The organization of conceptual materials: A methodology for measuring ideal and actual cognitive structures

The teaching-learning process is described in terms of a simple communication model with four components: the sender, the encoding structure, the decoding structure, and the destination. Within this context a method is proposed and illustrated for evaluating a student's understanding of the system of concepts underlying the topic areas in an elementary statistics and measurement course. The method, multidimensional scaling, involves determining the students' and instructor's cognitive maps for the various topics. A cognitive map represents a hypothetical cognitive structure of a student or instructor which characterizes his perceived organization of the concepts in a topic area. These individual cognitive maps were compared to the optimal organization or formal structure, as a basis for assessing the students' under-standing of the material. The present research was exploratory but demonstrated that:

1. With the help of experts it is possible to define the formal structure for the concepts in a topic area.
2. It is possible to measure, in a classroom setting, the cognitive maps that both the students and instructors have for a topic area.
3. By comparing individual students' cognitive maps to the instructor's cognitive map or to the formal structure, the student's understanding of the system of concepts defining the topic area can be evaluated.

     

Environnements Informatisés et Mathématiques: quels usages pour quels apprentissages?

Mathematics, seen as a model of pure science, often conveys the image of a science constructing itself in quite poor technological environments; it nevertheless develops by elaborating (and by exploiting) powerful material and symbolic tools. Actually mathematics teaching is closer to this image of mathematics than to mathematical practice: its goal seems to transmit a form of culture rather than efficient computation tools and theoretical means of their control (Kahane, 2002). This situation is viable if the tools can be held at distance, outside the classroom; it is no longer viable when computation tools (essentially calculators) are imported by students themselves inside the classroom and integrated into their mathematical practice. Thus established conflict between the social legitimacy of these tools and their school illegitimacy (Chevallard, 1992) deeply destabilises mathematics teaching itself. We present here a general framework to think about the integration of the tools in the teaching and learning of mathematics. More precisely, we propose:

1. A theoretical approach, which allows us to understand the influence of tools on human activity and in particular on professional and school education processes;
2. An analysis of computerized learning environments, which shows the importance of students' control of their own activity;
3. Some elements that help to think about the temporal and spatial organization of study in such environments and to guide students' activity;
4. A reflection about the conception of pedagogical resources, which is all the more necessary if one wants to facilitate an evolution of teachers' practices.

     

A hypertext open learning system for writers

In this article I describe three key design issues which underlie a CIRG project building an open learning hypertext package for teaching writing skills. These are issues in:

? combining flexible materials with fixed structures;

? giving students real flexibility in learning;

? the nature of interaction in hypertext writing teaching.

I outline a design strategy to meet problems in all these areas.     

The academic department as environment for teaching and learning

This study reviews the literature on academic environments with particular reference to the academic department which is seen as the most important factor in the teaching and learning environment. Departmental environment characteristics as identified by faculty and by students are described. For students the most important are:-

Student-Faculty Relationships;

Interest and Engagement in Teaching; and

Satisfaction with Instruction.

Differences between teaching and between learning environments are explained, especially differences between social science and natural science departments. These differences reflect the interaction between discipline, personal styles of faculty and students, and faculty-student relationships. Student academic satisfaction seems to be heavily dependent upon the relationships between students and faculty. Student achievement in relation to students' perception of the academic department seems to be dependent on the degree of their adaptation to the department. The studies reviewed clearly show that there are differences between departments. They also show that these differences may be explained not only by differences with regard to the characteristics of the academic discipline concerned, but also by differences concerning student-faculty relationships, faculty interest in students and teaching and the interaction between these factors. Teacher and student satisfaction and student achievement are affected by these variables.     

Résolution de problèmes de division au cycle elementaire dans deux types de situations didactiques

This study deals with the observation of a class composed of children aged 8–9 solving division problems. The analysis aims at differentiating the attitudes of pupils confronted with situations resulting from ‘EMPIRICAL’ learning from those observed in situations involving action resulting from ‘DIALECTIC’ learning. Two learning sequences are described in the course of the study:

* The first includes four classical terms which allow the use of empirical methods to find the quotient and the remainder.

* The second includes two terms elaborated so that they favour a dialectic of action with the children.

The observed differences reveal that:

* The repetition of drills of the same nature during the first learning sequence does not result in important variations as far as success and solution procedures are concerned.

* On the other hand, during the second learning sequence, all pupils use a more economical solution procedure with high level success rate.

     

The preference of Asian overseas students for the United States: An examination of the context

Asian students in increasing numbers have over the postwar period decided to go overseas for tertiary education, and an increasing proportion of those overseas students have selected the United States as their place of study. Eight elements of the changing context of Asian-American relations are identified which influence the Asian preference for American higher education:

1. The improving Asian-American political links
2. The increased volume of Asian-American economic exchange
3. The sharp increase in Asian immigration to the United States
4. The increasing similarity in the structure and content of Asian and American educational systems
5. The absorptive capacity of American higher education
6. The quality of American higher education
7. The complementarity of Asian demand and American supply
8. The opportunities provided in American higher education to cover educational costs through part-time work

     

Analysis of problem solving strategies on electricity problems in 12 to 13 year olds

Strategies implemented by 12–13 year olds to solve electricity problems are examined. Three factors account for observed strategies:

1. type of problem representation, itself dependent on the knowledge base;
2. cognitive personality dimensions;
3. form of problem statement.

Individual interviews were conducted. Each problem statement contained a perceptual ‘trap’ designed to induce contradictory responses. Strategies were coded for accuracy, latency, justification and control. Five types of problem solving strategies were observed:

1. a strategy based on misconceptions such as the vanishing current model;
2. a similar strategy but greater verbalization of doubt;
3. rush to use formulas;
4. sequential analysis of circuit;
5. application of principles learned in class.

Analysis shows that the target problems fell into two classes: problems that triggered automatic (canonical or calculatory) responses, and problems which were much more disruptive. The latter differentiated students who could handle contradictions and control their responses. Mention is also made of difficulties caused by the signified/signifier relationship.     

An investigation of the nature of the influences of item stem and option representation on student responses to a mathematics test

In teaching, representations are used as ways to illustrate the concepts underlying a specific topic. For example, use symbols (e.g., 1?+?2?=?3) to express the concept of addition. To compare students’ abilities to interpret different representations in mathematics, the symbolic representation (SR) test and the pictorial representation (PR) test were designed, and then administered to 681 sixth graders in Taipei, Taiwan. This study adopts two different modeling perspectives, the testlet perspective and the multi-ability perspective, to analyze this SR and PR test data in the context of item response theory. The main results show that:

1. Students scored on average significantly higher on the SR test than the PR test.
2. The effects of the item stem testlets could be large, but they are statistically non-significant; however, the influence of the number of items in the testlet should also be considered.
3. The nature of the option representations, SR and PR, represents two different mathematics abilities.
4. The main factor that influences students’ item responses is students’ abilities to interpret SR and PR, and the testlet effects generated from the shared item stem can be ignored.
5. Regarding the parameter estimates of the best-fitting model: (a) the person ability variance estimates show that the ability distributions on the SR and PR dimension may not be the same, (b) the correlation estimate between the SR and PR dimension indicates that these two abilities are moderately correlated, and (c) the item difficulty estimates for different models are similar.

Suggestions for teaching practice and future studies are provided in the Conclusion.     

Kuwait University and its evaluation program

As the only institution of higher education in Kuwait offering a four-year degree program, Kuwait University is expected to provide its society and its rapidly changing labor market with professionally trained Kuwaiti nationals in fields requiring up-to-date scientific and technical knowledge. Its location in the Arabian Gulf region requires KU to honor and preserve the Arab and Islamic tradition. Thus, the success of KU graduates in the job market and in society will depend on a combination of scientific knowledge and appreciation for local and regional values. With the introduction of the graduate studies program, KU is on the threshold of becoming a major institution of research and scholarship. With this step forward, KU increases its responsibility to offer a diversified academic program designed to meet the specialized manpower requirements of Kuwait as a major commercial center in the Middle East. To evaluate its programs, KU established the Center for Evaluation and Measurement in 1977 which introduced the Course and Instructor Evaluation project, and later expanded its activities through the KU Academic Evaluation Committee, to include program evaluation. The office of the Vice-Rector for Research was established in 1981 to encourage, support, and develop scientific research activities at Kuwait University. At present, KU has fully realized the importance of educational reform. A few of the issues, identified in this paper, can be outlined as follows:

1. The need for an admission policy to recruit more students competent in general subject matter knowledge as well as in English proficiency, and to assign them fairly to the subject areas of choice.
2. The need to design a research oriented curriculum with stronger emphasis on general education as required of an undergraduate studies program rather than stressing professionalism.
3. The need for an instructional program that deemphasizes students' total reliance on memorization and examinations for completing course requirements.
4. The need to improve instructional and research facilities, as well as make them available to students and to train students in their proper use.
5. The need to reappraise employment conditions for non-Kuwaiti teaching staff providing them with job security and career certainty.
6. The need for an administratively and financially independent KU, and long-range plan for a campus to accommodate the increasing number of students, faculty, and support staff.

fa]This report is based on studies conducted at the Center for Evaluation and Measurement and on the status reports of several foreign consultants, members of the KUAE Committee, who evaluated various departments. The author has highlighted those issues and added his interpretations in various areas of the academic program dealing with admission and recruitment of students and their career preparation, as well as curriculum, instruction, faculty, research, facilities, and introduction of graduate studies at Kuwait University.     

Career Guidance in Further,Higher and Continuing Education: — Expectations,programmes, training

This is a report on three working groups of the IRTAC European Consultation ‘Career Guidance in Further, Higher and Continuing Education’, University of London, December 16–20, 1983. The three working groups focused their discussion on the following themes:

- The expectations of those contemplating further and/or higher education.

- The selection and training of the career guidance team.

- The design, implementation and evaluation of career guidance programmes.

     

Teacher's role and reproducibility of didactical situations

Is it possible to specify teaching situations and to control their effects on students' learning? This general question is essential regarding the scientific character of research on mathematics education. It especially concerns the teacher's role in the class: can she ensure sufficient fidelity to a predefined scenario? This question is of special importance in the case of an experimental scenario the design of which is the result of a collaboration between a researcher and a teacher. This is considered here in the context of two case-studies. These case-studies exhibit two types of factors which tend to hamper fidelity in reproducing a given scenario:

- first, constraints on the teacher resulting from the didactical system: time constraints, success of the teaching process;

- second, teachers' conceptions about mathematics and learning. These results are considered with reference to prior research on didactical transposition and teacher's beliefs.

     

A new approach to the assessment of children's mathematical competence

The report is a translation of part of a Swedish paper entitled “On Students' Achievement in Mathematics after Finishing Comprehensive School”. The intention of the investigation was to

- diagnose the retention of some basic skills in some topics in algebra and geometry,

- reveal difficult steps in the learning processes in these topics.

Starting with a complicated question, e.g. the equation \(\frac{{3x - 2}}{2} = \frac{x}{3}\) a sequence consisting of 5–15 problems were constructed. Each new problem followed by the preceding one by taking away one or two details. \(\begin{gathered} 3(3x - 2) = 2x \\ {\text{ 9}}x - 6 = 2x \\ {\text{ 7}}x - 6 = 0 \\ {\text{ 7}}x = 6 \\ \end{gathered} \) is an example of a sequence belonging to the equation above. From about 10 complicated problems (“top-items”) and their sequences, in all 130 items, 10 sub-tests were put together in such a way that the pupils who took the test were not aware of the sequences but found no connection between the problems. Many surprising results were found, e.g., that the students scored higher on 14/(x+2)=2 than on 4/x=3, that the difficulty in finding the area of a triangle depended on the position of the triangle and that the problems “Simplify a/a ², a²/a, a/a” were of quite unequal difficulty. A discussion about the students' thinking in patterns and mechanically learning ends the report.     

Numeration a l'ecole elementaire

This paper presents results of research concerning the construction of the concept of natural integers by children. By testing the same children, whose school history was known with accuracy, at one year in tervals, we have sought to determine:

— How their competence in counting and numeration evolved during this period.

— What the mechanisms of this evolution were.

— What role school learning played.

     

Case study of a TeaM challenge game—e-PBL revisited

Today’s societies place challenging demands on individuals, who are confronted with complexity in many parts of their lives. What do these demands imply for key competencies that individuals need to acquire? Defining such competencies can improve assessments of how well prepared young people and adults are for life’s challenges, as well as identify overarching goals for education systems and lifelong learning. Why are competencies so important today? The PISA 2000 results underline the importance of student engagement. PISA found strong relationships between students’ attitudes, learning strategies and performance. In addition to skills related to specific parts of the school curriculum, students need to be equipped with some general competencies to solve life’s challenges. As they progress to adulthood, they need to learn to be able to complete not just pre-rehearsed exercises, but must also be able to solve problems set in unfamiliar situations by thinking flexibly and pragmatically. PISA 2003 therefore made a first-time assessment of students’ problem-solving skills. Findings revealed that just under one in five 15-year-olds in OECD countries are ‘reflective, communicative problem solvers’ able to tackle difficult tasks and also just under one in five students have problem-solving skills that cannot even be classified as ‘basic problem solvers’. What could be the basic problem and what resolution can be sought for? There are several examples in learning theory that suggests promises which need to be revisited. Barr and Tagg [From teaching to learning. Change. November/December pp. 13–25. Retrieved June 15, 2006 from http://critical.tamucc.edu/~blalock/readings/tch2learn.htm, 1995] defined the differences of paradigms in terms of learning theory comparing the notions of ‘teaching’ and that of ‘learning’, obviously expressing preferences to the later for its more in-depth effect on the learner. One of the main learner-centric approaches providing adequate positive results is problem based learning (PBL). This paper revisits the pedagogic theory behind PBL and examines it through a practical case study of a TeaM challenge game [TeaM challenge games: http://kihivas.ini.hu] with respect to its value in teacher education. It will concentrate on issues centred around:

• Traces of use of higher order thinking skills—according to Bloom’s taxonomy.
• Pedagogic pre-assumptions (designer’s side): requirements for design and supposed impact of students and teachers.
• Assignment within teacher training (training side): as the task of setting up such game is performed within Informatics teacher training at ELTE University and games were launched into public education.
• Pedagogic realities (facilitator’s side): how the teachers at a specific participant school viewed their role, the game, its impact and pedagogic value, its role in fulfilling the National Curriculum and its benefit for students.
• Indirect impact (staff’s side): how the game has affected the whole staff at school and what impact it had of the attitude of teachers.
• Results (evaluator’s side): how the game was evaluated in several ways and what new methods it has introduced into public education.

     

References of speech acts as characteristics of mathematical classroom conversation

In the article three parts of classroom conversation are studied with respect to the linguistic interference between teacher and pupils. Special attention is given to the reference of words and symbols of teacher and pupils. Some conclusions are:

- In classroom conversation we may consider the references of speech act as one of the basic features of learning.

- For succesful transfer of references between teacher and pupil, it is necessary that they are handling the same referential frameworks. Those frameworks are very fundamental in every day speech (‘form’ and ‘color’).

- Differences in references between teacher and pupils may lead to blockages in the learning. Sometimes they result in learning that is an imitation of teacher behaviour.

- To avoid these unwanted effects of learning, the teacher has to ensure that learning takes place within the everyday language of the pupils. So he will have to stimulate the pupils to explicate by themselves what they perceive and what they think.

     

Knowledge acquisition as a social phenomenon

The acquisition of knowledge, the development of the individual's knowledge bases, does not occur in a vacuum. The social context, both social structure (the perceived regularities in the social network) and social knowledge, appears to be related to the individual's acquisition of knowledge. In this article, the relationship between the social world and individual knowledge acquisition is explored. A general theory is postulated and then formulated as a model. The basic theory is predicated on the assumption that social interaction is the driving force behind knowledge acquisition. A selection of results pertaining to social learning will be presented. These include, but are not limited to the following:

• ? Social structure affects knowledge acquisition; e.g., individuals in tightly knit social groups develop similar cognitive structures, but not necessarily similar evaluations of those structures.
• ? Social knowledge evolves slowly and relative to shared experience.
• ? Individual knowledge acquisition is limited; e.g., individuals and groups talk past each other because of the lack of critical paths in their respective knowledge bases.

     

Building interfaces for on-line collaborative learning

For several years we have been engaged in the development and research of software environments for collaborative learning, for example in the recently completed CoLabs project (which we presented at the IFIP TC3 WG3.5 working conference in Budapest in 2004, see also http://matchsz.inf.elte.hu/Colabs/), also within lately defended long-range doctoral research, in which the co-author of this paper together with his undergraduate students had developed and evaluated cooperative computer activities for children aged 10 to 18. They observed children when using those environments and studied the influence of different approaches and solutions on the degree of their involvement and will to cooperate. We have also been involved in the London Knowledge Lab pilot project for developing a collaborative layered learning space travel games construction kit. Our department’s prior engagement in the development of collaborative activities also includes publishing a popular on-line journal (developed by A. Hrusecka and D. Lehotska, this on-line journal (in Slovak) can proudly boast up to 250,000 visits per month) for children, which intensively exploits on-line collaboration. This topic attracts us not only as a support for the learning process, but is a challenge for us as developers of educational programming tools as well. In our SuperLogo and Imagine environments we have always tried to provide users (ranging from children to developers) with new and powerful options to foster learning by exploring and developing. Thus we have equipped Imagine with the means for building objects and their behaviours in incremental loops, with parallel independent processes, event-driven programming and complex yet intuitive support for developing on-line environments for collaborative learning. In this paper we place our collaborative applications in the context of other related interfaces reported in literature. We use eight criteria to classify them and conclude that collaborative applications being developed by us and our students—future teachers—are distinguishable from others along two or three of those criteria: they combine in themselves typical features of Logo microworlds and inspiring support for on-line cooperation. We then analyze in detail our collaborative Imagine microworlds along four dimensions of their development. We specify means for establishing and maintaining on-line connection among any number of participants. We study tools for sending and receiving items (data, active characters with their behaviours, instructions etc.). We reflect on what can be shared by two or more participants in a collaborative activity. We examine all possible operations with common and private characters of a participant from the collaboration point of view. Our goals in this research and development are to:

1. Better understand potential the interfaces for on-line collaboration offer to support the learning process,
2. Place our Imagine Logo microworlds into context of other related applications,
3. Build a detailed map of all aspects important for their development (i.e., build a framework for the development),
4. Present the observations from our long-range experimental development and evaluation of the collaborative environments,
5. Point out how simple and natural it is (in the academic surroundings) to develop small and yet powerful collaborative microworlds—built for instance for immediate need in a classroom—with exceptional potential for interaction and openness.

Most of all, however, we want to motivate the endeavour to overcome all obstacles connected with the integration of on-line cooperation into children’s learning.     

School counseling in Israel. Issues and developments

This study investigated how Israeli teacher-counselors view their actual performance and what it is that teacher-counselors themselves feel should be their ideal roles. Counseling services were introduced into the educational system in Israel in 1960. Due to the fact that there was an urgent need to help students in their vocational plans and with their learning difficulties (Klingman and Ajzen, 1978), supervisors in The Ministry of Education suggested that teachers who have at least three years of teaching experience start a two year in-service training program in order to prepare them as specialists in helping pupils in the elementary schools plan for their future. A second objective was to help exceptional children with their learning problems. These goals caused the teacher with two years of special training to add a new role to his/her educational and teaching role. This dual role has been called ‘Teacher-counselor.’ In 1960, thirty four teacher-counselors started their work in different schools in Israel. Their major work was concentrated on disadvantaged children and with 7th and 8th graders helping them with their learning difficulties. To prevent overlapping with other helping professions and confusion concerning this new profession, a follow up study was conducted by Malinovski and Malinovski (1964) in order to define the role of the teacher-counselor. They have defined it to include eight activities which teacher-counselors were found to be involved with:

1. Help students adjust to school and community.
2. Help students reach self-understanding.
3. Provide information needed for vocational plans.
4. Help students understand their interests, values, and aptitudes.
5. Help students in human relationships.
6. To be a consultant for teachers and other professional workers.
7. Help parents in decision making concerning vocational plans for their children, and assist them in coping with behavioral problems.
8. Referral to special institutions when needed.

Since its origins in 1960, school counseling in Israel has been developed rapidly. This is reflected especially in the increasing number of teacher-counselors (43 teacher-counselors in 1964 to 800 teacher-counselors in 1976 and to 1366 teacher-counselors in 1981). Teacher-counselors now work not only in the Ministry of Education but also in the Ministry of Labor providing vocational services to teenagers who dropped out of school and who are encouraged to work and learn at the same time. As mentioned earlier, originally teacher-counselors were certified teachers who were selected after three years of experience in teaching and then they participated in a two-year program of in service training to become teacher-counselors. This state of affairs did remain for long. Soon after the introduction of the counseling services, universities responded to the newly created need and developed academic programs (for B.A. and then M.A. degrees) in counseling education. This evolution in training programs took place in the mid 1960's and brought a new sense of professionalism to the field of counseling. Until the mid seventies, universities limited admissions to counselor training to only those candidates who were already certified teachers with at least three years of experience. Currently, admission is not limited to teachers only but includes ‘fresh’ in-experienced students who can be admitted when they qualify on two criteria: Academic achievement and personality variables. The latter development has two significant meanings. First, the quality of students has become higher as they are selected from a larger population. Second, it is well known in Israel that for the teaching profession there exists what is called in Israel ‘negative selection: the less able go to teacher training seminaries to become teachers. Thus, by limiting admission to programs of training counselors only to graduates of these seminaries, the educational system's weaknesses were perpetuated. By widening the range of potential candidates not only has the quality of students and departments greatly improved, but also the educational system has gained much from these highly able counselors even though they are less experienced.     

El proyecto universidad desescolarizada: A feasibility study of teaching at a distance in Colombia S.A.

Plans for a nationwide system of education at a distance in Colombia S.A. are now under way to meet growing demands for higher education and to decentralize the current university system. Prior to this decision, a feasibility project was mounted in 1973–1976 by the University of Antioquia. Code-named El Proyecto UNIDES, its goals were:

- To check whether students could learn at a distance with no lowering of standards;

- To identify critical logistical conditions;

- To assess whether traditional university teaching methods could be renovated with systems resting on ideas from instructional technology.

UNIDES involved 70 staff of varying status and function who produced teaching materials and observed and assessed around 1500 students on and off campus under three instructional conditions covering a semester's work. D group students studied at a distance self-instructional materials in mathematics, psychology, and Spanish. S1 group students studied those materials individually on campus. S2 group students studied through conventional classes. Political confrontations with non-project students, staff anxieties, administrative, production, printing, distribution, and communication difficulties, and a 50–60 per cent dropout were unexpected events observed. This yielded valuable information about critical conditions in distance-teaching for practical decision-making in the future, but made assessment difficult. In academic performance, measured by common examinations for course credits, the groups ranked: S1, D and S2. There could be no clear-cut prediction from UNIDES. It suggested students can learn at a distance with no drop in standards, perhaps better through an autonomous system. Conventional systems might profit from adopting or adapting methods and materials developed for distance teaching.