Innovative Approaches in Math Teaching in Private Institutions

From the very beginning of my practice, I developed the goal to define the most successful and innovative strategies in teaching mathematics. I am perfectly aware that mathematics causes many difficulties for learners of different categories. I’ve chosen a complex approach to the problem. I tried to pay attention not only to teaching methods but also to additional factors, which can contribute to better academic success. I tried to combine practical and theoretical knowledge in my practice. I made a theoretical investigation of the number of progressive learning theories in the attempt to find ones, which could be applied for math classes. I discussed information with teachers and observed some methods in practice. I have also studied additional factors, which can attribute to academic success. According to my research and my personal observation, friendly classroom environment, supportive attitude and transformative leadership become effective means, which increase academic performance and create a healthy atmosphere in the classroom. I also had the chance to communicate with my future colleagues and make judgments about the methods and approaches they use in the classroom.

During one of teacher meetings, one of the participants mentioned the Singapore teaching method. I became interested in techniques and methods, which provided outstanding results in the shortest term. ‘’Singapore method’ provides outstanding results, especially for sciences and math’ (Learning Journal, October 15, 2018).  The method became especially interesting for me when I found out that math is one of the basic subjects in Singapore primary and secondary schools.  Singapore method was developed in the middle of the 1980s. Behavioral studies became the basis for the research. The most effective experience from different school of the world also became incorporated in the research.  Teaching professionals of Singapore made a decision to step away from rote-learning and made an ascent of problem-solving and teamwork. Singapore educational specialists used the method, introduced by Jerome Bruner (1965). Bruner developed the three-staged model, which consisted of using real objects, using pictures and learning through symbols. After reading additional literature on his method, I came to the conclusion that the method reflected stages of cognitive development, and thus made effective learning succession, which perfectly suited cognitive abilities. Textbook follow learning schema, which became the basis of the learning method. “The following sequence of activities is used in the textbook: the introduction of knowledge, informal assessment, and reflection of knowledge, reinforcement of math concepts, and computational and problem-solving skills through peer interaction in group activities and practice (Merttens, 2012, 34). These sequences help the learners develop cognitive abilities and logical thinking.   Singapore used a three-staged model while developing math learning course and modeling mathematical problems. The use of visual aids became one of the outstanding methods, which give the Singapore system much success. In general, visual aids make an important part of math learning. Colored blocks are used to learn counting. They are also used to represent fractions or ratios. The effectiveness of the methods is proved by high academic achievement.  These methods can easily be applied in the classroom. Psychological research states that younger children have very limited abstract thinking. At this point, the use of visionary aids becomes an effective way to represent abstract notions (Bruner, 1965). Visionary aids are usually actively used in during preschool lessons. At the same time,  progressive theoretical research and practical applications prove that visionary aids can be extremely helpful for presenting mathematical concepts on all stages of the learning process. Simple visionary examples with blocks provided good results in the classroom. “Learners become emotionally engaged, when they work with visionary aids” (Leanring Journayl, 20 October, 2018).   The methods got the name CPA heuristics, using the abbreviation of “Concrete-Pictorial-Abstract”. I paid special attention to the transitional stage,    between concrete and abstract concepts. This pictorial stage, often omitted in our educational system, is crucially important for our cognitive system. CPA heuristics presents stages, our brain passes through in its cognitive development. At this point, these stages are necessary for the successful acquisition of new abstract notions. Professor Fan, who developed about 80% of all math textbooks in Singapore, gives the essence of his CPA heuristics during his inaugural lecture.   “Showing a slide of two sets, one with 6 rabbits pictured and one with 7 rabbits  pictured, he demonstrated how the children could be shown a concrete representation of the addition 6 + 7. He then showed a pictorial representation consisting of two sets, one with 6 large dots, and one with 7 large dots. Finally, he moved on to reveal the abstract representation, 6 + 7 = 13 (Kheong, cited in Marrtens, 2012, p. 34).   The demonstration helps to get an idea of CPA heuristics. I believe that elements of Singapore model can be successfully applied in the classroom.

Curriculum and learning plan has a major influence on academic success and academic performance. I dedicated my time to studying this problem during my practice.    Some researches attract attention to the problem and point out that learners from private school demonstrate worse results after math tests. Lubidnskis and Crane (2009) defined five major reasons, which correlated to higher scores. They defined them as: “certified teachers; forward-thinking math programs that keep up with curricular trends; school size; class size; and parental involvement. Of these five, the report indicates that teacher certification and a reform-friendly curriculum were crucial factors in determining higher achievement (Lubienskis & Crane 2009). At this point, it becomes evident that a reform-friendly curriculum, as well as teacher certification,  should be in the focus of attention for private schools.  I decided to make an investigation into the curriculum, used in Singapore.  There is a difference in the Singapore curriculum as well. It is more stripped down at the primary level in comparison to the US curriculum. In primary school, Singapore children learn fewer topics, but they have the chance to study them in depth and get the necessary amount of practice. “When you look at England and the US, [their curriculums] are mile-wide and inch-deep. They teach a lot of things but at a shallow level. Mathematics in Singapore is not about knowing everything. It’s about thinking like a mathematician” ( Schleicher, cited in Lubidnskis and Crane, 2009). The approach, developed by Singapore educational specialists gives children the chance to perform the in-depth study, which becomes a key factor of effectiveness. In addition, young learners can study new material with comfortable speed and this helps to avoid additional stress.

During one of the meetings, Mrs. A started a discussion about gifted children, who possess inborn abilities to learning sciences in general and math in particular. In response to her arguments, I expressed my personal position. I also became absolutely fascinated by the approach to talents and abilities in Singapore. The western educational system is mainly based on the assumption that different children have inborn abilities in particular subjects. This system is not supported in Singapore, where they believe that diligence can help reach academic success at any subject.  What is notable, English academic system has finally applied this approach as well. As Tim Oates, who worked on the England’s national curriculum in 2010-2013 notes: “It is a different approach to ability — really, a major overhaul of the way in which children are viewed.  A switch from an ability-based model of individualized learning, to a model [which says that] all children are capable of anything, depending on how it is presented to them and the effort which they put into learning it”  (Oates, 2010, p. 114). This approach changes a lot in treatment to the educational process. Applying such an approach assumes that any student can reach success. This changes both – the attitude of teachers and the attitudes of learners. I was thinking about this idea lately. “All children are like seeds and the teacher becomes the one, who creates the soil for these seeds to grow or to become spoilt” (Learning Journal, October 12, 2018). This idea can have a major influence on the teaching math in private school. Using such an approach,  it is possible to teach the class as a whole, not breaking it into smaller groups according to abilities in math.  NCTM’s saying “people who understand and can use mathematics in a variety of environments will be successful in college and in life ” also reflects this basic idea (NCTM). Math is important for the future success in different spheres of lie and it is important to put all possible effort to help all learners reach success in it. It is important to challenge the notion” that mathematics is only for the select few. On the contrary … all students should have the opportunity and the support necessary to learn significant mathematics with depth and understanding” (NCTM). When attending the meeting at school, I was thinking of new methods and techniques. After reading these words, I came to the realization that new methods and techniques should come from one basic concept – “everyone can be successful in math” (Learning Journal, October 21, 2018).

Looking for other ways to enhance students’ academic performance, I also became interested in the question of the supportive learning environment. “supportive learning environment is an essential part of the learner’s success” (Learning Journal, October 19, 2018).  Creating safe and friendly surrounding is crucially important in order to give learners with a different learning style opportunity to express themselves and take an active part in the study process. It is important to keep in mind different learning styles and spend time in order to define learning styles, most suitable for each learner. In the diverse classroom, it would be useful to combine different styles for different learners to be able to perceive information in the most effective way. Learners should know about their learning styles in order to develop effective learning strategies. The creative and safe atmosphere will help learners with different abilities to get maximum use of the time spent in the classroom.

Changes in the contemporary education system should be reflected in the classroom environment as well. Learner-centered learning and multiple intelligences should become new focuses on the teaching process. “Recent years have seen a change in the trends of education from pedagogy to andragogy i.e. from a teacher-centered learning to a student-centered learning. Therefore, it is not only desirable but also essential for educators to recognize that adults have different learning styles and that they should tailor instructions to the characteristic ways in which the adults prefer to learn” (Kharb et al., 2013).  Tools which can be used for creating effective learning atmosphere may include friendly surrounding, inclusive learning,  universal design learning, and learner-centered learning.  Collecting necessary information about learners, their abilities and their learning styles can make an important contribution to the successful learning process.  The methods used for teaching may include lectures, practicals, tutorials, discussions, projects and problem solving.  It is also important to measure outcomes from different methods used, in order to be able to distinguish the most successful ones.

Looking for the innovative teaching methods, I paid special attention to the naturalistic education.  The Naturalistic or Authentic methods of an education center on creating a special learning environment, where learners are able to discover the knowledge. Natural or authentic approaches are learner-oriented approaches, where the learner is put in the center of the study process. These methods do not give students ready answers for their questions, but rather create necessary conditions and post questions for the learners to discover the answers. Naturalistic or authentic methods of learning assume less teacher’s participation in the study process if to compare with Instructional learning approaches.  These methods include: “discovery learning,  problem-based learning,   inquiry learning,  experiential learning,    and constructivist learning” (Kirschner, Sweller, and Clark, 2006,  p. 75). All these approaches include minimal guiding from the teacher.  Proponents of these approaches state that non-directive methods stimulate a desire for cognition, help learners to discover their own investigative mechanisms, take into account individuality of each learner, enforce motivation and, in general, have positive results on the learning process (Kuhn, 2007).  In natural approaches, learners are not given ready information, but rather get an opportunity to discover this information themselves. Such an approach helps them to develop independence of thinking, originality of thinking and creativity. Proponents of such approaches believe that learning results are higher when learners resolve learning tasks in information-rich settings. In addition, Authentic and Natural approaches do not center on only giving knowledge, but also on the general development of learner’s personality.  Opponents of such an approach center on cognition mechanisms and peculiarity of human psychics. For example, Kirschner, Sweller, and Clark state that it is important to take into account cognitive architecture, when choosing the learning approaches. According to them, the latest studies, as well as experiments in this field prove that ”minimally guided instruction is less effective and less efficient than instructional approaches that place a strong emphasis on guidance of the student learning process” (Kirschner, Sweller, and Clark, 2006,  p. 75).  In this way, the latest research shows that cognitive mechanisms works better when learners get direct instructions.  For the math class naturalistic approach can be successfully combined with the group work. Learners can unite their efforts to solve mathematical problems together. Group problem solving can become not only an effective learning method, but also a kind of communicative training, and team-building technique.

My study of innovative approaches in teaching math and study of the most effective methods of the world finally directed me to the method of problem-solving. Such methods as transformation learning (Mezirow), Problem-solving Method, Project method can be helpful in training practical skills, critical thinking, emotional intelligence, leadership skills, responsibility, time-management skills and ability to operate information. These skills make the priority in contemporary society. The first thing to do is to step aside from directive and autoreactive methods of teaching. Teaching training of the past, which made teacher the center of the educational process, does not bring the necessary skills to learners. Learners should get more freedom and should put more responsibility for their education. The methods of big projects, which requires to combine several learning subjects and different learning skills and abilities should be developed in order to teach students to combine different pieces of knowledge.

Problem-solving is successfully used for teaching different subjects including both, sciences and humanities. Problem-solving could be used as an effective method in math teaching as well. “ Discovery math – let students find out the solution” (Learning Journal, October 12, 2018).  Problem-solving uses the type of learning mechanism, which enables the learners not to drill and memorize information, but to find answers. This method lets learners develop critical thinking and learn to find solutions to the problem. In the process of  “discovering” math, they develop algorithms, which can be applied in different life situations.

During one of my school meetings, I became the participant of the discussion about the international learners. I found about difficulties, they meet during their learning process. Changes in the contemporary education system should be reflected in the healthcare assessment as well. Learner-centered learning and multiple intelligences should become new focuses on the teaching process.While reflecting on this issues, I made a note: “International learners need special attention and special care” (Learning Journal, October 6, 2018). After careful reflection, I made a list of important characteristics, which should be noted when planning a learning process for international students. International students, who enter learning institutions outside of their native countries have to meet not an only the language barrier, but also cultural and social differences. They have to adapt to a new lifestyle. While choosing teaching strategies for international students, it is important to keep in mind that they have to go through the complicated process of adaptation. Friendly attitude, gentle correction of mistakes, encouragement and supportive surrounding are very important for this category of students.

After the discussion about international learners,  I made a proposition to discuss other categories of students, which may vary from learner’s profile. Together with my colleagues we also defined such categories as non-traditional learners, multicultural learners, and physically challenged learners. We united effort to present defining characteristics for each category.

Non-traditional learners may have a different vision of themselves and people around them. This vision may derive from their life experience or from their cultural background. Inclusive education should make the main goal to help non-traditional students save their uniqueness, but, at the same time, get a positive learning experience and build good relations with the environment. 

Multicultural students live at the blend of several cultures. They often combine different cultural backgrounds. The most important educator’s task should become in teaching them to organically integrate their multicultural background in their everyday lives.

Physically challenged learners may need both, physical and moral support. They can meet physical limitations and this can become an obstacle for the successful learning process. The teacher and administration should make everything possible to create favorable and friendly learning conditions for them. In addition, moral support and encouragement can be important factors, which can bring additional comfort to physically challenged learners. The category of learners, who are at risk needs additional attention. Timely monitoring, psychological and social support are important for this category of learners.

Information about different categories of learners made me think about possible strategies, which could be successfully used while teaching them. I made up a plan to expand my knowledge about each category and prepare possible approaches, which could bring maximum benefits to learners.

During one of the meetings, we discussed the role of the teacher in the learning process. There is no doubt that the learning process itself goes to great transformation. Teachers meet new challenges and have to develop an answer to them.  At this point, the role of the teacher should also be changed and transformed. The teacher should definitely keep leadership position, but this leadership should correlate with the needs of the time. Transformational leadership is that kind of leadership, which describes Leadership in the teaching industry has certain peculiarities. The leader should be able to inspire learners and make them grow and develop as personalities. In addition, he also should be able to deal with different behavioral difficulties and disciplinary problems.  For this purpose, the leader should possess such qualities as honesty, non-judgmental attitudes, desire to help, desire to use innovative and integral approach. A good leader should possess good communication skills. He should be able to understand the needs of learners and to build good relations with the administration of the learning institution.  The leader in the educational sphere should be good professional his sphere of expertise. He should be not only able to explain new materials, but also make learners inspired with what they see and hear in the classroom. Compassion and empathy are also important characteristics of the effective leader, because these qualities enable to understand the learners’ need and choose the best strategy to fulfill these needs.

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The terms offer and acceptance. (2016, May 17). Retrieved from

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