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# IMPACT OF VIRTUAL AND CONCRETE MANIPULATIVES IN THE MATHEMATICS CLASSROOM

Does the use of manipulative materials affect the student learning of mathematics? It has been established that students acquire knowledge through an active process that engages them (Boggan, Harper, & Whitmire, 2010). According to Cockett and Kilgour (2015), one of the best strategies to introduce an active and engaging learning environment is to use the manipulative materials. Currently, many mathematics teachers use manipulative materials to support their classroom teaching. Due to the importance of manipulatives, the policy makers recommend that they should be used to teach mathematics at all levels of education. This essay examines the effects of using manipulatives for student learning of mathematics.

Cockett and Kilgour (2015) observe that mathematics classrooms require collaboration than most subjects taught in schools. However, achieving collaboration in teaching subjects like mathematics is sometimes challenging. Unlike other subjects, mathematics learning takes place across different stages. To move from one stage to the next, the student must properly synthesize whatever is being taught by the teacher. To begin with, the use of mathematics enhances the students’ thinking skills. According to Boggan, Harper, & Whitmire (2010), thinking and reasoning are some of the most important components of learning mathematics. The abstract nature of mathematics calls for proper reasoning for the students to understand the mathematical concepts. But how can the teacher enhance the student reasoning in the classroom? When the teacher uses manipulatives, he/she gives the students the opportunity to compare and operate on quantities. It is evident that mathematics learning is more about handling aspects of quantities. Teaching mathematics students with manipulatives such as the titles, pattern blocks, and cubes provides the relevant connection with handling the quantitative nature of mathematics.

According to Cockett and Kilgour (2015), the success by which the students understand mathematics also depends on the teacher’s use of manipulatives. Some teachers know how to choose the best type of manipulative to use within the mathematics classroom. Generally, learning is a long process that often involves several stages. Therefore, the manipulatives offer the students the opportunity to have a meaningful experience by offering a concrete form of learning. However, the mathematics teachers who seldom use manipulative materials in their mathematical teaching often encounter difficulties explaining various mathematic concepts to the students.

It has been established that the manipulatives support the student engagement during mathematics learning (Cockett & Kilgour, 2015). Students that are engaged are likely to gain more concepts and understanding of mathematics than students who are not engaged. Without the manipulatives, the process of engaging the students may not take long. They are likely to get bored easily and lose concentration. However, the manipulatives supports the student learning by making them engaged for the most part of the learning sessions. Most teachers agree that the students need to be engaged for the better part of the lessons for them to synthesize the mathematical concepts being taught. According to Cockett and Kilgour (2015), mathematics classes that are based on mere teaching are likely to be boring within a short time. By allowing the students to be actively involved, the students become more interested in the lesson and the subject being taught. Enjoyment in learning becomes interesting when it is linked to the tangible objects, and this can effectively be achieved by the use of manipulatives. Many teachers have confessed that the benefits of using manipulatives are mostly evident when introducing new mathematic concepts or in revisions. The nature by which a new mathematical concept is introduced affects his future understanding of the concept. When introducing the new concept, Boggan, Harper, and Whitmire (2010) agree that it is necessary to go beyond the theory toe enable quick understanding of whatever in being taught. When proper introduction is not done, there is a high chance that the student will not properly understand what is being taught in the classroom. Manipulatives provide the effective visuals needed to enhance mathematics study. According to Boggan, Harper, and Whitmire (2010), the visuals also enhance the student engagement and promote the understanding of mathematics among the students.

Cockett and Kilgour (2015) suggest that higher confidence levels are necessary for the student to understand whatever is being taught by the teachers. If the teacher cannot effectively enhance the student confidence, then there is a low probability that the student will pass the mathematics examinations. Boggan, Harper, and Whitmire (2010) also supports that lack of confidence alone is a big impediment to the student understanding of the basic concepts of mathematics. Without confidence, the students are likely to perceive mathematics as a big struggle in their academic life. Only proper use of manipulatives in mathematics teachings has the potential of countering the high levels of lack of confidence among the students. The teacher can allow the students to physically move the manipulative materials to enable them to comprehend the relationships being explained in the mathematics lesson. By stimulating the kinetics side of the learner, the confidence levels in such students are enhanced significantly.

Another effect of the manipulatives is associated with the individual needs of the mathematics students (Boggan, Harper, & Whitmire, 2010). Students have varying speed of understanding mathematical concepts. Therefore, some additional effort is needed to make them understand whatever is being explained by the teacher. The benefit of manipulative is that it can be used to manage different learning styles needed by the students in a mathematics classroom. Therefore, the teacher will simply use the manipulative to support a better understanding technique for the students who never understood from the initial concepts. Since mathematical figures cannot be touched or felt, abstract reasoning is necessary to enhance student learning. Without abstract reasoning, it would be very complicated for the students to understand the mathematical concepts taught in class.

For younger learners, it is evident that the use of manipulatives affects their comprehension of patterns and functions. According to Cockett and Kilgour (2015), students properly taught with manipulative materials are good in sorting and comprehending the different functions of mathematics. On the same note, the math teachers can easily use the manipulatives to enhance the number sense and other mathematic related abilities. On the other hand, the students who are taught mathematics with too much theory finds it hard to distinguish patterns and make proper generations from such patterns. However, the use of manipulatives can effectively be used to fill the gap by enabling the student to comprehend different patterns and make an appropriate generalization of such patterns. In relation to this, the use of manipulative supports the teaching of geometric shapes (Boggan, Harper, & Whitmire, 2010).

For young mathematic learners, the use of manipulatives is used to support the understanding of the mathematical numerical base 1,2,3,4,5…….. 10 (Cockett & Kilgour, 2015). During such sessions, the manipulatives will effectively be used to describe the relationship of one numeral and the next numeral. Besides, the use teachers use the manipulative materials to describe and explore the spatial relationships that exist in mathematical numerals. On the same note, the manipulatives are effectively used to instill the understanding of the basic mathematical operations such as addition, multiplication, subtraction, and division. Also, the manner in which these relationships occur can properly be explained by the use of manipulatives.

Mathematics teaching can never be complete without geometry. However, a proper understanding of geometric shapes is necessary for the students to pass their examinations. Cockett and Kilgour (2015) argue that manipulatives can be structured in the form of geometrical shapes to enhance the understanding of geometry. Mathematics learning also involves both the standard and the non-standard measurements. Teaching these measurements is sometimes complicated if there are no proper tools to illustrate how such measurements can be done.

Another potential benefit of using virtual or concrete manipulatives is evident in the description (Boggan, Harper, & Whitmire, 2010). There are several symmetrical relationships that need to be described and explained during mathematic courses. However, it becomes a big challenge for the student to describe these relationships if such student is not taught by the use of manipulatives. Mathematics is a wide course that is taught right from elementary schools to the top level university studies. The basic components of mathematics learned in earlier years can easily be forgotten by the students. However, the students that were heavily taught by the use of manipulatives experiences developed spatial memory. In future the mathematics classrooms, the student can utilize their spatial memory based on earlier manipulative descriptions to make the relevant connections needed in the mathematics classroom.

Active mathematics classrooms should involve lots of experimentations and transformations. Actually, most research in mathematics involves lots of experimenting with numbers to draw common conclusions and patters. According to Cockett and Kilgour (2015), experimentation in mathematics classrooms can effectively be enhanced by the use of manipulatives. Such experimentations and transformations help the students to develop proper problem-solving skills in mathematics. Generally, mathematics figures can be presented in various ways and forms. Sometimes, it becomes a challenge for the students to quickly comprehend the manner and the nature of connecting different mathematic concepts. Therefore, the manipulatives enable the students to develop the skills of representing mathematics in different ways. On the same note, the mathematical ideas can be communicated in different ways. According to Boggan, Harper, & Whitmire (2010), the manipulatives used in mathematics teaching can easily be manipulated to represent different concepts as they apply in mathematics. The mathematic students can effectively relate a real world situation to the mathematical symbols as used by the teacher in mathematical learning. Within the mathematics classroom, the teacher’s use of manipulatives helps the students to verbalize mathematical thinking. The other important section of mathematic teaching is making presentations. By the use of the manipulatives, the teacher or the student can take ownership of the learning experiences and make meaningful representations that is quite convincing.

In conclusion, the use of virtual and concrete manipulatives has positive effects in the mathematic classroom. The teachers achieve the necessary collaboration when using the manipulative tools to teach their students’. The proper use of manipulatives in mathematics teachings also has the potential of countering the high levels of lack of confidence among the students. Another effect of using manipulatives is that it can be used to manage different learning styles needed by the students in a mathematics classroom.

References

Cockett, A & Kilgour, P. W. (2015) “Mathematical Manipulatives: Creating an Environment for Understanding, Efficiency, Engagement, and Enjoyment,” TEACH COLLECTION of Christian Education: Vol. 1: Issue. 1, Article 5. Available at: http://research.avondale.edu.au/teachcollection/vol1/iss1/5

Boggan, M., Harper, S., & Whitmire, A. (2010). Using manipulatives to teach elementary Mathematics. Journal of Instructional Pedagogies. 3(5) 1-6, Retrieved from http://www.aabri.com/manuscripts/10451.pdf

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