The concept of educational materials is expected to serve pedagogical goals of the curriculum's as developing ideas in depth, promoting sense making, engaging students, and motivating learning. Piaget (1952) implied that children do not possess the mental maturity to grasp abstract mathematical concepts presented in words or symbols alone and require various experiences with concrete materials and drawings for learning to take place. Bruner (1960, 1986) underlined the role of physical objects by maintaining that children present their understandings in three stages of representation as the terms en-active, iconic and symbolic.
Skemp‟s (1987) postulations upholded the belief that students‟ early experiences and interactions with physical objects formed the basis for later learning at the abstract level. Prior to the early 1990s, manipulatives and learner collaboration were not adequately implemented in elementary mathematics education. The decision of National Council of Teachers of Mathematics (NTCM, 1989) on promoting the use of concrete materials in mathematics teaching played a critical role on the creativity began to emerge in implementation of manipulatives into educational environments. In response to NCTM's (2000) recommendations regarding the improvement of mathematics instruction, manipulatives have become highly popular and very detailed sources of both content and pedagogical information (Trafton, Reys, & Wasman, 2001). This intensive attention on using manipulatives took the form of manipulatives that modeled the addition, subtraction, multiplication, and division students used to have to memorize from practice. In fact, manipulatives can come in a variety of forms and they are often defined as “physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics” (Boggan, Harper, & Whitmire, 2010). Mathematical manipulatives can be classified as commercials and/or teacher-produced ones. Commercial manipulatives are those including tangrams; cuisenaire rods; numicon patterns; Dienes‟ blocks; interlocking cubes; base ten blocks; pattern blocks; colored chips; links; fraction strips, blocks, or stacks; color tiles; and geo boards (Van de Walle & Lovin, 2005). Teacher-made manipulatives used in teaching place value are listed as beans, bean stick, and popsicle sticks.
In order to help students to construct geometric ideas, concrete educational materials such as geometry rods, geo board, isometric papers, symmetry mirrors etc. are to utilized. This utilization also provides an opportunity for the teacher to assess and meet the needs of primary school students as they construct personal mathematical knowledge. The ultimate goal of using manipulatives in maths instruction is to help children handle abstract concepts and the symbols that are used to represent these concepts. Heddens (1986) claims that „since all mathematics comes from the real world, the real situation must be translated into the symbolism of mathematics for calculating. Dienes (1961) emphasizes using manipulative in order to provide a concrete referent for a concept, often at more than one level, instead of a referent for a given abstract idea or procedure. Heddens (1986) summarizes the pedagogical influences of using manipulative materials in teaching mathematics as helping students learn: to relate real world situations to mathematics symbolism, to work together cooperatively in solving problems, to discuss mathematical ideas and concepts, to verbalize their mathematics thinking, and to make presentations in front of a large group. The author also maintains that there are many different ways to solve problems and that mathematics problems can be symbolized in many different ways.
Exemplifying, while Breen (2000) found out that computer supported geometry instruction affects 8th graders geometry skills and conceptual development in a positive way, Sarı (2010) obtained the same conclusion with 4th graders. Considerably, as teacher education programs aim to develop teachers' knowledge of mathematics and their knowledge of students as learners, these programs "should develop teachers' knowledge of and ability to use and evaluate instructional materials and resources" (NCTM, 1989, p. 151). Incorporating the use of manipulative materials in mathematics supports teachers in learning to direct their attention toward the facilitation of students' understanding and conceptualization rather than drill and practice of rote procedures. Mathematical manipulatives play a key role in young children‟s mathematics understanding and development. These concrete objects facilitate children‟s understanding of important math concepts, and then later help them link these ideas to representations and abstract ideas. In addition, children often lead to use manipulatives in a rote fashion, with little emphasis and understanding of the mathematical concepts behind the procedures (Hiebert & Wearne, 1992). Thus, students need to learn to use manipulatives that support and scaffold children's leaming, as opposed to simply making mathematics fun and applicable to children's everyday lives.
Over the past few decades, researchers have studied the use of manipulatives in several different grade levels and in several different countries (Boggan, Harper & Whitmire, 2010; Cain-Caston, 1996; Castro, 2006; Kelly, 2006). The majority of the studies indicate that mathematics achievement increases when manipulatives are put to good use. Many studies also suggest that manipulatives improve children‟s long-term and short-term retention of math. Cain-Caston‟s (1996) research indicates that using manipulatives helps improve the environment in math classrooms. Kelly, (2006, p. 188) posits that “teachers need to know when, why, and how to use manipulatives effectively in the classroom as well as opportunities to observe, first-hand, the impact of allowing learning through exploration with concrete objects”. In a study investigating the impact of curriculum materials on the change in teachers' practice revealed that using the materials has changed teachers‟ instructional practice (Edwards, 1995). Castro (2006) also studied with elementary pre-service teachers and discussed how manipulatives as educational materials are used. The study including the descriptions of learners on how these materials can be used in the classroom pointed out two major outcomes: some students thought that curriculum materials could be used to help students learn, others saw these materials as tools that can support teachers' instructional decisions.
To sum up, while the findings of much research has shown that students who use manipulatives during mathematics instruction outperform students who do not (Driscoll, 1981; Sowell, 1989; Suydam, 1986), some others have shown student achievement levels to be related to teachers‟ experience in using manipulatives (Sowell, 1989; Raphael and Wahlstrom, 1989). Admittedly, the most important responsibility belongs to the teacher at the point of using of the teaching materials at the teaching process. The teachers who are the practitioners of the curriculum and facilitators of learning environment should be consciously aware of the critical impact of learning materials on providing the pupils with problem solving skills. On the other hand, using concrete materials to teach mathematics is currently a well-established pedagogical strategy throughout the world though, there‟s no concrete information on how teachers implement them into their actual teachings. By aiming to purport the manipulative use of classroom teachers at primary education settings, the current study may serve to raise educational stakeholders‟ awareness towards the importance of incorporating the manipulatives in mathematical learning process with a focus on geometry.
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