## Definition of Terms

### Manipulatives

According to Moyer (2001) explained that mathematics manipulatives are physical objects that represented concretely materials in mathematics ideas which is abstract. Manipulatives can be form in variety shape and they are used as teaching tools in order to engage students in the hands in learning of mathematics.

### Teaching

The meaning of teaching which is give an information or instruction in any subject or skill. Then, teaching is all about concentrated sharing of knowledge and experience to students. Teaching is similar with training, coaching, preparing or brainwash.

### Primary Level

The primary level was called an elementary grade. There are students in the primary school from standard One until standard Six. Thus, it is also typically the first stage of formal education.

## Literature Review

This chapter will discuss and explore more on the literature which is relevant to this study. Some previous researcher studies about the effect using manipulatives in teaching mathematics among teachers. This chapter begins with mathematics teachers using manipulatives, teaching mathematics using manipulatives and teaching mathematics using manipulatives at primary level. Then, the researcher presents the method of teaching mathematics using manipulatives and the effect using manipulatives in teaching mathematics at primary level.

### Mathematics teachers using manipulatives

Use of manipulatives could be very challenging in teaching especially when the teachers do not know the existence of manipulatives and do not know how to use manipulatives. This statement had stated by previous researcher who is McIntosh (2012) explained that when the teachers do not have enough knowledge or beliefs towards their training and confidence levels will dragged them in teaching their students mathematical misconceptions through manipulatives use. So that, the teachers should have knowledge in using manipulatives that can teach their students and assist them in right direction to understanding the concepts of mathematics correctly.

Next, another previous researcher had stated that as mathematics educator believe that students would be better learner if given a chance in experience the use of manipulatives. It can help and encourage students to visualizes, examine and develop the concepts of mathematics. Not just that, the teachers mathematics also responsible in order to illustrate the mathematical relationships with applications related with surrounding.

### Teaching mathematics using manipulatives

According to previous researcher John van de Walle (2013) explained that manipulatives as mathematical tool represents a topic of mathematics that can be imposed. Manipulatives also can be in physical objects, picture or drawing. It showed use of manipulatives can help teachers in teaching mathematics at primary level. Next, manipulatives as tools for teachers modelling and visualizes towards students which use to illustrate and discover mathematics concepts. This tools more effective and valid for use in the classroom instruction.

Moreover, another previous researcher Traver Holder (1993) has been proven and highly support that use of manipulatives effectively in teaching mathematics because use of manipulatives can be using at any grade levels in order to help students to understand concepts of mathematics. Then, use of manipulatives also give teachers chance to help students who is weak in mathematics especially the concepts of mathematics that always make students confusing. It is can give students to exploring and discover the problems in order using manipulatives.

Lastly, teaching mathematics using manipulatives would be interesting and fun learning in order to encourage students more motivate in learning mathematics. Previous researcher had proved that using manipulatives can help learners in development cognitive of mathematics.

### Teaching mathematics using manipulatives at the primary level

Since the early 1900s, use of manipulatives be part as essential in teaching mathematics at elementary school level. Then, as described by Dienes (1960) suggest that children learning in mathematics build their knowledge within understanding the concepts of mathematics and supported another theorist Jean Piaget (1952) suggest that children be able to understand symbols and abstract in experiencing using concrete materials.

Next, teaching with manipulatives can help students especially at primary level in order to understand mathematics concepts by experiencing hand on learning. Thus, it is can grab students attention which is play and explore concrete objects. When students touch, move and explore these objects. It can help them in developed their learning skills and thinking.

From here, students will be eager to asked question, connect ideas to find the solution of the problem. it showed that students are able to understand that concept with using manipulatives. Hence, the terms of concrete materials and manipulatives are often described as teaching tools. For example of manipulatives are fraction tiles, popsicle stick, pattern blocks and base ten blocks.

### Method of teaching mathematics using manipulatives

In order to use manipulatives effectively and correctly, an educator especially teachers need to design and create creativity activities in using manipulatives very carefully. According to Zahorik (1996) that found the educator felt use of manipulatives did not encouraged students in developing their lesson in mathematics even the hands – on activities is generating interest and promote students to love and learn mathematics.

Therefore, there are many method that we can keep manipulatives become a foundation basis in learning mathematics. Firstly, manipulatives should be directly parallel to the objectives or standard topic of mathematics that being taught. So that, students would gain deeper understanding in content of topic and also can save time the teacher in teaching. Use of manipulatives is long life time that can be used in the class for several years.

Secondly, use of manipulatives allow that students figure out in solving the problem by their own minds. It is also called manipulatives as self – correcting. The teaching styles in using manipulatives is heutagogy which the teachers as assistance that helping students if they really need help. Not just that, it is can allow students to develop their cognitive by their own pace.

Thirdly, manipulatives can come in variety of forms. Not just that, the manipulatives are multifunctional that can grabbed student’s attention and motivate them to learn and love mathematics. In the japan, children were introduced with small manipulatives at lower elementary grade that can teach them in discovered and solving the problem. However, this statement were supported by previous researcher who is Sowell’s (1989) stated that manipulatives is highly effective in order consistently used in a long period of time in teaching and learning.

Forth, as educator we need to build understanding of the concepts mathematics use of manipulatives. For example, when teaching the fractions topic in using manipulatives which is fraction tiles.

So that, students can more understand and can avoiding misconception. It is can encourage students to learn more topic of mathematics and increases their performance. Normally, young learner would us their fingers to counting especially multiplication. According to Siegler (1996) stated that use of manipulatives which is base ten blocks can develop more sophisticated in solving the problem and visualizes it.

Anglegs

- Anglegs used to learn polygons, perimeter, area, side length and more.

Attribute Blocks

- Attribute Blocks used to learn shape of 2D Dimension (triangle, square, rectangular, circle and hexagon).

Base Ten Blocks

- Base Ten Blocks used to study addition, subtraction, multiplication and division. It also can used in teaching area and volume.

Fraction Tiles

• Fraction Tiles used to study explore fraction in addition, subtraction, and mixed numbers.

Geared Clocks

- Geared Clocks are to accurate hour and minute relationship. It is allow young learner to now time and calculating elapsed time.

Pattern Blocks

- Pattern Blocks are used to learn measurement which is side length and width. It also to show that the sides have same length except trapezoid.

Snap Cubes

- Snap Cubes is used to study explore number sense and operations including counting, addition and subtraction.

### Effect using manipulatives in teaching mathematics at primary level

In fact, use of manipulatives are contribute to development of cognitive skills and communications. As described by Stein (2001) stated students are easily in remember about what they did and explain what they thinking in using manipulatives to solve the problem. There are many of effect using manipulatives in teaching mathematics at primary level which are use of manipulatives can increases student’s communications and thinking skills in order to present their solutions.

Next, teaching styles which heutagogy would be present in this system because of educator as assistant that assist students in order to find the solutions of the problems. It is can developed students in working groups or pair to present their ideas. This is a chance to improved themselves and shared the strategies in experiencing using manipulatives.

Hence, use of manipulative also build up the bridge between the concrete materials and abstract level of topic in mathematics. It is can improved and increasing student’s scores and performance. Manipulatives can serve as model to help and support students in learning mathematics and avoiding misconceptions. Manipulatives also can known as foundational basis in learning and teaching mathematics.

Lastly, according to Heddens (1986), Reisman (1982), Ross and Kurtz (1993) said that manipulatives is good objects in orders to help students and allows them learning based on experiencing about the abstract concept of mathematics. Thus, manipulatives is very important in teaching and learning especially mathematics in helping students to think more meaningful ways and developed their interest to love and learn mathematics.

## Conceptual and Theoretical Framework

This study guided by two theorist who are Jean Piaget and Montessori which is that young children learn best through concrete objects. As described by Jean Piaget, young learner’s thinker focused on concrete object based on experiencing and abstract as symbols.

From Piaget’s theory and Montessori’s theory that had discussed in background of the study had supported by James Burner (1996) that believed use of manipulatives help young learner’s thinking being active and focused. Not just that, James Burner suggest that different types of manipulatives helped young learner to touch and increases their development of cognitive.

Lastly, manipulatives is very useful and important towards educator in teaching mathematics to help students gain deeper understanding concepts of mathematics. It should be present as objects in teaching mathematics. So, it can showed that mathematics some subject very fun, interesting and easier to learn and score.