In my opinion, for mathematics problems, there are usually alternative paths towards their solution. Not all problems in mathematics have neat and exact solutions. As a result, students of different learning styles can approach a required solution from different angles. However, they need the teachers’ assistance for them to get to the solution. Various scholars gave different opinions on how mathematics teachers can assist students of varying learning styles to improve on their learning.
According to McLeod (2007), teachers should design instructions that offer students best opportunities to learn in their preferred manner. Mkonto (2015) supported by reiterating that teachers should develop balanced strategies. A balanced strategy according to Mkonto is one that accommodates the various learning styles displayed in the classroom. However, Mkonto thought that there is need for teachers to sometimes create intentional mismatches between teaching strategies and students’ learning styles so that students are forced to practise using their less preferred learning styles.
Sarasin (1999) outlined four steps that a mathematics teacher should follow in order to effectively assist students of different learning styles. According to Sarasin, the mathematics teacher should begin by assessing his or her own learning style. The teacher then assesses his or her students’ learning styles. He or she checks if his or her learning style matches the learning styles of his or her students. The third stage is when the teacher analyses and evaluates his or her teaching style. This stage is done in order for the teacher to match his or her teaching style with the students’ learning styles. In the fourth and final stage, the teacher plans an instruction that accommodates the students’ learning styles.
Evans and Sadler-Smith (2006) suggested some strategies which can be used by mathematics teachers when they teach their students. The two scholars suggested that when teachers teach according to students’ learning styles they should be sensitive to the students and employ learner-centred strategies. Teaching strategies should offer choice and flexibility to the students. According to Evans and Sadler-Smith, there are benefits for both matching and mismatching teaching strategies with students’ learning styles. Therefore teachers should use a variety of teaching styles. Those scholars thought that when teaching students according to their learning styles, the students should be made aware of their learning styles and be
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encouraged to learn in their less preferred learning styles. Evans and Sadler-Smith also suggested that teachers create suitable learning environments in which the aims of the learning programme are clearly stated and guidelines for the assessment requirements are given to students in advance. The scholars further advised that the teachers should avoid labelling their students as it may have negative effects on the students’ self-esteem.
According to the two scholars, the effects of culture on the development of learning styles should not be overlooked. Hence teachers were advised by the two scholars to properly guide their students so that culture does not affect the students negatively. Students should be allowed to discuss in groups. Evans and Sadler-Smith thought groups encourage diversity in learning. As a result, they encouraged teachers to take advantage of group work so that students learn from their peers. They also emphasised on the need for mathematics teachers to develop the students’ meta-cognitive skills.
Kolb (1984) suggested learning activities that can be used by mathematics teachers to assist students according to their learning styles. The activities were given under the classes of learners suggested under Kolb’s experiential learning styles model. Table 3.1 shows the classes of learners and the suggested learning activities.
Table 3.1: Kolb’s classes of learners and suggested learning activities Class of learners Suggested learning activities Convergers Performing technical tasks
Experimenting
Simulations
Laboratory assignments
Divergers Group discussions
Collecting information
Brainstorming
Field trips
Assimilators Reading notes and textbooks
Attending lectures
Analysing theoretical models
Doing independent research
Watching demonstrations
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Accommodators Exploring new experiences
Using trial and error
Hands-on
Experimenting
According to Kolb and Kolb (2013), each class of learners expect a mathematics teacher to behave in a particular way. In order to make sure that all the four learning styles displayed by the students in a mathematics class are catered for, the mathematics teacher should take four different roles. The four roles that the mathematics teacher should take are the following:
coach, facilitator, subject expert, standard setter and evaluator.
Mathematics teacher as a coach
According to Kolb and Kolb (2013), accommodators view a teacher as a coach. This implies that the teacher should work collaboratively with the students. He or she teaches each student on a one-on-one basis so that the students’ weaknesses and strengths are found. The teacher should always encourage self-discovery. Students should be motivated so that they ride on their strengths. Students should take advantage of their strengths for them to acquire new experiences. The teacher as a coach looks for remedies which overcome students’
weaknesses. As the teacher works with his or her students, he or she is expected to give immediate feedback to the students on their performance. By so doing, the students are encouraged to keep on trying and exerting effort in their learning.
Mathematics teachers as a facilitator
Divergers view their mathematics teacher as a facilitator (Kolb, 1984). Kolb and Kolb (2013) stated that when a teacher takes the role of a facilitator, he or she should promote inside-out learning in students. By this statement, Kolb and Kolb meant that the teacher should make sure that the students comprehend the new knowledge taught and they should be able to show understanding by change in behaviour. When a teacher facilitates learning, student-centred teaching strategies are used. Such teaching strategies include the inquiry method which entails that the teacher gives students a problem to solve and the students carry out researches to find possible solutions. In order for the teacher to effectively facilitate learning, the teacher should create conducive personal relationship with the students. The teacher should always promote dialogue with the students. Students must be free to interact
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with the teacher. A teacher-facilitator motivates students to keep on working hard despite hardships faced in the process.
Mathematics teacher as a subject expert
According to Kolb (1984), assimilators view their mathematics teachers as experts in the field of mathematics. In their role as subject experts, mathematics teachers must possess abilities to systematically analyse statements in mathematics. The teachers are also expected to organise the subject matter in such a way that the students can easily grasp. This involves planning instructions so that topics to be covered are arranged in sequential order. Arranging concepts in sequential order ensures that the students learn simple concepts first and then progress to concepts that are more challenging. As explained by Kolb and Kolb (2013), a teacher who is viewed by students as a subject expert should be convincing, respectable, dependable and trustworthy. He or she must be a deep thinker. Kolb and Kolb suggested that when the expert teacher teaches learners that fall under a group of learners referred to as assimilators, he or she can make use lectures and texts.
Mathematics teachers as a standard setter or evaluator
Convergers view their mathematics teachers as standard setters (Kolb, 1984). The teachers as standard setters are expected to be objective. They should teach for a purpose and they seek to achieve particular goals. The students expect them to be result oriented all the time.
Mathematics teachers take this role when they set tests or examinations for their students.
They set performance objectives for their students. The teachers set the evaluation criteria and they evaluate their students’ performance using the set criteria. As put forward by Kolb and Kolb (2013), when convergers learn mathematics they work in order to convince their teachers that they can do well.
Honey and Mumford (1992) also suggested learning activities that can be used by, mathematics teachers as they teach students of different learning styles. Table 3.2 gives the classes of learners and the suggested learning activities.
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Table 3.2: Honey and Mumford’s classes of learners and suggested learning activities Class of learners Suggested activities preferred
Activists problem solving
group discussion
puzzles
competitions
role-play
Pragmatists Applying learnt concepts to real life situations
problem solving
discussions
Theorists following role models
gathering statistics
using quotes
seeking background information
applying theories
Reflectors paired discussions
completing self-analysis questionnaires
observing activities
getting feedback from others
coaching others
interviewing others
According to Honey and Mumford (1992), pragmatists prefer learning through hands-on.
Their preferred learning techniques are experimenting and continuous practice. They expect their teacher to show them what to do before they get an opportunity to practise on their own.
Activists and theorists look for challenging situations. They enjoy facing challenges that are associated with problem solving. Theorists always look for background information behind theories, formulae and algorithms. They prefer exploring complex situations. Activists always desire to be the best performers. They like competition. Therefore teachers should
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allow them to compete in solving problems in mathematics. Reflectors on the other hand, should be given time to assimilate new knowledge and reflect upon it.
Honey and Mumford (1992) stated that teaching students according to their learning styles takes two dimensions. The two dimensions are: concrete versus abstract and safety versus challenge.
Concrete versus abstract
As put forward by Honey and Mumford (1992), the first dimension of the strategy of teaching students according to their learning styles has concrete on one end and abstract on the other end. The preference for concrete involves dealing with real life experiences whist the preference for abstract involves dealing with manipulation of symbols. Pragmatists and activists have preference for concrete whilst theorists and reflectors have preference for abstract. That means pragmatists and activists prefer dealing with real life experiences. They prefer dealing with concrete ideas. Theorists and reflectors on the other hand can easily deal with symbols and texts.
Safety versus challenge
Honey and Mumford stated that the other dimension has safety on one side and challenges on the other. Activists and theorists seek challenges when they learn while on the other hand pragmatists and reflectors look for safety. Pragmatists need enough time to practise and reflectors need time to reflect on new knowledge. Safety can be provided by the teacher through providing the students with ample time to practise and to reflect. This can be achieved if the teacher delivers lessons in a step by step manner without rushing to finish.
Challenge can be given to students through provision of more demanding tasks. Students should be allowed to experiment, hypothesise or try alternative methods. They should be given an opportunity to control their learning environment. They should be provided with chances to reverse their decisions when they feel the decisions are not appropriate.
Figure 3.1 illustrates the dimensions that the strategy of teaching students according to their learning styles can take.
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Pragmatists activists
Safety Challenge Reflectors Theorists
Abstract
Figure 3.1: Illustration for Honey and Mumford’s two dimensional teaching strategy
The interpretation for figure 3.1 is as follows: Pragmatists are concrete-safety learners. They prefer to learn from real life situations and they need time to practise. Activists are concrete- challenges learners. They learn from real life experiences and they need to be provided with more challenging or demanding tasks. Theorists are abstract-challenges learners. Theorists can learn through symbols and they need more demanding tasks. Reflectors are abstract- safety learners. They prefer learning through manipulation of symbols and they need time to reflect on their new experiences.
Due to the diverse nature of students’ learning styles, Perini, Silver, and Strong (2000) advised mathematics teachers to use a variety of teaching strategies. They recommend that students be permitted to work in their preferred learning styles but to be advised to use the strategy as a way of developing confidence to use the other three learning styles so that they become balanced. According to Perini et al., students should be assisted in recognising their learning styles through the use of four dimensions of mathematics learning. Perini et al.
argued that it is important for mathematics teachers to align teaching and assessment strategies with students’ learning styles as they go through the four dimensions of mathematics learning. The four dimensions are computation, explanation, application and problem solving. The descriptions of the four dimensions are as follows:
Computation
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Computation involves making some calculations. These calculations are done following specific rules, formula or algorithms.
Explanation
Explanations involve expressing oneself to others. In order words it means communicating one’s mathematical ideas or one’s way of thinking. It also involves describing mathematical processes.
Application
Application is when a learner applies mathematical concepts in real life situations, for example, when one uses the concept of addition to find the total number of cattle in a village.
Problem solving
This dimension involves using mathematical concepts in coming up with solutions to real life problems, for example calculating the time and amount of fuel required to travel from point A to point B.
In order to assist mathematics teachers, Perini, Silver and Strong (2000) suggested some learning activities that can be done by mathematics students in the four classes suggested by their model. They made use of their classification of learners in order to come up with the activities for each class. The activities matched the description of the learners in each class.
Table 3.3 shows the classes of learners and the suggested learning activities.
Table 3.3: Perini, Silver and Strong’s classes of learners and suggested learning activities
Class of learners Suggested learning activities
Mastery maths learners Application of algorithms, formulae and theorems
Computing
Producing mathematical reports Interpersonal maths
learners
Group discussions
Applying mathematical concepts in solving real life problems Understanding maths
learners
Proving why concepts work in real life
Individual work
Identifying mathematical patterns
Constructing scientific arguments
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learners
Solving non-routine problems
Solving project-like problems
Developing mathematical models
Designing
Bender and Waller (2011) advocated differentiated teaching to ensure that all learners benefit from the learning process. Differentiated teaching as defined by Tomlinson (2001) entails tailoring instruction so as to meet the individual needs of the learners. Laura (2017) added by stating that differentiated teaching means the teacher observes and understands differences and similarities among their students and uses the information to plan instruction. Weselby (2017) summarised differentiated teaching as designing a lesson based on students’ learning styles. According to Weselby, differentiated teaching involves continuous formative assessment and adjustment of lesson content until it meets students’ needs. Tomlinson (2001) suggested that differentiated teaching can be done in three areas of teaching which are content (what the learner learns), process (how the content is mastered by the learner) and product (how the learning process is assessed and evaluated). When differentiating the content, the teacher can vary his or her instruction so that it includes questions that demand the use of different skills. The following is an example of a balanced instruction found in the reviewed literature. This instruction was given to a junior secondary class. The class of learners catered for are given in brackets. These were based on the model by Perini et al.
(2000).
(i) Use the formula for area of a rectangle to compute the area of the irregular shape given below.(Mastery maths learners)
8cm
3cm
5cm 12cm 11cm
11cm
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(ii) Create your own area problem by connecting four rectangles. The rectangles can be of any measurements. Arrange them in any way you want and find the area of the irregular shape formed.(Self- expressive maths learners)
(iii)Picture your own home. Think about each room in your house. Draw a floor plan of the house indicating the dimensions of each room. Suppose you want to carpet each room, how much carpet would you need.(understanding maths learners and interpersonal maths learners) (Perini, Silver &Strong, 2007)
Umugiraneza and Bansilal (2017) purported that the most common strategies that are used in mathematics learning are direct instruction, cooperative learning and problem based instruction. However, Moore (2012) proposed alternative mathematics learning strategies which include manipulation of objects, real life application of mathematics concepts, and integration of information and communication technology (ICT) devices and use of games.
Of these strategies, Moore emphasised on the use of games in mathematics learning by saying that games help in developing mathematical thinking.
White (2012) noted that the use of manipulative objects like drawing instruments and computers create more concrete representations of mathematical concepts in learners than any other method. The Ministry of Primary and Secondary Education (MOPSE) Mathematics Syllabus in Zimbabwe for Forms 1-4 (2015) suggested the following teaching strategies to be used in teaching mathematics concepts: discussions, expositions, demonstrations, simulations, educational tours and presentations by experts. As reported by Mangwende and Maharaj (2018), the MOPSE syllabus suggests that mathematics teachers use relevant texts, information and communication technology tools, the environment, Braille materials, talking tools and software. Yousuf and Behlol (2015) supported the use of information and communication technology (ICT) systems when teaching mathematics by reporting that the application of ICT as a teaching strategy was found to be effective as compared to traditional strategies. ICT as defined by Mohanty (2011) refers to all technological tools and resources used to communicate, create, disseminate, store and manage information. It includes computers, the internet, broadcasting technologies (radio and television), cell phones and calculators. Mohanty proclaimed that ICT has many benefits to students. One of the benefits is that it gives students an opportunity to collaborate on assignments with people inside and outside school through flexibility of anywhere, anytime access. Tinker (2017) also supported
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by reporting that different computer software packages were used with positive results in schools in Mathematics teaching. Tinker reported that the most widely used packages in teaching mathematics concepts like functions were ClarisWorks, Microsoft works, Alice and Stella.
Ozgen and Bindak(2012) carried out a study in order to find the opinion of students with different learning styles on the use of ICT in mathematics learning. Qualitative and quantitative methods were used in collecting the data. The study revealed that students with diverging and accommodating learning styles had positive opinions towards the use of computers in mathematics learning compared to those with assimilating and converging learning styles.
However, a study carried out in Ghana revealed that mathematics teachers were not effectively integrating ICT in their mathematics instruction (Agyei & Voogt, 2010).
According to Agyei and Voogt, despite the benefits of ICT in assisting students of varying learning styles, mathematics teachers in Ghana lacked knowledge about how ICT can be integrated in mathematics teaching. As given by Agyei and Voogt, this impacted negatively on the teaching of students of different learning styles.
Apart from teaching methods that are student-centred and sensitive to students’ learning styles, assessment of the learning process is also a very important practice in mathematics teaching. Boaler (2016) proposed continuous assessment of students’ learning styles with the aim of improving their understanding of mathematics concepts. Boaler reiterated that mistakes made by students should present a powerful learning opportunity which teachers should take advantage of by providing immediate feedback on students’ actions and how the actions can be improved.