This study contributes to the scholarship of teaching and learning (SoTL) by examining how case-based teaching and threshold concepts promote culturally inclusive pedagogical practices among pre-service teachers (PSTs). Our research design reflects SoTL principles by taking a systematic, transparent, iterative, and collaborative approach to collecting, analysing, and sharing data. Our work is explicitly aligned with theoretical frameworks, and we address unresolved issues in order to facilitate transformative learning. We aimed to explore how PSTs perceive culturally inclusive pedagogy and professional competence in a case-based course. Three key findings emerged: increased awareness of classroom diversity, a change in the PSTs’ understanding of culturally inclusive teaching, and resistance to exploratory learning designs. Many PSTs demonstrated transformative learning and sound professional judgment. However, some expressed resistance and uncertainty, underscoring the importance of scaffolding and support. The findings align with the literature on threshold concepts as gateways to boundary crossing and a deeper understanding of diversity in SoTL. The results highlight the potential of case-based teaching to encourage metacognitive reflection and to promote inclusive educational practices in teacher education programs. The study demonstrates that designing inquiry-based learning activities that integrate case studies and threshold concepts can facilitate critical reflection and metacognition among PSTs.
Epistemic integration offers a way to specify the intellectual demands of vocational undergraduate study: students use concepts and evidence to justify a professional decision. This article develops that argument through a conceptual synthesis, two national teaching standards, and descriptive statistics from five education bulletins. China's vocational undergraduate enrollment rose from 129,300 in 2021 to 518,300 in 2025 as the number of providers increased from 32 to 87. Private institutions accounted for 68.8% of providers at the start of the period and 27.6% at its end. Against this changing institutional background, the proposed assessment procedure follows a student's reasoning through the framing of a problem, explanation of choices, verification of results, and application to changed conditions. Occupational performance and intellectual justification receive separate judgments based on evidence from the same learner and task. Curriculum coherence, joint educational provision, progressive practice, and teaching team capability form the organizational basis for this work. Their 24 diagnostic indicators connect program arrangements to evidence of learning. Three propositions specify how task design, guidance, and responsibility for review are expected to support integration. The research agenda concerns the consistency of these judgments and their use in improving subsequent learning opportunities.
Many education systems aim to support teachers in moving toward conceptually oriented mathematics instruction. The 2023 California Mathematics Framework provides one example of this effort by organizing standards around big ideas and emphasizing mathematical connections. In this study, we report on an early investigation of teachers’ learning about, and efforts to enact, the framework’s big ideas approach. We followed a cohort of elementary teachers who participated in a year-long professional learning fellowship. Drawing on multiple qualitative data sources, we examine the affordances and constraints teachers experienced as they learned to teach mathematics conceptually through big ideas, as well as the ways that the framework's conceptual structure supported their instructional decision-making. Teachers reported meaningful shifts in their teaching, which they attributed to increased student engagement, a sense of instructional freedom, and growing confidence in themselves as mathematical thinkers. Classroom observations corroborated these reported shifts by documenting teachers' enactment of key features of conceptual mathematics instruction. At the same time, teachers identified important constraints, particularly tensions between conceptual teaching and procedural district assessment systems. Across teachers, the big ideas approach provided a shared conceptual structure for organizing instruction around connected mathematical ideas while supporting teachers’ professional judgment in how those ideas were enacted in classrooms. To illustrate variation in teachers’ experiences, we present four cases representing different trajectories of learning and enactment. We conclude with implications for the design of professional learning and the use of coherent conceptual frameworks to support teachers' learning and instructional decision-making.
بسیاری از نظام‌های آموزشی در پی حمایت از معلمان برای حرکت به سوی آموزش ریاضیات مبتنی بر مفاهیم هستند. چارچوب ریاضیات کالیفرنیا ۲۰۲۳ نمونه‌ای از این تلاش است که استانداردها را حول ایده‌های بزرگ سازمان‌دهی کرده و بر ارتباطات ریاضی تأکید می‌کند. در این مطالعه، گزارشی از یک بررسی اولیه درباره یادگیری معلمان و تلاش‌های آن‌ها برای اجرای رویکرد ایده‌های بزرگ این چارچوب ارائه می‌شود. ما یک گروه از معلمان ابتدایی را که در یک دوره یک‌ساله یادگیری حرفه‌ای شرکت کردند، دنبال کردیم. با استفاده از منابع مختلف داده‌های کیفی، به بررسی فرصت‌ها و محدودیت‌هایی که معلمان در فرآیند یادگیری آموزش مفهومی ریاضیات از طریق ایده‌های بزرگ تجربه کردند، و همچنین نحوه حمایت ساختار مفهومی چارچوب از تصمیم‌گیری‌های آموزشی آن‌ها پرداختیم. معلمان تغییرات معناداری را در شیوه تدریس خود گزارش کردند که آن را به افزایش مشارکت دانش‌آموزان، احساس آزادی آموزشی و افزایش اعتماد به نفس خود به عنوان اندیشمندان ریاضی نسبت دادند. مشاهدات کلاسی این تغییرات گزارش‌شده را با مستندسازی اجرای ویژگی‌های کلیدی آموزش مفهومی ریاضیات توسط معلمان تأیید کرد. همزمان، معلمان محدودیت‌های مهمی را شناسایی کردند، به‌ویژه تنش میان آموزش مفهومی و نظام‌های ارزیابی رویه‌ای منطقه‌ای. در میان معلمان، رویکرد ایده‌های بزرگ ساختار مفهومی مشترکی برای سازمان‌دهی آموزش حول ایده‌های مرتبط ریاضی فراهم کرد و در عین حال از قضاوت حرفه‌ای معلمان در نحوه اجرای این ایده‌ها در کلاس حمایت نمود. برای نشان دادن تنوع تجربیات معلمان، چهار مطالعه موردی ارائه می‌شود که مسیرهای متفاوت یادگیری و اجرا را نمایان می‌کند. در پایان، پیامدهایی برای طراحی یادگیری حرفه‌ای و استفاده از چارچوب‌های مفهومی منسجم جهت حمایت از یادگیری معلمان و تصمیم‌گیری‌های آموزشی آن‌ها ارائه می‌شود.
