فکر بنیانبانک مقالات روان‌شناسی

instructional decision-making

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Critique-mediated lesson redesign as a perspective on emerging pedagogical reasoning: Preservice mathematics teachers teaching the equal sign

Zaheera Jina Asvat; Shalom Nokuthula Ndhlovana African Journal of Teacher Education and Development, 2026, Vol. 5, Issue 1, pp. a230 https://doi.org/10.4102/ajoted.v5i1.230

چکیده

Background: Preservice teachers may solve equality tasks correctly while still explaining them procedurally, suggesting that correct performance does not necessarily reflect a relational understanding of the equal sign. When planning lessons, they must translate their mathematical understanding into instructional decisions, making lesson redesign a useful context for examining developing pedagogical reasoning. Aim: This study explored what critique-mediated lesson redesign revealed about preservice mathematics teachers’ emerging pedagogical reasoning when planning Grade 7 lessons on the equal sign. Setting: The study took place in a mathematics methodology course at a South African university. Methods: A qualitative multiple-case artefact-analysis design was used. Three group lesson redesigns were compared using lesson plans, written rationales and lecturer critique. The Knowledge Structures of Teaching in Emerging Practice (K-STEP) framework was used to interpret how the groups’ reasoning developed during redesign. Results: Redesign prompted greater attention to relational meanings of the equal sign, conceptual sequencing and learner understanding, although procedural routines and limited responses to anticipated learner thinking persisted. Conclusion: Critique-mediated lesson redesign made visible the uneven nature of developing pedagogical reasoning. The groups began to move towards more relational and learner-responsive lesson designs, although this development remained incomplete. Contribution: The study shows how lesson redesign can be used not only to improve planning but also to explore how preservice teachers interpret, revise and justify instructional decisions.

متن کامل دسترسی آزاد

Preparing Preservice Special Educators for Learner Variability: Integrating Universal Design for Learning and Differentiated Instruction in Coursework

آماده سازی مربیان ویژه برای قابلیت یادگیری: یکپارچه سازی طراحی جهانی برای یادگیری و تمایز در دوره کار

Lauren Fischbacher; Gospel Kim; Da-Eun Lee Journal of Special Education Preparation, 2026 https://doi.org/10.33043/df2fkj9qnb

چکیده

As inclusive education expands, PreK–12 classrooms increasingly include learners with diverse strengths, needs, and learning profiles. Teacher preparation programs are expected to prepare educators to support this diversity in inclusive settings. Preservice educators also bring varied backgrounds, experiences, and learning needs to coursework, requiring teacher educators to design learning environments that are responsive to this variability while preparing special education candidates to support diverse learners in PreK–12 classrooms. However, instructional approaches in teacher preparation do not always reflect these principles, and preservice educators may learn about inclusive instructional frameworks without experiencing how they are enacted in practice. This article introduces the Plan–Model–Embed framework, which integrates universal design for learning and differentiated instruction within teacher preparation coursework. The framework supports teacher educators in planning for learner variability, modeling instructional decision-making, and embedding opportunities for reflection and application across coursework. Drawing on course-based examples, the framework is illustrated through approaches to differentiating content, process, and product to support preservice educators with diverse backgrounds, experiences, and learning needs. These practices position preservice educators to both experience inclusive instructional approaches and examine their application within authentic learning contexts.

با گسترش آموزش فراگیر، کلاس‌های پیش‌دبستانی تا دوازدهم به طور فزاینده‌ای شامل یادگیرندگانی با توانمندی‌ها، نیازها و پروفایل‌های یادگیری متنوع می‌شوند. انتظار می‌رود برنامه‌های تربیت معلم، آموزگاران را برای حمایت از این تنوع در محیط‌های فراگیر آماده کنند. دانشجومعلمان نیز با پیشینه‌ها، تجربیات و نیازهای یادگیری متفاوت وارد دوره‌های آموزشی می‌شوند و این امر مستلزم آن است که مدرسان تربیت معلم محیط‌های یادگیری را به گونه‌ای طراحی کنند که به این گوناگونی پاسخ دهد و در عین حال داوطلبان آموزش ویژه را برای حمایت از یادگیرندگان متنوع در کلاس‌های پیش‌دبستانی تا دوازدهم آماده سازد. با این حال، رویکردهای آموزشی در تربیت معلم همواره بازتاب‌دهنده این اصول نیستند و دانشجومعلمان ممکن است درباره چارچوب‌های آموزشی فراگیر بیاموزند بدون آنکه تجربه‌ای از اجرای عملی آن‌ها داشته باشند. این مقاله چارچوب Plan–Model–Embed را معرفی می‌کند که طراحی جهانی برای یادگیری و آموزش تفکیکی را در دوره‌های تربیت معلم ادغام می‌کند. این چارچوب به مدرسان تربیت معلم کمک می‌کند تا برای گوناگونی یادگیرندگان برنامه‌ریزی کنند، تصمیم‌گیری‌های آموزشی را مدل‌سازی نمایند و فرصت‌هایی برای تأمل و کاربرد در سراسر دوره‌های آموزشی فراهم آورند. با بهره‌گیری از نمونه‌های مبتنی بر دوره، این چارچوب از طریق رویکردهایی برای تفکیک محتوا، فرایند و محصول به منظور حمایت از دانشجومعلمان با پیشینه‌ها، تجربیات و نیازهای یادگیری متنوع، تبیین می‌شود. این شیوه‌ها دانشجومعلمان را در موقعیتی قرار می‌دهد تا هم تجربه رویکردهای آموزشی فراگیر را داشته باشند و هم کاربرد آن‌ها را در زمینه‌های یادگیری اصیل مورد بررسی قرار دهند.

متن کامل دسترسی آزاد

The instructional justification of formal concept entry in science education: a concept genesis framework

توجیه آموزشی ورود مفاهیم رسمی در آموزش علوم: چارچوب تکوین مفهوم

G. Sivasubramanian Frontiers in Education, 2026, Vol. 11 https://doi.org/10.3389/feduc.2026.1958667

چکیده

Science education seeks not only to expand learners' knowledge but also to develop scientific ways of explaining natural phenomena. This requires more than transmitting disciplinary information. Learners must recognise why scientific concepts become necessary, how they extend or revise existing explanations, and under what conditions they provide meaningful accounts of the physical world. The educational challenge therefore concerns not only which concepts should be taught, but also the instructional reasoning surrounding their introduction.Science education research has generated substantial knowledge through conceptual change, inquiry-based learning, model-based instruction, learning progressions, productive preparation, and related traditions. These approaches have shown the importance of engaging prior ideas, recognising explanatory limitations, refining representations, and applying knowledge across contexts. Yet one decision connecting many of these processes often remains implicit: the introduction of formal scientific concepts (Duit and Treagust, 2012;Méheut and Psillos, 2004;Steenhof et al., 2020;Minner et al., 2010;Campbell et al., 2015).In this article, formal concept entry refers to the point at which a scientific construct is presented in an explicit disciplinary form, for example as a named concept or definition, symbolic or mathematical representation, law, model, or related formal structure. Such constructs frequently enter instruction through curricular sequence, textbook organisation, or teaching convention. These arrangements may be appropriate, but the educational justification for formal concept entry is seldom examined directly: not whether the construct belongs in the curriculum, but whether its formal presentation is coordinated with the explanatory work Commented [S[1]: 'U' was missing in '.edu'. Now that is included learners are expected to perform. This issue has renewed practical importance as learners increasingly encounter completed definitions, derivations, simulations, and explanations through digital platforms and generative artificial intelligence before instruction has established their explanatory significance. Greater access to formal scientific information does not itself establish when a construct becomes meaningful within learners' developing understanding (Kumar et al., 2026). This Opinion therefore argues that formal concept entry deserves explicit consideration as an instructional decision. The central question is not whether formal scientific concepts should be introduced early or late, but whether their introduction is instructionally justified by the explanatory work learners are expected to perform.To support reflection on this question, I propose the Concept Genesis Framework (CGF). CGF is an instructor-facing conceptual architecture for examining how formal scientific concepts are prepared, introduced, interpreted, and integrated within learning. It neither replaces established educational theories nor prescribes a universal teaching sequence. Its contribution is to provide a coherent language for considering the instructional justification of formal concept entry.CGF does not arise from a single theory of learning. Its design draws on several established traditions that converge on a common instructional concern: learners interpret new scientific ideas through prior understanding, may need to recognise limitations in existing explanations, and require representational and explanatory support to integrate new disciplinary constructs.Conceptual-change scholarship provides one foundation through its attention to existing conceptions, explanatory inadequacy, and the restructuring of understanding (Strike and Posner, 1982;Duit and Treagust, 2012). Nersessian (1989) adds a representational perspective by emphasising that scientific understanding involves the construction and coordination of conceptual and mathematical representations rather than the reception of completed definitions alone. Inquiry and teaching-learning sequence research further situate such conceptual development within deliberately organised instructional activity (Sandoval and Reiser, 2004;Méheut and Psillos, 2004).CGF does not depend on a single philosophical doctrine. Its orientation is epistemic and instructional: scientific concepts are treated as disciplinary resources for explanation, representation, and prediction rather than as isolated verbal or symbolic entities. ThisReviewer comment 1 has been addressed Paragraph beginning -Concepts, equations------and ending (Kumar et al., 2026), has been replaced with the new paragraph-starting -In this article---------and ending (Kumar et al., 2026).orientation is compatible with constructivist perspectives insofar as it recognises prior understanding and active meaning-making. CGF is not, however, proposed as a constructivist theory of learning, nor does it assume that learners independently rediscover disciplinary knowledge. Its narrower concern is whether the instructional conditions surrounding formal concept entry allow a scientific construct to perform meaningful explanatory work within a learning situation.The ten elements of CGF are consequently described as instructional functions rather than whether it can be used across related contexts (Disciplinary Transfer); and how it supports subsequent learning (Forward Linkage). The framework does not claim that these ten functions are empirically invariant or that all must occur in a fixed order. Depending on the concept, discipline, learners, and instructional purpose, they may overlap, recur, be compressed, or be unnecessary.Scientific concepts are not merely definitions, symbols, or equations. They are intellectual tools developed to explain, organise, and predict phenomena. Although learners often encounter them in completed disciplinary form, instruction must determine how they can become meaningful explanatory resources rather than isolated information.CGF organises ten instructional functions around this problem. The number ten reflects this analytical differentiation of instructional work surrounding formal concept entry rather than an assumed set of invariant cognitive stages. These functions describe a flexible educational logic, not fixed learner stages or a mandatory sequence. Depending on the concept, discipline, learners, and instructional purpose, they may overlap, recur, be compressed, or be unnecessary. (Sandoval and Reiser, 2004;Rea-Ramirez et al., 2009). Its educational value lies in orienting learners towards a meaningful explanatory objective.As learners attempt to address the question, they may recognise that their current explanations or reasoning strategies are insufficient. CGF describes this recognition as Cognitive Tension.It is neither required nor sufficient for conceptual change, but it can help learners recognise the limits of their existing explanatory resources (Strike and Posner, 1982;Rea-Ramirez et al., 2009).: correction of the wording in Figure 1 from "comprises of ten instructional functions" to "comprises ten instructional functions." Minor typographical errors identified within the figure have also been corrected.Recognition of these limitations may generate Epistemic Need: an appreciation that an additional scientific construct is required to explain, organise, or predict observations more adequately. Epistemic need differs from curiosity alone because it concerns the perceived explanatory necessity of a new concept. It may emerge spontaneously or through instructional guidance (Lee et al., 2021).Instruction may then examine the boundaries, assumptions, or inadequacies of existing explanations. A model may fail under new conditions, conflict with evidence, or prove too limited for a broader domain (Rea-Ramirez et al., 2009;Sommeillier et al., 2021).Identifying such limitations does not require rejecting earlier explanations entirely. Scientific understanding often develops through extension, refinement, and specification rather than complete replacement.Historical reconstruction can show why concepts emerged, but it is only one route to explanatory necessity. The need for a concept may also become visible through experimental anomalies, engineering constraints, mathematical inconsistency, model comparison, simulation, or unresolved disciplinary questions (Matthews, 1992). The objective is not to reproduce scientific history, but to clarify the explanatory conditions that justify introducing a formal scientific concept.Concept Genesis denotes the instructional point at which the formal scientific construct is explicitly introduced, stabilised, or recognised as an appropriate response to the identified explanatory problem. It does not imply that learners independently reinvent disciplinary knowledge or experience a single moment of discovery. Terminology or representations may appear earlier, but Concept Genesis marks the point at which they acquire coherent disciplinary meaning (Stamovlasis et al., 2005;Cook, 2006).Concepts gain precision through equations, symbols, graphs, diagrams, models, or other disciplinary representations. CGF defines formalisation broadly because representationalPeriod is included, which was missing practices differ across scientific fields. Concept Genesis and Formalisation are analytically distinct but educationally interconnected and may develop recursively.Correctly manipulating a representation does not necessarily indicate understanding (Stamovlasis et al., 2005). Scientific Interpretation connects formal constructs with their explanatory meaning, assumptions, domains of applicability, predictive capacity, and disciplinary significance. It therefore links procedural use with conceptual understanding.Understanding becomes educationally valuable when learners can extend it beyond the immediate instructional setting. Disciplinary Transfer involves applying a concept across related problems, conditions, contexts, or scales. Transfer should not be assumed from success on familiar tasks but treated as an outcome requiring instructional design and observation (Lobato and Hohensee, 2021).Through Forward Linkage, a newly acquired concept becomes a resource for subsequent models, explanations, and disciplinary learning. Formal concept entry is therefore not only about introducing an individual construct, but also about supporting the progressive organisation of scientific understanding across a curriculum.Taken together, these functions enable educators to examine how formal scientific concepts are prepared, introduced, interpreted, extended, and connected. CGF does not prescribe a universal route to learning. It provides a structured language for considering whether formal concept entry is instructionally justified within a particular educational context.CGF is a conceptual lens for instructional planning and reflection, not a new theory of learning, a validated instructional model, or a prescriptive teaching method. It does not replace inquirybased learning, conceptual change, model-based instruction, productive preparation, learning cycles, teaching-learning sequences, or related evidence-informed approaches (Méheut and Psillos, 2004;Minner et al., 2010;Duit and Treagust, 2012;Campbell et al., 2015).Instead, it organises instructional functions recognised across these traditions around the specific question of formal concept entry.The framework does not require all ten functions to appear, nor does it prescribe their order. Scientific disciplines differ in conceptual structure, mathematical demands, representational practices, and curricular constraints. Learners also differ in prior knowledge, educational goals, cognitive resources, and learning contexts. The functions may therefore overlap, recur, or be omitted.CGF also does not advocate delayed instruction. Early introduction of terminology, diagrams, notation, or simplified models may sometimes provide necessary scaffolding (Cook, 2006). In other situations, learners may benefit from first recognising an explanatory limitation. The relevant judgement concerns not timing in isolation, but whether a formal scientific concept can support the explanatory work required within the learning situation.The framework may be especially useful for concepts that are abstract, counterintuitive, mathematically constituted, foundational for later learning, or commonly presented only in completed formal form. It may be unnecessary for straightforward factual knowledge, routine procedural skills, directly observable phenomena, or situations in which immediate explicit instruction is clearly appropriate.Its educational value remains an empirical question. CGF should therefore be treated as a conceptual proposition that invites evaluation across disciplines, educational levels, and instructional settings.Learners may reproduce definitions, derivations, or equations while remaining uncertain about why a construct became necessary, what problem it addresses, or where it applies. Procedural competence remains educationally important, but it does not always develop together with explanatory understanding (Stamovlasis et al., 2005). Formal concept entry should therefore be judged not only by what learners can perform, but also by the understanding that the construct is intended to support.Concept introduction is also rarely a single event. Terminology, qualitative descriptions, diagrams, equations, computational procedures, and canonical explanations need not enter instruction simultaneously. Each may serve a different role. Formal concept entry is therefore better understood as a distributed instructional process whose components can be introduced according to their explanatory function.This perspective also refines the idea of learner readiness. Readiness is not simply the completion of prerequisite activities. It concerns the relationship between the explanatory demands of a learning situation and learners' capacity to integrate a new construct meaningfully. Prior knowledge, representational support, cognitive demands, recognition of limitations, and instructional guidance all shape this capacity (Cook, 2006;Steenhof et al., 2020).Learner difficulty alone does not justify introducing a formal scientific concept. Productive struggle is not an educational goal in itself, and immediate explanation does not necessarily prevent understanding. Effective teaching requires judgement about when exploration, representation, explanation, and direct guidance are most educationally useful (Steenhof et al., 2020).Because these judgements vary across thermodynamics, quantum chemistry, biology, engineering, and other disciplines, CGF remains deliberately flexible. Its purpose is not to standardise concept introduction, but to make the reasoning behind it more visible.The principal contribution of CGF is to make explicit an instructional decision often embedded within broader pedagogy: why a formal scientific concept is introduced at a particular point in learning. This perspective complements existing educational research rather than competing with it. Diverse traditions may organise teaching differently, yet many confront the transition from provisional or intuitive explanations to formal scientific concepts. Treating that transition as an object of reflection may create a useful point of dialogue across approaches.The framework also has implications for curriculum design and educational research. Curricula typically specify what should be taught but provide less guidance about the reasoning supporting the introduction of particular concepts, representations, or mathematical formulations (Méheut and Psillos, 2004). Attention to formal concept entry may help educators align curricular expectations, learner preparedness, explanatory demands, and instructional support. In research, it may offer an additional dimension for describing interventions and interpreting differences across learning environments.Its relevance is heightened by contemporary digital learning. Learners may now encounter formal scientific language and representations before an instructional context has established their explanatory significance (Kumar et al., 2026). The educator's role therefore extends beyond providing information towards helping learners understand when and why formal constructs become useful.Several limitations remain. CGF has not undergone systematic empirical validation and does not claim that explicit attention to concept entry will necessarily improve understanding or transfer. Its functions may not operate uniformly across disciplines, learner populations, or educational levels. Instructional decisions also remain shaped by curriculum, assessment, institutional constraints, teacher expertise, available time, and learner diversity.Future studies may investigate how educators currently justify formal concept entry, how such judgements vary across disciplines, and whether making them explicit influences conceptual understanding, transfer, curriculum design, teacher education, or research reporting. These studies would not seek a universal rule for early or delayed instruction. They would examine whether greater transparency regarding the reasoning behind concept entry contributes meaningfully to science education.In conclusion, the educational significance of a formal scientific concept lies not only in its disciplinary content, but also in the instructional judgement governing when it becomes meaningful within learners' developing explanations of the natural world. CGF offers a conceptual architecture for examining that judgement. Recognising formal concept entry as an explicit instructional decision may help clarify how scientific knowledge becomes meaningful during learning.

آموزش علوم نه تنها به گسترش دانش فراگیران می‌پردازد، بلکه هدف آن توسعه شیوه‌های علمی تبیین پدیده‌های طبیعی نیز هست. این امر فراتر از انتقال صرف اطلاعات تخصصی است. فراگیران باید دریابند چرا مفاهیم علمی ضرورت می‌یابند، چگونه این مفاهیم تبیین‌های موجود را گسترش داده یا اصلاح می‌کنند و تحت چه شرایطی می‌توانند تبیین‌های معناداری از جهان فیزیکی ارائه دهند. بنابراین، چالش آموزشی صرفاً به این محدود نمی‌شود که کدام مفاهیم باید آموزش داده شوند، بلکه استدلال آموزشی پیرامون معرفی آن‌ها نیز اهمیت دارد. پژوهش‌های آموزش علوم از طریق تغییر مفهومی، یادگیری مبتنی بر پژوهش، آموزش مبتنی بر مدل، پیشرفت‌های یادگیری، آمادگی مولد و سنت‌های مرتبط، دانش قابل توجهی تولید کرده‌اند. این رویکردها اهمیت درگیر کردن ایده‌های پیشین، شناسایی محدودیت‌های تبیینی، اصلاح بازنمایی‌ها و به‌کارگیری دانش در زمینه‌های مختلف را نشان داده‌اند. با این حال، تصمیمی که بسیاری از این فرایندها را به هم پیوند می‌دهد، اغلب ضمنی باقی می‌ماند: ورود مفاهیم علمی رسمی (Duit و Treagust، ۲۰۱۲؛ Méheut و Psillos، ۲۰۰۴؛ Steenhof و همکاران، ۲۰۲۰؛ Minner و همکاران، ۲۰۱۰؛ Campbell و همکاران، ۲۰۱۵). در این مقاله، ورود رسمی مفهوم به نقطه‌ای اشاره دارد که یک سازه علمی به صورت صریح و تخصصی، مانند یک مفهوم یا تعریف نام‌گذاری‌شده، بازنمایی نمادین یا ریاضی، قانون، مدل یا ساختار رسمی مرتبط ارائه می‌شود. این سازه‌ها اغلب از طریق توالی برنامه درسی، سازماندهی کتاب درسی یا عرف تدریس وارد آموزش می‌شوند. این ترتیبات ممکن است مناسب باشند، اما توجیه آموزشی برای ورود رسمی مفهوم به ندرت به طور مستقیم بررسی می‌شود: نه اینکه آیا سازه باید در برنامه درسی باشد، بلکه آیا ارائه رسمی آن با کار تبیینی که از فراگیران انتظار می‌رود هماهنگ است. این مسئله با توجه به اینکه فراگیران بیش از پیش با تعاریف کامل، استنتاج‌ها، شبیه‌سازی‌ها و تبیین‌ها از طریق بسترهای دیجیتال و هوش مصنوعی مولد پیش از آنکه اهمیت تبیینی آن‌ها در آموزش تثبیت شده باشد مواجه می‌شوند، اهمیت عملی تازه‌ای یافته است. دسترسی بیشتر به اطلاعات علمی رسمی به خودی خود تعیین نمی‌کند که چه زمانی یک سازه درک معناداری در فهم در حال رشد فراگیران پیدا می‌کند (Kumar و همکاران، ۲۰۲۶). بنابراین، این مقاله بر این باور است که ورود رسمی مفهوم شایسته توجه صریح به عنوان یک تصمیم آموزشی است. پرسش اصلی این نیست که آیا مفاهیم علمی رسمی باید زود یا دیر معرفی شوند، بلکه این است که آیا معرفی آن‌ها با کار تبیینی که از فراگیران انتظار می‌رود، توجیه آموزشی دارد یا خیر. برای حمایت از تأمل در این پرسش، چارچوب تکوین مفهوم (CGF) پیشنهاد می‌شود. CGF معماری مفهومی برای مدرسان است تا بررسی کنند که چگونه مفاهیم علمی رسمی آماده، معرفی، تفسیر و در یادگیری ادغام می‌شوند. این چارچوب جایگزین نظریه‌های آموزشی موجود نیست و توالی تدریس جهان‌شمولی را تجویز نمی‌کند. سهم آن ارائه زبانی منسجم برای تأمل درباره توجیه آموزشی ورود رسمی مفهوم است. CGF از یک نظریه واحد یادگیری نشأت نمی‌گیرد. طراحی آن مبتنی بر چند سنت تثبیت‌شده است که بر یک دغدغه مشترک آموزشی تمرکز دارند: فراگیران ایده‌های علمی جدید را از طریق فهم پیشین تفسیر می‌کنند، ممکن است لازم باشد محدودیت‌های تبیین‌های موجود را شناسایی کنند و برای ادغام سازه‌های تخصصی جدید به حمایت بازنمایی و تبیینی نیاز دارند. پژوهش‌های تغییر مفهومی با توجه به تصورات موجود، ناکافی بودن تبیین‌ها و بازسازی فهم، یکی از بنیان‌ها را فراهم می‌کنند (Strike و Posner، ۱۹۸۲؛ Duit و Treagust، ۲۰۱۲). Nersessian (۱۹۸۹) با تأکید بر اینکه فهم علمی مستلزم ساخت و هماهنگی بازنمایی‌های مفهومی و ریاضی است و نه صرفاً دریافت تعاریف کامل، دیدگاه بازنمایی را می‌افزاید. پژوهش‌های یادگیری مبتنی بر پژوهش و توالی تدریس-یادگیری نیز این تحول مفهومی را در فعالیت آموزشی سازمان‌یافته قرار می‌دهند (Sandoval و Reiser، ۲۰۰۴؛ Méheut و Psillos، ۲۰۰۴). CGF به یک مکتب فلسفی خاص وابسته نیست. رویکرد آن معرفت‌شناختی و آموزشی است: مفاهیم علمی به عنوان منابع تخصصی برای تبیین، بازنمایی و پیش‌بینی تلقی می‌شوند، نه صرفاً موجودیت‌های لفظی یا نمادین منفرد. این رویکرد با دیدگاه‌های سازنده‌گرایانه تا جایی سازگار است که فهم پیشین و ساخت فعال معنا را به رسمیت می‌شناسد. با این حال، CGF به عنوان نظریه سازنده‌گرای یادگیری پیشنهاد نمی‌شود و فرض نمی‌کند که فراگیران به طور مستقل دانش تخصصی را بازکشف می‌کنند. دغدغه محدودتر آن این است که آیا شرایط آموزشی پیرامون ورود رسمی مفهوم اجازه می‌دهد یک سازه علمی در یک موقعیت یادگیری کارکرد تبیینی معنادار ایفا کند یا خیر. به همین دلیل، ده عنصر CGF به عنوان کارکردهای آموزشی توصیف می‌شوند، نه اینکه آیا می‌توان آن را در زمینه‌های مرتبط به کار برد (انتقال تخصصی) و چگونه از یادگیری بعدی حمایت می‌کند (پیوند رو به جلو). این چارچوب ادعا نمی‌کند که این ده کارکرد به طور تجربی ثابت یا همه باید به ترتیب مشخصی رخ دهند. بسته به مفهوم، رشته، فراگیران و هدف آموزشی، ممکن است این کارکردها همپوشانی، تکرار، فشرده یا غیرضروری باشند. مفاهیم علمی صرفاً تعاریف، نمادها یا معادلات نیستند. آن‌ها ابزارهای فکری هستند که برای تبیین، سازماندهی و پیش‌بینی پدیده‌ها توسعه یافته‌اند. اگرچه فراگیران اغلب آن‌ها را به صورت کامل و تخصصی دریافت می‌کنند، آموزش باید تعیین کند که چگونه می‌توانند به منابع تبیینی معنادار تبدیل شوند، نه اطلاعات منفرد. CGF ده عنصر را سازمان می‌دهد.

متن کامل دسترسی آزاد

Conceptual, connected mathematics: the path from teacher learning to classroom practice

ریاضیات مفهومی و مرتبط: مسیر از یادگیری معلم تا عمل کلاسی

Marjorie M. Hahn; Miriam S. Leshin; Jo Boaler; Jack A. Dieckmann; Megan E. Selbach-Allen Journal of Mathematics Teacher Education, 2026 https://doi.org/10.1007/s10857-026-09784-9

چکیده

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.

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