Disadvantages Of Math Manipulative PDF

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Disadvantages Of Math Manipulative...

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Disadvantages Of Math Manipulative Teaching math can be a daunting task, especially in the lower grades. Teaching mathematical concepts through lecture and paper and pencil work isn’t enough to achieve deep understanding, math reasoning or problem solving skills. Math manipulatives are “hands on” or virtual materials designed to engage students in active investigation to gain higher levels of understanding. Manipulatives not only allow students to explore concepts, but also allow teachers to see what students are thinking. “The National Council of Teachers of Mathematics (NCTM) Principles and Standards for School Mathematics emphasizes the importance of using manipulatives and visual representations, as well as mathematical modeling, in each of its standards at all grade levels” (Shaw, 2002). The use of manipulatives in the classroom are also supported by educational theory. Jean Piaget’s theory of cognitive development indicates that elementary school students are typically in the concrete operational stage of cognitive development. This stage encompasses the development of organized rational thought. Students begin to develop the abilities of conservation and

reversibility. Although students are able to approach problems in a logical way, they typically struggle with thinking abstractly or hypothetically (McLeod, 2010). Manipulatives are an excellent way to bridge the gap. Students are able to work with materials to create concrete experiences which help lead to abstract reasoning. Mathematic manipulatives come in many forms, and have both advantages and disadvantages. Four classic manipulatives used in today’s classrooms are: fraction strips, base ten blocks, counters, and pattern blocks. Fraction strips are a manipulative designed to represent and compare fractions. They are rectangular pieces of plastic, foam, or paper which represent different parts of a whole. They are various sizes and colors based on their denominators, and can be used to help students visualize explore the concepts of fraction equivalency, adding and subtracting fractions, and comparison of size. Fraction strips are a versatile manipulative that allow students to manipulate concrete objects to understand a complex concept. However, they are somewhat limited and do not necessarily help with the mental process of working with fractions.

One advantage of fraction strips is that this manipulative is easy to produce. Fraction strips made of hard plastic or soft foam can be purchased, but they can also easily be created for free from paper. Fraction strip templates can be downloaded and printed, and students can cut out the fractions to use. This is an advantage because they can be mass produced, and when the small pieces get lost or damaged, they can easily be replaced. A second advantage of fraction strips is the variety of fraction concepts at different learning levels they can be used for. When first introducing students to the concept of fraction; fraction strips can be used to demonstrate fractions as parts of a whole. They can then be used at a higher learning level to facilitate a visual representation of equivalent fractions and comparison of sizes. As students transition into the mathematical functions of fractions, the strips can be used to help add and subtract with like and unlike denominators. Fraction strips are a cheap and easy manipulative which can be used over many grade levels for many purposes. Fraction strips also have some disadvantages. One disadvantage is that there are a limited selection of denominators that can be used.

While they work well for initially learning the concepts, they do not accommodate the full range of denominators that students will need to work with. The second disadvantage of fraction strips is that they do not necessarily help with the mental action of working with fractions that students should be able to do. Working with manipulatives does not always translate into understanding. Students may be able to perform the correct actions to demonstrate the concepts with the fraction strips, but if they do not make the connection to the mental action of what is happening with the fractions they do not really understand the concept. Base ten blocks are a manipulative designed to represent the base ten or decimal system. They are pieces of plastic or wood formed into four different components. The first, is a single unit representing the number one. The second, is a rod of ten cubes representing the number ten. The third, is a flat block made up of ten rods representing the number 100. The fourth, is a cube made up of ten flats representing the number 1000. Base ten blocks help students visualize the concepts of counting, number sense, place values, addition, subtraction, perimeter and area.

One advantage of this manipulative is its ability to help build mathematic reasoning. Base ten blocks are tactile objects that students can manipulate to physically reason and problem solve. Conceptual explanation and logical justification can be difficult for students; base ten blocks allow them to experiment and show their thought process. Working with base ten blocks is a major advantage over modeling with pictures drawn on paper primarily because students can use the manipulatives to build and modify their ideas fluidly without having to stop their train of thought to erase and reorder their ideas. Another advantage of base ten blocks is the range of concepts that they can be used for. This manipulative is appropriate to use in classrooms from kindergarten to high school for concepts from basic counting to algebra and geometry. Base ten blocks are not “novelty” manipulatives that are necessarily considered “babyish”. Their use as a modeling and justification tool appeal to a wide range of students. Base ten blocks are not without their disadvantages. One disadvantage of this manipulative is the distraction and loss factor. The small pieces make tempting projectiles, building blocks, and other

imaginative toys, so keeping students on task may be a challenge. In order to combat this disadvantage, a teacher needs to have an appropriate classroom management plan in place. Kits can also be costly and the pieces are easily lost or taken. An academic disadvantage of this manipulative is while base ten blocks help model procedure, they do not help with academic language or verbal explanation. Students using this manipulative to help problem solve and reason will be able to create a model of how they worked the problem, but when asked to explain the concept may struggle. Base ten blocks do not help with the academic language or vocabulary of the concepts they are being used to explore. Counters are a manipulative designed to assist in understanding basic math skills. While most useful in the younger grades to teach the concepts of counting, sorting, and basic addition and subtraction; they can be effectively used at all grade levels to teach concepts of multiplication, division, ratios, and algebra. Counters are simply tokens which represent units or numbers. The counters that teachers can purchase are usually small, round, coin sized plastic disks. However, counters can be anything.

The biggest advantage of counters as a manipulative is the ease of acquiring them. Counters are tokens which represent units or numbers, so they can be anything. Teachers can cheaply acquire or make a bulk amount of counters to use. Some examples of what teachers often use for this manipulative are: dried beans, popcorn kernels, jelly beans, colored paper squares, marshmallows or Fruit Loops style cereal. Another advantage of this manipulative is their ease of use. Students can use counters intuitively, it does not take much instruction time explaining how to use them. A teacher can maximize guided and independent practice with this manipulative and clearly see what the students are thinking. There are a couple disadvantages to this manipulative. The first disadvantage is management of the objects. Since counters are smaller items dispersed in quantity, often being used by young children, they will end up everywhere. Spilled, thrown, knocked off desks, and possibly eaten; the loss of these manipulatives is high. The second disadvantage is that they are really only useful for teaching basic skills, such as working with simple math and small numbers. It becomes difficult to use counters to express large numbers and

complex expressions. At that point, the manipulative actually hinders learning because the students are focused more on organizing and managing the counters than on exploring the concept. Finally, pattern blocks are manipulatives designed to represent geometric shapes. They consist of color coded shapes such as triangles, squares, parallelograms, rhombuses, trapezoids, and hexagons. This manipulative is used primarily to explore pattern relationships, fractions and geometric principles. One advantage of pattern blocks is that they are a manipulative that will help more symbolic, artistic, and spatial thinkers. The nonlinear nature of pattern blocks create opportunities for students to explore mathematic concepts in more creative ways. Colorful concrete shapes can be used to help students achieve the abstract elements of a concept, or help creative, abstract thinkers work back to the linear process. Pattern blocks are a manipulative that can be used in many different ways by many different types of students. Another advantage of pattern blocks is there versatility. They can be used for so many different concepts, from teaching basic math skills, to exploring complex ideas. They can be used as counters with each shape

representing different numbers. They can be used like fraction strips to illustrate how shapes can be part of a whole. Students can use them for learning patterns, sorting, making pictures, ratios, algebra, and geometry. Pattern blocks offer such a wide range of possibilities that they are almost a “must have” manipulative. Pattern blocks have some significant disadvantages. The first disadvantage is that pattern blocks can be costly. Since the sides on the shapes need to be congruent, and fit together correctly, they are hard to self-create. The purchased kits have many pieces, and it is inevitable that there will be loss or damage. The benefits of this manipulative may not be worth the potential financial investment. Another disadvantage is that the concepts being explored with pattern blocks may not easily translate into understanding. Pattern blocks can be fun and creative, and have uses at all grade levels; however they are often used for more complex concepts such as pattern relationships, spatial relationships, and geometric principles. The concrete manipulative is being used to represent much more abstract concepts and the connections may take more time....