Assessing Low-attaining Pupils in Arithmetic Word Problem Solving

This paper describes a standing alone computer based assessing system called ASSA (Adaptive System for Student Assessment), able also to be a part of a larger intelligent tutoring system. It is designed to support the assessment of pupils of age 8-12 who show a very low performance in solving simple arithmetic word problems. The main aim of the system is to tackle the lowattaining student’s ability to state what calculation should be used in order to solve a practical problem, involving the operation of addition or subtraction. The system uses any of the models of the operation and in any appropriate context and is able to interpret the answer. The main purpose of the underlying research is to study the difficulty a computer system faces to adapt to the student’s individualities concerning his learning preferences, his real learning strengths but also his current motivational state. INTRODUCTION One of the challenges for the application of artificial intelligence (AI) to education is the introduction of AI tools in everyday classroom school life. Two questions are included in the concept of didactics, according to the classical theory of Bildung (Klafski 1963), namely what to teach and how to teach. One of the requirements for a successful AI educational tool is that to be adaptive it must have a wide range of instructional strategies (Ohlsson, 1987). ITSs need to represent different teaching strategies so that most suitable one can be applied to a particular student, or in a particular situation. (Ohlsson, 1987). A teaching strategy is responsible for the selection of the appropriate presentation and assessing methods, and for sending them to the interface administrator, where they become concrete interactions with the student. Today’s ITSs have very limited pedagogy and underpinning models of learning and teaching. Most AI researchers just put together different pedagogies in order to take decisions about teaching styles. However there is an increased emphasis on student-centred learning, learning through inquiry, as opposed to a more didactic or drill-and-practice approach that many ITSs favour. If ITSs don’t have a foundation for didactic tutoring they have an even less principled approach to these styles. They lack the ability to tutor flexibly, to adopt different teaching styles and strategies when appropriate, and to permit students to use different learning styles. Such systems moreover cannot assist the low-attaining students to advance in their learning.Some researchers are still producing ITSs, trying to push into more complex words more complex pedagogies within the ITS framework, really a very tough objective to succeed. In this paper an intelligent assessing system, called ASSA is presented, having the general structure of an ITS. ASSA is designed to assess students of elementary school who show low performance in arithmetic word problem solving. In order to teach low-attainers in mathematics there is the need of the existence of an individualised curriculum, in other words the use of a teaching strategy in accordance with the student’s strengths (Haylock, 1991). A first aim of the system is to be able to adapt its performance to the student’s knowledge state and mainly to his individual characteristics and strengths, using different appropriate dynamically generated assessing strategies. A second aim of the system is to show motivation-based tactics as defined by Malone and Lepper (1987) and Keller (1983) and become a motivational competent tutor as suggested in (Lepper, Woolverton, Mumme, & Gurtner, 1993). In the next paragraphs we will consider ASSA’s knowledge representation and architectural ideas which permit to the system to adapt low-attaining student’s behaviour in order to find the best performance with her. THE DOMAIN ASSA assesses the student’s understanding of a major objective of numeracy in today’s word, namely whether he knows what calculation to choose, even if she has to use a calculator, for the whole range of numerical situations which might encountered in everyday life. The system asks the student to solve simple problems of addition and subtraction, expressed verbally, keeping the quantities of the problem ‘situated’, according to what can be called the objectives-and-assessment approach: specify a sequence of objectives to be attained by the pupils, assess the pupils’ current attainment against these objectives, and then design a learning program to move them forward. (Duncan, 1978; Ainscow and Tweddle, 1979). The objectives-and-assessment approach for mathematical low-attaining pupils can only be endorsed if the target objectives are realistic and relevant. They must be reasonable targets for the pupils concerned to aim for, given the teacher’s judgements about their abilities and intellectual deficiencies, and they must be relevant to the real needs of the pupils in the world in which they live and in which they are growing up (Haylock, 1991),. Greeno and his colleagues have considered a new schema to categorise basic problems of addition and subtraction, based to their semantic relations. According to this they distinguished three main categories of verbal arithmetic problems, problems of change, composition and comparison. Each of these three categories is further subdivided in different types of problems according to which is the quantity in demand and whether the problem is a problem of augmentation or reduction (. (Duncan, 1978; Ainscow and Tweddle, 1979) In ASSA, a similar analysis has been followed, proposed by Haylock (1991), considered as more relevant to the real needs of the low-attainers, where six different categories of contexts (sets of things, money, length and distance, weight, capacity and liquid volume, time) are used. According to the above analysis six models have been considered for addition and subtraction (aggregation, augmentation, partitioning, reduction, comparison, inverse of addition) and have been identified thirty-four classes of problems, that relate contexts with models in an appropriate way. Following this analysis the system is concerned only with assessing the appropriate operation for a calculation which might arise in the chosen contexts.