Authentic assessments for learning

Students’ academic and personal problems in institutions of learning can be identified and resolved in a number of ways that are familiar to educational psychologists, special educators, school counselors, and educational researchers. Normally, students’ problems tend to be numerous, multifaceted and complex in nature and require an interdisciplinary approach to understand them adequately. This then calls for a variety of procedures to be employed when investigating and addressing students’ problems in schools.

These are studies that combine quantitative and qualitative research paradigms in an attempt to compare or contrast the findings and understand the presenting problem(s) more fully. A researcher may, for example, investigate the same problem in a two step wise fashion or strategy starting as an exploratory quantitative survey and ending as an in-depth qualitative case study. Mixed methods research designs also use a mixture of data collection approaches (e.g. tests, questionnaires, observations, interviews, documents, and projects) and adopt a wide range of data analysis techniques (both quantitative and qualitative). Investigators who use mixed method research designs also often report and interpret data and findings in different ways. In all these strategies, the data and findings are triangulted to confirm their validity. Mixed method research designs have several advantages and disadvantages but only three examples of each of these will be given here. The three main advantages of the strategy are that it: (1) incorporates the strengths of both qualitative and quantitative approaches; (2) provides a more comprehensive view of the problem or phenomena being studied; and (3) does not limit the data being collected. The major disadvantages or limitations are that it: (1) requires high-level expertise in both quantitative and qualitative methods to use it competently; (2) needs extensive data collection and resources; and (3) is prone to being used superficially such as claiming to have used several methods when in actual fact and reality only one was used. There are three main specific designs that are associated with the mixed method research approach and these are: (1) explanatory design - occurs when quantitative data are collected first followed by qualitative data collection; (2) exploratory design - whereby qualitative data are gathered first with quantitative data collection following later; and (3) the triangulation design – in which quantitative and qualitative data are collected simultaneously to provide a more comprehensive and complete set of data. As is the case with other research methods, the investigator’s decision and choice to use a mixed methods approach is often arrived at after a long and careful thought based on the consideration of a number of important factors such as the type/nature of problem to be researched, specific research questions or hypotheses to be probed, the feasibility of the research strategy, rationale or justification for using the method, and expertise in using appropriate data collection, analysis and interpretation techniques. It is pointless and redundant for eclectic investigators to use a research method

when it is not warranted.

In the past, student academic evaluations focused mainly on the assessment of learning (the quantity of knowledge and skills a student obtains as a result of attending school and receiving instruction from teachers – i.e quantifying what one gets from undergoing a course of instruction). This quantity was usually reflected in test/examination scores and grades as manifested on the school report or transcript. Emphasis was placed on the so-called summative norm-referenced assessments that were used to mark the end of an educational cycle / level as well as rank and compare students for various purposes such as offering them admission, scholarship or employment. By doing so, examinations dominated the scene in schools and educational systems became examination-oriented (Mundia, 2010). Both teachers and students became obssessed with coaching and preparation for examinations respectively. In this way, examinations undermined good teaching which emphasizes understanding.

On the contrary, authentic assessments for learning stress that student evaluations should help learners to understand and master the knowledge and skills that they receive through teaching. These evaluations include both formal criterion-referenced assessments as well as the informal formative assessments such as observations, experiments, interviews, portfolios, lesson studies, and assessments by the self, peers, and parents. There are no norms derived from the informal authentic assessments and the results cannot be used for comparison purposes. Despite this, these informal authentic assessments are seen or considered to be the key to meaningful learning based on understanding. They enable teachers and parents to identify the conditions and circumstances under which a student can maximize her/his potential to learn. Emphasis here is on assessing the learner holistically/globally for both academic and personal problems. The assessment results form the basis for improved teaching and learning. Though still relatively new and unknown, authentic assessments are already becoming well known in some developing countries (see Engelbrecht et al., 1999).

Sources of problems in learning mathematics Many students at all levels of education in developing countries have problems in learning mathematics. The causes of these difficulties are many and wide ranging. Five of the numerous broad factors appear to be outstanding. First, some students seem to be negatively influenced by the stereotype beliefs held by many people that mathematics is a difficult subject (Heward, 1996). Second, for a number of learners their problems appear to stem from unsatisfactory teaching and the resultant lack of experience of success (Mundia, 1996; 1998). Third, still for other students their difficulties seem to be linked to the procedures used in evaluating mathematics learners (Somerset, 1987; Murray, 1996). Fourth, there are also students who unfortunately may have a genuine specific learning disability in mathematics (; Thornton et al., 1983; Hall, 1994; Mercer, 1997; Bos & Vaughn, 2002). Fifth, poor performance in mathematics might also be attributed to inadequate funding of education which results in fewer teaching/learning resources and low quality of education (Kelly; 1986; 1991). The child described in the present triadic study (nick-named B) required the joint efforts of an educational psychologist / school counselor, one of the child’s parents (referrer) and a special educator, to solve. Dettmer, Thurston and Dyck (2002) discuss the viability and benefits of collaborative intervention strategy.

Development and persistence of math anxiety and phobia Students who do not perform well in mathematics often develop math anxiety and phobia. Math anxiety and phobia in the context of the present study refer to the unreasonable worries about and fear of mathematics. This condition can be severe and persistent if not treated effectively through either educational interventions (e.g. provision of remedial instruction, learning support, and individualized educational plans), or via counseling. There are several counseling / therapeutic techniques that are used in treating anxiety and phobia. They include rational emotive therapy (RET), implosive therapy, systematic desensitization, operant conditioning, modeling, cognitive restructuring, and behavior therapy. Fogiel (1989) and Thompson (2003) discuss most of these procedures in detail.

This mixed-methods study incorporated elements of the survey, case study and action research approaches in investigating the research problem. From the diagnostic test, an error analysis, and a think-aloud clinical interview, the study identified some of the child’s difficulties. The major presenting problems included: inability to use the four arithmetic operations (addition, subtraction, multiplication, and division) efficiently; not understanding the relationship between units, tens and hundreds; using any two of the four arithmetic processes (+, - , x, ÷) in combination within one operation; treating each column as a  separate problem; place value problems or wrong alignment of numbers; poor eye-hand coordination leading to dysgraphia; and short-term memory / memory lapses. The other problems that became apparent through this investigation and are implied in the findings include possible causal factors such as dyscalculia, dyslexia, low self-esteem, low self-efficacy, and math anxiety / phobia. Further assessment and research is recommended to probe and confirm the role of these variables in young learners with math difficulties such as student B, to gain additional insights. Future research should also be directed at examining the learning styles and study strategies in mathematics of young children with high support needs in this subject.