Search

In mathematics education, researchers often contrast conceptual and procedural teaching approaches, although labels and conceptualizations often vary across studies. Prior research has extensively examined empirical relationships between the two teaching approaches and mathematics achievement. In our study, we aimed to extend this research by exploring whether one teaching approach moderates the relationship between the other teaching approach and algebra achievement. Specifically, we investigated whether the relationship between one teaching approach and algebra achievement differs depending on the degree to which the other teaching approach is implemented. We used data from the High School Longitudinal Study (HSLS:2009) that was conducted in the USA. In our study, procedural teaching was measured as the amount of emphasis that teachers placed on objectives related to procedures and computational skills, whereas conceptual teaching was measured as the amount of emphasis that teachers placed on objectives related to understanding, application, and motivation. Hierarchical linear modeling (HLM) was used to analyze the data, thus accounting for clustering of students within classes and classes within teachers. We found a statistically non-significant interaction effect. This result suggests that the association between one teaching approach and algebra achievement is similar across the degrees of the other teaching approach. Furthermore, we found a statistically significant association between conceptual teaching and algebra achievement. Specifically, conceptual teaching was positively related to algebra achievement. For procedural teaching, we found a statistically non-significant association. Hence, we did not find evidence that procedural teaching is related to algebra achievement.

This paper reports on a two-year project to form teaching development groups in engineering departments. The goal of each group was to discuss and implement interactive teaching strategies (e.g., in-class problem solving). The research design used meetings notes, feedback from group leaders and a case study of one participant to describe how the groups can be designed to support teaching development. This research was grounded in the following questions: What are the design principles underlying a successful, ongoing, small-group model for faculty teaching development? What logistical and structural features are important for ongoing faculty teaching development in a small-group format? This paper presents the five principles identified in the study and provides a case study of an engineering faculty member's teaching innovations over the several years during and after his participation in the faculty development group.

Reform efforts in the teaching of undergraduate science, technology, engineering, and mathematics (STEM) have included introducing faculty to specific teaching strategies and engaging them in collaborative initiatives. This study examined the experiences of STEM faculty learning interactive teaching strategies while also learning and applying self-study methodology in a year-long faculty self-study learning community. We used self-study methodology as an innovative design to support STEM faculty's research about their teaching. Drawing on multiple sources of data, the researchers found that although participants reported that learning self-study methodology was unique and complex, they embraced the problematic and sophisticated nature of self-study to examine their teaching while recognizing the close link between teaching and research. As they reflected on their professional identities as teachers, they gained a better understanding of their role in their students' learning. Supporting faculty's small changes in teaching can lead to larger changes over time. Self-study methodology can reinforce the change process. The self-study learning community design may be useful as a catalyst for developing an advanced teaching trajectory for STEM faculty and useful for faculty from various disciplines. Implications for impacting individual and institutional capacity in higher education are discussed.

The purpose of this study was to explore how university researcher professional development design decisions built and sustained K-8 partnerships which foregrounded mathematics in integrated STEM via model-eliciting activities (MEAs). We applied a self-study methodology to facilitate a longitudinal examination of our practice in this multi-year project. We used the Decision-Making Protocol for Mathematics Coaching to understand our collaboration with division stakeholders as they worked toward integrating MEAs with district curriculum and pacing. Analysis of professional development artifacts, evidence of scholarship, and researcher memos revealed four recalibration points driven by district initiatives and leadership changes. Coaching with MEAs created opportunities for equitable student engagement and formative assessment. Implications for designing professional development that emphasizes explicit connections between the constraints of mathematics curriculum and the possibilities of teaching and learning through STEM integration are presented.

Mathematics specialists support the teaching and learning of K-12 mathematics and attend to school-based responsibilities and needs. This study examined the shifts in responsibilities of mathematics specialists during the COVID-19 pandemic to better-understand their current and potential future influence on mathematics teaching. An online survey was administered nationally to reveal how school-based mathematics specialists adapted their responsibilities in response to the changing school conditions. Responses from school-based mathematics specialists were analyzed using a mixed methods approach to capture self-reported shifts in responsibilities, as well as challenges and opportunities. Findings indicate that the school-based mathematics specialists were able to rapidly reprioritize their responsibilities in response to both teachers' professional learning and instructional needs. These findings illuminate the importance of mathematics specialists as school-based leaders who must continually navigate relationships and apply leadership knowledge and skills in novel ways to support shifts in mathematics teaching and learning.

To encourage growth in instructional practice, the authors describe various formats, plans, and scheduling options for mathematics coaches and other stakeholders to consider when determining effective ways to enhance the teaching and learning of mathematics.

For the past forty years, United States school districts have increasingly hired mathematics specialists to support the teaching and learning of mathematics. Despite the prevalence of this professional development structure, this is a relatively new research topic for the mathematics education field. In this paper, we report findings from an exploration of literature between 1981 and 2018 to examine the role of mathematics specialists (MSs). In particular, we examine: (1) MS positioning across research; (2) historical trends of school-based MS research; and (3) orientations of school-based MSs within research. Using the McGatha and Rigelman framework as an analytic lens, we found that beyond the positions identified in their framework (coach, intervention specialist, teacher), there were four additional MS positionings within the research (learner, other p-12 stakeholder, university stakeholder, unknown). Ultimately, we forward an expansion to the McGatha and Rigelman framework to include these new categories, as well as contextual descriptions and working definitions to support future research in more accurately and robustly capturing the ways in which MSs are investigated and reported on in research.

This paper suggests implications for researchable questions about mathematics teacher development. We ask the following: what is necessary for research that includes mathematics specialists or other hidden school-based roles within a project beyond classroom teachers and students? Mathematics specialists (e.g. mathematics coaches, mathematics teacher leaders) support teacher learning and development using different models of school-based professional development. They can play a critical role in connecting research and practice. However, research in mathematics education has regularly neglected to examine their role in studies of professional development. We suggest there are two needs for creating and examining researchable questions about such hidden players in studies of professional development: (1) defining practices and hidden players involved in systematic school change and (2) identifying the unit of analysis and scaling up professional development. We summarize existing studies and present considerations for future research.

This article uses a self-study research methodology to explore teaching an online course for mathematics specialists. The course included weekly videoconferencing sessions and focused on supporting their development as mathematics coaches working with K-8 teachers to enhance mathematics teaching and learning. The central question for the self-study was about the design of the course and the characteristics of the learning environment that resulted from the design. The study included journal reflections and survey data. Three themes emerged in the analysis of the instructional decision making for the course: student autonomy and engagement, authenticity and practicality, and fostering community.

In this article we describe our engagement in self-study as part of an examination of design-based research for education. We focus on graduate-level online teacher education as an example of how self-study provided a means of examining deeply our teaching and our roles as teacher and designer in the learning environment. We posit that online learning environments are particularly well suited for self-study to enhance design perspectives because the interactions between teacher and students are informed by personal context and mediated by technological tools. The graduate students in our courses were teacher leaders in literacy or mathematics who were learning how to support professional development for other teachers. Throughout our self-study research we found ourselves drawing upon our previous design research experiences, which aided our ability to engage in self-study: We were part of the classroom system, focusing on our roles within the teaching and learning process as designers of the online learning environment. Three key design principles resulted from our self-study process: focusing on systems of learning and teaching, designing pedagogical tools and products, and using iterative processes. Engaging in self-study enhanced our understanding and implementation of synchronous online instruction, particularly regarding our use of technological tools to enhance student learning and support learning communities.

The purpose of this study is to examine prospective mathematics specialists' engagement in an instructional sequence designed to elicit and develop their understandings of random processes. The study was conducted with two different sections of a probability and statistics course for K-8 teachers. Thirty-two teachers participated. Video analyses within a collaborative course design were used to support a teaching experiment about teachers' conceptions of random processes. In particular, teachers were asked whether the outcomes of "Rock-Paper-Scissors" (RPS) are generated randomly or not, were presented with a definition for random selection, and were asked to come to a conclusion about RPS. Teachers struggled to reconcile the equality of winning outcomes for each player with the potential for human interference in the process of generating outcomes. Ultimately, teachers concluded the outcomes were not generated randomly, but encountered a variety of unexpected obstacles along the way. (Contains 2 figures and 3 tables.)

Results of analysis of responses to a first-year undergraduate engineering activity are presented. Teams of students were asked to develop a procedure for quantifying the roughness of a surface at the nanoscale, which is typical of problems in Materials Engineering where qualities of a material need to be quantified. Thirty-five teams were selected from a large engineering course for analysis of their responses. The results indicate that engagement in the task naturally led teams to design a sampling plan, use or design measures of center and variability, and integrate those measures into a model to solve the stated problem. Team responses revealed misunderstandings that students have about measures of center and variability. Implications for instruction and future research are discussed. (Contains 4 tables and 2 figures.)

Defining challenging curriculum first requires an examination of what is meant by curriculum. This discussion of challenging curriculum is motivated by the evaluation of the National Science Foundation's Math and Science Partnership Program. Standards frameworks, textbooks, software, and pedagogy are some aspects of curricula. The level of challenge of a curriculum is a locally defined, qualitative characteristic that depends on the curriculum system. The structure of a curriculum system is proposed to investigate the purposes, representations, and conceptual systems inherent in models of curriculum that are part of mathematics teaching and learning initiatives. Three types of models are proposed: content focused, pedagogically focused, and learner centered. The models draw on examples from the Math and Science Partnership portfolio and from other areas of the literature on mathematics curriculum. (Contains 1 table and 1 footnote.)

The study investigated tool development by three middle school mathematics teachers. The tools they designed were intended to support the use of model-eliciting activities (a form of instruction related to problem-based learning) and particularly the students' presentations of their solutions for the whole class. The study examined the design and purposes for the presentation tools and resulted in a framework for categorizing teachers' purposes for tools. The framework addressed the unit of analysis for the tools (individual students or groups of students) and the nature of teachers' purposes for the tools. Design research was used as a theoretical perspective for conducting the investigation.

The study examined first-year engineering students' responses to a statistics task that asked them to generate a procedure for quantifying variability in a data set from an engineering context. Teams used technological tools to perform computations, and their final product was a ranking procedure. The students could use any statistical measures, and they needed to explain their ranking procedure in detail. The responses were first categorized by the statistical measures used. The responses were categorized using a cyclic model development perspective moving from primitive to more sophisticated responses. The modeling cycle framework provided a developmental view of students' responses and use of statistics. The study raised questions related to the measurement of variability, the application of statistics, and the process teams go through when designing an analysis procedure.

We have designed model-development sequences using a common context to provide authentic problem-solving experiences for first-year students. The model-development sequence takes a model-eliciting activity a step further by engaging students in the exploration and adaptation of a mathematical model (e.g., procedure, algorithm, method) for solving a problem for a realistic client. Here we describe an entire model-development sequence in which first-year engineering students are asked to develop, explore, and adapt a model for quantifying the size of aluminum crystals using digital images in response to the needs of an aluminum manufacturer. The intent of this paper is to highlight, by example, the components and educational value of a model-development sequence. [For "Quantifying Aluminum Crystal Size Part 1: The Model-Eliciting Activity," see EJ1063793.]

Model-eliciting activities (MEA), specially designed client-drive, open-ended problems, have been implemented in a first-year engineering course and in secondary schools. The educational goals and settings are different, but the design of an MEA enables it to be versatile. This paper will introduce the reader to the principles that guide MEA design and demonstrate the flexibility of implementation by describing the use of an MEA, Aluminum Crystal Size, in these two educational settings. [For "Quantifying Aluminum Crystal Size Part 2: The Model-Development Sequence," see EJ1063797.]