Computer Aided Assessment of Mathematics Using STACK

Abstract

Assessment is a key component of all teaching and learning, and for many students is a key driver of their activity. This paper considers automatic computer aided assessment (CAA) of mathematics. With the rise of communications technology this is a rapidly expanding field. Publishers are increasingly providing online support for textbooks with automated versions of exercises linked to the work in the book. There are an expanding range of purely online resources for students to use independently of formal instruction. There are a range of commercial and open source systems with varying levels of mathematical and pedagogic sophistication. History and BackgroundAssessment is a key component of all teaching and learning, and for many students is a key driver of their activity. Computer aided assessment (CAA) has a history going back over half a century, for example (Hollingsworth 1960) reports a "grader" programme which automatically checked some aspects of students' computer programmes. "We are still doing considerable hand filing of punched cards at this stage. This large deck of cards which includes the grader program is then run on the computer. Our largest single run has been 106 student programs covering 9 different exercises." By the mid-1960s computers were being used to teach arithmetic, e.g. (Suppes 1967), and by the 1980s there were a number of separate strands of research in this area including the artificial intelligence (AI) community, e.g. (Sleeman and Brown 1982). The ambitious goals of such artificial intelligence-led systems have only been achieved in confined and specialized subject areas. These difficulties were acknowledged early, for example in their preface to (Sleeman and Brown 1982).

Advantages of Using Automatic Formative Assessment for Learning Mathematics

“…Research centers and universities have developed systems that are able to process openended answers from a mathematical point of view and to establish if they are equivalent to the correct solutions, in order to widen the possibilities of student interaction with the digital tools. Example of similar Automatic Assessment Systems (AAS) are CALM, developed by the Heriot-Watt University in the programming language of Pascal [9]; STACK, developed by the University of Edinburgh and relying on the Computer Algebra System (CAS) Maxima for its Mathematics capabilities [10]; Moebius Assessment, developed by the University of Waterloo and running on the engine of the Advanced Computing Environment (ACE) Maple [11]. By Exploiting programming languages or mathematical packages, these AASs allow instructors to build interactive worksheets based on algorithms where answers, feedbacks and values are computed over random parameters and can be shown in different representational registers.…”

Про Засоби Сдо Moodle Для Підготовики Навчальних Матеріалів Для Курсів Хімічного Та Фармацевтичного Спрямування

“…Суттєвою перевагою СДО Moodle є можливість розширення функціональних можливостей системи за допомогою зовнішніх додатків (https://moodle. org/plugins/), що забезпечує адаптацію даної СДО до особливостей навчального процесу при викладанні спеціальних дисциплін та курсів [6][7][8][9][10][11][12] Висновки. В роботі представлено результати авторів щодо удосконалення процесу налагодження СДО Moodle для підготовки навчальних матеріалів з хімічних та фармацевтичних дисциплін, що містять хімічні формули та схеми реакцій.…”

A design science research methodology for developing a computer-aided assessment approach using method marking concept

“…However, the software packages for mathematical assessment, have been developed are to implement the partial credit concept. These software are used to design through questions, collected answers and assessed them in the same way (Beevers et al 1999;Jones 2008;Livne et al 2007;Passmore et al 2011;Sangwin 2012). In these cases, to implement partial credit concept, MSQs have been redesigned by breaking them into sub questions that require only one step to solve thereby enabling partial credit concept implementation.…”

“…For the learners the assessment is the most significant activities that influence their approach to learning (Price et al 2011;Sangwin 2012). There are three well known types of assessment (namely summative, formative and diagnostic) in education; however the focus of the study is limited to formative assessment that is used to check current learners' status; where they aim to head and how to reach their targets (Wiliam 2011).…”