A PEDAGOGY OF TEACHING THE TEST Du Toit Erna, Department of Education, Sol Plaatje University, Kimberley & Du Toit Jacqueline, Student support Services, Wellness Centre, Central University of Technology,Welkom, South Africa: erna.dutoit@spu.ac.za Abstract Mathematics is undoubtedly an essential subject needed to equip learners in mastering many other subjects. The inability to comprehend mathematics has become a major issue relating to the decline in learners mathematical performance. The objective of good mathematics teaching should not be to "cover the curriculum" or as in the context of this research teach learners the test but to show learners how to explore mathematics. In focusing on a pedagogy that merely addresses the need to pass or obtain good marks the focus is largely on irrelevant and uninteresting set of learning objectives and not engaging for learners. In the context of this study evidence was gathered that mathematics in most cases were taught as a series of computations rather than a tool for solving open-ended and interesting problems. Moreover most learners were identified with a preference to the auditory learning style which implicated that learners are not actively constructing knowledge. The importance of relevance in teaching mathematics cannot be over-stated. Furthermore many learners disengage from learning mathematics because of an unsatisfactory pedagogy of coercion to force them into learning an unsatisfying curriculum such as only to improve the annual national assessment (ANA) mark. Therefor this study suggests a pedagogy that is more diversified to address a wider variety of learning styles and thus to improve the students' academic achievements in mathematics and enhance learning. Introduction The current status in many South Africa schools are that practically no learning is taking place during the year (Spaull,2013) and more over in Mathematics. A survey conducted by the National School Effectiveness (2013) revealed shocking results on the performance of grade 5 learners on ordinary calculations at a grade 2 level. The results revealed that 70% of learners from the quintile 1, 2 and 3 schools could not answer most of the questions. Despite of spending 500 extra hours teaching time, learners could still not master the arithmetic needed at this level. In researching for possible reasons to this phenomenon, the popular response was that many South African teachers have very low levels of content knowledge (Spaull, 2013). The South African Consortium for Monitoring Educational Quality (SACMEQ, 2011) stated that 32% of grade 6 math s teachers have desirable subject knowledge. Teachers hence cannot teach what they do not know. The same tendency was identified in certain parts of the grade 6 curriculum and revealed that only 46% of the teachers could answer the questions correctly and in comparison that 22% of grade 6 learners will answer it correctly. At this stage the argument is: If the teachers do not know, what is it that they teach and moreover what are the students learning from listening to their teachers. In conclusion many SA teachers have shocking low levels of content knowledge and learners are performing badly in mathematics. The reality is if the lack of content knowledge on the one side and the pedagogy to convey that knowledge on the other side is not addressed the longer learners will remain illiterate and innumerate (Spaull,2013). A new problem however has arouse in an attempt to raise the mathematics marks namely a pedagogy of teaching the test. This dichotomy in some instances can improve the marks but not necessarily improve mathematical knowledge or understanding. This lead to the research question: Can learners
learning styles and teachers teaching styles contribute to the weak performance of learners in mathematics? Learning styles Brown (2000) in Gilakjani and Branch (2012) defines learning styles as the manner in which individuals perceive and process information in a teaching learning situation. This indicates the choice that the individual makes of one learning style or condition over another. Learning styles can also be characterised as the cognitive, affective, social and physiological behaviours that serve as stable indicators of how they perceive and interact to the learning environment (Celce-Murcia, 2001 cited in Gilakjani & Branch, 2012). Celce-Murcia elaborates that learning styles is a general approach that students acquire to learn something new in a manner that he/she perceives, interacts with and responds to the environment. The three general learning styles that should be visible in the mathematics classroom are: visual, where learners think in pictures and learn best in visual images for example figures and models; auditory, where learners discover information through listening, interpreting and assimilating information by means of reading out aloud; and thirdly, the kinaesthetic learner that learns best through a hands on approach and favours interaction with the physical world by means of constructing knowledge on a flat surface or by means of three dimensional structures. Garner (2006) in Gilakjani and Branch views this type of learning as multiple intelligences that reflect a mixed view of personal tools that each individual possess. Individuals make sense of the new information in their own unique way and store it in such a way that they are able to retrieve it again. Different intelligences are of neutral value and not one is considered as superior to the other. Gathered from what was discussed in the previous paragraphs two aspects namely that learners perceive information in their own unique way and that current teachers in South Africa have a very low level of content knowledge lead to the main argument in this study is: How will the learning style of the learners be affected by the teaching style (pedagogy) of the teachers? Various studies have indicated that 20-30% of the learners are auditory; 40% visual and 30-40% are tactile/kinaesthetic or visual/ kinaesthetic. The incorporation of a variety of learning styles alone will however not solve the problem and is it important that time should also be spend on: the basic stimuli affecting each individual whether it is environmental, emotional, sociological, physiological and psychologically. What takes place at the individual level is essential. One should also be aware of what affects the learner s motivation, concentration and retention to be able to match it with a style that focuses on learning and what is perceived as difficult and new (Dunn & Griggs, 2007 cited in Boström, 2011). The problem of poor performance is also situated in a much broader context where learners are failing in large numbers and not completing the secondary grades in Mathematics (Becker, 2013). Further research into possible factors of the didactical interaction between learners and teachers is necessary to identify possible problems (Boström, 2011). Questions to be investigated are: Is there is not a need to expand educational strategies and an in depth didactic discussions of practical activities?; and are schools flexible enough in terms of student learning needs? International research on successful education highlight the following four aspects to why some educations systems are successful: the quality of a school cannot exceed the quality of its teachers; to improve outcomes is to improve teaching; high performance requires each learner to be successful; and that schools need good leaders (Barber & Mourshed,2007). Chau (1996) already stated this in 1996 that quality education needs quality teachers. Therefore teacher s competence is crucial for students academic achievement. If teachers
tend to teach as they themselves learn this may be one explanation of the difficulty learners have assimilating the information (Steinberg, 2005 in Boström, 2011). Teachers therefor should be aware of how learners are learning and of their own learning and teaching style (Boström, 2011). Research conducted in Norway revealed that education based on learning styles affects teacher s perceptions and their actions of competence (Boström, 2011). Teachers that bear learning styles in mind when they teach adapt themselves more often to students learning preferences and are more open to change. The more teachers are aware of learning styles the more they provide opportunities for addressing student s individual learning. Knowing how students learn is an important starting point for instruction both individually and in groups. Teachers should reflect on their own style to understand their own strategy that gives greater insight into their own and others behaviours and be aware of the repercussions it has on teaching (Steinberg, 2004) cited in Boström, 2011). To ensure success it is important: to identify individual profiles and group profiles and make suggestions on how to accommodate the learners; that each student becomes aware of his best way to learn; to encourage students to study according to their strengths; to propose individual study strategies rather than study skills (Whitley & Littleton, 2000 in Boström,2011). If the focus thus is on learning styles it will require a pedagogy to be taught that will accommodate all learning styles. Stensmo (2006) emphasises the importance of differentiation instruction to address the phenomena and the implications it has for teaching. Implications for teaching Research has indicated that students often fail because they are not exposed to didactic skills that will support or enhance their learning. The implications for teaching is that it should be a collaborative attempt that caters for a variety of learning experiences until all learning styles have been addressed. This however asks for the cooperation of different individuals or teams where certain concepts in various subjects can be integrated. Schools should assign enough time to the diversity of learning styles as well as innovation in this field. The main essence is to find a balance between the extremes and each learning dimension. To be able to achieve this in the teaching learning context in the mathematics classroom it is necessary to: provide a context where a variety of mathematic concepts can be addressed as well as the connection between relevant material and the experience of the learner; make use of figures and diagrams to support verbal information; make use of numerical as well as algebraic examples to illustrate abstract concepts; provide time for both active student participation and reflection on the material presented (Montgomery & Groat, 1996). It is common practice that learners will bring to the classroom a great diversity of learning styles. Not addressing or acknowledging the problem may lead to potential conflicts and misunderstandings that can undermine student learning. More over the acknowledgment of students preferred learning styles can empower the student (Randall, 1995; Grasha,1996 in Montgomery & Groat,1996). It is therefore recommended that the teachers be self-reflective on their pedagogical goals and strengths in their teaching. Teachers should also modify their teaching style to be framed within a broader conceptual context. Teachers must be aware that neither learning style nor teaching style is absolute. Moreover teachers must be attentive that it takes time and can be modified for different purposes in different classroom contexts.
Lastly teachers can be assured that it will be to the benefit of the class to gradually introduce class activities that substantially accommodate their learning style preference. McKeachie (1995) clearly states that the matching of teaching styles and learning styles is not the ultimate solution to solve all classroom conflicts. He refers to other factors such as classroom climate, previous background motivation, gender and multicultural issues that can influence the quality of learning. However being self-reflective and acknowledging the role of learning styles can make teaching more rewarding and enhance student learning at the same time. Pedagogical content knowledge Successful teachers draw from specialised knowledge that distinguishes them from only applying subject knowledge and general pedagogical principles and practices. Common practice often is the evaluation of general pedagogical practices regardless of the content knowledge that teachers convey. It is therefore assumed that these practices are instructionally effective despite the academic quality or the grade level being taught (Rowan, Schilling, Ball & Miller, 2001). Schulman (1986) in Rowan et al (2001) makes an analytical distinction between the teacher s subject matter knowledge and teacher s knowledge of pedagogy (PCK). The practice knowledge that Schulman refers to is used by teachers to guide their actions in in highly contextualised classroom setting. These actions entail how to structure and represent the academic content as well as making use of specific teaching strategies to address common conceptions, misconceptions, and difficulties that students encounter with learning. Teacher s mathematics knowledge plays a significant role in shaping the quality of their teaching. Moreover in many cases the Mathematics knowledge is also inadequately understood as well as the application of the mathematical knowledge. The endless concerns on student s basic mathematics are evidence that the teaching and learning of mathematics needs improvement. The standard of what should be learnt is possible if direct attention is paid to the practice of teaching. Especially in the context of this study where teachers lack the basic content knowledge and more over learners are exposed to the pedagogy of teaching the test. Various efforts of the past have shown that good instruction can make a difference (Ball, 2003). The effective application of the curriculum and going about standards in a responsible way depends on if the subject matter was understood. How students conceptualise mathematics is central to their capacity to perceive the information that was instructed. It is essential that the teaching learning context must be structured in such a way that students learn. Thus the improvement of students learning depends on skilful teaching and skilful teaching depends on capable teachers and what they know and can do. Moreover the quality of mathematics depends on the teacher s knowledge of the subject. Teachers that lack sound mathematical understanding and skill are often teachers that are graduates from the system. The learners from these circumstances become the adults and many become teachers with the same mathematics education of how they were taught. The goal therefor is not to produce teachers who know more mathematics but to improve learners learning. Teaching should thus be regarded as a professional practice and teachers must possess knowledge and skills beyond what is visible from the curriculum (Ball, 2003). Research has indicated that meaningful" learning produces better skill performance than rote learning. (The New York Times, 2013).
Research methodology The positivistic and post-positivistic paradigms were chosen to capture possible reasons why grade 6 learners perform badly in Mathematics. Qualitative and quantitative methods were employed to gain insight into the problem (Pietersen & Maree, 2007). In an attempt to seek answers why Maths learners in grade 6 perform badly a research project in the Lejwelapitswa district was identified. A research team was identified which consisted of education researchers and a psychometrist. A variety of research instruments such as class observations, interviews with teachers and questionnaires on teacher teaching styles and learners learning styles, TriMaths (basic maths, maths vocabulary, study orientation);gsat (number series, pattern completion, number problems) and a document analysis (work books, teaching portfolios, assessment activities, results of ANA tests) were used to collect data from 11 teachers and 140 learners. This section of the research focused on the learning styles and teacher styles. Results and discussions The data from the learners learning styles revealed that the most (63) were auditory learners, 41 were tactile learners and 29 were visual learners. The data from the teaching styles revealed that the teachers prefer analysis to rote learning but do not focus on practical applications (algorithms/recipe procedures); teachers prefer analysis to rote learning and focuses on familiar applications (apply algorithms on familiar problems); teachers prefer to have students learn through hands on activities completed in a collaborative way. It seems that a mismatch exists between the need of these learners and the teachers and the failure to acknowledge and solve the potential conflicts and misunderstandings that undermine student learning. These individual differences in learners have certain implications for the school or learning environment. It is therefore necessary to structure a learning environment to develop a variety of ways on how to process information. It is not possible to accommodate each individual but by means of changing the way you teach you can accommodate learners on a regularly basis. McCarthy (1997: 49) alludes that if the specific preference is addressed learner s high order thinking skills are stimulated which implies that learners have more control over how they learn. Conclusion Matching teaching style and learning style is not a cure to solve classroom conflicts. In the case of this study the manner how instruction was conducted simply did not accommodate most of the learners or engage them during the learning process. Evidence gathered indicated that mathematics in most cases was taught as a series of calculations rather than a tool for solving open-ended and interesting problems. The slight improvement in the performance of the learners ANA marks has prompted some progress but unfortunate testing was overemphasized and misused in the schools. Test-driven changes indicate an improvement but despite of this, schools are not up to par with the high-performing nations in maths, science and even literacy instruction.
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