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Examination of the literature on methodologies for verifying and validating complex computer-based Problem Solving Systems led to a general hypothesis that there exist measurable features of systems that are correlated with the best testing methods for those systems. Three features (Technical Complexity, Human Involvement, and Observability) were selected as the basis of the current study. A survey of systems currently operating in over a dozen countries explored relationships between these system features, test methods, and the degree to which systems were considered valid. Analysis of the data revealed that certain system features and certain test methods are indeed related to reported levels of confidence in a wide variety of systems. A set of hypotheses was developed, focused in such a way that they correspond to linear equations that can be estimated and tested for significance using statistical regression analysis. Of 24 tested hypotheses, 17 were accepted, resulting in 49 significant models predicting validation and verification percentages, using 37 significant variables. These models explain between 28% and 86% of total variation. Interpretation of these models (equations) leads directly to useful recommendations regarding system features and types of validation methods that are most directly associated with the verification and validation of complex computer systems. The key result of the study is the identification of a set of sixteen system features and test methods that are multiply correlated with reported levels of verification and validation. Representative examples are: • People are more likely to trust a system if it models a real-world event that occurs frequently. • A system is more likely to be accepted if users were involved in its design. • Users prefer systems that give them a large choice of output. • The longer the code, or the greater the number of modules, or the more programmers involved on the project, the less likely people are to believe a system is error-free and reliable. From these results recommendations are developed that bear strongly on proper resource allocation for testing computer-based Problem Solving Systems. Furthermore, they provide useful guidelines on what should reasonably be expected from the validation process.

A research report submitted in partial fulfilment of the requirements for the degree of Master of Science in Education to the Wits School of Education, Faculty of Science, University of Witwatersrand, Johannesburg, 2017 / This research problematised the teaching and learning of the grade 8 topic of simplifying algebraic expressions via the errors and misconceptions learners’ show on that topic. The study conducted at a secondary school in Johannesburg identified the nature of grade 8 learners’ errors and misconceptions on simplifying algebraic expressions. A teaching intervention through using those errors as resource to help learners reduce them was undertaken. There was an implementation of discovery learning as an intervention strategy to help learners to explore algebraic concepts with the minimum involvement of the researcher. The researcher used constructivism, sociocultural learning and variation theories since these theories affect the learners learning of algebra. The researcher used an interpretive paradigm which is concerned about the individuals’ interpretation of the world around them. Purposive and convenience sampling were used in the study. Data was collected using a sample of thirty grade 8 learners. The learners wrote a pre-test as one of the assessment task in the study. The purpose of the pretest was to identify learners’ errors on simplifying algebraic expressions. After the learners’ errors were identified and analysed, the researcher conducted a semi-structured, focus group interview with six learners in the study. The selection of the interviewees depended on the type and frequency of errors they have displayed in their pre-test scripts. The purpose of the interview was to investigate the reasons behind the learners’ errors as identified in the pre-test. An intervention strategy which implemented guided discovery learning was employed to learners with the use of the identified errors as a resource to help learners reduce them. After the intervention, the learners wrote a post-test to check if there was an improvement in learners’ performance after the intervention. Pre- and post-tests results were analysed for errors revealed by learners. The teaching intervention periods were introduced to create learning opportunities for learners. The findings of the study revealed that before intervention learners encountered a lot of difficulties when simplifying algebraic expressions but the learners’ performance improved after the intervention. The recommendations of the study are, teachers should welcome learners’ errors in teaching and learning of mathematics and use them as a resource to help learners reduce them in solving mathematical problems Key words: Learners’ errors, misconceptions, simplification of algebraic expressions. / XL2018

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The two-trial concept identification task is particularly appropriate for studying inferential capabilities of young children. When instances are presented in specified ways, the correct concept may be determined regardless of whether it occurs on both, only one, or on neither of the two trials. In addition, when attributes are dimensional in nature and limited to two values per dimension, information about one value is information about the other value. Previous experimenters have used the two-trial inference problem to study the child's ability to infer a conjunctive concept (Huttenlocher, 1964, 1967), to infer a single value from two dimensions (Scholnick, 1970, 1971a, b, c; Daehler, 1972), and to infer a single attribute from one dimension (Daehler, 1972). Training and stimulus materials were varied in the present experiment to study their influence on the child's processing of dimensionalized values in an inference task.

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