportional relationships. The results of the study provide evidence that a curricular activity system in which teacher professional development is coherently aligned to technology-embedded curriculum impacts teachers’ ability to teach as well as students’ learning of proportional relationships.

Examining the Pattern of Middle Grade Mathematics Teachers’ Performance: A Concurrent Embedded Mixed Methods Study

Background:The purpose of this study was to reveal the pattern in a structure of teachers’ instructional performance. Specifically, seven teachers’ performances (Standards and Objectives, Presenting Instructional Content, Lesson Structure and Pacing, Activities and Materials, Academic Feedback, Grouping Students, and Teacher Content Knowledge) were investigated.Materials and methods:An embedded mixed methods approach analyzed 426 reports concerning 175 classroom-capturing videos.Results:The findings showed a structured pattern and the relationships among the teachers’ performances. Also, multiple group analysis was employed to examine the differences between beginning and experienced teachers’ performance patterns. The beginning and experienced teachers presented different paths regarding the four performances: Activities and Materials, Grouping Students, Standards and Objectives, and Lesson Structure and Pacing.Conclusions:The findings of the current study have implications for teacher professional development.

Exploring Relationships Between Setting Up Complex Tasks and Opportunities to Learn in Concluding Whole-Class Discussions in Middle-Grades Mathematics Instruction

This article specifies how the setup, or introduction, of cognitively demanding tasks is a crucial phase of middle-grades mathematics instruction. We report on an empirical study of 165 middle-grades mathematics teachers' instruction that focused on how they introduced tasks and the relationship between how they introduced tasks and the nature of students' opportunities to learn mathematics in the concluding whole-class discussion. Findings suggest that in lessons in which (a) the setup supported students to develop common language to describe contextual features and mathematical relationships specific to the task and (b) the cognitive demand of the task was maintained in the setup, concluding whole-class discussions were characterized by higher quality opportunities to learn.

Blended-format professional development and the emergence of communities of practice

In this paper, we draw on Wenger’s (1998) conception of communities of practice to observe the emergence of a community of practice among middle grades mathematics teachers who participated in a two-year blended-format (online synchronous, online asynchronous, and face to face) professional development program designed to increase middle-grades mathematics teachers’ content and pedagogical content knowledge, as well as foster the evolution of local communities of practices. Results indicate that the professional development program supported the development of a community of practice among a subset of participating teachers, while others failed to develop what constitutes a community of practice. Issues related to professional development design in light of these findings are discussed.

Mathematics Teachers' Reasoning About Fractions and Decimals Using Drawn Representations

This qualitative study considers middle grades mathematics teachers' reasoning about drawn representations of fractions and decimals. We analyzed teachers' strategies based on their response to multiple-choice tasks that required analysis of drawn representations. We found that teachers' flexibility with referent units played a significant role in understanding drawn representations with fractions and decimals. Teachers who could correctly identify or flexibly use the referent unit could better adapt their mathematical knowledge of fractions validating their choice, whereas teachers who did not attend to the referent unit demonstrated four problem-solving strategies for making sense of the tasks. These four approaches all proved to be limited in their generalizability, leading teachers to make incorrect assumptions about and choices on the tasks.

Integrating Literature to Support Mathematics Learning in Middle School

Supporting all students' learning is a challenge for middle grades mathematics teachers. One approach that holds promise is integrating mathematics and literacy, a practice consistent with middle school philosophy. While reading and language arts are typically easy to integrate with other subjects, some have cautioned that integrating mathematics with other subjects may be difficult to do in ways that lead to deep understanding of mathematics content (Klein, 1996; Shanahan, 1997) In particular, new research supports integrative approaches that use literature with mathematical themes to support and extend the conceptual understanding of complex mathematical development (Austin, Thompson, & Beckman, 2005; Bean, 2000). This is because familiar contexts allow students to draw on their prior knowledge to bring meaning to the mathematics (Miller, 1998; Murphy, 1999; Whitin, Mills, & O'Keefe, 1990; Whitin & Wilde, 1992). Integrating mathematics and literacy creates opportunities to introduce new vocabulary, make connections among abstract concepts, and showcase ways that mathematics applies across curriculum (Whitin & Wilde, 1992). In addition, integrating multicultural literature in the mathematics classroom can provide familiar contexts for culturally diverse students and it can present content from various viewpoints. This can help students develop cultural awareness and sensitivity as it strengthens their mathematical content knowledge and literacy skills (Bean, 2000). One possible reason teachers have difficulty integrating mathematics and literacy is the perceived lack of materials recommended and readily available to middle grades teachers. In this article, we identify a wealth of short stories, novels, and texts that not only represent rich language but also complex mathematical thought. For the purpose of this article, we focus on literature that could be easily integrated into mathematics classrooms. We developed a framework for classifying texts based on the complexity of the mathematics content, and we have organized our discussion according to this framework. Reviewing texts The authors searched extensively to find novels and short stories with mathematical content. Using advanced searching mechanisms and keywords such as math or numbers, we examined online book warehouses (e.g., Amazon.com) and literature databases (e.g., Children's Literature Comprehensive Database). These resources provided all types of literature; however, for the purposes of this article, we limit our discussion to only young adult literature. The second author's website features a complete list of titles, including a brief synopsis of each (http://ksuweb.kennesaw.edu/~fwallac1/). We used national standards for teaching middle grades mathematics to determine the type of mathematical content within these young adult texts (see Figure 1). Broad categories of content in middle grades mathematics classrooms include numbers and operations, algebra, geometry, measurement, data analysis and probability, and problem solving. As we read each text and identified the mathematical content, we found that the potential for using the books to support integrated instruction varied in relation to the complexity of the mathematics. Consequently, we developed categories related to the potential opportunities to teach rich mathematics. In other words, the higher the level of mathematical complexity within a story, the greater the number of opportunities for using integration to support the development of rich mathematical ideas for students. To develop the categories, we compared each new text read with each previously read text and asked questions such as: How does the story support the development of mathematical ideas? What is the purpose of the mathematical content within the story? How is the mathematical content presented? and How are solutions to mathematical problems described? Integrating mathematics and literature Our examination of literature found that middle school mathematical concepts found in the national standards are represented in young adult literature and offer possibilities for integration. …

Change in beliefs after first-year of teaching: The case of Turkish national curriculum context

Abstract The impact of national curriculum context on mathematics related beliefs of 12 beginning middle grades mathematics teachers was investigated after the teacher education program and first-year teaching through interviews and a combination of three belief frameworks. National curriculum requirements, lack of effective mentoring programs, and preservice tutoring experiences were detected as the major factors impacting beliefs. Participants simultaneously had teacher-centered and student-centered beliefs, causing inconsistency in beliefs and practices. While participants’ preservice and first-year experiences contrasted, they developed contextual beliefs to deal with the difficulties. Reflections on teacher education and beginning teacher support policies in national curriculum contexts were discussed.

Beneath the Tip of the Iceberg: Using Representations to Support Student Understanding

A common challenge for middle-grades mathematics teachers is to find ways to promote student understanding of mathematics. When an algorithm for adding or subtracting fractions is explained as clearly as possible and students have opportunities to practice it, the reality is that many students will continue to confuse the procedures and forget how they work. The primary intervention used to address student confusion is to reteach common procedures and give additional practice in the hope that the students will understand over time.

Different Assessments, Common Practice? Mathematics testing and teaching in the USA and England and Wales

Recently, the state has used testing more extensively to influence instructional practice. But how much do assessments actually influence practice? To explore this issue, we observed middle-grade mathematics teachers in England and Wales with their highly aligned curriculum and assessment system and two US states with performance-based assessment systems promoting more thoughtful instruction. Maryland's tests had higher stakes attached to them than Maine's. Our observations suggest that testing policies can influence the content taught and promote certain kinds of teaching to the test but that basic instructional practices, like the kind of explanation teachers offer to students and the intellectual challenge of the work, are more difficult to influence. We suggest three hypotheses for the apparent stability in underlying teaching practice. First, some testing policies do not challenge those practices. Second, assessments that do challenge current practice may not be accompanied by adequate professional development to help teachers change practice. Finally, teachers' knowledge and beliefs about teaching mathematics are so deeply embedded that they are difficult to influence.

Impact of the Missouri Middle Mathematics Project on the Preparation of Prospective Middle School Teachers.

The goal of the project was to improve the teaching and learning of middle school mathematics through collaborative Standards-based mathematics curriculum investigations. The project not only contributed to the improvement of teaching mathematics in the participants’ classrooms, but it also significantly affected the program for prospective middle school mathematics teachers at the University of Missouri-Columbia. This teacher education program is described in this article. An essential ingredient in the successful transition to Standards-based practice at the middle school level is the development of teacher education programs that reflect the fundamental principles of the NCTM Standards (1989). In particular, the mathematical preparation of prospective middle grade teachers, which traditionally had been integrated into the programs for elementary teachers, needs careful consideration. The Mathematical Association of America, in A Call for Change (MAA, 1991), outlined recommendations for the mathematical preparation of middle grade teachers. These recommendations differ significantly from recommendations for the preparation of elementary teachers and provide guidance to those developing new programs for middle grade mathematics teachers. Currently, as in the case of the M 3 Project, much attention is being focused on the improvement of the knowledge and instructional skills of inservice teachers. This is important in order to stimulate immediate and substantive change. However, it is imperative that preservice education be simultaneously improved, so that new teachers entering the field are knowledgeable and can collaborate with their more experienced colleagues in transforming the classrooms in which middle grade students study mathematics. In response to this urgency, college and university faculty throughout the nation are examining and restructuring their teacher preparation courses and programs. These academic activities have created