Visual Structure Editing of Math Formulas

Math formulas can be large and complex resulting in correspondingly large and complex LaTeX math strings for expressing them. We design operations to visually edit the typeset LaTeX formulas. The operations are invoked via the formula\u27s control points, which are created as a way to specify an operation associated with the point\u27s location relative to a symbol in the formula. At the control points, formulas can be extended in multiple ways, LaTeX can be inserted locally by typing, an existing formula can be inserted, or part of the formula itself can be moved to that point. Parts of formulas can be selected by clicking on a symbol or dragging a rectangle over an area in the formula, and the subtree for the selection can be replaced, deleted, moved to another point in the formula, or lifted out of the formula into a chip floating above the canvas. Formula chips can be used as arguments to operations, including a set of existing formulas provided in a symbol palette. Operations can be performed either by making a selection, selecting a control point operation, and then specifying an argument, or by dragging an argument to one of the control points in the formula. We perform an online formula editing experiment to examine if these visual editing operations can be used to reduce the time and actions spent in order to make edits to formulas. With 35 participants completing 18 formula editing tasks split between 3 input conditions of LaTeX only, Visual only, or LaTeX and Visual, we find that on average participants spend the least amount of time on the editing tasks when both editing capabilities are available

Towards semantic mathematical editing *

Currently, there exists a big gap between formal computer-understandable mathematics and informal mathematics, as written by humans. When looking more closely, there are two important subproblems: making documents written by humans at least syntactically understandable for computers, and the formal verification of the actual mathematics in the documents. In this paper, we will focus on the first problem. For the time being, most authors use T E X, L A T E X, or one of its graphical frontends in order to write documents with many mathematical formulas. In the past decade, we have developed an alternative wysiwyg system GNU T E X MACS , which is not based on T E X. All these systems are only adequate for visual typesetting and do not carry much semantics. Stated in the MathML jargon, they concentrate on presentation markup, not content markup. In recent versions of T E X MACS , we have started to integrate facilities for the semantic editing of formulas. In this paper, we will describe these facilities and expand on the underlying motivation and design choices. To go short, we continue to allow the user to enter formulas in a visually oriented way. In the background, we continuously run a packrat parser, which attempts to convert (potentially incomplete) formulas into content markup. As long as all formulas remain sufficiently correct, the editor can then both operate on a visual or semantic level, independently of the low-level representation being used. An important related topic, which will also be discussed at length, is the automatic correction of syntax errors in existing mathematical documents. In particular, the syntax corrector that we have implemented enables us to upgrade existing documents and test our parsing grammar on various books and papers from different sources. We will provide a detailed analysis of these experiments

Online assessment through moodle plataform

The differences between secondary education and Higher Education (HE) are numerous, both in terms of teaching methodologies and as well as evaluation/validation procedures. Until a few years ago, the HE assessment practices were reduced, with some exceptions from practical/laboratory curricular units, to written exams, carried out on the same day and at the same time by all, or, at most, two frequencies (tests) over the course of the semester or year. With growing concerns in terms of learning outcomes and students’ success, globalisation and the massification of education, several alternative models have been tested, both in terms of teaching/learning methodologies (flipped, project-based, “blended”, among others) and assessment practices (portfolio, continuous, segmented, formative, and others). The fast development of electronic devices has been promoting the development and sharing of several digital educational tools and their use seem to be a good choice to promote actual students’/professors’ interaction and corresponding socialization, even in some assessment tasks. In this particular case, online activities can be transformed into powerful self-assessment resources for students, stimulating reflection and promoting independent learning. Moodle, as an open Learning Management System (LMS), has all the requisites and potential features to be a fine supporting tool to several activities, specifically to assessing ones. In this paper, we will briefly describe Moodle potentialities, with some application examples based on literature review and present the work developed on several Mathematic curricular units from different schools of the Polytechnic of Porto, where Moodle is used as an online assessment tool, to promote a continuous/segmented model with specific and different activities designed for each course.info:eu-repo/semantics/publishedVersio

Mathematical model and software for investigation of internal ballistic processes in high-speed projectile installations

This paper describes a software package that allows to explore the interior ballistics processes occurring in a shot scheme with bulk charges using propellant pasty substances at various loading schemes, etc. As a mathematical model, a model of a polydisperse mixture of non-deformable particles and a carrier gas phase is used in the quasi-one-dimensional approximation. Writing the equations of the mathematical model allows to use it to describe a broad class of interior ballistics processes. Features of the using approach are illustrated by calculating the ignition period for the charge of tubular propellant

Solving tasks from linear programming using GeoGebra

Each student from every new generation, soon or latter, encounters difficulties when solving mathematical problems, even the best ones. Some students have problems with mastering the material, others with solving homework assignments, others have problems with quickly forgetting what they have learned, others think that they would lose a lot of time for solving the task and, in the end, they might get an incorrect result, which reduces their motivation for finding a solution and so on. Mathematical content that is presented graphically and mathematical problems whose solution may be obtained graphically remains best in the student’s memory. Moreover, if an appropriate software is used during the solving of a given mathematical problem, if its graphical representation is precise enough and the final solution can be clearly seen from it, then most of the stumbling blocks for students will be surmounted. In this paper we will present the graphical solution method for linear programming problems using GeoGebra. The software allows graphic editing to be done in a quick and simple way which is very important for students

Analysis of Conceptual, Factual, Principle, and Skill Errors Based on Students' Thinking Ability: How is it Connected to Science Learning?

This study aims to describe misconceptions about concepts, facts, principles and skills based on thinking skills that were made by fifth grade students at SD Inpres 6 Lolu in solving multiplication fraction problems. This research is descriptive qualitative research which is based on the problem solving steps put forward by Polya. The research subjects were taken by 6 students based on the level of thinking skills determined using the Standard Deviation (SD) calculation. Data collection methods used are test and interview methods. The study's findings reveal that students make different types of errors based on their thinking ability in the process of solving mathematical problems. These errors can be categorized into four main areas namely: factual errors, conceptual errors, skill errors, principal errors. In summary, the study highlights that students' thinking ability is closely linked to the types of errors they make when solving mathematical problems. These errors primarily involve faulty facts, conceptual misunderstandings, skill-related issues, and principal errors. Understanding these patterns of errors can guide educators in developing targeted interventions to improve students' mathematical problem-solving skill

A Numerical approach for Ship Energy Analysis

This master´s thesis has focused on energy analysis of ships and ship designs by developing a tool and a method for numerical analysis for evaluation of emissions, efficiency and costs. The overall focus has been on making the tool simple and understandable for the concerned user. This has been done by combining simple inputs filled in by the user and advanced inputs by predefined, editable values. The tool has been tailored for a passenger vessel, a live fish carrier and a double-ended car ferry but can also easily be modified to other vessel types such as offshore wind vessels and bulk carriers. The tool is presenting CO2, NOx, CO, PM and SO emissions as well as carbon footprint from combustion and production of fuels. Lifetime costs estimations for the systems analyzed in the tool are also included. Diesel, LNG, Hydrogen and batteries are energy carriers analyzed in the tool. The tool also provides a mean for comparing different powertrains and energy carriers at an early stage of a design process, in order to select the best available concept and/or to possibly exclude some of the powertrains evaluated, before entering a detailed design phase. It is developed a methodology where the four disciplines ship design, route studies, engine setup and costs are included. By adding precise values for selected inputs in the four disciplines the result is expected to be relatively exact. The relative difference between the engines studied are in order with the market trends. The tool and results have been compared with observations made onboard NFT Steigen in Vestfjorden, Norway February 2018. A study trip to Tokyo, Japan has played a role to the master´s by observations and data collected. The amount of data collected from the industry used to present state-of-the-art engine curves has made the tool modern and representative for new technology. Batteries are found to be the 40% cheaper and 57% more efficient than diesel engines for double-ended car ferries operating shorter crossings along the Norwegian coast. By use of the tool it has also been shown why batteries are less favorable for cruise ships and live fish carriers due to charging time, costs and weight. This report does not include studies or discussions of availability of materials used in batteries or limitation of production. Hydrogen still face challenges regarding several factors such as infrastructure, rules and regulations, costs, availability and public awareness. The tool can be used to analyze the effect of cost reductions of fuel cells and hydrogen and improved efficiency. By doing this, it has been shown that hydrogen can compete with traditional fuels such as LNG and diesel in the future. By use of hydrogen produced from renewable energy, the carbon footprint from hydrogen can be kept low. To ensure that the tool stays a state-of-the art aid for analyzing ship emissions and efficiency, the data and content has to be constantly updated. Several add-ins such as rest-heat-recovery, carbon footprint from production of engines and an engine optimization tool will, if added to the tool, improve the tools functionality.Oppgåva har fokusert på energianalyser for skip og skipsdesign ved å utvikle eit verktøy og ein metode for numerisk analyse av utslepp, effektivitet og kostnad. Fokuset har vore retta mot å sette saman eit verktøy på ein enkel og brukarvennleg måte. Ved å kombinere enkle innstillingar som brukaren sjølv må fylle inn og avanserte innstillingar som er førehandsinnstilte men moglege å endre har verktøyet vorte handterbart for brukarar med meir eller mindre erfaring innanfor fagdisiplinane. Verktøyet har vorte skreddarsydd for eit passasjerfartøy, ein brønnbåt og ei ferje, men kan også lett modifiserast til bulkskip, offshore-vind fartøy og fleire. Verktøyet reknar ut CO2-, NOx-, CO-, PM- og SO-utslepp. Det finn også karbonfotavtrykket frå produksjon, transport, mellomlagring og forbrenning av dei ulike drivstoffa. Levetidskostnadar er også utrekna. Diesel, flytande naturgass, hydrogen og batteri er dei fire energiberarane som er inkluderte i verktøyet. Dette er også eit grunnlag for å samanlikne forskjellige energioppsett og energiberarar tidleg i designprosessen, for å best kunne velje det mest ideelle konseptet og/eller om mogleg å kunne ekskludere nokre av alternativa, før ein går vidare i detalj-prosjektering av skipet. Det er utvikla ein metode der dei fire disiplinane skipsdesign, rutestudier, energisystemoppbygging og kostnad er inkludert. Ved å legge inn eksakte verdiar for innstillingane er det forventa relativt eksakte resultat. Den relative skilnaden mellom dei forskjellige energisystema stemmer også overeins med dei forventa trendane i moderne energiteknologi. Verktøyet og resultata har vorte samanlikna med observasjonar gjort om bord på brønnbåten NFT Steigen i Vestfjorden, Norge i februar 2018. Ein studietur til Tokyo, Japan utført oktober 2017 har også spela ei viktig rolle for utviklinga av verktøyet gjennom observasjonar og datainnsamling. Mengda av data samla inn gjennom industrien for å anvende moderne effektivitetskurver har gjort verktøyet moderne og representativt for nyare motorteknologi. Batteriteknologi har vist seg å vere 40% billegare å 57% meir effektivt enn dieselmotorar for bilferjer i operasjon langs Norskekysten i følgje verktøyet. Ved å bruke verktøyet, har ein også vist at for eksempel brønnbåtar og cruiseskip vil ha utfordringar med å nytte batteri grunna ladetid, kostnad og vekt. Rapporten inkluderer ikkje studiar eller diskusjonar rundt materiale som er viktige for å produsere batteri, og kor vidt denne produksjonen er berekraftig eller ikkje. Hydrogenteknologi har framleis ein veg å gå når det kjem til infrastruktur, reglar og retningslinjer, kostnad, tilgjengelegheit og allmenn aksept. Verktøyet kan verte brukt til å analysere effektane av kostnadsreduksjonar for brenselceller og hydrogen og forbetra effektivitet. Ved å gjere desse analysane har det vorte avdekka resultat som indikerer at hydrogen kan konkurrere med tradisjonelle drivstoff. Ved å anta at hydrogen er produsert ved fornybarteknologi, får ein også eit relativt lågt karbonfotavtrykk. For å sikre at verktøyet opprettheld sin status som moderne og representativt må datasetta regelmessig oppdaterast. Forskjellige tilleggsfunksjonar som restvarmeutnytting, karbonfotavtrykk frå produksjon av energisystema og eit motoroptimaliseringsverktøy vil kunne gjere verktøyet endå meir funksjonelt.Masteroppgåve i energiMAMN-ENERGENERGI39

Developing interactive e-contents for a mathematic Ersmus+ Project: challenges and experiences

Stimulating students for learning is a regularly recurring theme that never seems finished, remaining in the frontline of teachers’ day to day struggle, and this recurrent factor is exponentiated when the subjects are directly related with Mathematics. In November 2018 the European Project EngiMath started work the development of a common Mathematics course for engineering students from the 6 countries of the consortium – Estonia, Ireland, Poland, Portugal, Romania and Spain. This course will be an online course with all the usual features and e-contents, however the project partners have been particularly focused on the pedagogical features and real digital competences when developing all the materials and interactive e-contents. An exhaustive search has been developed for the best way to build interactive content that would stimulate students to improve their basic mathematical skills, dealing with all the time and financial constraints, common to European higher education. This paper will describe, in a detailed way, all the steps of the construction of the theoretical contents, in English, which are the basis of the course proposed by the project and that are now being translated to each of the five distinct mother languages to avoid the frequent interpretation misleading problems for students and other cultural hitches. These e-contents are based on the construction of SCORM packages (Shareable Content Object Reference Model) for the Moodle platform, created over animated presentations to promote students’ interaction and avoid drop out behaviours.info:eu-repo/semantics/publishedVersio

Spreadsheet-Based Sudoku as a Tool for Teaching Logical Deduction

Drawing on the contributions of two recent studies by Sugden (2007) and Luterbach, Rodriguez, and Milling (2010) in Spreadsheets in Education, this study illustrates that Excel-based Sudoku is an effective tool for teaching logical deduction. This study also illustrates some essential Sudoku techniques, all based on logical deduction. Relevant information from the Sudoku grid is extracted by using Excel features, thus making it easier for students to explore opportunities to apply suitable Sudoku techniques throughout the solution process