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This paper describes a pilot study that explores students learning how to program via a multi-disciplinary approach. The study participants were eleven 6th grade students who learned programming fundamentals via music activities in a Scratch 3.0 environment. These activities included the programming of familiar melodies and the development of suitable animations or computer games. For that matter, a study unit termed MelodyCode was developed in the spirit of the STEAM education approach and the spiral learning method and included exploration tasks based on individual learning. Via the programming of familiar melodies, they became acquainted with programming concepts such as functions, variables, repetition and control commands, parallel processes, and more. Competitions that win awards were held from time to time, which prompted students to invest efforts in their projects to reach first place and gain the teacher and classmates' appreciation. The study was conducted in the form of action research. The data analysis yielded references to the effect of MelodyCode on common stereotypes students hold regarding programming (masculine profession, necessitates good mathematics knowledge), cognitive aspects (cognitive load, linking music concrete use to abstract programming concepts), and affective aspects (joyful and relaxing class atmosphere, motivation, curiosity, self-efficacy).

This article describes a unique ongoing experience of learning programming via engagement in music programming of known melodies. Seventh and eighth graders participated in 10 lessons of weekly activity. Via the programming of melodies, using the Scratch 2.0 environment, they became acquainted with basic concepts of programming such as methods, variables, repetition and control commands, parallel processes, and more. The study was conducted in the form of an action research. The study units were designed in the spirit of the spiral learning method, in which the learning concepts are revisited several times while their level of complexity rises. From the data analyzed so far, four categories emerged: enjoyment, interest, gaining programming knowledge, and experiencing feelings of success. The students were enthusiastic during the learning lessons, and they were curious to learn and use advanced concepts. The music programming provided them with practical meaning for the learned programming structures and concepts.

The present study examines the difficulties novice data modelers face when asked to provide a data model addressing a given problem. In order to map these difficulties and their causes, two short data modeling problems were given to 82 students who had completed an introductory course in database modeling. Both problems involve three entity sets with relationships between them, either ternary or binary. The students' solutions were classified according to the types of errors they committed. More than half of the students provided faulty solutions. After an analysis of these results, open interviews were conducted with a selected group of students in order to figure out the reasons underlying the students' erroneous decisions regarding the data model. Among the reasons for their erroneous solutions were insufficient experience, lack of reflection on their solution, and lack of immediate feedback. In addition, the authors suggest instructional modifications derived from the research results.

Aim/Purpose: Multi-threaded software design is considered to be difficult, especially to novice programmers. In this study, we explored how students cope with a task that its solution requires a multi-threaded architecture to achieve optimal runtime. Background: An efficient exploit of multicore processors architecture requires computer programs that use parallel programming techniques. However, parallel programming is difficult to understand and apply by novice programmers. Methodology: The students had to address a two-stage problem--(1) design an optimal runtime solution to a given problem with no additional instructions; and (2) provide an optimal runtime multi-threaded design to the same problem. Interviews were conducted with a representative group of students to understand the underlying causes of their provided designs. We used qualitative research methods to gain refined insights regarding the students' decision making during the design process. To analyze the gained data, we used content analysis tools. Contribution: The case study presented in this paper will help the teacher to stress the merits and limitations of various parallel architectures and confront students with the consequences of their solutions via performances' benchmark. Findings: Analysis of the student's solutions to the first stage revealed that the majority of them did not provide a multi-threaded solution ignoring the optimal runtime requirement. At the second stage, seven various architectures were provided differing in the number of involved threads, the data structures used, and the synchronization mechanism employed. The majority of the solutions were sub-optimal and only a few students provided an optimal one. Recommendations for Practitioners: We recommend conducting class discussions that will follow a task similar to the one used in this study. Recommendation for Researchers: To be able to generalize the received results this research should be repeated with larger study participant groups from various academic institutions. Impact on Society: Understanding the difficulties of novice programmers may lead to quality software systems. Future Research: To be able to generalize the received results this research should be repeated with larger study participant groups from various academic institutions.

In this paper there is a description of a case in which mathematical argumentation emerge and develop between 7th grade students working in an interactive computerized environment without a deliberate mentoring. The computerized environment has its influence on the characteristics of this argumentation which include mathematical regularities based on concrete examples of geometrical shapes (stars and regular polygons) and mathematical considerations relating to numbers' properties. [For complete proceedings, see ED489538].

Many students view mathematics as a collection of theorems and facts that were discovered by intelligent mathematicians and all they have left to do is to study them carefully. Some believe it is important to help students change this view (Lavy & Shriki, 2003). One possible way is to enable students to modify the attributes of a given situation, and then pose problems that concern the newly generated situation (Brown & Walter, 1993). In this paper, the authors wish to demonstrate the simplicity of such a process, and exemplify the idea that even a fundamental situation can serve as a trigger for discovering unknown patterns.

In this study, a practicum-based approach to bridge the gap between industry expectations and Information Systems graduates skills is presented and discussed. Students participate in the practicum project during their last study year, and take part in various professional activities in the industry in accordance with their professional aspirations and their desired specialty. Semi-structured questionnaires and interviews with students who participated in the project in the last four years were conducted in order to reveal the students' perceived contributions of the project. The students experienced real workplace environments, acquired extended knowledge and skills, built social infrastructure to assist them with future job seeking, and above all gained real world experience that help them to build their professional image, and gain confidence in their traits and abilities. In addition, the practicum-based approach was compared with other common approaches used to bridge the gap, and its relative advantages and disadvantages were discussed.

In this study, we examined aspects relating to the impact of integrating question-asking activities and providing answers to these questions while reading historical mathematical texts on prospective mathematics teachers' self-reported cognitive load. The research design of the study was quasi-experimental. The study participants included two groups of 20 students each (experimental and control). The experimental group was instructed to ask questions while coping with the texts, whereas the control group received no special instructions. The experimental group participants were asked to think aloud while coping with the texts and audio record themselves. These records were transcribed into written protocols. Both groups had to respond to a self-esteem index questionnaire in which they had to report the level of difficulty they experienced during their attempts to cope with the texts, as an indicator of their sense of cognitive load. This process was repeated at three time points, relating to three different texts. The data were analyzed using quantitative and qualitative methods. Two main observations were obtained: (1) A significant difference was found between the control and the experimental groups regarding the decrease in cognitive load along the time points. Because the only difference between the control and experimental groups was the activity of question-asking, it might be concluded that question-asking affects the reduction in cognitive load. (2) Question-asking supports the assimilation of new information up to a specific limit, depending on the gap between existing knowledge and new information. [ABSTRACT FROM AUTHOR]

One aspect of professional development of mathematics teachers relates to the development of assessment skills. The aim of this study is to examine the effects of engaging prospective mathematics teachers in peer assessment, both as assessors and assessees, on the development of their assessment skills in general and assessment of geometrical proofs in particular. The research was conducted within a Method course in which peer assessment activities were employed. Sixteen prospective mathematics teachers participated in the research and had to act both as assessors and assessees. Analysis of the research data reveals that during the various phases of the study the prospective teachers developed skills concerning the selection of categories and weights for the assessment of their peers' work. In the criteria set they selected for the peer assessment, they referred to meanings and roles of mathematical proof. In their reflections, the prospective mathematics teachers also referred to the effects of the peer assessment on their mathematical knowledge, asserting that by being exposed to different solution strategies and new problems they were able to widen their mathematical knowledge.

In this study we explored the effects of providing ninth-grade students with the chance to take part in decision making concerning the mathematics level they would be assigned to in high school. Decisions concerned their self-competence regarding their mathematical abilities, their learning goals and the class atmosphere. The students were taught three mathematics topics during the ninth grade in two levels (regular and extended) and after each topic they were examined in the level they identified as appropriate for himself/herself. After each exam the students were asked to fill in a questionnaire in which they had to address issues referring to their choice. The results revealed that the students learnt how to better monitor their learning. The students' learning goals were mainly performance and mastery goals and the class atmosphere changed completely and frustration and dissatisfaction were no longer expressed. (Contains 2 tables and 3 figures.)

This study examines how Information Systems Engineering School students on the verge of their graduation understand the mechanism of exception handling. The main contributions of this paper are as follows: we construct a questionnaire aimed at examining students' level of understanding concerning exceptions; we classify and analyse the students' responses to the questionnaire in order to determine their level of understanding of the mechanism; and we discuss the students' reflections concerning exceptions. The students were required to demonstrate their understanding of various aspects of Java exception handling: exception throwing and catching, fluency of code in the presence of exceptions, multiple catch clauses, common and different reactions to the various exceptions, passing an exception up the calling chain, proper use of the exception hierarchy, re-throwing an exception, and overriding a method which throws exceptions. The results obtained reveal that almost all the participants understood the basics of throwing and catching an exception, but only a few demonstrated the highest level of understanding of the exception mechanism. As the level of understanding required to address the questionnaire problems increased, the number of study participants who were able to answer correctly decreased substantially. In fact, most of the study participants were not familiar with all the possibilities encompassed by the exception mechanism and so were not able to use them properly. The students' reflections were classified into the following categories: perceptions concerning the benefits of using exceptions; perceptions concerning the complexity of the exception mechanism; and issues concerning the development environment. According to the results obtained we recommend several modifications to the curriculum with the aim of improving the students' ability to properly utilize the advanced properties of exceptions to produce higher quality software. (Contains 4 figures and 1 table.)

Recent reforms in mathematics education have increased the need for teachers to attend professional development programs. In order to motivate teachers to attend such programs and to maximize their effect on teachers' development, we believe it is important to adapt the contents of such programs to teachers' perceived needs. The current study was designed to explore the professional needs of Israeli mathematics teachers, as they perceived them. Our results show that teachers are mainly concerned with developing their mathematical knowledge and acquiring knowledge that relates to the way in which students comprehend various mathematical concepts. However, these concerns stem from different positions that can be attributed to their teaching experience: new teachers appear to be self-centered; therefore their concern with developing their knowledge might be a result of a need to gain self-confidence. More experienced teachers are able to consider the effect of their teaching on students' learning, and it appears that their wish to acquire knowledge stems from this perspective. Highly experienced teachers, like new teachers, are also self-centered, believing they know everything about teaching and learning, and therefore express interest in acquiring knowledge merely for satisfying their own curiosity. (Contains 3 notes, 2 tables, and 1 figure.)

This study discusses and presents various strategies employed by novice programmers concerning exception handling. The main contributions of this paper are as follows: we provide an analysis tool to measure the level of assimilation of exception handling mechanism; we present and analyse strategies to handle exceptions; we present and analyse solutions provided by novice programmers; we classify and analyse the participants' reflections concerning their solutions. Modern programming languages, such as Java, provide the programmer an elaborated object oriented exception mechanism; enable him to handle exceptions in a more convenient way. The aim of this study was to discover the strategies novice programmers are using to handle exceptions and whether they utilise the advantage of the modern exception handling mechanism. For that matter the participants (college students) had to provide a written solution to a given problem with a special focus on exception handling. In addition each of them was interviewed. The analysis of the solutions provided was carried out according to a set of software quality criteria (clarity, modularity and extensibility) adapted to exception handling characteristics. These criteria were used to explain the advantages and disadvantages of the solutions from a software engineering perspective. The solutions provided were also analysed according to a classification of levels of assimilation concerning the structure of exceptions, based on the SOLO taxonomy. The first level of assimilation refers to solutions in which no exception mechanism was used, and the errors were handled in the old fashion way (local handling or return of an error code). The fifth and last level refers to solutions that used adequate hierarchy of exception classes allowing easy extension according to future requirements and enabling the handling of multiple exception altogether or handle each separately. In between these levels there are strategies that used exception mechanisms without the exhausting of its advantages. The results obtained reveal that only few participants (7 out of 56) provided a solution that was classified to one of the two highest assimilation levels, while many (23 out of 56) did not use exception mechanism at all. The rest of the students (25 out of 56) used the exception mechanism poorly (i.e., used only Exception class or did not use hierarchy of exceptions). The participants had difficulties in utilising the advanced exception handling mechanisms and in exhibiting a high level of abstraction with regard to the proper design of a hierarchy of exceptions. The students' statements collected during the interviews were classified into the following categories: misconceptions concerning code quality; misconceptions concerning exception handling; difficulties in understanding the exception handling mechanism; the perceived importance of exception handling; and a lack of programming experience. During the interviews the students provided explanations concerning the reasons they were not fully utilized the exception mechanism. Among them are: lack of practice, too few demonstrated examples, focussing merely on providing a working solution without considering quality issues. Finally we recommend on some modifications to the curriculum, among them: to expose the students earlier to the exception mechanism; to throw built-in Java exception to address validation errors; and to put more attention to quality issues. (Contains 5 tables and 3 figures.)

In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the "What If Not?" (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs' portfolios reveals that they believe that engaging in the inquiry-based activity enhanced both their mathematical and meta-mathematical knowledge. As to the mathematical knowledge, they deepened their knowledge regarding the geometrical concepts and shapes involved, and during the process of creating the problem and checking its validity and its solution, they deepened their understanding of the interconnections among the concepts and shapes involved. As to meta-mathematical knowledge, the PTs refer to aspects such as the meaning of the givens and their relations, validity of an argument, the importance and usefulness of the definitions of concepts and objects, and the importance of providing a formal proof. (Contains 1 figure and 2 tables.)

The present study was carried out within a systems analysis and design workshop. In addition to the standard analysis and design tasks, this workshop included practices designed to enhance student capabilities related to non-technical knowledge areas, such as critical thinking, interpersonal and team skills, and business understanding. Each task was reviewed and assessed by both the students and the instructor. The main research study objective was to examine the effect of team-based peer-review on the students' learning process in an information systems workshop, What is presented is data referring to the grading process, to students' enhanced learning reflected in the narrowing gap between the instructor's and the students' grading, as well as the students' reflections demonstrating their perception of the workshop's components. (Contains 2 tables and 3 figures.)

One of the subjects that undergraduate students learning Object Oriented (OO) design find hard to apply is the construction of class hierarchies in general, and the use of interface classes in particular. The design process requires decomposition and reconstruction of problems in order to model software classes. The common attributes and behaviors are usually modeled using class inheritance except when the common behaviors do not belong to the same class hierarchy; in such case, an interface class is preferred. In order to be able to properly design, the designer has to demonstrate the abstraction abilities on various levels. In this study, we aimed at examining the students' demonstration of abstraction levels during design of class hierarchy in general, and whether or not they use interface classes in particular. The results of the study reveal that a majority of students were able to build a reasonable class hierarchy; however, many of them did not use interface classes as a tool for expressing common behaviors. Nevertheless, all of them could identify and choose the best solution for a particular problem among four different solutions, which included the use of interface class. (Contains 1 table and 13 figures.)

Various terms are used to describe mathematical concepts, in general, and statistical concepts, in particular. Regarding statistical concepts in the Hebrew language, some of these terms have the same meaning both in their everyday use and in mathematics, such as Mode; some of them have a different meaning, such as Expected value and Life expectancy; and some have the opposite meaning, such as Significance level. Spoken language plays an important role in shaping how the informal statistical definitions taught in schools are remembered. In the present study we examine the impact of the everyday use of terms on the students' informal definitions of various statistical concepts. Though all the study participants were familiar with the concepts they were asked to define, a high percentage of them failed to provide correct definitions of the given statistical concepts. Analysis of the incorrect definitions revealed that the everyday use of the terms used to label the concepts, influenced the informal definitions provided by the students. (Contains 1 end note and 3 tables.)

Prospective teachers' (PT) beliefs and views regarding teaching and learning affect the way they teach after they have graduated. Often, these views are a consequence of their past experience as pupils themselves. In recent years there has been a great effort toward changing the teaching and learning of mathematics, which raises the need to generate a change in views and beliefs. The present study aims at exploring the effect of learning via computerized project-based learning (CPBL) on the change in views of third year prospective mathematics teachers regarding the image of the "good teacher." To assess the change in views of our pre-service teachers regarding the image of the "good teacher," an integrated tool was employed: two open questionnaires, written portfolios, and transcripts of class discussions. In this paper we focus mainly on results obtained from the questionnaires, supported by evidence from the portfolios, and show that CPBL is an effective approach for supporting the change in views of our pre-service mathematics teachers regarding the image of the "good teacher."

This paper reports an example of a situation in which university students had to solve geometrical problems presented to them dynamically using the interactive computerized environment of the "MicroWorlds Project Builder". In the process of the problem solving, the students used ten different solution strategies. The unsuccessful strategies were then classified into three main categories: distracting, reducing and confusing. One student group had to solve the same problem in its non-dynamic version. The results received from both groups were compared and analysed. Analysis of the solution strategies and the process of the categorization revealed that the percentage of success in both groups was similar and in the case of the given problem, the dynamic visual mode of the problem distracted the students' attention away from proper handling of the solution of the problem. (Contains 6 figures and 3 tables. Solutions are appended.)

This paper presents a description of the different types of arguments that emerged as two students, working in a computerized environment, engaged in an investigation of several number theory concepts. The emerging arguments are seen as a result of the influence of the computerized environment together with collaborative learning. Using qualitative research methods, data are analyzed to show how the students constructed four types of mathematical arguments: basic, compound, elaborated, and general-presented-as-specific. These example-based arguments could serve as a knowledge base for developing formal mathematical proofs. (Contains 11 figures.)

To investigate mechanisms of failure in mathematics, we adopt the "communicational approach to cognition," which describes thinking as an activity of communication and learning mathematics as an initiation to a certain type of discourse. In the search for factors that impede students' participation in arithmetic communication, we examine the arithmetical discourses of two 18-year-old girls with long histories of learning difficulties. The resulting "arithmetical discourse profiles" of the two students help us substantiate the following two claims: (1) Almost any person may become a skillful participant of arithmetical discourse, provided, first, that a discursive mode is found that makes the best of this person's special strengths and second, that in the process of teaching, the general sociocultural context of learning is taken into account as having a central role in enabling or barring one's access to literate discourses; (2) if the potential for successful participation remains often unrealized, it is mainly because of certain widely practiced abuses of literate mathematical discourse. (Contains 2 figures, 6 tables and 14 footnotes.)

This paper describes a pilot study that explores students learning how to program via a multi-disciplinary approach. The study participants were eleven 6th grade students who learned programming fundamentals via music activities in a Scratch 3.0 environment. These activities included the programming of familiar melodies and the development of suitable animations or computer games. For that matter, a study unit termed MelodyCode was developed in the spirit of the STEAM education approach and the spiral learning method and included exploration tasks based on individual learning. Via the programming of familiar melodies, they became acquainted with programming concepts such as functions, variables, repetition and control commands, parallel processes, and more. Competitions that win awards were held from time to time, which prompted students to invest efforts in their projects to reach first place and gain the teacher and classmates' appreciation. The study was conducted in the form of action research. The data analysis yielded references to the effect of MelodyCode on common stereotypes students hold regarding programming (masculine profession, necessitates good mathematics knowledge), cognitive aspects (cognitive load, linking music concrete use to abstract programming concepts), and affective aspects (joyful and relaxing class atmosphere, motivation, curiosity, self-efficacy). [ABSTRACT FROM AUTHOR]

We present a case study of two students engaged in an investigation of number theory concepts in the computer environment, "Geoboard". The two students struggle with significant problems to communicate mathematics, and the computer plays a vital role in helping them overcome these difficulties. In fact, the students constantly use the screen images to help them make sense of each other's vague ideas and incomplete utterances. Using the qualitative research methods of discourse analysis, we construct the learning profiles of the two students and show how the characteristics of each contributed to the shared process, and how they used the computer presence to enable this process. We trace this process through the students' construction of two mathematical concepts that arose in their activities, the "n-star" and "common denominators".