Teaching University-Level Mathematics Using Mathematica

This paper considers the use of the computer algebra system Mathematica for teaching university-level mathematics subjects. Outlined are basic Mathematica concepts, connected with different mathematics areas: algebra, linear algebra, geometry, calculus and analysis, complex functions, numerical analysis and scientific computing, probability and statistics. The course “Information technologies in mathematics”, which involves the use of Mathematica, is also presented - discussed are the syllabus, aims, approaches and outcomes.

Tessellation with some Irregular Poligons

An idea for the use of problems of tessellation with irregular polygons in the optional activities in Information Technologies teaching are presented.

A Software Platform for Teaching Programming with Grading Systems

Красимир Манев, Милослав Средков, Петър Армянов - Състезателните системи (СС) са незаменимо средство за организация на състезания по програмиране. Напоследък СС се използват и в обучението по програмиране. В статията е предложена платформа, която да интегрира възможностите на СС, създадени или използвани от авторите. Целта е изграждането на проста и ефективна среда за обучение по програмиране, подпомагаща учебния процес. Специфицирани са основните елементи на платформата, като резултат от предходно изследване, и една нейна възможна архитектура.

Discover the Thracians - An Approach for Use of 2D and 3D Technologies for Digitization of Cultural Heritage in the Field of E-learning

Information and communication technologies (ICT) offer an easier access to and a multi-perspective view of cultural heritage artifacts and may also enrich and improve cultural heritage education through the adoption of innovative learning/teaching methods. This paper examines the different practices and opportunities for digitization of cultural artifacts with historical significance and describes the work on a pilot project concerning the development of e-learning materials in the Thracian cultural and historical heritage. The proposed method presents an approach based on a combination of 2D and 3D technologies to facilitate the overall process of digitization of individual objects. This approach not only provides greater opportunities for presenting the Thracian heritage but also new perspectives for studying it - students, scientists, PhD students will have the opportunity to work with the materials without having access to them.

Creative thinking experimentations for entrepreneurship with a disruptive, personalised and mobile game-based learning ecosystem

Based on an unprecedented need of stimulating creative capacities towards entrepreneurship to university students and young researchers, this paper introduces and analyses a smart learning ecosystem for encouraging teaching and learning on creative thinking as a distinct feature to be taught and learnt in universities. The paper introduces a mashed-up authoring architecture for designing lesson-plans and games with visual learning mechanics for creativity learning. The design process is facilitated by creativity pathways discerned across components. Participatory learning, networking and capacity building is a key aspect of the architecture, extending the learning experience and context from the classroom to outdoor (co-authoring of creative pathways by students, teachers and real-world entrepreneurs) and personal spaces. We anticipate that the smart learning ecosystem will be empirically evaluated and validated in future iterations for exploring the benefits of using games for enhancing creative mindsets, unlocking the imagination that lies within, practiced and transferred to multiple academic tribes and territories.

Special education teachers' perspectives on teaching middle school students with severe emotional disturbance

The voices of special education teachers who educate middle school students with severe emotional disturbance (SED) have been largely unheard in the educational forum and in the discussion about raising the academic achievement of middle school students with SED. These students continue to have high attrition rates and low levels of academic achievement. This study described and analyzed the perspectives of five special education teachers regarding appropriate instructional strategies for educating middle school students with SED. It also explored these teachers' opinions concerning difficulties they experienced in raising the academic achievement of students with SED and some of the solutions for overcoming these challenges. The professional literature emphasizes the importance of teacher knowledge (Altrichter, Posch, & Somekh, 1996; Clandinin & Connelly, 1996) and also offers suggestions for appropriate instructional strategies for educating students with SED (Bauer, Keefe, & Shea, 2002; Heward, 2000; Kauffman, 2001; Polloway, Patton, & Serna 2001). ^ A qualitative case study was employed to describe and analyze the five participants' perspectives on teaching middle school students with SED. The sources of data collection were interviews, observations and analysis of documents. Data presentation was from the perspective of the participants in dialogue with the interpretations of the researcher and against the backdrop of the professional literature and the researcher's critical theory philosophy. One of the major themes that emerged from the analysis was the teachers' insistence on the students' need for discipline tempered with teacher nurturing and playfulness. One concern was the need for teacher training in current appropriate, research-based instructional strategies for educating students with SED. ^ As a result of this study, one of the recommendations made was for more rigorous standards of re-certification and professional development of certified teachers who educate students with SED. ^

Mechanistic studies on the degradation of gasoline oxygenates by advanced oxidation technologies and the reaction of 4-methyl-1,2,4-triazoline-3,5-dione with tetracyclopropylethylene

Gasoline oxygenates (MTBE, methyl tert-butyl ether; DIPE, di-isopropyl ether; ETBE, ethyl tert-butyl ether; TAME, tert-amyl ether) are added to gasoline to boost octane and enhance combustion. The combination of large scale use, high water solubility and only minor biodegradability has now resulted in a significant gasoline oxygenate contamination occurring in surface, ground, and drinking water systems. Combination of hydroxyl radical formation and the pyrolytic environment generated by ultrasonic irradiation (665 kHz) leads to the rapid degradation of MTBE and other gasoline oxygenates in aqueous media. ^ The presence of oxygen promotes the degradation processes by rapid reaction with carbon centered radicals indicating radical processes involving O 2 are significant pathways. A number of the oxidation products were identified. The formation of products (alcohols, ketones, aldehydes, esters, peroxides, etc) could be rationalized by mechanisms which involve hydrogen abstraction by OH radical and/or pyrolysis to form carboncentered radicals which react with oxygen and follow standard oxidation chain processes. ^ The reactions of N-substituted R-triazolinediones (RTAD; R = CH 3 or phenyl) have attracted considerable interest because they exhibit a number of unusual mechanistic characteristics that are analogous to the reactions of singlet oxygen (1O2) and offer an easy way to provide C-N bond(s) formation. The reactions of triazolinedione with olefins have been widely studied and aziridinium imides are generally accepted to be the reactive intermediates. ^ We observed the rapid formation of an unusual intermediate upon mixing tetracyclopropylethylene with 4-methyl-1,2,4-triazoline-3,5-dione in CDCl 3. Detailed characterization by NMR (proton, 13C, 2-D NMRs) indicates the intermediate is 5,5,6,6-tetracyclopropyl-3-methyl-5,6-dihydro-oxazolo[3,2- b][1,2,4]-triazolium-2-olate. Such products are extremely rare and have not been studied. Upon warming the intermediate is converted to 2 + 2 diazetidine (major) and ene product (minor). ^ To further explore the kinetics and dynamics of the reaction activation energies were obtained using Arrhenius plots. Activation energies for the formation of the intermediate from reactants, and 2+2 adduct from the intermediate were determined as 7.48 kcal moll and 19.8 kcal mol−1 with their pre-exponential values of 2.24 × 105 dm 3 mol−1 sec−1 and 2.75 × 108 sec−1, respectively, meaning net slow reactions because of low pre-exponential values caused by steric hindrance. ^

The effects of word prediction and text-to-speech technologies on the narrative writing skills of students with specific learning disabilities

This study investigated the effects of word prediction and text-to-speech on the narrative composition writing skills of 6, fifth-grade Hispanic boys with specific learning disabilities (SLD). A multiple baseline design across subjects was used to explore the efficacy of word prediction and text-to-speech alone and in combination on four dependent variables: writing fluency (words per minute), syntax (T-units), spelling accuracy, and overall organization (holistic scoring rubric). Data were collected and analyzed during baseline, assistive technology interventions, and at 2-, 4-, and 6-week maintenance probes. ^ Participants were equally divided into Cohorts A and B, and two separate but related studies were conducted. Throughout all phases of the study, participants wrote narrative compositions for 15-minute sessions. During baseline, participants used word processing only. During the assistive technology intervention condition, Cohort A participants used word prediction followed by word prediction with text-to-speech. Concurrently, Cohort B participants used text-to-speech followed by text-to-speech with word prediction. ^ The results of this study indicate that word prediction alone or in combination with text-to-speech has a positive effect on the narrative writing compositions of students with SLD. Overall, participants in Cohorts A and B wrote more words, more T-units, and spelled more words correctly. A sign test indicated that these perceived effects were not likely due to chance. Additionally, the quality of writing improved as measured by holistic rubric scores. When participants in Cohort B used text-to-speech alone, with the exception of spelling accuracy, inconsequential results were observed on all dependent variables. ^ This study demonstrated that word prediction alone or in combination assists students with SLD to write longer, improved-quality, narrative compositions. These results suggest that word prediction or word prediction with text-to-speech be considered as a writing support to facilitate the production of a first draft of a narrative composition. However, caution should be given to the use of text-to-speech alone as its effectiveness has not been established. Recommendations for future research include investigating the use of these technologies in other phases of the writing process, with other student populations, and with other writing styles. Further, these technologies should be investigated while integrated into classroom composition instruction. ^

Scaling geospatial searches in large spatial databases

Modern geographical databases, which are at the core of geographic information systems (GIS), store a rich set of aspatial attributes in addition to geographic data. Typically, aspatial information comes in textual and numeric format. Retrieving information constrained on spatial and aspatial data from geodatabases provides GIS users the ability to perform more interesting spatial analyses, and for applications to support composite location-aware searches; for example, in a real estate database: “Find the nearest homes for sale to my current location that have backyard and whose prices are between $50,000 and $80,000”. Efficient processing of such queries require combined indexing strategies of multiple types of data. Existing spatial query engines commonly apply a two-filter approach (spatial filter followed by nonspatial filter, or viceversa), which can incur large performance overheads. On the other hand, more recently, the amount of geolocation data has grown rapidly in databases due in part to advances in geolocation technologies (e.g., GPS-enabled smartphones) that allow users to associate location data to objects or events. The latter poses potential data ingestion challenges of large data volumes for practical GIS databases. In this dissertation, we first show how indexing spatial data with R-trees (a typical data pre-processing task) can be scaled in MapReduce—a widely-adopted parallel programming model for data intensive problems. The evaluation of our algorithms in a Hadoop cluster showed close to linear scalability in building R-tree indexes. Subsequently, we develop efficient algorithms for processing spatial queries with aspatial conditions. Novel techniques for simultaneously indexing spatial with textual and numeric data are developed to that end. Experimental evaluations with real-world, large spatial datasets measured query response times within the sub-second range for most cases, and up to a few seconds for a small number of cases, which is reasonable for interactive applications. Overall, the previous results show that the MapReduce parallel model is suitable for indexing tasks in spatial databases, and the adequate combination of spatial and aspatial attribute indexes can attain acceptable response times for interactive spatial queries with constraints on aspatial data.

What Teaching Strategies Can I Employ to Improve Student Achievement in the Addition of Fractions with Different Denominators?

The purpose of this action research was to determine what instructional strategies could be used to improve student achievement in fraction addition. An eighth grade intensive math class practiced multiplication facts and hands-on applications of fractions concepts for 2 months. Pretests/posttests were used to measure improvement in computation and understanding.

Evaluating the Effectiveness of Discrete Trial Procedures for Teaching Receptive Discrimination to Children with Autism Spectrum Disorders

Research has found that children with autism spectrum disorders (ASD) show significant deficits in receptive language skills (Wiesmer, Lord, & Esler, 2010). One of the primary goals of applied behavior analytic intervention is to improve the communication skills of children with autism by teaching receptive discriminations. Both receptive discriminations and receptive language entail matching spoken words with corresponding objects, symbols (e.g., pictures or words), actions, people, and so on (Green, 2001). In order to develop receptive language skills, children with autism often undergo discrimination training within the context of discrete trial training. This training entails teaching the learner how to respond differentially to different stimuli (Green, 2001). It is through discrimination training that individuals with autism learn and develop language (Lovaas, 2003). The present study compares three procedures for teaching receptive discriminations: (1) simple/conditional (Procedure A), (2) conditional only (Procedure B), and (3) conditional discrimination of two target cards (Procedure C). Six children, ranging in age from 2-years-old to 5-years-old, with an autism diagnosis were taught how to receptively discriminate nine sets of stimuli. Results suggest that the extra training steps included in the simple/conditional and conditional only procedures may not be necessary to teach children with autism how to receptively discriminate. For all participants, Procedure C appeared to be the most efficient and effective procedure for teaching young children with autism receptive discriminations. Response maintenance and generalization probes conducted one-month following the end of training indicate that even though Procedure C resulted in less training sessions overall, no one procedure resulted in better maintenance and generalization than the others. In other words, more training sessions, as evident with the simple/conditional and conditional only procedures, did not facilitate participants’ ability to accurately respond or generalize one-month following training. The present study contributes to the literature on what is the most efficient and effective way to teach receptive discrimination during discrete trial training to children with ASD. These findings are critical as research shows that receptive language skills are predictive of better outcomes and adaptive behaviors in the future.

Massive inclusion of digital technologies in schools : Argentinian young adolescents? appropriation of computers and the Internet in popular and middle classes

Since the implementation of the Programa Conectar Igualdad (PCI) (Connecting Equality Program) in 2010 in Argentina, numerous Social Science specialists started to research how massive ICT introduction in schools would radically affect teaching and learning processes, knowledge building and youth behaviour. Nevertheless, there is still not much empirical evidence showing the ways in which these technologies are appropriated. This situation discloses the need of placing research questions locally situated with regard to those potential changes. What existing access methods does PCI encounter? And how does its implementation participate in the design of personal and family heterogeneous trajectories of ICTs appropriation? How do the students themselves perceive the infl uence of PCI on their own technologic abilities and competence? How do knowledge and aptitudes associated to new digital media articulate with the knowledge manners promoted by the school format and institutionalism? How does the massive introduction of netbooks affect the interaction among different school actors (students-teachers)? What happens in other sociability and socialization spaces, such as the house and cybercafé?

Enlivening, Invigorating & Enhancing Science:This session explores learning from a range of Primary Science Teaching Trust projects focused on invigorating the experience of children, teachers and whole school communities with primary science.

This session will provide you with opportunity to find out what is being achieved and explore the implications for your own practice.

Gender Differences in Early Reading Strategies: a Comparison of Synthetic Phonics Only with a Mixed Approach to Teaching Reading to 4-5 Year-Old Children

A survey of primary schools in England found that girls outperform boys in English across all phases (Ofsted in Moving English forward. Ofsted, Manchester, 2012). The gender gap remains an on-going issue in England, especially for reading attainment. This paper presents evidence of gender differences in learning to read that emerged during the development of a reading scheme for 4- and 5-year-old children in which 372 children from Reception classes in sixteen schools participated in 12-month trials. There were three arms per trial: Intervention non-PD (non-phonically decodable text with mixed methods teaching); Intervention PD (phonically decodable text with mixed methods teaching); and a ‘business as usual’ control condition SP (synthetic phonics and decodable text). Assignment to Intervention condition was randomised. Standardised measures of word reading and comprehension were used. The research provides statistically significant evidence suggesting that boys learn more easily using a mix of whole-word and synthetic phonics approaches. In addition, the evidence indicates that boys learn to read more easily using the natural-style language of ‘real’ books including vocabulary which goes beyond their assumed decoding ability. At post-test, boys using the nonphonically decodable text with mixed methods (Intervention A) were 8 months ahead in reading comprehension compared to boys using a wholly synthetic phonics approach.

A Haptic System for Depicting Mathematical Graphics for Students with Visual Impairments

When teaching students with visual impairments educators generally rely on tactile tools to depict visual mathematical topics. Tactile media, such as embossed paper and simple manipulable materials, are typically used to convey graphical information. Although these tools are easy to use and relatively inexpensive, they are solely tactile and are not modifiable. Dynamic and interactive technologies such as pin matrices and haptic pens are also commercially available, but tend to be more expensive and less intuitive. This study aims to bridge the gap between easy-to-use tactile tools and dynamic, interactive technologies in order to facilitate the haptic learning of mathematical concepts. We developed an haptic assistive device using a Tanvas electrostatic touchscreen that provides the user with multimodal (haptic, auditory, and visual) output. Three methodological steps comprise this research: 1) a systematic literature review of the state of the art in the design and testing of tactile and haptic assistive devices, 2) a user-centered system design, and 3) testing of the system’s effectiveness via a usability study. The electrostatic touchscreen exhibits promise as an assistive device for displaying visual mathematical elements via the haptic modality.