The success of education is attributed to the use of modern teaching methods that have been developed in the last few years. These methods include project work, providing meaningful choices for students, self-directed learning, literature-based reading, and problem-based curriculum. A well-prepared learning environment facilitates excellent learning outcomes.
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Consequently, the Montessori education system focuses on proving a learning environment that enables students to acquire knowledge by exploring and engaging in different learning experiences. Piaget (1970, p. 30) asserts that the primary role of intelligence is to promote understanding and invention among learners. The origin of our “intellectual operations is, thus, to be sought for as far back as an initial stage of the development characterized by sensory motor actions and intelligence”.
This implies that successful learning has a strong correlation with the development of primary sensory motor actions. Children are likely to do abstract mental operations if they undertake regular practice with sensorial activities. Imitation, developing mental images, drawing, and language development are the main learning characteristics of students who are between 2 and 8 years.
Thus, children prefer symbolic and semiotic functions at this age. Students should be guided to generate ideas and to discover mathematical relations on their own, rather than forcing them to accept those generated by adults. Educators should help students to gain experience in using mathematical skills at their own pace.
This can be achieved by encouraging the students to engage in regular practice that enables them to develop and to use deductive reasoning in mathematics. Piaget (1970) emphasizes the importance of allowing children to do their work independently by asserting that “even in the sphere of image-recall and memory, it can be shown how much structure and even the conservation of memories is linked to the schemata of actions and operations” (p. 35).
Piaget (1970, pp. 35-36) illustrated this argument through an experiment that involved a comparison of the memories that different teams of young learners can retain in an exercise that involves grouping cubes in terms of whether the groupings are perceived, looked at, reconstructed by the learner, or an adult as the young learner observes. The memories exhibited in each case were superior.
This means that the presentations by the adult produced mere perceptions. Consequently, vital information is often lost each time an experiment is done as the child observes, rather than allowing the child to perform the experiment on her own.
Maturation and exercise of intelligence can be achieved through practical experiments, as well as, independent thinking. According to Piaget (1970, p. 36), children will always demonstrate high maturity and advanced level of thinking if they are guided to do independent work. This observation holds regardless of the condition in which the child lives in.
Thus, children should engage in practical math experiences in order to develop neurological thinking. Even though mathematical experience is essential for the development of intelligence, it is not a sufficient condition because it occurs with empiricism. Nonetheless, abstract math enhances the development of logical reasoning. Hence, didactics mathematics should be used to strengthen students’ math power.
Teachers must guide students and help them to develop logical reasoning. Nicholl (1998, p. 37) opine that teaching interventions should focus on knowledge acquisition, as well as, the development of the learners’ character, wisdom, and emotional maturity. The education system that is used in most schools benefits only a small number of students.
This is because majority of students in most schools have inadequate creativity and analytical skills, as well as, flexibility in thought. Nicholl (1998, p. 37) notes that students have multiple intelligences, which differ in terms of context, linguistic skills, as well as, their ability to read and write. Logical-mathematical intelligence determines a student’s ability to reason and to think logically.
Visual-spatial intelligences reinforce a student’s ability to conceptualize future outcomes in terms of mental pictures. Thus, it enables students to engage in thought provoking experiences that enable them to plan and to strategize for the future. Musical intelligence enables students to develop rhythm and to improve their ability to compose music.
Bodily-kinesthetic intelligence is also important because it enables individuals to solve problems, generate ideas, and develop products. Interpersonal intelligences are essential because they enable us to work effectively with others and to evaluate our strengths and weaknesses. Finally, naturalist intelligence boosts the ability to identify the differences in the natural world.
Nicholl (1998, p. 39) asserts that linguistic, logical and numerical abilities are the most important determinants of individual success. According to Montessori (1995, p. 12), the greatness of a person starts at the early stages of development in his mother’s womb. Children often open up their mind for learning immediately after being born.
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Thus, educators have a great opportunity to help children to unfold their psychic power at an early age. The infancy stage is considered as the most important development phase in learning since the child’s interest to learn is at its peak. Currently, several teaching methods that seem to be effective in promoting learning are available.
Nonetheless, the education systems in various parts of the world are still struggling to provide a program that meets all the learning needs of students. This situation is attributed to the use of conventional teaching methods, which limit students’ ability to explore their world. In this regard, “the world of education is like an island where people are cutoff from the world, and are prepared for life by exclusion from it.
Only a pressure from outside can change, renovate, and find remedies for that manner of education at every level”. Mental development facilitates the acquisition of manual skills. The desired work outcomes can only be achieved if a person has fine motor movements and is able to pay attention to details. The ability to utilize the hand is the greatest advantage that human beings have.
Consequently, it is essential to use our hands to acquire knowledge. The hand and the mind works in unison in order to achieve the highest level of knowledge, as well as, intelligence. In Montessori education, teachers focus on developing children’s sensorial and motor skills in their early years. They use sensorial and motor skill materials to identify the sensorial and motor skill capabilities of every child.
Conventional education systems, on the other hand, use a method referred to as object lessons in which educators provide a limited skill set. Montessori (1995, p. 28) asserts that educators should use every resource at their disposal to enhance learning among children. A Montessori teacher’s role is to guide learners. Consequently, they must focus on continuous professional development, as well as, using their knowledge to support children in order to achieve the best learning outcomes.
One of the advantages of Montessori education is that it provides lessons that cater for the learning needs of all students. It does not limit students’ ability to learn. Teachers should always evaluate the ability of each child to perform prior to the introduction of new learning materials. They should keenly observe students in order to determine whether they require repetition.
Robinson (1991, p. 17) emphasizes the importance of evaluating the use of the best teaching practices. Group work can be effective if there is a student who understands the material that is being studied, and is able to explain it to his colleagues. The benefit of this strategy is that the student who is explaining the material to others develops an in-depth understanding of the content.
However, too much repetition can cause constant reviews. Teachers must organize cooperative learning groups in a manner that reduces the ‘free rider’ effect. This can be achieved if the responsibility of explaining the learning materials or giving instructions is shared among the group members.
This strategy is important because talented students are likely to consider disproportionate sharing of responsibilities, and the failure of team members to contribute in heterogeneous groups to be unfair and frustrating. Sternberg, Grigorenko and Ferrari (2004, p. 2) asserts that the process of measuring intelligence and success requires advanced expertise.
Concisely, the process requires “meta-components of thinking, which include recognition of problems, definition of problems, formulation of strategies, representation of information, allocation of resources, as well as, monitoring and evaluation of solutions to various problems”. The acquisition of these skills or expertise is attributed to gene-environment, co-variation, and interaction.
The conventional tests that are used to evaluate intelligence and related abilities focus on past achievements. These tests include vocabulary, oral analogies, conceptual reasoning, and solving mathematical problems. The weakness of these tests is that they propose a causal relationship whereby, the tests reveal a construct that seems to be a causal of, rather than a mere temporary antecedent of later success.
A large percentage of human characteristics reveal the co-variation and the association between genetic and contextual factors. Nonetheless, it is not possible to perform an explicit measure of the influence of genes on the development of intelligence. Thus, only a fraction of the expressed intelligence can be measured.
The part of intelligence that can be measured includes the expressions of developing expertise, as well as, the type of expertise that can possibly facilitate reflection among teaching practitioners. In this regard, intelligence measures should be correlated with later success. Sternberg, Grigorenko and Ferrari (2004, p. 2), identified three domains of intelligence namely analytical, creative, and practical.
Individuals can exhibit analytical, creative, or practical expertise without having the other domains. Meta-cognitive skills refer to an individual’s understanding of his own cognition. These skills describe a person’s knowledge of solving arithmetical problems in terms of the procedures to be followed and how they should be executed.
Explicit learning takes place when a student makes an effort to learn. Implicit learning, on the other hand, occurs when a student acquires knowledge incidentally without making deliberate or systematic efforts. The most important thinking skills that students need include critical thinking, creative thinking, and practical thinking.
Both declarative and procedural knowledge are essential in mathematics. Declarative knowledge involves the use of facts and well-established principles, whereas procedural knowledge involves following well-defined course of action and strategies. Learners need procedural tacit knowledge because it enables them to understand how various systems operate.
Competence and achievement are important sources of motivation in the study of mathematics. Achievement-oriented learners usually focus on solving problems that are challenging. Competent learners, on the other hand, focus on finding solutions to existing problems. The main weakness of conventional tests for intelligence is that they are based on the assumption that individuals operate in a de-contextualized environment.
The results of these tests are often interpreted based on a person’s internal characteristics. However, the participants in these tests usually do not operate in a fixed environment. Educators can modify the tests in order to suit the type of expertise that is needed in any given cultural milieu. Conventional tests are important because they enable educators to forecast school performance.
However, the tests can only measure a small portion of the types of developing expertise that are essential for life success. Most conventional tests cannot forecast more than 10% of the variations in individual differences in terms of the indicators of success in adulthood. Students should receive training on cognitive and social skills both in their homes and in their schools.
This is because these skills are important in acquiring academic knowledge and solving life challenges. Educators should expand their understanding of abilities and realize that measuring them involves assessing students’ expertise. This will enable them to avoid overestimating the abilities of learners with expertise in math, but lack similar expertise for future success in life.
The instruction methods used by teachers should focus on enhancing reflective, analytical, creative, as well as, practical thinking within a knowledge base. Additionally, teaching interventions should take into account the students diverse styles of learning and thinking in order to promote high academic performance. Students’ thoughts must be focused on learning in order to achieve the best outcomes.
Most teachers believe that they can help students by using different teaching strategies. Curriculum compacting is one the methods that have been used successfully by teachers to enhance learning. Regular training programs enable teachers to develop new knowledge and procedures that promote learning.
Furthermore, teachers can improve the existing body of knowledge about the best teaching practices by sharing their knowledge through formal and in formal discussions. Watters (2010, pp. 222-238), studied the teacher attributes that support students’ interests. The characteristics, which he identified included teachers’ ability to link pedagogical practices with students’ interest, creating relevant learning experiences, good classroom management skills and being able to explain complex concepts or ideas.
Furthermore, teachers should have adequate content knowledge and passion for a particular subject matter such as mathematics. Hirsch (1928, p. 10) opine that excellent learning outcomes can be achieved if students see, and feel the subject that is being taught. Consequently, he encourages traditional schools to adopt the use of multisensory instructional methods in their curriculum.
Montessori education system is effective because it allows students to learn in one classroom for three years. During this period, the child gets to interact with younger and older learners. Moreover, the children benefits from integrated instructions, which enable them to understand how things fit together. Integrated instructions also reinforce the content that is being taught by providing different contexts.
The education system should encourage the teaching of reality in order to achieve the best learning outcomes. In this regard, teachers should focus on choosing interesting topics in order to keep their students engaged. In addition, education systems should focus on individualized instructions, rather than teaching the majority. This will facilitate achievement of the best results.
Hirsch (1928, p. 134) describes high-order thinking as a process that involves cross checking through different interfaces using several concepts that are related. Individuals, conceptualize a problem in their mental space through a cross checking process that utilizes preexisting knowledge as a guide. According to Hirsch (1928, p. 134), conventional test are not capable of measuring high-order thinking.
Using the conventional tests among children can encourage memorization. However, this strategy has negative effects on students’ achievements in learning. In particular, it focuses on quick memorization of isolated information, rather than generation of new ideas. In addition, the tests do not cover all the aspects of knowledge and performance that students should achieve.
In this regard, the conventional tests are ineffective because they place students in a passive and reactive role instead of focusing on evaluating their abilities to structure tasks, to generate ideas, and to find solutions to problems. Rimer (2008) asserts that schools in the United Sates have not been able to improve mathematical skills among boys and girls.
Girls who usually score the highest grade in math are often immigrants or children of immigrants who migrated from nations in which math is highly valued. Even though girls have great talent in math, such talent is hardly available in the United States. One of the factors that explain the poor performance in math in the United Sates is that talent in mathematics is not highly valued in the culture of the country (Rimer, 2008).
This discourages children from putting more effort in the subject. The country’s culture creates a perception that high performance in math can only be achieved among Asians and nerds. Countries in which students excel in mathematics usually have comprehensive math curricula. Furthermore, the cultures and educational systems of these countries usually value talent in math.
They encourage and support learners who are able to excel in math. Students who excel in mathematics believe that high performance can be achieved through intuition and creativity (Rimer, 2008). Research indicates that student-centered and teacher-directed approaches to teaching are ineffective. Thus, they should not be used to teach math in schools.
Recent studies indicate that improvements in math performance can be achieved through cooperative learning methods. Team assisted individualization (TAI) is one of the cooperative learning approaches that is increasingly being used to hence students’ performance in mathematics (Rimer, 2008). The characteristics of this approach include heterogeneous groups of learners assisting each other, specific teacher guidance, and performance-based rewards.
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