Instruction Repertoire Research Articles

Mathematics in Art and History Museums: An Informal Mathematics Education Case for Teachers’ In-Service Training

Recognizing the omnipresence of mathematics across various contexts, this paper addresses the untapped potential of museums as rich venues for informal mathematics learning beyond traditional educational settings like classrooms. This paper presents the InformalMath program, designed for the professional development of primary and middle school teachers using integrating mathematics education within art and history museums through designing mathematics visit workshops. Specifically, the focus is placed on Phase 1 of the program, in which teachers participated in two informal mathematics education workshops at two museums in Turin, Italy, and were asked to reflect on their participation through a written essay. The analysis of the essays reveals significant engagement, appreciation of mathematics as a cultural artifact, and the emergence of creativity and inclusion among participating teachers. These findings highlight the benefits of such interdisciplinary approaches in enhancing mathematical understanding and pedagogical strategies. Conclusions emphasize the program’s success in not only enriching teachers’ instructional repertoire but also in promoting a more holistic, engaging, and contextualized approach to mathematics education, suggesting a promising avenue for future educational practices and research in informal learning environments.

VTS: From the Museum into the ENL Classroom

Visual thinking strategies (VTS) is a museum-based technique with promising potential for English learners' (ELs') language development and content learning. Educators in museums and school settings have enthusiastically adapted VTS to their instructional repertoires in order to bolster students' aesthetic appreciation, literacy development, critical thinking, language learning, and content learning. In this article, the authors present a vignette from a high school classroom to illustrate the powerful potential of VTS for classroom use with linguistically diverse learners. The article also considers how language teachers may modify typical VTS to constructively scaffold ELs’ learning.

Ecology of E-Learning

Purpose. The paper deals with the role of new digital technologies in learning. 
 The tasks for the research are the following: to bring readers with an up-to-date range of new learning and teaching technologies, explore the notion of "ecology of e-learning" by analyzing the dynamics of student and teacher interactions in e-learning environments, investigate critically the ways in which technologies can create openings for new pedagogical practices, and also at times fossilize old pedagogical practices that perhaps should have been already abandoned, explore the "affordances" framework as a checklist used to analyze educational technologies and their associated pedagogical practices. 
 Methodology. The methods of the educational research context, data collection, data analysis and reporting of the students’ responses have been applied. Some interviews have been conducted in this study to receive the answers of different students and lecturers at Kharkiv University of Humanities ‘People’s Ukrainian Academy’. The basis for our research has been scientific and pedagogical studies relevant to future foreign languages teachers’ professional training in distance education conditions.
 Results. Didactic and reflexive pedagogy have been analyzed and compared. The following aspects have been analyzed: ubiquitous learning, active knowledge making, multimodal meaning, recursive feedback, collaborative intelligence, metacognition, differentiated learning. It is emphasized that digital ecologies and the new learning spaces afforded by technologies provide us with the availability to have a group of learners in a space where not all of them have to be tracking the same page, the same task at the same time. It is possible to create learning experiences for individuals and for groups with specific needs and to be able then to pace either the whole group or to pace the individual, to track an individual or to track the whole class depends on the learning process, either for the whole class or the individual, in order to adjust the instruction, the data, the information that the learner or the class has, so that they are able to meet their goals. It is highlighted that every child in the classroom even if they are the same age, or if they are the same background are unique in some way. The orientation to learning or their behavior, or their understanding of their purpose is molded by each one’s life experience. Educators have a responsibility to show that every learner is transformed, progresses, is able to understand and engage with and represent knowledge in a way that meets their needs of being an educated person that can move through the formal school system.
 Conclusions. Working within digital spaces allows us to harness the attention of every learner, to tailor educational process for their needs, to track whether they are performing or not and to adjust what we are doing. It provides us with the ability to make sure that all learners can be engaged. It means a different kind of plan. It certainly means collaborating. Collaborative intelligence for teachers in preparing, work and instruction in this space is also a key to the kinds of solutions that possible. 
 It means designing lessons with the learners in mind, not only with just pacing ones way through the standards or with any kind of curriculum, it is aligning the standards to individual's needs and deconstructing them and reconstructing them in order to pace individuals and groups so that they can progress towards higher or to goals. It means for the teacher expanding their instructional repertoires to be able to address all the learners in the classroom and as well as expanding the capacity to work with others to bring in experts through the digital ecologies that might be able to support individual learners.

An integrated model for teacher continuing professional learning in Zimbabwean primary schools

Background: Rapid changes in the classroom and out-of-school life characteristics of this knowledge society make continuing professional learning for teachers an imperative. But what kind of continuing training model could be effective in diverse work situations such as under-resourced rural school environments?Aim: The aim of the project was to capacitate primary school teachers in their teaching of mathematics to encompass numeracy learning outcomes among their pupils.Setting: This article describes an intervention service-cum-research project undertaken in three rural school districts of Zimbabwe.Method: Underpinned by the notion of change and lifelong learning, the intervention project deployed a modified cascade action research design to train 70 teacher leader mentors and 35 community leader mentors as drivers of the change in the three districts. Twelve of the 70 teacher leader mentors were further developed into expert status on numeracy pedagogy for continuity and sustainability of the change.Results: The service dimension of the project succeeded in infusing numeracy pedagogy in the schools’ instructional repertoires at the level of cultural practice within communities of practice.Conclusion: The main challenges faced in trying to implement pedagogy intended to foster mathematical numeracy are those related to costs, sustainability and continuity, some if not all of which can be dealt with through collaboration between experts, teachers and community.Contribution: The research dimension resulted in revealing a potentially powerful model of teacher continuing professional development characterised by fusing centre (district), school and community elements while retaining the cascade format. This model is worth exploring in similar and diverse school environments elsewhere.

Visual thinking strategies for English learners: Learning language through the power of art

AbstractVisual thinking strategies (VTS) is a museum‐based technique with exciting potential for English learners' (ELs') language development. Originally used to engage novice viewers in discussing art pieces, English language arts and ESOL educators have enthusiastically adapted VTS to their instructional repertoires in order to bolster students' literacy development, language learning, and content learning. In this article, the authors consider the classroom use of VTS with linguistically diverse learners. They present its classic form through a vignette to illustrate how the visual stimulus, coupled with three questions—What's going on in this picture? What makes you say that? What else can we find?—can help students produce linguistically scaffolded content. The researchers draw from the literature and identify ways that VTS implementation has been shown to support learners' development of language modalities, critical thinking, and affective skills. Finally, the authors encourage educators to explore and expand their teaching practices with ELs to try this refreshing technique in their classrooms.

The first 5 years of teaching science: The beliefs, knowledge, practices, and opportunities to learn of secondary science teachers

AbstractThe early years of teaching are important for science teachers, but little is known about how science teachers develop professionally in their early years. This mixed methods study took a longitudinal view of the early years of teaching. Following 95 secondary science teachers over a 5‐year period, this study examined the beliefs, pedagogical content knowledge (PCK), and practices of the teachers during and after their induction programming. It drew upon the conceptual framework of opportunities to learn to contemplate the experiences of the teachers in relationship to their beliefs, PCK, and practices. Interviews and observations comprised the data in the study, which were analyzed quantitatively and qualitatively and then integrated to understand the teachers' development. The quantitative analysis revealed that the early career teachers experienced no significant change in their beliefs over time but did experience significant change in their PCK and in some of their instructional practices. The qualitative analysis highlighted the difficulty in changing the instruction of the teachers, administrative decisions that constrained or contributed to the learning of the new teachers, and the different professional learning opportunities new teachers drew upon over time. These results suggest that early professional development experiences provided some support for the newly hired teachers, but not enough to challenge their beliefs or establish the instructional repertoires envisioned in the science education reforms. To better support the development of early career science teachers, they need strategic learning opportunities over time that involve administrators, colleagues, and science teacher educators.

The general technological competency model for vocational teachers in Kazakhstan

Like in many Global South countries, the vocational education and training system in Kazakhstan has some weaknesses, including low-competent educators poorly applying digital technologies in their instructional repertoire, which highlights the need for motivating teachers towards incorporating technologies representing students' everyday life in the educational process. Meanwhile, there are no practically applicable competency frameworks for Kazakhstani vocational teachers to date. This paper aimed to gather students’ opinions on which skills are more or less important for vocational educators to outline a technological competency framework for Kazakhstani vocational teachers based on Digital Competency Profiler, with content validity tested by five experts. A set of nineteen items measured on a five-point Likert scale, organized into technical, communicational, informational, and epistemological domains, was uploaded to an online survey platform and distributed among Master degree students enrolled in vocational programs in Kazakhstan. Based on survey data, the construct validity of the model was assessed by confirmatory factor analysis, which yielded high entire reliability and internal consistency. The learners assigned importance to all the four domains. However, they estimated vocational teacher’s ability to utilize productivity tracking tools as almost futile, which allegedly indicates the surveyees’ insufficient awareness about those applications and their purposes. Generally, the participants tend to prioritize vocational educators’ capacities to process mathematical computations, visualize numerical data, and operate with electronic text files and projectors, as well as their readiness for effective communication through messengers and electronic mail. The framework that emerged from this research can be used as a blueprint for synchronizing and improving educational programs in Kazakhstan.
 
 Keywords: education; survey; technology; ICT; vocational education and training.

Community languages school teachers’ pedagogical habitus in transition: an Australian perspective

ABSTRACT This research investigated Australian community languages school (CLS) teachers’ emerging pedagogical habitus, focussing specifically on key dynamics effecting the adaptation in their pedagogical understanding and practice. Following an interview-based case study design, the research analyzed in detail major factors and their interplay that had impacted the development of an expanding pedagogical habitus of three overseas-trained CLS teachers. Findings indicated that the teachers’ pedagogical habitus could have been shaped by their overall experience and understanding of the diverse contexts. The prior experience of the participants and their new learning from the professional development programs could help enhance and effect a change in their pedagogical habitus in a new educational context. A related finding was that teachers’ varied prior experiences and expertise may have determined the extent of their expanding pedagogical habitus in that it enriched (or inhabited) their instructional repertoires, through a process of engagement, reflection, negotiation and integration in a new context. Implications for teacher professional development were also considered.

Leveraging Positive Behavior Supports to Improve Engagement in Virtual Settings

High-levels of classroom engagement and on-task behavior have been linked to positive outcomes for students. In traditional classroom settings when levels of on-task behaviors are low, teacher integration of Positive Behavior Interventions and Supports (PBIS) can facilitate improvement in student engagement. PBIS strategies such as creating clear routines and expectations, explicit instruction on expected behaviors, acknowledging behavior, and a high level of opportunities to respond have demonstrated efficacy for improving engagement across grade levels. As teachers increasingly adjust their teaching to virtual platforms these evidence-based practices should continue to be a part of their instructional repertoire. Unfortunately, teachers may have little experience in leveraging such practices to improve engagement in virtual classrooms. With the recent shift to virtual instruction due to the pandemic, it is important teachers are equipped with knowledge and skills to implement PBIS in virtual classroom settings to improve student outcomes. This manuscript provides a how-to guide to support teachers and administrators in effective and efficient use of PBIS in online platforms to bridge the gap in practice. Steps and an implementation checklist are included to improve virtual learning engagement by utilizing tools within online platforms such as Zoom and GSuite to clarify virtual expectations and increase student demonstration of expected behaviors.

Learning Together: Teachers’ Evolving Understanding of Coordinated Word Study Instruction Within an RTI Framework

Despite evidence that tiered instruction within response to intervention (RTI) frameworks is important for students with reading difficulties, no complementary professional development (PD) research demonstrates how teachers can develop knowledge necessary to implement coordinated evidence-based instruction across instructional tiers. One promising PD approach combines lesson study (LS) with content-focused PD sessions; PD sessions introduce teachers to new knowledge, while LS supports teachers in integrating knowledge into their instructional repertoires. We used grounded theory methods to investigate how teams of upper elementary teachers’ ( n = 7) understandings of coordinated, tiered reading instruction changed through participation in Project InSync, a year-long PD consisting of content-focused PD workshops and LS cycles. Results indicate that, through interactions during LS sessions, teachers developed more sophisticated and integrated understandings of word study content, pedagogical practices, students’ struggles with literacy, and coordinating instruction across instructional tiers. Results have implications for teacher PD within RTI frameworks.

Agency

Agency

What Constitutes Poor Teaching? A Preliminary Inquiry Into the Misbehaviors of Not-So-Good Instructors

Across three phases, we investigated college students’ perceptions of poor college teaching to develop a typology of poor teaching behaviors. In Phase 1, students generated a list of qualities representative of poor teaching. In Phase 2, another group of students assigned behavioral correspondents to these qualities, resulting in a list of 15 poor teaching qualities and their attendant misbehaviors. Finally, in Phase 3, yet another group of students generated a “top 5” list of qualities and behaviors that their most ineffective teachers have exhibited. Across participants in Phase 3, the top 5 list included, in order, being disrespectful, offering unrepresentative and unfair student learning assessments, having unrealistic expectations for student learning, being less than knowledgeable on course content, and having poor communication skills. These findings provide practical guidance on which particular behaviors teachers should avoid adopting in their instructional repertoires.

Challenges of Integrating Mobile Technology into Mathematics Instruction in Secondary Schools: An Indonesian Context

ABSTRACTImplementing mobile learning in curriculum-based educational settings faces challenges related to perceived ethical and learning issues. This study investigated the affordances of mobile technologies to support mathematics instruction by teachers. An exploratory study employing questionnaires and semi-structured interviews revealed that, while mathematics instruction can be augmented with mobile learning, the majority of schools in Indonesia have banned student use of mobile phones in classrooms. Teachers are concerned about the improper use of mobile phones that could impact their students' mental well-being and distract them from learning. Most teachers perceive mobile technologies to be disruptive and seem reluctant to use them for teaching delivery. However, teachers are eager to experiment with digital technologies within mathematics instruction. Our findings suggest infusing alternate technologies that fit better with the school's teaching and learning environment. This includes web-based applications that can run on different digital devices ranging from desktop computers, laptops, and tablets, to mobile phones. We propose setting up communities of practice for mathematics teachers to share their instructional repertoire on integrating digital technologies within the classroom.

Writing in the content areas: a Norwegian case study

Since 2006, literacy skills have been mandated as an integral part of all subject areas at all levels (grades 1–13) in Norwegian schools. With the exception of reading, evaluation reports show that teaching in general seems to be little affected by this reform. During the last few years, however, there has been a noticeable growth in interest in writing in the content areas. The article presents quantitative and qualitative data from a network of secondary schools that have established cross-curricular school-based writing projects. Teachers in these schools meet regularly, sharing experiences about students’ writing and ways of organizing writing sessions. While they had to deal with differences in subject-specific text norms, they discovered similarities across subject areas they could work collectively on. A major effect for the participants was the development of a broader instruction repertoire and more goal-related use of scaffolding strategies in the classroom, most of which was in accordance with a process approach to writing. We discuss these data in the light of similar studies in Norway and abroad, and we highlight some reflections about implications for practice.

Exploring changes to a teacher’s teaching practices and student learning through a volleyball content knowledge workshop

This paper describes how improving a teacher’s content knowledge changes his teaching practices and its subsequent effects on student learning during a middle school volleyball instructional unit. The study was designed to challenge teacher educators’ thinking about the importance of in-depth content knowledge for effective teaching by demonstrating the effects of a content knowledge workshop on a teacher’s teaching practices and student learning. A mixed-method research design was adopted with one male physical education teacher’s qualitative teaching data and his 24 eighth-grade students’ quantitative learning data. Two separate classes of volleyball were observed for 5 days before and after the content knowledge workshop ( n = 20 lessons total). Audio and videotaped recordings were made of each lesson. Descriptive and constant comparative analyses were used to analyze the data. The results of the study indicated that the teacher used more task progressions, integrated skill practices, small-sided games, content adaptations, and diverse verbal instructional repertoires after developing content knowledge. These changes ultimately impacted the students’ game performance and involvement as well as cognitive understanding of content. The findings verify that there are strong relationships among the teacher, content, and student learning by showing how the other components are changed when the teacher’s level of content knowledge is altered. The research effort may guide teacher educators’ professional development efforts aimed at increasing pre-service and in-service teachers’ professional knowledge for teaching.

Exploring iconic interpretation and mathematics teacher development through clinical simulations

Field placements serve as the traditional ‘clinical’ experience for prospective mathematics teachers to immerse themselves in the mathematical challenges of students. This article reports data from a different type of learning experience, that of a clinical simulation with a standardized individual. We begin with a brief background on medical education’s long-standing use of standardized patients, and the recent diffusion of clinical simulations to teacher and school leader preparation contexts. Then, we describe a single mathematics simulation and report data from prospective mathematics teachers’ interactions with a standardized student on the issue of iconic interpretation. Findings highlight teachers’ diagnostic, explanatory, mathematical, and instructional repertoires, as they guide a standardized student through two different graphing problems. Implications focus on the trends in teachers’ instructional decisions, contextualized explanations, and the use of clinical simulations to enhance mathematics teacher development.

Developing a Theory of Ambitious Early-Career Teacher Practice

Current theories of novice teacher learning have not accounted for the varied influences of pedagogical training, subject matter knowledge, tools, identity, and institutional context(s) on the development of classroom practice. We examined how 26 beginning secondary science teachers developed instructional repertoires as they participated in two types of communities, one infused with discourses and tools supportive of ambitious teaching and another that reinforced traditional practices. We found three trajectories of practice—each with distinctive signatures for how novices engaged students intellectually. Differences were explained by: the communities with which teachers most closely identified, the degree to which teachers’ discourses about student thinking were developed within these communities, and how teachers used tools from the communities to shape their practice.

Form-focused social repertoires in an online language learning partnership

This study explores how mutual language learning partners, a native speaker (NS) and learner of Italian as a foreign language, use conversational repair as an authentic resource for out-of-class social interaction and focus-on-form during online text chat sessions. Specifically, it analyses the sequential organization of prototypical form-focused exposed correction sequences where the NS both initiates and completes repair of the learner's non-target grammar in the same turn, also known as recast. Findings indicate that despite the face-threatening nature of exposed correction within an unequal speech exchange system, participants maintain social solidarity by orienting to expert-novice roles and integrating recasts into phatic action-accepting and appreciation routines to bring form-focused trajectories to a polite conclusion prior to returning to topical talk. The learner's role as interaction manager is evident in her regular transformation of NS-initiated pedagogical actions-in-progress into social ones. Comparison of these form-focused pedagogical-social trajectories with a prototypical teacher-fronted instructional repertoire, the Initiation-Response-Feedback (IRF) sequence, reveals previously unidentified differences in how participants manage their interactions, especially exposed correction, in a formal-pedagogical and an informal social-pedagogical environment. While IRF is only one of many instructional repertoires in which correction activity is nested, fundamental structural differences suggest that online dyadic chat within language learning partnerships provides a potentially empowering and spontaneous alternative to classroom-based instructional repertoires, in preparation for real-life interaction in the target language.

Shifting the Focus to Student Learning: Characteristics of Effective Teaching Practice As Identified by Experienced Pre-service Faculty Advisors

Cochrane-Smith and Power identify trends in teacher education programs with some relating to heightened teacher accountability for students’ learning. In this paper we provide a model that identifies characteristics believed to be critical elements related to a teacher’s conceptual focus shifting from an emphasis on their teaching to their students’ learning and we have grounded these characteristics in current educational research. Through focus group inquiry, we have identified those teacher characteristics thought to account for effective teaching practice. These characteristics include: a professional growth perspective, passion and enthusiasm for the content, pedagogical content knowledge, a rich instructional repertoire of strategies, awareness of assessment for, as, and of learning, ability to read the body language of the learner, caring classroom management strategies, and instructional efforts (e.g., social justice). Our research data provide a conceptual framework for further study.

Developing Imagination, Creativity, and Literacy through Collaborative Storymaking: A Way of Knowing

Early in her life, Nancy King discovered that stories are rich sources of wisdom, imagination, creativity, and comfort. In this essay, King describes her personal experiences developing and using the collaborative storymaking process with young people and adults in various school settings. The author states that collaborative storymaking establishes opportunities for students to create stories from stories, using imagemaking and abstract prompts. She maintains that the iterative process expands and improves students' oral and written expression. King invites other educators to include collaborative storymaking in their instructional repertoire to stimulate their own and their students' reading, writing, and speaking skills, and to foster a supportive learning community.