Towards New Teaching in Mathematics How to Realize Inquiry Based and Problem Oriented Mathematics Lessons?

Дагмар Рааб Математиката е вълнуваща и забавна. Можем ли да убедим учениците, че това може да стане действителност. Задачите са най-важните инструменти за учителите по математика, когато планират уроците си. Планът трябва да съдържа идеи как да се очертае и как да се жалонира пътят, по който учениците ще стигнат до решението на дадена задача. Учителите не трябва да очакват от учениците си просто да кажат кой е отговорът на задачата, а да ги увлекат в процеса на решаване с подходящи въпроси. Ролята на учителя е да помогне на учениците • да бъдат активни и резултатни при решаването на задачи; • самите те да поставят задачи; • да модифицират задачи; • да откриват закономерности; • да изготвят стратегии за решаване на задачи; • да откриват и изследват различни начини за решаване на задачи; • да намират смислена връзка между математическите си знания и проблеми от ежедневието. В доклада са представени избрани и вече експериментирани примери за това как учители и ученици могат да намерят подходящ път към нов тип преживявания в преподаването и изучаването на училищната математика.

Content-Based Image Retrieval for Computer Tomography Images Using Wavelet Descriptors

An approach to building a CBIR-system for searching computer tomography images using the methods of wavelet-analysis is presented in this work. The index vectors are constructed on the basis of the local features of the image and on their positions. The purpose of the proposed system is to extract visually similar data from the individual personal records and from analogous analysis of other patients.

The strengths, weaknesses, opportunities and threats of using social software in higher and further education teaching and learning

Social software is increasingly being used in higher and further education to support teaching and learning processes. These applications provide students with social and cognitive stimulation and also add to the interaction between students and educators. However, in addition to the benefits the introduction of social software into a course environment can also have adverse implications on students, educators and the education institution as a whole, a phenomenon which has received much less attention in the literature. In this study we explore the various implications of introducing social software into a course environment in order to identify the associated benefits, but also the potential drawbacks. We draw on data from 20 social software initiatives in UK based higher and further education institutions to identify the diverse experiences and concerns of students and educators. The findings are presented in form of a SWOT analysis, which allows us to better understand the otherwise ambiguous implications of social software in terms of its strengths, weaknesses, opportunities and threats. From the analysis we have derived concrete recommendations for the use of social software as a teaching and learning tool.

An innovative approach to teaching structural induction for computer science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding and performance of computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: (1) identifying sources of computer science students’ difficulties with proofs by induction, and (2) developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

Subject -centered and problem -based approaches to teaching clinical competence in physical therapy

Physical therapy students must apply the relevant information learned in their academic and clinical experience to problem solve in treating patients. I compared the clinical cognitive competence in patient care of second-year masters students enrolled in two different curricular programs: modified problem-based (M P-B; n = 27) and subject-centered (S-C; n = 41). Main features of S-C learning include lecture and demonstration as the major teaching strategies and no exposure to patients or problem solving learning until the sciences (knowledge) have been taught. Comparatively, main features of M P-B learning include case study in small student groups as the main teaching strategy, early and frequent exposure to patients, and knowledge and problem solving skills learned together for each specific case. Basic and clinical orthopedic knowledge was measured with a written test with open-ended items. Problem solving skills were measured with a written case study patient problem test yielding three subscores: assessment, problem identification, and treatment planning. ^ Results indicated that among the demographic and educational characteristics analyzed, there was a significant difference between groups on ethnicity, bachelor degree type, admission GPA, and current GPA, but there was no significant difference on gender, age, possession of a physical therapy assistant license, and GRE score. In addition, the M P-B group achieved a significantly higher adjusted mean score on the orthopedic knowledge test after controlling for GRE scores. The S-C group achieved a significantly higher adjusted mean total score and treatment management subscore on the case study test after controlling for orthopedic knowledge test scores. These findings did not support their respective research hypotheses. There was no significant difference between groups on the assessment and problem identification subscores of the case study test. The integrated M P-B approach promoted superior retention of basic and clinical science knowledge. The results on problem solving skills were mixed. The S-C approach facilitated superior treatment planning skills, but equivalent patient assessment and problem identification skills by emphasizing all equally and exposing the students to more patients with a wider variety of orthopedic physical therapy needs than in the M P-B approach. ^

The impact of standards -based practices in mathematics on the achievement of low -performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

The efficacy of an interactive computer system for teaching developmental mathematics to college students

Many students are entering colleges and universities in the United States underprepared in mathematics. National statistics indicate that only approximately one-third of students in developmental mathematics courses pass. When underprepared students repeatedly enroll in courses that do not count toward their degree, it costs them money and delays graduation. This study investigated a possible solution to this problem: Whether using a particular computer assisted learning strategy combined with using mastery learning techniques improved the overall performance of students in a developmental mathematics course. Participants received one of three teaching strategies: (a) group A was taught using traditional instruction with mastery learning supplemented with computer assisted instruction, (b) group B was taught using traditional instruction supplemented with computer assisted instruction in the absence of mastery learning and, (c) group C was taught using traditional instruction without mastery learning or computer assisted instruction. Participants were students in MAT1033, a developmental mathematics course at a large public 4-year college. An analysis of covariance using participants' pretest scores as the covariate tested the null hypothesis that there was no significant difference in the adjusted mean final examination scores among the three groups. Group A participants had significantly higher adjusted mean posttest score than did group C participants. A chi-square test tested the null hypothesis that there were no significant differences in the proportions of students who passed MAT1033 among the treatment groups. It was found that there was a significant difference in the proportion of students who passed among all three groups, with those in group A having the highest pass rate and those in group C the lowest. A discriminant factor analysis revealed that time on task correctly predicted the passing status of 89% of the participants. ^ It was concluded that the most efficacious strategy for teaching developmental mathematics was through the use of mastery learning supplemented by computer-assisted instruction. In addition, it was noted that time on task was a strong predictor of academic success over and above the predictive ability of a measure of previous knowledge of mathematics.^

A practical system for hands-off computer interaction based on electromyogram (EMG)/eye gaze tracking (EGT)

Effective interaction with personal computers is a basic requirement for many of the functions that are performed in our daily lives. With the rapid emergence of the Internet and the World Wide Web, computers have become one of the premier means of communication in our society. Unfortunately, these advances have not become equally accessible to physically handicapped individuals. In reality, a significant number of individuals with severe motor disabilities, due to a variety of causes such as Spinal Cord Injury (SCI), Amyothrophic Lateral Sclerosis (ALS), etc., may not be able to utilize the computer mouse as a vital input device for computer interaction. The purpose of this research was to further develop and improve an existing alternative input device for computer cursor control to be used by individuals with severe motor disabilities. This thesis describes the development and the underlying principle for a practical hands-off human-computer interface based on Electromyogram (EMG) signals and Eye Gaze Tracking (EGT) technology compatible with the Microsoft Windows operating system (OS). Results of the software developed in this thesis show a significant improvement in the performance and usability of the EMG/EGT cursor control HCI.

Investigating the Effects of Cognitive Apprenticeship-Based Instructional Coaching on Science Teaching Efficacy Beliefs

The overall purpose of this collected papers dissertation was to examine the utility of a cognitive apprenticeship-based instructional coaching (CAIC) model for improving the science teaching efficacy beliefs (STEB) of preservice and inservice elementary teachers. Many of these teachers perceive science as a difficult subject and feel inadequately prepared to teach it. However, teacher efficacy beliefs have been noted as the strongest indicator of teacher quality, the variable most highly correlated with student achievement outcomes. The literature is scarce on strong, evidence-based theoretical models for improving STEB. This dissertation is comprised of two studies. STUDY #1 was a sequential explanatory mixed-methods study investigating the impact of a reformed CAIC elementary science methods course on the STEB of 26 preservice teachers. Data were collected using the Science Teaching Efficacy Belief Instrument (STEBI-B) and from six post-course interviews. A statistically significant increase in STEB was observed in the quantitative strand. The qualitative data suggested that the preservice teachers perceived all of the CAIC methods as influential, but the significance of each method depended on their unique needs and abilities. STUDY #2 was a participatory action research case study exploring the utility of a CAIC professional development program for improving the STEB of five Bahamian inservice teachers and their competency in implementing an inquiry-based curriculum. Data were collected from pre- and post-interviews and two focus group interviews. Overall, the inservice teachers perceived the intervention as highly effective. The scaffolding and coaching were the CAIC methods portrayed as most influential in developing their STEB, highlighting the importance of interpersonal relationship aspects in successful instructional coaching programs. The teachers also described the CAIC approach as integral in supporting their learning to implement the new inquiry-based curriculum. The overall findings hold important implications for science education reform, including its potential to influence how preservice teacher training and inservice teacher professional development in science are perceived and implemented. Additionally, given the noteworthy results obtained over the relatively short durations, CAIC interventions may also provide an effective means of achieving improvements in preservice and inservice teachers’ STEB more expeditiously than traditional approaches.

An Innovative Approach to Teaching Structural Induction for Computer Science

Proofs by induction are central to many computer science areas such as data structures, theory of computation, programming languages, program efficiency-time complexity, and program correctness. Proofs by induction can also improve students’ understanding of and performance with computer science concepts such as programming languages, algorithm design, and recursion, as well as serve as a medium for teaching them. Even though students are exposed to proofs by induction in many courses of their curricula, they still have difficulties understanding and performing them. This impacts the whole course of their studies, since proofs by induction are omnipresent in computer science. Specifically, students do not gain conceptual understanding of induction early in the curriculum and as a result, they have difficulties applying it to more advanced areas later on in their studies. The goal of my dissertation is twofold: 1. identifying sources of computer science students’ difficulties with proofs by induction, and 2. developing a new approach to teaching proofs by induction by way of an interactive and multimodal electronic book (e-book). For the first goal, I undertook a study to identify possible sources of computer science students’ difficulties with proofs by induction. Its results suggest that there is a close correlation between students’ understanding of inductive definitions and their understanding and performance of proofs by induction. For designing and developing my e-book, I took into consideration the results of my study, as well as the drawbacks of the current methodologies of teaching proofs by induction for computer science. I designed my e-book to be used as a standalone and complete educational environment. I also conducted a study on the effectiveness of my e-book in the classroom. The results of my study suggest that, unlike the current methodologies of teaching proofs by induction for computer science, my e-book helped students overcome many of their difficulties and gain conceptual understanding of proofs induction.

The impact of standards-based practices in mathematics on the achievement of low-performing students

This study examined standards-based mathematics reform initiatives to determine if they would improve student achievement on the part of low-performing students. New curricula, the Carnegie Learning Cognitive Tutor®, were provided for algebra and geometry students. The new instructional strategy relied on both the teacher-led instruction and the use of computers to differentiate instruction for individual students. Mathematics teachers received ongoing professional development to help them implement the new curricula. In addition, teachers were provided with ongoing support to assist them with the transformation of the learning environments for students using standards-based practices. This quasi-experimental (nonrandomized) study involved teachers in two matched urban high schools. Analyses (ANCOVAs) revealed that the experimental group with an appropriately implemented program had significantly higher learning gains than the comparison group as determined by the students' 2007 mathematics Developmental Scale Score (DSS). In addition, the experimental group's adjusted mean for the second interim mathematics assessment was significantly higher than the comparison group's mean. The findings support the idea that if the traditional curriculum is replaced with standards-based curriculum, and the curriculum is implemented as intended, low-performing students may make significant learning gains. With respect to the teaching practices as observed with the Classroom Observation Protocol (COP), t-tests were conducted on four constructs. The results for both the algebra and geometry teachers on the constructs were not significant. The COP indicated that teachers in both the experimental and comparison groups used traditional instruction strategies in their classrooms. The analyses of covariance (ANCOVA) on the use of technology revealed no significant main effects for computer use.

An alternative to BlackboardTM? Student use of web-based textbook teaching and learning material

This paper investigates the use of web-based textbook supplementary teaching and learning materials which include multiple choice test banks, animated demonstrations, simulations, quizzes and electronic versions of the text. To gauge their experience of the web-based material students were asked to score the main elements of the material in terms of usefulness. In general it was found that while the electronic text provides a flexible platform for presentation of material there is a need for continued monitoring of student use of this material as the literature suggests that digital viewing habits may mean there is little time spent in evaluating information, either for relevance, accuracy or authority. From a lecturer perspective these materials may provide an effective and efficient way of presenting teaching and learning materials to the students in a variety of multimedia formats, but at this stage do not overcome the need for a VLE such as Blackboard™.

From phenomenography study to planning teaching

A phenomenographic study uncovers variations in the way that the subjects are aware of a phenomenon. In the categories of description that represent the variations in awareness there are features that, through their variation, define the characteristics of the categories. Teaching seeks to foster a change in the way that the learner is aware of a phenomenon through opening up a space of learning. This paper outlines the way that the outcome spaces from a phenomenographic study can be used to plan a teaching programme that utilises variations in the features. It discusses a strategy for teaching programming based on a phenomenographic study of practitioner conceptions of an object-oriented program. The strategy covers features related to the nature of an object-oriented program. Copyright 2010 ACM.

Practice-based film education for children: teaching and learning for creativity, citizenship and participation

Practice-oriented film education aimed at children has been hailed for various reasons: at a personal level, as a means of providing tools for self-expression, for developing creativity and communication skills. And at a social level, it is argued that children must now become competent producers, in addition to critical consumers, of audiovisual content so they can take part in the global public sphere that is arguably emerging. This chapter discusses how the challenges posed by introducing children to filmmaking (i.e. digital video) are being met at three civil associations in Mexico: La Matatena AC, which seeks to enrich the children’s lives by means of the aesthetic experience filmmaking can bring them. Comunicaciòn Comunitaria, concerned with the impact filmmaking can have on the community, preserving cultural memory and enabling participation. And Juguemos a Grabar, with a focus on urban regeneration through the cultural industries.

Assessment of the EEE-4 oral test: a discourse analysis based on complex networks.

With the development of information technology, the theory and methodology of complex network has been introduced to the language research, which transforms the system of language in a complex networks composed of nodes and edges for the quantitative analysis about the language structure. The development of dependency grammar provides theoretical support for the construction of a treebank corpus, making possible a statistic analysis of complex networks. This paper introduces the theory and methodology of the complex network and builds dependency syntactic networks based on the treebank of speeches from the EEE-4 oral test. According to the analysis of the overall characteristics of the networks, including the number of edges, the number of the nodes, the average degree, the average path length, the network centrality and the degree distribution, it aims to find in the networks potential difference and similarity between various grades of speaking performance. Through clustering analysis, this research intends to prove the network parameters’ discriminating feature and provide potential reference for scoring speaking performance.