It is critical to recognize that programs for advanced study share many of the objectives of other programs in the same discipline; these design principles, therefore, also apply to the design and development of mathematics and science courses at all levels. While each of the four key elements is addressed separately here, in practice they work together synergistically and need to be aligned in mutually supportive ways.
Without such alignment and interdependence, deep conceptual understanding is more difficult to achieve. The systemic and dynamic relationship among the four elements also means that changes in one element affect and require changes in the others. In addition, it is essential to recognize the critical role of the learning environment in fostering learning with understanding. The learning environment of the school and the classroom in which these components of educational programs interact affects the degree to which teachers can integrate curriculum, instruction, and assessment to promote learning with understanding National Research Council [NRC], b.
A curriculum for understanding is intentionally designed around the organizing principles and essential concepts of the domain and provides opportunities for in-depth exploration in a variety of contexts design principles for curriculum are summarized in Box Such a curriculum emphasizes depth of understanding over breadth of coverage. It is designed to provide genuine opportunities for high-quality instruction and multiple points of entry into mathematics and science Au and Jordan, ; Brown, ; Heath, ; Tharp and Gallimore, A mathematics or science curriculum for advanced study that promotes learning with understanding:.
Structures the concepts, factual content, and procedures that constitute the knowledge base of the discipline around the organizing principles big ideas of the domain. Links new knowledge to what is already known by presenting concepts in a conceptually and logically sequenced order that builds upon previous learning within and across grade levels.
Focuses on depth of understanding rather than breadth of content coverage by providing students with multiple opportunities to practice and demonstrate what they learn in a variety of contexts. Includes structured learning activities that, in a real or simulated fashion, allow students to experience problem solving and inquiry in situations that are drawn from their personal experiences and real-world applications.
Incorporates language, procedures, and models of inquiry and truth verification that are consistent with the accepted practice of experts in the domain. Emphasizes interdisciplinary connections and integration and helps students connect learning in school with the issues, problems, and experiences that figure prominently in their lives outside of the classroom. Therefore, in designing a curriculum for understanding, the key concepts and processes of the discipline should be clearly identified, explicated, and organized in a coherent fashion around the big ideas Mintzes, Wandersee, and Novak, ; National Council of Teachers of Mathematics [NCTM], ; NRC, The organization of curriculum plays a critical role in helping students reconstruct misconceptions and see connections between what they are currently learning and what they have learned before.
Curriculum for understanding represents more than a collection of activities or bits of information: it provides for the holistic performance of meaningful, complex tasks in increasingly challenging environments Resnick and Klopfer, A curriculum for understanding takes the shape of topical strands that are highly interconnected in ways that are consistent with the knowledge structure used by experts in tackling complex tasks in their discipline Marin, Mintzes, and Clavin, The deep disciplinary understanding of experts encompasses a vast amount of knowledge, but generally only a subset of that knowledge is used in the solution of any given problem.
Experts not only have acquired extensive and deep knowledge and conceptual understanding, but also are skilled at discerning, identifying, and retrieving knowledge that is relevant to the solution of a particular problem. Their knowledge is organized into meaningful patterns and structures and is conditionalized situated , meaning that what they know is accompanied by a specification of the contexts in which it is useful Glaser, ; Simon, Many curricula and instructional materials, however, are not designed to help students conditionalize their knowledge.
For example, textbooks are more likely to tell students how to do something than to help them understand the conditions under which doing it will be useful Simon, , p. Having students work in laboratory settings is a familiar strategy for helping them develop conditionalized knowledge that supports problem solving. Well-designed laboratory experiences also encourage students to apply their knowledge and skills to concrete, real-world problems or novel situations Resnick, Students presented with vast amounts of content knowledge that is not organized into meaningful patterns are likely to forget what they have learned and to be unable to apply the knowledge to new problems or unfamiliar contexts Haidar, Curriculum for understanding provides ample opportunity for students to apply their knowledge in a variety of contexts and conditions.
This helps them transfer their learning to new situations and better prepares them for future learning Bransford and Schwartz, Providing students with frequent opportunities to apply what they learn in multiple contexts requires a reallocation of instructional time.
Forging the American Curriculum: Essays in Curriculum History and Theory
Allowing time for in-depth learning means decisions must be made about what knowledge is of most worth. For this reason, the curriculum needs to specify clearly the appropriate balance between breadth and depth of coverage in terms of student learning outcomes.
It is well accepted that students draw on their families, communities, and cultural experiences to create meaning and understanding. If students are able to draw on their cultural, social, and historical experiences in problem-solving situations, they are more likely to deepen their understanding. This can be accomplished by design through structured activities that, in real or simulated fashion, allow students to experience problem solving and inquiry in situations drawn from their personal experiences.
An effective curriculum allows for incorporating socialization into the discourse and practices of academic disciplines and provides frequent opportunities for students to apply the modes of inquiry and truth verification strategies and processes characteristic of each domain.
An appreciation of the distinctive features of disciplines, however, should not lead to their isolation from each other or from the everyday world. Rather, strong curriculum design emphasizes interdisciplinary connections, integration, and authenticity in the relationship between learning in and out of school. These features not only make learning more challenging, exciting, and motivating, but also help students develop their abilities to make meaningful connections by applying and transferring knowledge from one problem context to another. The emphases of a curriculum for supporting learning with understanding are presented in Table Instruction in advanced courses in mathematics and science should engage students in a variety of learning activities that are purposefully designed to connect with what they already know and motivate them to work.
Underlying disciplinary principles and processes sequenced to optimize learning. Isolated concepts presented in relation to a single context or topic with no the connection to other topics. Continuity and interdisciplinary integration through emphasis on relationships of unifying concepts and processes to many topics. Example: A curriculum guide specifies that 8 percent of the advanced biology course should include topics related to cell energy, including cellular respiration and photosynthesis.
The teacher schedules 1 week for a unit on cellular respiration. During this time, students carry out a variety of activities and laboratory exercises in class and complete out-of-class assignments. At the end of the week they take a unit test. The class goes on to the next unit, photosynthesis.
Example: A curriculum specifies four statements of essential knowledge about the production and utilization of energy in cells that are critical to building an understanding of the processes of photosynthesis and respiration. Prior relevant knowledge possessed by students is assessed using quizzes or student concept maps. The teacher schedules 3 days for activities that focus on this knowledge. A rubric is written so that both teacher and students know how the knowledge will be demonstrated. Students carry out a variety of activities in class and complete out-of-class assignments.
The Making Of The Curriculum: Collected Essays (Studies in Curriculum History Series, 21)
At the same time, they must demonstrate their knowledge of each of the four specified outcomes before they can receive credit for the unit. Students continue to work on essential knowledge and present evidence when they are ready, even as activities for the next unit may be beginning. Curriculum developed for one course at a time without articulation among the levels of schooling. Curriculum that is well articulated between the elementary grades and between high school and college and makes recognized connections with other disciplines.
Curriculum that can be adapted to meet the diverse needs of students and situations. Standards-driven changes in courses, leading to advanced high school and introductory college courses through modification of content and pedagogy at the advanced course and college levels. Instruction should focus students on the central concepts and fundamental principles of the discipline. It also should assist them in constructing a framework for organizing new information as they explore concepts in depth and in a variety of contexts and develop problem-solving strategies common to the discipline Novak, The design principles for instruction are summarized in Box Teaching for conceptual understanding in advanced mathematics and science courses:.
Is based on careful consideration of what students already know, their ideas and ways of understanding the world, and the patterns of practice they bring with them into the classroom. Is designed to provide the appropriate degree of explicitness for the situation and the abilities of the learners. Engages students in worthwhile tasks that provide access to powerful mathematical and scientific ideas and practices; moves students to see past the surface features of problems to the deeper, more fundamental principles; and develops their conceptual understanding and skills.
Structures learning environments in which students can work collaboratively to gain experience in using the ways of thinking and speaking used by experts in the discipline. Orchestrates classroom discourse so that students can make conjectures, present solutions, and argue about the validity of claims, thus helping them explore old understandings in new ways, reveal misconceptions, and generalize and transfer their learning to new problems or more robust understandings. Provides explicit instruction in metacognition as part of teaching in the discipline.
Creates expectations and social norms for the classroom that allow students to experience success and develop confidence in their abilities to learn. Instruction should take into account common naive concepts held by students, as well as the effects of their cultural and experiential backgrounds on their learning.
- Immunochemistry in Clinical Laboratory Medicine: Proceedings of a symposium held at the University of Lancaster, March, 1978.
- EU Prospectus Law: New Perspectives on Regulatory Competition in Securities Markets (International Corporate Law and Financial Market Regulation);
- Oxford modern sci writing.
- Khwateen-e-Islam ki Behtreen Masjid.
Activities and strategies should be continually adapted and refined to address topics arising from student inquiries and experiences. It is important for instruction in advanced courses in mathematics and science to engage students in inquiry using a variety of activities and strategies, including experimentation, critical analysis of various sources of information, and the application of technology in problem solving. In this way, students combine knowledge in the domain with reasoning and thinking skills as they are engaged collaboratively in asking questions, constructing, testing and analyzing explanations, communicating the explanations, and considering alternatives Townes and Grant, Learning experiences are worthwhile when they represent concepts and procedures; foster skill development, reasoning, and problem solving; and help students make connections among mathematical and scientific ideas and to real-world applications NCTM, Such experiences prompt the learner to see past the surface features of a problem to deeper, more fundamental principles.
Accomplishing this complex endeavor requires a qualified teacher. The National Board for Professional Teaching Standards NBPTS describes a qualified teacher as one who effectively enhances student learning and demonstrates the high level knowledge, skills, abilities, and commitments reflected in the following five core propositions: 2.
Teachers know the subjects they teach and how to teach those subjects to students. To promote understanding, explicit instruction in metacognition should be integrated into the curriculum. Thus, instruction should create tasks and conditions under which student thinking can be revealed so that students, with their teachers, can review, assess, and reflect upon what they have learned and how.
Additionally, teachers should make their reasoning and problem-solving strategies visible to students whenever possible Collins and Smith, ; Lester et al. Effective instruction in advanced courses should involve building and nurturing a community of learners. A community of learners encourages students to take academic risks by providing opportunities for them to make mistakes, obtain feedback, and revise their thinking while learning from others with whom they are engaged in inquiry and cooperative problem-solving activities. To nurture the capacity of students to generalize and transfer their learning to new problems, teachers must help students explore old understandings in new ways.
Since intrinsic motivation is self-sustaining, instruction should be planned so as to maximize the opportunity for developing a strong intrinsic motivation to learn. Students benefit when they can experience success and develop the confidence of a successful learner—one who has the tools to ask relevant questions, formulate problems and reframe issues, and assess his or her own knowledge and understanding Alaiyemola, Jegede, and Okebukola, ; Stipek, Table illustrates the emphases of instructional practices to support learning with understanding.
Understanding assessment results requires that the user draw inferences from available data and observations that are supported by the assessment. Presenting scientific knowledge through lecture, text, and demonstration, with activities centered on the teacher.
- Studies in Curriculum Theory Series - Routledge.
- What is curriculum? Exploring theory and practice.
- 1st Edition.
- Forging the American Curriculum: Essays in Curriculum History and Theory - CRC Press Book!
- IN ADDITION TO READING ONLINE, THIS TITLE IS AVAILABLE IN THESE FORMATS:.
- Theoretical Atomic Physics.
- A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity.
Guiding students through active and extended inquiry and facilitating student-centered learning. Strategies that incorporate collaboration among students and foster the development of classroom learning communities. Establishing blocks of time and designing lessons such that all students are required to learn the same thing in the same way at the same rate.
Flexible scheduling and learning experiences that provide students with enough time, space, resources, guidance, and feedback for learning. Students doing numerous, often simplistic and unconnected laboratory activities and being exposed to many different procedures. Students conducting extended investigations and inquiry and having opportunities to progress through cycles of assessment and revision.
Focusing on interactions between students and materials, as well as teacher—student and student— student interactions. Laboratory exercises in which students are provided with all relevant background and procedures and are asked to follow the steps, fill in the data, and answer a few questions, after which the class moves on. Teachers, life histories and studies of curriculum and schooling. London: Falmer Press. Education as a practical matter: Some issues and concerns.
Professional knowledge, professional lives: Studies in education and change. Maidenhead, Philadelphia: Open University Press. Routledge: Abingdon. London, New York: Routledge. Tierney Eds. Life history research in educational settings: Learning from live. Buckingham, Philadelphia: Open University Press. Biography, identity and schooling: Episodes in education research. Hargreaves, A. Dissonant voices: Teachers and the multiple realities of restructuring. Revisiting voice.
Educational Researcher, 25 1 , 12— Hargreaves, D. Deviance in classrooms.
Harvey, D. The condition of postmodernity: An enquiry into the origins of cultural change. Oxford: Basil Blackwell. Hobsbawm, E. Age of extremes: The short twentieth century, — London: Michael Joseph. Lawn, M. From responsibility to competency: A new context for curriculum studies in England and Wales. Levinson, D. New York: Ballantine Books. New York: Alfred A. Lortie, D. Schoolteacher: A sociological study. Chicago: University of Chicago Press. Basically what he proposed was greater division of labour with jobs being simplified; an extension of managerial control over all elements of the workplace; and cost accounting based on systematic time-and-motion study.
All three elements were involved in this conception of curriculum theory and practice. For example, one of the attractions of this approach to curriculum theory was that it involved detailed attention to what people needed to know in order to work, live their lives and so on.
One telling criticism that was made, and can continue to be made, of such approaches is that there is no social vision or programme to guide the process of curriculum construction. As it stands it is a technical exercise. The Progressive movement lost much of its momentum in the late s in the United States and from that period the work of Ralph W. Tyler, in particular, has made a lasting impression on curriculum theory and practice. His theory was based on four fundamental questions:. Tyler Step 7 : Determination of what to evaluate and of the ways and means of doing it.
Taba The attraction of this way of approaching curriculum theory and practice is that it is systematic and has considerable organizing power. Central to the approach is the formulation of behavioural objectives — providing a clear notion of outcome so that content and method may be organized and the results evaluated. There are a number of issues with this approach to curriculum theory and practice.
The first is that the plan or programme assumes great importance. The problem here is that such programmes inevitably exist prior to and outside the learning experiences. This takes much away from learners. They can end up with little or no voice. They are told what they must learn and how they will do it. The success or failure of both the programme and the individual learners is judged on the basis of whether pre-specified changes occur in the behaviour and person of the learner the meeting of behavioural objectives.
If the plan is tightly adhered to, there can only be limited opportunity for educators to make use of the interactions that occur. It also can deskill educators in another way. The logic of this approach is for the curriculum to be designed outside of the classroom or school, as is the case with the National Curriculum in the UK. Educators then apply programmes and are judged by the products of their actions. It turns educators into technicians. Second, there are questions around the nature of objectives.
This model is hot on measurability. It implies that behaviour can be objectively, mechanistically measured. There are obvious dangers here — there always has to be some uncertainty about what is being measured. We only have to reflect on questions of success in our work. It is often very difficult to judge what the impact of particular experiences has been. Sometimes it is years after the event that we come to appreciate something of what has happened.
For example, most informal educators who have been around a few years will have had the experience of an ex-participant telling them in great detail about how some forgotten event forgotten to the worker that is brought about some fundamental change. Yet there is something more. In order to measure, things have to be broken down into smaller and smaller units. The result, as many of you will have experienced, can be long lists of often trivial skills or competencies.
This can lead to a focus in this approach to curriculum theory and practice on the parts rather than the whole; on the trivial, rather than the significant. It can lead to an approach to education and assessment which resembles a shopping list. When all the items are ticked, the person has passed the course or has learnt something.
The role of overall judgment is somehow sidelined.
Work samples | The Australian Curriculum
Third, there is a real problem when we come to examine what educators actually do in the classroom, for example. Much of the research concerning teacher thinking and classroom interaction, and curriculum innovation has pointed to the lack of impact on actual pedagogic practice of objectives see Stenhouse ; and Cornbleth , for example. One way of viewing this is that teachers simply get it wrong — they ought to work with objectives. I think we need to take this problem very seriously and not dismiss it in this way.
The difficulties that educators experience with objectives in the classroom may point to something inherently wrong with the approach — that it is not grounded in the study of educational exchanges. It is a model of curriculum theory and practice largely imported from technological and industrial settings. Fourth, there is the problem of unanticipated results. The focus on pre-specified goals may lead both educators and learners to overlook learning that is occurring as a result of their interactions, but which is not listed as an objective. The apparent simplicity and rationality of this approach to curriculum theory and practice, and the way in which it mimics industrial management have been powerful factors in its success.
A further appeal has been the ability of academics to use the model to attack teachers:. I believe there is a tendency, recurrent enough to suggest that it may be endemic in the approach, for academics in education to use the objectives model as a stick with which to beat teachers. The demand for objectives is a demand for justification rather than a description of ends… It is not about curriculum design, but rather an expression of irritation in the problems of accountability in education.
Stenhouse We have seen that the curriculum as product model is heavily dependent on the setting of behavioural objectives. The curriculum, essentially, is a set of documents for implementation. Another way of looking at curriculum theory and practice is via process. In this sense curriculum is not a physical thing, but rather the interaction of teachers, students and knowledge. In other words, curriculum is what actually happens in the classroom and what people do to prepare and evaluate. What we have in this model is a number of elements in constant interaction.
It is an active process and links with the practical form of reasoning set out by Aristotle. This form of words echoes those of Lawrence Stenhouse who produced one of the best-known explorations of a process model of curriculum theory and practice. He suggests that a curriculum is rather like a recipe in cookery. It can be criticized on nutritional or gastronomic grounds — does it nourish the students and does it taste good?
A curriculum, like the recipe for a dish, is first imagined as a possibility, then the subject of experiment. The recipe offered publicly is in a sense a report on the experiment. Similarly, a curriculum should be grounded in practice. It is an attempt to describe the work observed in classrooms that it is adequately communicated to teachers and others.
Finally, within limits, a recipe can varied according to taste. So can a curriculum. Stenhouse shifted the ground a little bit here. He was not saying that curriculum is the process, but rather the means by which the experience of attempting to put an educational proposal into practice is made available. The reason why he did this, I suspect, is that otherwise there is a danger of widening the meaning of the term so much that it embraces almost everything and hence means very little. More specifically, if curriculum is process then the word curriculum is redundant because process would do very nicely!
The simple equation of curriculum with process is a very slap-happy basis on which to proceed. We also need to reflect on why curriculum theory and practice came into use by educators as against policy-makers. It was essentially as a way of helping them to think about their work before, during and after interventions; as a means of enabling educators to make judgments about the direction their work was taking.
This is what Stenhouse was picking up on. As a minimum, a curriculum should provide a basis for planning a course, studying it empirically and considering the grounds of its justification.
Recommended For You
It should offer:. Principle for the selection of content — what is to be learned and taught. Principles for the development of a teaching strategy — how it is to be learned and taught. Principles on which to diagnose the strengths and weaknesses of individual students and differentiate the general principles 1, 2 and 3 above, to meet individual cases. Principles on which to study and evaluate the progress of students. Principles on which to study and evaluate the progress of teachers. Guidance as to the feasibility of implementing the curriculum in varying school contexts, pupil contexts, environments and peer-group situations.
Information about the variability of effects in differing contexts and on different pupils and an understanding of the causes of the variation. A formulation of the intention or aim of the curriculum which is accessible to critical scrutiny. There are a number of contrasts in this model of curriculum theory and practice as compared with the product model. First, where the product model appeals to the workshop for a model, this process model looks to the world of experimentation. Thus, in this sense, a curriculum is a particular form of specification about the practice of teaching.
It is not a package of materials or a syllabus of ground to be covered. It is not like a curriculum package which is designed to be delivered almost anywhere. Third, outcomes are no longer the central and defining feature. Rather than tightly specifying behavioural objectives and methods in advance, what happens in this model of curriculum theory and practice is that content and means develop as teachers and students work together.
Fourth, the learners in this model are not objects to be acted upon. They have a clear voice in the way that the sessions evolve. The focus is on interactions. This can mean that attention shifts from teaching to learning. The product model, by having a pre-specified plan or programme, tends to direct attention to teaching. For example, how can this information be got over? A process approach to curriculum theory and practice, it is argued by writers like Grundy , tends towards making the process of learning the central concern of the teacher.
This is because this way of thinking emphasizes interpretation and meaning-making. As we have seen each classroom and each exchange is different and has to be made sense of. However, when we come to think about this way of approaching curriculum in practice, a number of possible problems do arise. The first is a problem for those who want some greater degree of uniformity in what is taught.
The Making Of The Curriculum: Collected Essays (Studies Curriculum History)
This approach to the theory of curriculum, because it places meaning-making and thinking at its core and treats learners as subjects rather than objects, can lead to very different means being employed in classrooms and a high degree of variety in content. As Stenhouse comments, the process model is essentially a critical model, not a marking model. It can never be directed towards an examination as an objective without loss of quality, since the standards of the examination then override the standards immanent in the subject.
This does not mean that students taught on the process model cannot be examined, but it does mean that the examinations must be taken in their stride as they pursue other aspirations. And if the examination is a by-product there is an implication that the quality the student shows in it must be an under-estimate of his real quality. It is hence rather difficult to get the weak student through an examination using a process model. Crammers cannot use it, since it depends upon a commitment to educational aims. To some extent variation is limited by factors such as public examinations.
The exchange between students and teachers does not float free of the context in which it arises. At the end of the day many students and their families place a high premium on exam or subject success and this inevitably enters into the classroom. This highlights a second problem with the model we have just outlined — that it may not pay enough attention to the context in which learning takes place more of this later.
The major weakness and, indeed, strength of the process model is that it rests upon the quality of teachers. If they are not up to much then there is no safety net in the form of prescribed curriculum materials. The approach is dependent upon the cultivation of wisdom and meaning-making in the classroom. If the teacher is not up to this, then there will be severe limitations on what can happen educationally.
Related The Making Of The Curriculum: Collected Essays (Studies in Curriculum History)
Copyright 2019 - All Right Reserved