H OW D O P RESERVICE M ATHEMATICS T EACHERS U SE M ANIPULATIVES TO T EACH M ATHEMATICS ?

: The aim of the research was to examine and evaluate how preservice mathematics teachers’ use of manipulatives to teach mathematics. In the current research, one of the qualitative research methods, case study was used. The research was conducted with 21 preservice mathematics teachers. Ten instructional sessions with manipulatives were carried out during a five-week period by researcher. After the instructional sessions preservice teachers made lesson plans and they designed a learning environment that teaches mathematics with manipulatives. The findings of the research indicated that most of the preservice teachers could not use manipulatives effectively and appropriately for the purposes. In addition, some preservice teachers had difficulty in making connections between mathematical concepts, daily life and manipulatives.


Introduction
Teachers are one of the main factors of the learning and teaching process as they have a crucial function and a determining and guiding role for gaining the behaviors predicted by the educational process (Atav, Kunduz, & Seçken, 2014).Therefore, the teacher training program constitutes a large part of the efforts to increase the quality of education.The importance of teacher training programs is also stressed for their important role in terms of preparing preservice teachers for their future classroom (Simon, 2013) so teacher competencies and teacher training is one of the issues that teacher educators frequently research on.General Competencies of the teacher profession refer to the knowledge, skills, attitudes and values that a teacher should have.Teacher competencies include competencies in the field, professional knowledge and general culture (Çelik, Yorulmaz & Çokçalışkan, 2019).It can be thought that teachers with these competencies will provide a qualified education.In this context, teachers and preservice teachers should be equipped and developed with the general and special field competencies that teachers should have in preservice and inservice training programs (Sarpkaya-Aktaş, 2017).In this framework, preservice teachers are provided with sufficient proficiency in subjects such as classroom management, measurement and evaluation, using strategy, method, technology and instructional materials (Shulman, 1986).
The competencies that teachers should have are considered as pedagogical content knowledge, mathematical content knowledge and curriculum knowledge (Ministry of National Education [MoNE], 2006;Shulman, 1986).In order to help to students learn, teachers must have sufficient knowledge of the subjects they will teach.This knowledge forms the content knowledge.Content knowledge is not sufficient for effective teaching (Ball & McDiarmid, 1990).Therefore, another competency, pedagogical content knowledge is essential.Pedagogical content knowledge as one of the components of teachers' knowledge is the type of knowledge that includes the most useful representations, simulations, examples and explanations that enable the understanding of frequently taught concepts specific to the field (Shulman, 1986).According to Shulman's (1995, s.130) model, teachers who have strong pedagogical content knowledge are more successful in designing effective teaching and learning environments, in understanding of what makes the learning of mathematics topics easy or difficult and in representing and formulating the subject that make it comprehensible to others.
Acta Didactica Napocensia, ISSN 2065ISSN -1430 One of the skills that should be acquired by preservice mathematics teachers is using manipulatives since the effective use of manipulatives in mathematics lessons depends on teachers (Sowell, 1989;Kelly, 2006).In order to facilitate learning by using manipulatives, teachers need to create effective learning environments and know when and how to use manipulatives on teaching mathematical concepts (Marshall & Swan, 2008;Moore, 2012).Manipulatives can only help the children's learning when they are used correctly in class (Boggan, Harper & Whitmire, 2010).Teachers should allow their students to have free time to play with the manipulatives (Boggan, Harper & Whitmire, 2010) and to explore them.On the other hand, teachers also need to know how to manage the learning environment when they use manipulatives (Marshall & Swan, 2008).
Despite the importance of using manipulatives in mathematics lessons, teachers had difficulties in using manipulatives, establishing connections between manipulatives and mathematics symbols (Kamina-Iyer, 2009).Moyer (2001, p.194) stated that, "it is difficult for teachers to transfer students' representations of their mathematical thinking and represent connections among mathematical ideas".In order to teach mathematics effectively, teachers should have a deep understanding about mathematics, they should know how to use manipulatives to support the development of a specific mathematical concept (Marshall & Swan, 2008).
Teacher educators should guide preservice teachers in the proper use of manipulatives in their teaching practices (Willis & Browning, 2013).Yetkin-Özdemir (2008) revealed that although preservice elementary teachers had knowledge and skills about manipulatives, they had difficulties to guide students to make connections between mathematical concepts and manipulatives.One of the reasons of difficulties is that even though the preservice teachers learned how to use manipulatives in teaching, there was not enough time to become a competent user of the manipulatives (Pişkin-Tunç, Çakıroğlu, & Bulut, 2020).
Preservice teachers should develop knowledge and skills to use manipulatives for mathematical subjects appropriately (Yetkin-Özdemir, 2008).For that reason, it is important for preservice teachers to gain skills of using manipulatives.In this context, the aim of the research is to examine and evaluate the skills of preservice mathematics teachers about using manipulatives to teach mathematics.Findings of this research can give clues about how preservice teachers will teach mathematics with manipulatives in their future classroom.Exploring preservice mathematics teachers' use of manipulatives in mathematics teaching will also give some important ideas to teacher educators about how to design learning environments to improve preservice teachers' knowledge of using manipulatives.

Conceptual Framework
Bruner's theory promoted the use of manipulatives in education.Besides Bruner's theory Piaget's theory also pointed the use of manipulatives (O'Meara, Johnson, & Leavy, 2020).In literature concrete mathematical tools are named as manipulative (Kamina-Iyer, 2009;Moyer, 2001), material (Furner & Worrell, 2017), concrete models (Sowell, 1989) and manipulative materials (Swan & Marshall, 2010).In this research "manipulatives" are used to define concrete mathematical tools.Moyer (2001) defined manipulatives as objects that are designed to represent abstract mathematical context concretely.Bellonio (2012) defined manipulatives as "objects that can be touched and moved by students to introduce or reinforce a mathematical concept".Manipulatives consist of objects used in daily life such as money, matches or measuring tools, or objects such as base ten blocks, algebra tiles (Yetkin-Özdemir, 2008) and can be in many forms, like fraction set, geometry strip, graph paper, empty cartons, etc.On the other hand, manipulatives can be in concrete, pictorial, and abstract or symbolic form (Sowell, 1989).Concrete manipulatives are objects that students can use and carry such as geo-boards, bean sticks; visual manipulatives are tools such as pictures, diagrams and graphics or videos, and abstract (symbolic) manipulatives are materials such as books, worksheets and pens that students use while working.
Base ten blocks, geo-board, geometry strip, tangrams, fraction sets, fraction cards, counters, pattern blocks, algebra tiles, unit cubes, geometric objects, symmetry mirror, volumes set, multi-squares set, multi-cubes set are used as manipulatives in mathematics lessons (Ministry of National Education, [MoNE], 2017).By using the geo-board, polygonal models, congruent and similar shapes can be constructed by students.It is also possible to construct polygon models with geometry stripes.Base ten blocks can be used to teach operations with natural numbers and decimals.The symmetry mirror allows Volume 15 Number 2, 2022 students to take the reflection symmetry of geometric shapes.The volume set can be used to teach the volumes of geometric objects.One of the mathematics manipulatives, counters are tools that can be used to model integers and operations with integers.Many new shapes can be created using tangrams which develop students' spatial skills.Another manipulative pattern blocks are tools to make patterns and tessellations.Fraction cards and fraction sets are manipulatives that can be used teaching fractions and operations with fractions.Algebra tiles are tools that can be used to express algebraic expressions.A set of multi-squares are useful materials to teach area and perimeter.On the other hand, unit cubes and multi-cubes can be used to teach geometric objects and develop spatial visualization skills.
These manipulatives especially concretize abstract mathematical concepts (Moyer, 2001) and establish connections between daily life experiences, mathematical concepts and symbols (Swan & Marshall, 2010;Uttal, Scudder & DeLoache, 1997).Szendrei (1996) stated that manipulatives help students develop a deep understanding of mathematical concepts and critical aspects of mathematics.As a matter of fact, some researches indicated that manipulatives make mathematical concepts easier to understand (Allen, 2007;Izsak, 2004;Kennedy & Tipps, 1994;Moyer, 2001;Suh & Moyer-Packenham, 2007) and increase achievement (Aburime, 2007;Boggan, Harper & Whitmire, 2010;Manches, O'Malley & Benford, 2010;Martelly, 1998;Martin & Shwartz 2005;Sowell, 1989;Swan & Marshall, 2010).Ünlü (2018) revealed that preservice teachers stressed the contributions of manipulatives such as increasing permanent learning, reification of abstract concepts, facilitation of learning and understanding, provision of visualization, conceptual learning, visualization in the mind/spatial thinking, effective teaching and reinforcement of subjects.On the other hand some researches indicated that using manipulatives does not have an effect on performance (Thompson, 1994) since the effectiveness of manipulatives depends on the teacher's skills and their instruction that is implemented (Pişkin-Tunç, Çakıroğlu & Bulut, 2020).
As a result of reviewing the literature, it has been determined that some preservice teachers have difficulty in making connections between mathematical concepts and manipulatives (Kamina-Iyer, 2009;Yetkin-Özdemir, 2008).Despite this, the number of studies examining in detail what the preservice teachers experienced while using the manipulatives and what difficulties they encountered is quite limited.Gökkurt-Özdemir, Uygun, Gün ve Koçak (2020) found that, although many preservice teachers wanted to use the manipulatives for the purpose of teaching the subject, they could not go beyond using for the purpose of practicing.Yazlık (2018) emphasized that teachers should make plans for the lessons in which they will use manipulatives and carefully prepare instructions for using manipulatives.In line with these researches, considering the role of teachers in the teaching process, it is important to investigate the skills of preservice teachers about using manipulatives.Moyer (2001) stated that teachers use manipulatives to enrich activities or as a game at the end of the mathematics lessons and students only used the manipulatives by following the teachers' directives.

1. Research Design
This research aimed to examine and evaluate the skills of preservice mathematics teachers' about using manipulatives in mathematics lessons.For this reason, one of the qualitative research methods, case study were used.In the case study, environments, individuals or processes are evaluated as a whole in real context (Patton, 2015).It allows an in-depth investigation of a particular group (Yıldırım & Şimşek, 2008).The case study was realized on a group of preservice elementary mathematics teachers.They were selected to examine their skills about using manipulatives.In this study, this method was preferred because the skills of using manipulatives of the preservice teachers in the natural environment were examined and more than one data collection tool (documents related to the lesson plans, field notes taken by the researcher during the observation process) were used.

Participants
The current research was conducted with 21 preservice mathematics teachers who were enrolled in a mathematics teacher education program at a state university.Preservice teachers who were taken a Material Design in Mathematics Education course were purposefully chosen for this research.In this course, instructional technologies and manipulatives which were used in teaching mathematics were taught and at the end of the course preservice mathematics teachers designed a concrete material about mathematics subjects.

Data Collection
During the implementations, theoretical information was given about designing and using manipulatives.Manipulatives that were used in mathematics teaching were introduced by the researcher.Examples were given and courses were designed to learn and discuss how to use manipulatives in mathematics classes.Detailed data collection process was presented in Table 1.Designing a learning environment that teaches mathematics with manipulatives and applying the lesson plans integrated acquisitions.
14 Evaluation According to Table 1, in 2-6 th weeks, activities related to manipulatives were conducted.It took 10 sessions and every session was 50 minutes duration.In 7 th week, preservice teachers prepared their lesson plans and in 8-13 th weeks, they presented their lesson plans.After the presentations in the 14 th week, preservice teachers and researcher evaluated their process.Manipulatives used in instructions and corresponding concepts were presented in Table 2.As seen in Table 2, the first session consisted of manipulatives such as base-ten blocks that can be used for teaching natural numbers and decimals.Activities with these manipulatives were carried out for modelling natural numbers and decimals, comparing and ordering decimals, and operations with natural numbers and decimals.In the second session the activities about equivalent fractions, comparing and ordering fractions, and operations with fractions were explored by using fraction cards and fraction bars.
In the third session, activities with hundred tables and counters were made.In the fourth session, algebra tiles were used to model algebraic expressions and operations with these expressions.In the fifth session, the participants were asked to construct polygons and to explore the relationships between triangle's edges by using geometry strips and geo-boards.In the sixth session, they were asked to construct different shapes by using squares sets and then estimate and calculate the areas and perimeters of these shapes.In the seventh session, activities with a symmetry mirror were carried out for the subjects of symmetry.In the eighth session pattern blocks and tangrams were used for teaching concepts of transformation geometry.In the ninth session such as unit cubes, cubes set, isometric dot paper that can be used for teaching three-dimensional shapes and spatial visualisation were introduced.Preservice teachers were expected to draw two-dimensional views (top, front, and sides) of the three-dimensional shapes.In the tenth session preservice teachers were supposed to construct a cube, a rectangular prism and a square prism with unit cubes and then to explore the volumes of these three-dimensional shapes.
After the instruction, every preservice teacher made a lesson plan and designed a learning environment that teaches mathematics with manipulatives within 20-30 minutes in class.Teaching practices were video-recorded and after the lessons, the recordings were analysed by the researcher.While collecting the data of the study, unstructured observation was also used.Case studies utilize multiple sources of evidence.One of these source types is direct observations that focus on human activities, the physical environment, and real-world events (Yıldırım & Şimşek, 2013).As a result of the observations, answers to the following questions were sought.
1. Did the preservice teacher know how to use manipulatives? 2. Did the preservice teacher introduce the manipulatives ? 3. Did the preservice teacher allow the student to use manipulatives? 4. Did the preservice teacher give correct instructions and directives while using the manipulatives? 5. Did the preservice teacher give feedback to the student about the use of manipulatives? 6. Did the preservice teacher make connections between manipulatives and the mathematical concept? 7. Did the preservice teacher concretize the mathematical concept using manipulatives? 8. Did the preservice teacher make connections between manipulatives and daily life?9. Did the preservice teacher able transform manipulatives to mathematical symbols?10.Did the preservice teacher manage class while using the manipulatives?

Data Analysis
The current research was carried out within a 14-week period with the participation of the preservice mathematics teachers.Manipulatives used by preservice teachers and the mathematics subjects they used in mathematics teaching are given in Table 3.During the implementation, skills of preservice mathematics teachers' about using manipulatives were evaluated by the researcher.Data from preservice teachers were obtained through document analysis, observation and video records.In order to establish validity and reliability, video-records were analyzed and categorized by different mathematics education researchers independently.Then these sets of categories were compared with each other and their final form was given.The themes and sub-themes and their frequencies (f) were presented.In this study, direct quotations about the observations, and lesson plan of the preservice teachers were included for the reliability of the research.After the coding process, for making required corrections, the issues on which there were "agreements" and "disagreements" were discussed.In order to calculate the reliability of the research, the reliability formula Reliability = Agreement/ (Agreement + Disagreement) was used (Miles & Huberman, 1994).
In the current research, the reliability was calculated to be 91%.

Findings
In this section, according to the documents, video-records and observations, the findings related to the skills of preservice mathematics teachers about using manipulatives are presented in Table 4. Initially, lesson plans of the preservice teachers' were examined.Some of the preservice teachers had adequate knowledge of using manipulatives in lesson plans (f=13).It has been observed during their teaching process that some of the preservice teachers have knowledge about where and how the manipulatives will be used.Despite this lesson plans were generally superficial, the preparation, teaching and evaluation stages of the course were not detailed enough in their lesson plans.For example, the lesson plan of preservice teacher S1, is not adequate to teach mathematics with manipulatives.
"Preparation: First of all, the subject and acquisition of the lesson are explained.Then the geo-boards were given to the students and the students are told to construct equal and similar polygons using the geo-board.
Process: First, they are told to construct 2 different triangles on the geo-board to see if they can be constructed or not.Secondly, they are asked to construct 2 identical triangles and to compare these triangles.It is expected to do the same steps with the rectangle and the square.After that properties of rectangles and squares are discussed.Then ask students to construct the same shape on the circular geo-board.At the end, it is concluded that it is constructed congruent geometric shapes.

Conclusion: Students understand the concept of congruence and similarity of geometric shapes."
According to the plan, preservice teacher S1 only gave directives to the students but it is not possible to teach congruence and similarity concepts in such a way.During his implementation, he allowed students to use manipulatives but he could not give correct directives and clear explanations.As a result, preservice teacher could not use geoboard for the purpose of concept learning and go beyond using them for the purpose of practicing.
Another preservice teacher S14's plan, "Preparation: First, fraction cards are introduced and an example is shown about the use of fraction cards.After that fraction cards are given to the students and they are asked to multiply fractions with these fraction cards.As an example, two fractions are written on the board and a student is chosen from the class and asked to multiply these two fractions.The student models the multiplication by placing these two fraction cards painted in different colours on top of each other, one vertically and the other horizontally.When the fraction cards are put on top of each other, the total number of squares formed constitutes the denominator of the fraction, and the total number of squares with colour change forms the numerator of the fraction.It is also represented concepts such as equivalent fractions using fraction cards.
Result: An abstract subject such as multiplication with fractions becomes concrete by modelling them with fraction cards.Evaluation: Multiply 2 5 by 3 4 using fraction cards.Choose different fractions and make comparisons between two fractions by using fraction cards.
During his presentation, he allowed students to use manipulatives but he did not give correct directives and clear explanations.It is not possible to make connections between mathematical concepts and manipulatives in such a way since the result was found by applying the given instructions rather than teaching the multiplication with fractions conceptually.As a result, he taught multiplication with fractions traditionally.
According to the observation results, some preservice teachers (f=10) started lesson by introducing the manipulatives to the students in the learning-teaching processes.For example, preservice teacher S16 stated to give information about manipulatives in the lesson plan such as "First of all, the manipulatives are introduced to the class.Then, algebra tiles are given to the students…."In the lesson, S16 started the lesson after introducing manipulatives; on the contrary, half of the preservice teachers started teaching the concepts directly without introducing manipulatives in any way (f=11).This situation may cause misuse of manipulatives as students do not have knowledge about where and how to use manipulatives.
According to the findings obtained as a result of video recordings and observations, all of the preservice teachers allowed the students to use the manipulatives individually or in the form of group work in the learning-teaching processes.They gave all of the manipulatives to the students before the lessons.Thus, Acta Didactica Napocensia, ISSN 2065-1430 it would be possible for students to gain experiences about manipulatives and explore mathematical concepts by using manipulatives.
While some preservice teachers gave clear, understandable and correct instructions in their teaching process (f=12), some of them could not give correct instructions to the students (f=9).For example, S3 asked to construct 3-4-5 triangles firstly and 3-4-10 triangles with the geometry strip to see if it is possible to construct this triangle or not.Then triangles were compared.The reason why it can be constructed or not was discussed and explained in class.After that angle-edge relations were discussed.Another preservice teacher S21 gave instructions such as "Similar or non-similar polygon models are drawn on the worksheet.From these polygons which polygons are similar?Why are they similar?Name similar polygons.Determine congruent angles and proportional edges.Find the similarity ratios of similar polygons?"This instruction was not understood very well in the lesson and the preservice teachers did not know exactly what to do.
As a result of the research, the findings obtained from the videos and lesson plans showed that most of the preservice teachers concretized abstract mathematical concepts (f=14).For example, preservice teacher S13 taught equivalent fractions with fraction cards."Represent by using fraction cards.Now, put these fraction cards on top of each other.What did you see?" What can you say about these fractions?Are they equivalent?"In this example preservice teacher represented fraction with fraction cards and concretized the concept of fraction.On the other hand, some preservice teachers did not concretize abstract mathematical concepts (f=7).
Another important finding obtained from the research is that only two preservice teachers made connections between daily life experiences and manipulatives.It was determined that other preservice teachers could not make connections between daily life experiences and manipulatives, neither in their lesson plans nor in the learning-teaching processes.For example, S6 gave this example and made connections between daily life and decimal numbers and base ten blocks."Melek was born with a weight of 3.44 kilograms and Şeyma was born with a weight of 3.35 kilograms.Accordingly, let's find out how many kilograms more Melek was born than Şeyma.The problem is written on the board.They are asked to represent the given numbers with base ten blocks.It is discussed which operation the problem requires and students asked to represent the operation.Preservice teacher S6 thought that…..Decimal numbers, which can also be encountered in daily life, are handled visual, thereby ensuring its retention in mind." Half of the participants (f=11) made connections between mathematical concepts and manipulatives.According to the preservice teacher S18' s teaching process "Work sheet was given to the students and it was expected to fill the table that consisted of an area and largest perimeter of multi squares.The set of multi-squares were examined.First, area of manipulative was calculated and the table was filled on the work sheet.For the possible largest perimeter of multi-square was examined and noted on table.Second, the area of another multi-square was calculated and the largest perimeter was found.For the possible largest perimeter of manipulative is examined and so on… Finally, the pattern between the area and the largest possible perimeter was found.It was concluded that multi-square set with the same area may have different perimeters.",preservice teacher S18 made connections between concepts of area, perimeter and multi-square set.Some preservice teachers transformed manipulatives to mathematical symbols (f = 13).Preservice teacher S7 taught absolute value by using a symmetry mirror.According to the plan, S7 designed learning environment: "Ask students to draw number lines on squared paper.It is requested to put the symmetry mirror at the zero point on the number line.Ask students to say the pairs of numbers that overlap on the symmetry mirror.Discuss and compare distances of these pairs of numbers from zero.It is noticed that the distances of the number pairs from zero are equal.The definition of distance to zero is absolute value and it is represented by " (-2) from zero (absolute value of -2)], thus |2|=|-2|=2.The result is that the absolute value comes out as positive, whether the number inside is positive or negative.|a|>|b| if a>b is true or false, it is explained by giving examples."As a result of observation, S7 transformed manipulatives to mathematical symbols.
In the teaching process, only 9 preservice teachers gave feedback about the use of manipulatives.During the lesson, they walked around the classroom, checked the students' representations with manipulatives and guided the students.They also corrected students' mistakes who used manipulatives wrongly.
Another important factor is classroom management.Every preservice teacher managed the classroom during the distributing and retrieving manipulatives.According to the finding, S6 stressed that "I think that classroom management will become difficult when teaching with manipulatives.Because some students may see manipulatives as a game.This can make teaching mathematics difficult."Another preservice teacher S7:"I think we need to guide students correctly about using manipulatives while teaching mathematics in the classroom.Otherwise, classroom management can become difficult."Most of the preservice teachers (f=13) were good at communication.They used gestures, mimics and the tone of voice properly and communicated with preservice teachers by getting them to participate in the lesson.14 preservice teachers could manage time effectively.Another 7 preservice teachers coul not finish activities on time.

Conclusion
According to the findings, it has been determined that some of the preservice teachers have a general command of using manipulatives.In light of the results of the study, it was observed that they chose suitable manipulatives for mathematics subjects and mathematics acquisitions.However, most of the preservice teachers could not use manipulatives effectively and appropriately for the purposes.Although many preservice teachers wanted to use the manipulatives for the purpose of teaching the subject, they could not go beyond using them for the purpose of practicing.These findings are correspond to findings of related literature (Gökkurt-Özdemir et al., Moyer, 2001).Whereas teachers should create effective learning environments and know when and how to use manipulatives on teaching mathematical concepts (Marshall & Swan, 2008;Moore, 2012).For that reason, it is crucial for preservice teachers to learn to use manipulatives correctly in the correct place in teacher education.Therefore, it is recommended to increase the number of courses in which manipulatives are used in teacher education program.It is also recommended to teacher educators to guide preservice teachers in the proper use of manipulatives in their teaching practices (Willis & Browning, 2013).
Another important issue is making lesson plans by using manipulatives.Approximately half of the preservice teachers could plan their lessons appropriately.Teachers should make plans for the lessons in which they will use manipulatives and prepare instructions for using manipulatives carefully (Yazlık, 2018).If preservice teachers have enough knowledge about making lesson plans with manipulatives, they will plan their future lessons effectively when they become teachers.Thus, it helps them to develop knowledge and skills to select and use appropriate manipulatives (Yetkin-Özdemir, 2008).
According to the findings obtained from this research, most of the preservice mathematics teachers started the teaching process without introducing the manipulatives sufficiently.In order to understand how to use the manipulatives, students need to learn the manipulatives.Otherwise, it will be difficult for them to use manipulatives effectively.
The preservice teachers allowed to use manipulatives during the lessons.For this reason, they gave all of the manipulatives to the students before starting the lessons.In this context, they gave enough time to use manipulatives during the lessons.They used manipulatives individually or in the form of group work in the learning-teaching processes.This situation enabled preservice teachers to interact with manipulatives.Boggan, Harper and Whitmire (2010) stated that teachers should allow their students to have free time to play with the manipulatives.However preservice teachers are not given enough time to become a competent user of the manipulatives in teacher education programmes (Pişkin-Tunç, Çakıroğlu & Bulut, 2020).On the contrary, it is expected from preservice teachers to give enough time to their students to explore and use manipulatives.For this reason, giving manipulatives to students to make practice is good evidence for preservice teachers to become competent users of manipulatives.
While some preservice teachers gave correct directives, clear and understandable explanations in their lessons, others did not.Students should learn mathematical concepts conceptually.Moyer (2001) stated that students used the manipulatives following the teachers' directives.So they learn mathematics Acta Didactica Napocensia, ISSN 2065-1430 traditionally.However, if preservice teachers could not give correct directives, clear and understandable explanations in their lessons, students could not understand what to do with manipulatives.
As a result of the research, some preservice teachers concretized abstract mathematical concepts.Mathematics involves many abstract concepts.Manipulatives are important tools that concretize abstract mathematical concepts (Moyer, 2001) and they make mathematical concepts easier to understand (Allen, 2007;Izsak, 2004;Kennedy & Tipps, 1994;Suh & Moyer, 2007).If preservice teachers and teachers concretize abstract concepts with manipulatives, students will learn mathematics more quickly.
When the lesson plans and teaching process of preservice teachers' were examined, it was determined that the preservice teachers mostly experienced difficulty in making connections between daily life experiences and manipulatives.Many researches also indicated that preservice teachers have difficulty in making connections between daily life and manipulatives.A few related studies show that making connections in mathematics teaching is far below the predicted level and quality (Gainsburg, 2008).For this reason, it is important to relate mathematical concepts with daily life for understanding mathematics.In addition, associating with real life motivates students and increases students' interest in mathematics (Stylianides & Stylianides, 2008).In spite of that, teachers generally choose real-life contexts to motivate their students, engage them, and show that mathematics is more understandable when it is related to real life (Gainsburg, 2008).
Half of the participants made connections between mathematical concepts and manipulatives.Despite this, it has been determined that some preservice teachers have difficulty about making connections between mathematical concepts and manipulatives (Kamina-Iyer, 2009;Yetkin-Özdemir, 2008).Manipulatives provide students with an additional perspective about mathematical concepts (Johnson, O'Meara, & Leavy, 2020).However, manipulatives are not automatically meaningful to students they need to be connected to the situations being represented (Kilpatrick, Swafford & Findell, 2001).Yetkin-Özdemir (2008) revealed that although preservice teachers had knowledge and skills about manipulatives, they had difficulty in guiding students to establish connections between mathematical concepts and manipulatives.Therefore, it may be useful to increase the number of examples that preservice teachers can relate mathematics concepts to manipulatives in teacher education courses.
The findings of the research revealed that only 9 preservice teachers gave feedback to the student about using manipulatives.Feedback is an information that is given about the student ś performance or understanding (Hattie & Timperlay, 2007).If teachers give feedback about using manipulatives, students will be aware of their misuse and misunderstanding and they will have a chance for correcting their mistakes.
More than half of the participants transformed manipulatives to mathematical symbols.Despite this, it has been determined that some preservice teachers have difficulty in transforming manipulatives to mathematical symbols.Some researchers also indicated that preservice teachers have difficulty in establishing connections between mathematical concepts and symbols (Swan & Marshall, 2010;Uttal, Scudder & DeLoache, 1997).
Another important factor is classroom management.Teachers should know to manage the learning environment when they use manipulatives (Marshall & Swan, 2008).They managed the classroom during the distributing and retrieving manipulatives.Most of the preservice teachers were able to communicate with their classmates and could manage time effectively.On the other hand, teachers also need to know how to manage the learning environment (collection and distribution of materials).These research findings are parallel to findings researches.Pişkin (2010) emphasized that the preservice teachers think that the greatest difficulty while teaching mathematical concepts by using manipulatives is classroom management.Ünlü (2018) found that some pre-service teachers think that manipulatives should not be used in elementary classrooms as they make the classroom management difficult.
In order for manipulatives to be recognized and used by the preservice teachers, it is recommended that the lecturers give the preservice teachers plenty of opportunities to gain experience with the manipulatives.One of the important sources of gaining experiences is direct experiences, so preservice teachers to live direct experiences of using manipulatives.By creating classroom environments in which preservice teachers feel psychologically and physically comfortable, they can make practice about teaching mathematics.As a conclusion, incorporating such practices into teacher training programs is believed to make contributions to the attempts made to train more qualified teachers.These practices can help preservice teachers develop skills in terms of using manipulatives effectively, classroom management and time management.Therefore, such implementations can be conducted in the courses of Teaching Practicum and Teaching Methods courses.Moreover, such researchs can be conducted for teachers.In this way, teachers can also see their mistakes and shortcomings in the use of manipulatives.

Table 1 .
Data collection process and activities Conducting activities related to manipulatives.As manipulatives: Geo-board, geometry strip, base ten blocks, tangrams, fraction cards, fraction bars sets, unit cubes, algebra tiles, symmetry mirror, multi-square set, multi-cubes set and volume set were used 7 Preparation of lesson plans Providing preservice teachers mathematics acquisitions in middle school mathematics curriculum, choosing one of them and making lesson plans 8-13 Presentation of lesson plans

Table 2 .
Manipulatives used in instruction and corresponding concepts

Table 3 .
Manipulatives used in preservice teachers' instruction and corresponding concepts

Table 4 .
Skills of preservice mathematics teachers' about using manipulatives