Preface Chapter 1 The challenge Chapter 2 The nature of the evidence: A synthesis of meta-analyses Chapter 3 The argument: Visible teaching and visible learning Chapter 4: The contributions from the student Chapter 5 The contributions from the home Chapter 6 The contributions from the school Chapter 7 The contributions from the teacher Chapter 8 The contributions from the curricula Chapter 9 The contributions from teaching approaches - I Chapter 10 The contributions from teaching approaches - II Chapter 11: Bringing it all together Appendix A: The 800 meta-analyses Appendix B: The meta-analyses by rank order References

Visible Learning: A Synthesis of Over 800 Meta-Analyses Relating to Achievement

generalize create, solve unseen problems, extrapolate to unknown domains 22831.indb 124 6/15/11 2:11 PM Designing intended learning outcomes 125 • the verb at the appropriate level of understanding or of performance intended; • the topic content the verb is meant to address, the object of the verb in other words; • the context of the content discipline in which the verb is to be deployed. The ILOs for the course The Nature of Teaching and Learning illustrate these points: 1 Explain why a particular course topic is important to teaching. 2 Apply a course topic to your own teaching. 3 Refl ect on your teaching in terms of a working theory you have gained from the course. 4 Evaluate a situation that has gone wrong and apply a solution. The fi rst refers to declarative knowledge: the students have to reach a level of understanding that requires them to explain something, not just describe or list it: the latter only display multistructural levels of understanding, but explaining requires students to be able to relate the topic to the context of teaching and is at a relational level of understanding. The second is a functioning knowledge example also at the relational level as it requires a level of understanding that enables the student to apply the topic to teaching. The other two are also about functioning knowledge and should be at the relational to extended abstract level of understanding, depending on the originality of the student’s response. The content in (3) is the student’s own working theory and the context the student’s own teaching, and in (4), the content is the theory used in evaluating and the context the problematic situation in teaching. As a note on the number of ILOs per course, we stated earlier that there should be no more fi ve or six ILOs for any course, even though there may be up to ten topics that need addressing. The answer is to write integrating ILOs that address several topics, or, as in ILOs (1) and (2) above, the ILO allows the student to select just one topic for demonstrating ability to achieve the ILO. Another thing to watch out for are redundant ILOs, such as ‘Describe and explain . . .’. ‘Describe’ is redundant because if the student can explain the topic, he or she can certainly describe it. The other matter one should keep in mind at this stage is that desirable but unintended outcomes, or outcomes unforeseen by the teacher, may emerge. This is the nature of extended abstract responses by the student, and they will be accounted for in the normal assessment, but others may simply be things that the student sees as important and relevant learning. This matter becomes a practical issue during assessment, and we address it in Chapter 10. You should now be in a position to design and write your own ILOs for a course you are teaching (Task 7.1). 22831.indb 125 6/15/11 2:11 PM 126 Designing constructively aligned outcomes-based teaching and learning Task 7.1 Writing course ILOs Take a course that you are teaching. Consider the course aim and write the course ILOs by identifying: a the kind of knowledge to be learned (declarative or functioning). b the content or topic to be learned. c the level of understanding or performance to be achieved. d any particular context in which the outcome verb is to be enacted. The following grid may be a useful framework to help you think. Kind of knowledge Level of Content topic Context Declar/function understanding (outcome verb) ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ ______________________________________________________________ Now go across the rows and write out the course ILOs by stating the intended level of understanding or performance (outcome verb), topic and the context in which the verb is to be enacted. There is no need to include the kind of knowledge in the ILO as that is defi ned by the verb(s) you use. To recap an example of a course ILO from our course The Nature of Teaching and Learning : Students should be able to: Refl ect (level of understanding and performance) on your teaching (context) in terms of a working theory you have gained from the course (content). Now write your course ILOs. Students should be able to: ILO1: _______________________________________________________ ILO2: _______________________________________________________ ILO3: _______________________________________________________ 22831.indb 126 6/15/11 2:11 PM Designing intended learning outcomes 127 Aligning ILOs at three levels: curriculum mapping Now that we have written the course ILOs, we have the task of checking to see that the three levels of intended outcomes, graduate, programme and course, are aligned. We can achieve this by curriculum mapping (Huet et al. 2009), which is a systematic means of ensuring alignment between programme ILOs and graduate outcomes, and course ILOs and programme ILOs. Graduate outcomes and programme ILOs Table 7.4 shows a simply way of checking the alignment between graduate outcomes and programme ILOs. The table is a device to ensure that the match between programme ILOs and graduate outcomes has at least been considered. Programme ILOs should not be forced to match graduate outcomes that don’t belong in the programme. Because of the different natures of different disciplines or professions, different programmes may have different emphases in addressing the graduate outcomes. It is not necessary that every programme should address all graduate outcomes to the same extent because some may not be relevant to the programme. Programme ILOs are simply the reasons that the programme is being taught, which is a matter of professional and academic judgment. However, university policy will prevail on this. Task 7.2 parallels Table 7.4: it asks you to align programme ILOs with the graduate outcomes of your university, if it has any. If the programme ILOs ILO4: _______________________________________________________ ILO5:_______________________________________________________ ILO6:_______________________________________________________ Review the ILOs to see whether: a the kind of knowledge, content and level of understanding or performance are relevant to achieve the course aim. b they cover all the main reasons for teaching the course. c they are clearly written, especially in identifying the level of understanding or performance to be achieved by the students, and the context (if appropriate). d the number is manageable for designing aligned teaching/learning activities and assessment tasks. How does this new set of course ILOs compare to your existing course ‘objectives’? Does the existing set need to be rewritten? 22831.indb 127 6/15/11 2:11 PM 128 Designing constructively aligned outcomes-based teaching and learning haven’t yet been articulated, discuss them with the programme coordinator and derive a set, then match them with the graduate outcomes. This should give you a clearer idea of how graduate outcomes can suitably be addressed in your teaching. How does your attempt gel with your university’s policy on this? Gelade and Fursenko (2007) also describe a tool for systematically mapping courses and programmes for graduate outcomes. Task 7.2 Aligning programme ILOs with graduate outcomes 1 Take a programme in which you are teaching and either list the programme ILOs if they are already articulated or, if they are not, sit down with the programme coordinator or programme committee chairperson and fi rst write the aims of the programme and a list of programme ILOs that meet those aims. 2 What are the graduate outcomes of your university? List them in the left-hand column in the grid below. 3 In the right-hand column list the programme ILOs that would address the graduate outcomes. Are all graduate outcomes addressed somewhere? Which are not? Does it matter?’ Graduate outcomes Programme ILO 1 2 etc. Table 7.4 An example of aligning programme ILOs with graduate outcomes Graduate outcomes Programme ILO Competent in professional Analyse and apply principles to real-life practice accounting situations Communicate effectively Communicate as a professional with clients and colleagues in real-life accounting situations Teamwork Operate effectively and ethically as a team member in real-life accounting situations Ethical professional As above 22831.indb 128 6/15/11 2:11 PM Designing intended learning outcomes 129 Programme ILOs and course ILOs The next level of alignment is between the programme and the course ILOs. As each programme is served by its constituent courses, it is important that, when aligning course ILOs to the programme ILOs, the course ILOs in total address all aspects of the programme ILOs. Often a programme ILO will be addressed by several courses, from different and increasingly more complex angles. You may attempt this in Task 7.3. Task 7.3 Aligning course ILOs with programme ILOs For individual teachers 1 List the programme ILOs of the programme. 2 List the course ILOs of the courses that you are teaching in a given programme. 3 Consider what programme ILO(s) each of the course ILOs addresses in the following table. Programme ILOs Course 1 ILOs Course 2 ILOs Course 3 ILOs

Teaching For Quality Learning At University

Objectives: Lao Juan (LJ, 劳倦) is a syndrome described in Chinese medicine (CM) that manifests with : Lao Juan (LJ, 劳倦) is a syndrome described in Chinese medicine (CM) that manifests with fatigue, fever, spontaneous sweating, indigestion, work-induced pain, weakness of the limbs, and shortness of breath. fatigue, fever, spontaneous sweating, indigestion, work-induced pain, weakness of the limbs, and shortness of breath. The present study was conducted to examine the reliability and validity of a Lao Juan Questionnaire (LJQ). The present study was conducted to examine the reliability and validity of a Lao Juan Questionnaire (LJQ). Methods: A total of 151 outpatients and 73 normal subjects were asked to complete the LJQ. Seventy-three normal subjects A total of 151 outpatients and 73 normal subjects were asked to complete the LJQ. Seventy-three normal subjects were additionally asked to complete the Chalder Fatigue Scale (CFS). Twelve clinicians determined whether the were additionally asked to complete the Chalder Fatigue Scale (CFS). Twelve clinicians determined whether the 151 outpatients exhibited LJ or not. The internal consistency and construct validity for the LJQ were estimated using 151 outpatients exhibited LJ or not. The internal consistency and construct validity for the LJQ were estimated using data from the outpatient subjects. The CFS data were used to examine the concurrent validity of the LJQ. Total LJQ data from the outpatient subjects. The CFS data were used to examine the concurrent validity of the LJQ. Total LJQ scores and the clinicians' diagnoses of the outpatients were used to perform receiver operating characteristics (ROC) scores and the clinicians' diagnoses of the outpatients were used to perform receiver operating characteristics (ROC) curve analyses and to defi ne an optimum cut-off score for the LJQ. curve analyses and to defi ne an optimum cut-off score for the LJQ. Results: The 19-item LJQ had satisfactory internal : The 19-item LJQ had satisfactory internal consistency (α=0.828) and concurrent validity, with signifi cant correlations between the LJQ and the CFS subscales. consistency (α=0.828) and concurrent validity, with signifi cant correlations between the LJQ and the CFS subscales. In the test of construct validity using principal component analysis, a total of six factors were extracted, and the overall In the test of construct validity using principal component analysis, a total of six factors were extracted, and the overall variance explained by all factors was 59.5%. In ROC curve analyses, the sensitivity, specifi city, and area under the variance explained by all factors was 59.5%. In ROC curve analyses, the sensitivity, specifi city, and area under the curve were 76.0%, 59.2%, and 0.709, respectively. The optimum cut-off score was defi ned as six points. curve were 76.0%, 59.2%, and 0.709, respectively. The optimum cut-off score was defi ned as six points. Conclusions: Our results suggest that the LJQ is a reliable and valid instrument for evaluating LJ. Our results suggest that the LJQ is a reliable and valid instrument for evaluating LJ. KEYWORDS Chinese medicine, chronic fatigue syndrome, Chinese medicine-pattern Chinese medicine, chronic fatigue syndrome, Chinese medicine-pattern

Development and Validation of A

Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: * Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. * Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.

Adding It Up: Helping Children Learn Mathematics

It is said that there’s nothing so practical as good theory. It may also be said that there’s nothing so theoretically interesting as good practice 1 . This is particularly true of efforts to relate constructivism as a theory of learning to the practice of instruction. Our goal in this paper is to provide a clear link between the theoretical principles of constructivism, the practice of instructional design, and the practice of teaching. We will begin with a basic characterization of constructivism identifying what we believe to be the central principles in learning and understanding. We will then identify and elaborate on eight instructional principles for the design of a constructivist learning environment. Finally, we will examine what we consider to be one of the best exemplars of a constructivist learning environment -- Problem Based Learning as described by Barrows (1985, 1986, 1992).

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Problem Based Learning: An instructional model and its constructivist framework

Growing up Constructivist - Languages and Thoughtful People Unpopular Philosophical Ideas - A History in Quotations Piaget's Constructivist Theory of Knowing The Construction of Concepts Reflection and Abstraction Constructing Agents - The Self and Others On Language, Meaning and Communication The Cybernetic Connection Units, Plurality, and Number To Encourage Students' Conceptual Constructing.

Radical constructivism : a way of knowing and learning

The existence of objective knowledge and the possibility of communicating it by means of language have traditionally been taken for granted by educators. Recent developments in the philosophy of science and the historical study of scientific accomplishments have deprived these presuppositions of their former plausibility. Sooner or later, this must have an effect on the teaching of science. In this paper I am presenting a brief outline of an alternative theory of knowing that takes into account the thinking organism’s cognitive isolation from ‘reality’. This orientation was proposed by Vico at the beginning of the 18th century, disregarded for two hundred years, and then propounded independently by Piaget as a developmentaly grounded constructivist epistemology. The paper focuses specifically on the adaptive function of cognition, Piaget’s scheme theory, the process of communication, and the subjective perspective on social interaction. In the concluding section it then suggests some of the consequences the shift of epistemological presuppositions might have for the practice of teaching.

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Cognition, Construction of Knowledge, and Teaching

The experiencing consciousness creates structure in the flow of its experience, and that structure is what conscious cognitive organisms experience as “reality.” Since that reality is created almost entirely without the experiencer’s awareness of his or her creative activity, it comes to appear as given by an independently “existing” world. Once knowing is no longer understood as the search for an iconic representation of ontological reality but, instead, as a search for fitting ways of behaving and thinking, the traditional problem of epistemology disappears. Knowledge can now be seen as something which the organism builds up in the attempt to order the as such amorphous flow of experience by establishing repeatable experiences and relatively reliable relations between them. The possibilities of constructing such an order are determined and perpetually constrained by the preceding steps in the construction. That means that the “real” world manifests itself exclusively where our constructions break down. Moreover, we can describe and explain these breakdowns only in the very concepts that we have used to build the failing structures.

An Introduction to Radical Constructivism

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Teaching experiment methodology: Underlying principles and essential elements

I: On the Construction of the Counting Scheme.- Children's Counting.- The Counting Types.- Perceptual Unit Items.- Figural Unit Items.- Motor Unit Items.- Verbal Unit Items.- Abstract Unit Items.- Ontogenetic Analysis.- Stages.- Adaptation.- Counting as a Scheme.- The First Part of the Counting Scheme.- The Third Part of the Counting Scheme.- Other Sources of Numerosity.- Perceptual Mechanisms.- Spatial Patterns.- Meaning Theory.- Reflection and Abstraction.- II: The Construction of Motor Unit Items: Brenda, Tarus, and James.- 1. Brenda.- The Perceptual Period.- The Motor Period.- Discussion of Brenda's Case Study.- The Perceptual Period.- The Motor Period.- 2. Tarus.- The Perceptual Period.- The Motor Period.- Discusion of Tarus's Case Study.- The Perceptual Period.- The Motor Period.- 3. James.- The Perceptual Period.- The Motor Period.- Discussion of James's Case Study.- The Perceptual Period.- The Motor Period.- Perspectives on the Three Case Studies.- Period Criterion.- The Incorporation and Invariant Sequence Criteria.- The Reorganization Criterion.- III: The Construction of Verbal Unit Items: Brenda, Tarus, and James.- 1. Brenda.- Discussion of Brenda's Case Study.- 2. Tarus.- Discussion of Tarus's Case Study.- 3. James.- Discussion of James's Case Study.- Perspectives on the Case Studies.- The Verbal Period as a Subperiod in the Figurative Stage.- Counting-on.- IV: The Construction of Abstract Unit Items: Tyrone, Scenetra, and Jason.- 4. Tyrone.- The Motor Period.- The Abstract Period.- Discussion of Tryone's Case Study.- 5. Scenetra.- The Motor Period.- The Verbal Period.- The Abstract Period.- Discussion of Scenetra's Case Study.- 6. Jason.- The Motor Period.- Creating Verbal Unit Items.- The Abstract Period.- Discussion of Jason's Case Study.- Perspectives on the Case Studies.- Stages.- Incorportation Criterion.- Transition to the Abstract Period.- The Reorganization of Counting.- V: Lexical and Syntactical Meanings: Brenda, Tarus, and James.- 1. Brenda.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of Brenda's Case Study.- The Perceptual Stage.- The Figurative Stage.- 2. Tarus.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of Tarus's Case Study.- The Perceptual Stage.- The Figurative Stage.- 3. James.- The Perceptual Period.- The Motor Period.- The Verbal Period.- Discussion of James's Case Study.- The Perceptual Stage.- The Figurative Stage.- Perspectives on the Case Studies.- The Perceptual Stage.- Finger Patterns.- The Figurative Stage.- Mobile Finger Patterns.- Sophisticated Finger Patterns.- Spatio-Auditory Patterns.- Dual Meanings of Number Words.- Counting as the Meaning of Number Words.- Summary of the Types of Preconcepts and Concepts.- Meanings of "Ten".- Ten as an Enactive Concept.- Ten as a Countable Figural Unit.- Ten as a Countable Motor Unit.- Adding Schemes.- The Perceptual Stage.- The Figurative Stage.- Comments on Prenumerical Children.- VI: Lexical and Syntactical Meanings: Tyrone, Scenetra, and Jason.- Systems of Integration.- Integrations.- Sequential Integration Operations.- Progressive Integration Operations.- Part-Whole Operations.- 4. Tyrone.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Discussion of Tyrone's Case Study.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Unit Types of the Unit of Ten.- 5. Scenetra.- Recognition and Re-Presentation of Patterns.- The Emergence of the Integration Operation.- The Period of Sequential Integration operations.- The Period of Progressive Integreation Operations.- Discussion of Scenetra's Case Study.- The Emergence of the Integratoin Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- Unit Types of the Unit of Ten.- 6. Jason.- Recognition and Re-Presentation of Patterns.- The Emergence of The Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive integration Operations.- The Period of Part-Whole Operations.- Discussion of Jason's Case Study.- The Emergence of the Integration Operation.- The Period of Sequential Integration Operations.- The Period of Progressive Integration Operations.- The Period of Part-Whole Operations.- Unit Types of the Unit of Ten.- Perspectives on the Case Studies.- The Emergence of the Integration Operation.- Numerical Patterns.- Number Sequences.- Stages in the Construction of the Numerical Counting Scheme.- Piaget's Invariant Sequence and Incorporation Criteria.- The Reorganization Criterion.- Units of One.- The Unit of One in Sequential Integration Operations.- The Unit of One in Progressive Integration Operations.- The Unit of One in Part-Whole Operations.- Units of Ten.- The Stage of Sequential Integration Operations.- The Stage of Progressive Integration Operations.- The Stage of Part-Whole Operations.- Other Perspectives.- VII: Strategies for Finding Sums and Differences: Brenda, Tarus, and James.- Brenda.- Independent Solutions.- Number Word Coordinations.- Tarus.- Independent Solutions.- Number Word Coordinations.- James.- Independent Solutions.- Number Word Coordinations.- Perspectives on the Case Studies.- Number Facts.- VIII: Strategies for Finding Sums and Differences: Tyrone, Scenetra, and Jason.- Sequential Integration Operations.- Jason.- Tyrone.- Scenetra.- Discussion: Sequential Integration Operations.- Progressive Integration Operations.- Jason.- Tyrone.- Scenetra.- Discussion: Progressive Integration Operations.- Part-Whole Operations.- Jason.- Tyrone.- Perspective on the Case Studies.- Arithmetical Context.- Thinking Strategies and Integration Operations.- Thinking Strategies and the Basic Facts.- Thinking Strategies and the Construction of Part-Whole Operations.- Goals for Teaching Thinking Strategies.- IX: Modifications of the Counting Scheme.- Predicting Modifications of the Counting Scheme.- Mathematical Learning.- The Perceptual Stage.- Temporary Modifications.- Procedural Accommodations.- Engendering Accommodations.- Isolated Procedural Accommodations.- The Figurative Stage.- Procedural Accommodations.- Temporary Modifications.- Retrospective Accommodations.- Re-presentation and Review of Prior Activity.- The Figurative Stage: Tyrone, Scenetra, and Jason.- Procedural Engendering Accommodations.- Temporary Modifications.- Metamorphic Accommodations.- Stages in the Construction of Part-Whole Operations.- Sequential Integration Operations.- Procedural Accommodations.- Engendering Accommodations.- Progressive Integration Operations.- Internal Reorganizations.- Part-Whole Operations.- Phylogenetic Perspectives.- Zones of Potential Development in Retrospect.- Figurative Stage.- Sequential Integration Operations.- Progressive Integration Operations.- Part-Whole Operations.- Final Comments.- References.

Ernst von Glasersfeld

Papers

Radical constructivism : a way of knowing and learning

Cognition, Construction of Knowledge, and Teaching

An Introduction to Radical Constructivism

Teaching experiment methodology: Underlying principles and essential elements

Construction of Arithmetical Meanings and Strategies