Reflections from the Application of Different Type of Activities : Special Training Methods Course *

Abstract: The aim of this study is to reveal the benefits gained from “Special Training Methods II” course and the problems prospective mathematics teachers encountered with it. The case study method was used in the study. The participants in the study were 34 prospective mathematics teachers studying at a Primary School Mathematics Education Department. The data collection tools were a form composed of open-ended questions and semi-structured interviews. Descriptive analysis of the quantitative data was carried out. In the “Special Teaching Methods II” course, beginning in the spring term of the 2015-2016 academic year, teaching activities on “multiple intelligences”, “discovery”, “group work”, “problem-solving”, “history of mathematics” and “computer-assisted teaching” were developed and implemented. It was concluded that these activities helped students like mathematics more, understand the importance of helping each other and cooperation and have more enjoyable lessons, as well as aiding their cognitive, social and emotional development. It was also found that through these activities participants improved their belief in themselves and increased their confidence regarding teaching mathematics. The participants also faced with some difficulties during the application process. They mostly mentioned that preparing worksheets was time-consuming, finding a school to perform the activity was hard and students were reluctant.


Introduction
Activity may be defined as a planned task which aims to provide the students with the gains in the curriculum (Bransford, Brown and Cooking, 2000) and applications which allow students to use mathematical expressions and symbols, create models and engage in reasoning and abstraction (Baki, 2008).In other words, activity may be defined as a task, which attracts the interest of the student, is a part of everyday life and puts the student in the center (Bukova-Guzel & Alkan, 2005).An activity should be interesting and educational, selected from daily events, have a defined purpose, enable students to interact and collaborate, allow students construct their knowledge by using their previous experiences and preliminary learning, make efficient use of time, motivate students and encourage them to think, discuss and predict (Dreyfus & Tsamir, 2004;Doolittle, 2000;Epstein & Ryan, 2002;Ishi, 2003;Kerpic, 2011;Ozmantar & Bingolbali, 2009;Saunders, 1992;Watson, 2008).On the other hand, Ainley, Pratt and Hansen (2006) emphasizes that purpose and applicability principles are important when developing an activity.
Mathematical tasks are given great importance in the United States in order to improve the quality of mathematics education and support the learning of a certain concept (Simon and Tzur, 2004).National Council of Teachers of Mathematics (NCTM) highlights the importance of student-centered mathematics education through application of various activities (NCTM, 2000).In the updated middle school mathematics curriculum and textbooks in Turkey, it is noted that subjects should be taught through activities (Ministry of National Education [MNE], 2013).The curriculum aims to create situations where students make discoveries on their own through learning-based activities and easily learn by understanding (Bulut, 2008).Considering that the curriculum expects subjects or concepts are taught through activities (MNE, 2005), it seems that there is a conflict instead of a common perception as far as the application of the curriculum through activities goes and therefore there are problems about the quality and the implementation style of activities (Bozkurt, 2012).On the other hand, some studies reveal that teachers are not able to develop activities or perform developed activities in their classes (Duatepe-Paksu and Akkus, 2007) or are not interested in and willing to perform activities due to certain reasons (Bal, 2008;Ozpolat, Sezer, Isgor and Sezer, 2007).
The content of the Special Training Methods (STM-I and STM-II) course involves field-specific basic concepts and the relation of these concepts with the teaching in the field; general objectives of the teaching in the field; methods, techniques, tools and materials used; and review and assessment of the relevant curriculum and textbooks.In addition, the course requires teaching of problem-solving, numbers and operations, algebra, geometry, measurement, data processing and probability and involves planning, presentation and assessment activities (CoHE, 2007).Therefore, prospective teachers are expected to be informed about strategies, methods and techniques required by the STM course which they take at undergraduate level and be able to apply these strategies, methods and techniques when they start their service.However, it is reported in the literature that teachers prefer teaching methods and techniques such as direct instruction or question-answer, are not sufficiently equipped (Okur-Akca, Akcay & Kurt, 2016) and usually use the question-answer technique, the expository teaching strategy and discussion and direct instruction methods (Temizoz & Ozgun-Koca, 2008).Teachers show the busy curriculum and the concern for not being able to keep up with the schedule as the reasons behind this situation and express that they do not use different teaching methods in different classes (Temizoz, 2005).Although studies on activities are available in the literature, there is no study in which prospective teachers apply activities which they developed in the STM-II course to middle school students and which points out to resulting situations to the best of our knowledge.For this reason, this study is significant in that it reveals opinions of prospective teachers about the applicability of activities which they developed and determines potential gains of middle school students via these activities.In this context, prospective teachers developed mathematical activities in accordance with principles specified in the curriculum and the study addressed how these activities are applied within the process.Thus, the purpose of this study is to reveal outcomes achieved through and problems encountered during the application of activities related to multiple intelligences, discovery, group work, problem-solving, history of mathematics, mathematical rules and computer-assisted teaching.To this end, the study seeks to answer the following questions: 1. What are the difficulties encountered by prospective mathematics teachers during the "STM-II" course?2. What are the opinions of prospective mathematics teachers about gains provided by activities developed in the "STM-II" course for middle school students?3. What are the gains provided by activities developed in the "STM-II" course for prospective teachers?

Methodology
The study utilizes the qualitative research approach.The qualitative research method is used for the systematic examination of meaning derived from the experiences of individuals participating in the research (Ekiz, 2013).Qualitative studies have important characteristics such as creating an awareness of the natural environment, adopting a holistic approach, revealing the perceptions of participants, being flexible and performing an inductive analysis (Yildirim & Simsek, 2011).Taking these characteristics into account, the present study was designed as a case study approach which requires the use of multiple data collection tools by the researcher to gather detailed and in-depth information about real life events, a certain situation, a certain time period or limited situations within a group (Creswell, 2013;Yildirim & Simsek, 2011).The present study focuses on a limited situation and attempts to gather in-depth information, thus employs the case study method.

Participants
The study was carried out with 34 prospective teachers attending the fourth-year of Elementary School Mathematics Teaching Department, Faculty of Education in a state-owned university.28 of the participants were female and 6 were male.The prospective teachers participating in the study were coded as P1, P2, P3, P4, P5, ..., P34 in accordance with research ethics.

Data Collection and Analysis
A form consisting of open-ended questions was used in this study in order to reveal opinions of participants about gains achieved through and problems encountered during mathematical activities which they constructed and applied in the STM-II course.The form included questions regarding gains achieved through and problems encountered during the application of activities related to multiple intelligences, discovery, group work, problem-solving, history of mathematics, mathematical rules and computer-assisted teaching.The questions in the form used in the study were prepared with the help of the literature and opinions of two experts on the subject were received.The content and prediction validity of questions in the form was ensured by receiving opinions of three faculty members specializing on the field.Lastly, comprehensibility of the questions was examined by a Turkish language professor and the form took its final shape.
The qualitative findings obtained using the form were applied descriptive analysis.Tables were created based on common views of the participants.Frequency values were used when creating the tables.It is of great importance in terms of validity in a qualitative research to report the data collected in detail, include direct quotes from the participants and present results obtained (Yildirim & Simsek, 2005).For this reason, direct quotes were used in this study to reflect the opinions of the participants and present findings to the reader in a organized and interpreted manner.Quotes from prospective teachers were included with each code.

The Application Process of The Activities Constructed by The Participants
The prospective teachers made use of experiences of the researcher and various studies in the literature when developing the activities given in the table below.The title, the purpose and the participant count of each activity carried out in the STM-II course can be seen in the table below.It should be mentioned that prospective teachers received help from experts to develop the activities.12 Safety in Numbers To allow students to collaborate toward a common goal and gain confidence.

13
From The Specific to The General, from The General to The Most General To perform activities aimed at examining number and shape patterns and arithmetic sequences and expressing the rule of the sequence using a variable (e.g.n).

Pinocchio and The Money Pouch
To ensure active participation and effective communication through group work.
15 Working with Whole Numbers To compare and sort whole numbers.

A Basket of Apples and The Car Dealer
To solve a higher-order problem using Polya's problemsolving steps.
As shown in the table above, the participants prepared 16 "Group Work" activities dealing with different subjects.To arouse interest in and willingness to learning, increase learning responsibility and improve versatile thinking skills in decision-making process.
As shown in the table above, the participants prepared 17 "Problem-solving" activities dealing with different subjects.

Activity's Name
Activity's Purpose

Number of Participants 1 Sieve of Eratosthenes
To allow students learn the historical development of mathematics and value mathematics.

Ataturk and Geometry
To allow students learn about the history of mathematics by showing the importance placed by and contributions of Ataturk to mathematics.

Fractals in Our Lives
To raise awareness in students by pointing out the place of fractals in the history of mathematics.

Ancient Egyptian Mathematics
To help students understand place values of digits in the decimal number system and the reason behind the transfer in addition.

Euclid's Algorithm
To allow students to discover Euclid's cathetus correlation.

Dealing with The Sieve of Eratosthenes
To help students find prime numbers up to 100 using the sieve of Eratosthenes. 7

Getting to Know Pythagoras and His Relation
To help student establish the Pythagorean relation and solve problems by teaching them the place of Pythagoras in the history of mathematics.

Guess and Find
To help students explain and share their mathematical ideas in a logical way by using the mathematical terminology and language correctly.9 Leonardo Da Fibonacci To allow students to discover that mathematics exists in nature and everywhere and realize beauties of mathematics. 10

Getting to Know al-Khwarizmi
To inform students about the history of mathematics by introducing al-Khwarizmi.
11 Pearls from Sierpinski To introduce the famous Polish mathematician Waclaw Sierpinski and his contributions to science.
12 Sino-Japanese Numbers To examine the development processes of mathematics in different civilizations.

Solving A Eratosthenes Puzzle
To explain Eratosthenes' contribution to the history of mathematics.To allow students see relations between concepts, reach generalizations, make estimations based on the rule and improve inductive and mathematical thinking skills.

Studying Fractions with Smurfs
To teach how to compare unit fractions, make denominators equal and recognize equivalent fractions.
12 Not Without Rules To point out the importance of mathematical rules which we use in everyday life.

Whole Numbers in My Mind
To choose the right strategy for mental addition and subtraction with natural numbers.
14 Think About It To teach students the rules of division and help them transfer these rules to new situations or associate the rules with everyday life.
15 How About Working with Cylinders?
To calculate the volume of the cylinder and find the pattern between volumes of two cylinders whose diameters are doubled 16 Party Hat To give examples for the use of cone in everyday life and help them find volume and area of cone.
As shown in the table above, the participants prepared 16 ".Rule Teaching" activities dealing with different subjects.To identify diagonals and interior and exterior angles of polygons and calculate the sum of interior and exterior angles.
2 Finding Formulas To construct new knowledge using the preliminary knowledge of students and thus show them how formulas are derived.
3 My Sugar Cube To establish the volume relation through models considering that the cube is a special case of the rectangular parallelepiped.

Angles in My Body
To name and draw polygons and recognize main elements of polygons such as the edge, interior angle, corner and diagonal.

Linear Equations
To draw graphs of linear equations and express how two variables with linear correlation change depending on each other via tables, graphs and equations.
6 Brain Storming To form structures whose drawings from different perspectives are given.
7 My Absolute Value To teach how to determine the absolute value of a whole number.

The Discovery of The Day
To find the general pattern by finding the relation between the edge length of a square drawn in a circle, whose radius changes at each step, and the area of the isosceles right triangle in each square.
9 Learning The Square Root To teach students how to determine the relation between square natural numbers and square roots of these numbers.

Let's Discover Together
To create the image of a planar shape created as a result of successive displacements and reflections.
11 Vulture Circle To measure the length of a circle and the arc of a circle and the area of a circle and a circle segment.

Let's Play with Legos
To calculate the volume of a shape by counting unit cubes.

I Found A Model
To associate a percentage with a fraction or decimal notation corresponding to the same greatness and show conversions between these notations via a model.
14 My Exponential Numbers To find and show the square and the cube of a natural number.

Percentages on Windows
To allow students to calculate the amount corresponding to a certain percentage of a quantity and express a quantity as the percentage of another quantity.

Acute, Right and Obtuse Angles
To teach students form acute, right and obtuse angles and recognize acute, right and obtuse angles.17 Let's Make Lemonade To teach students liquid measuring units and conversions between these units and help them make comparisons.

18
Let's Find The Perfect

Square and The Difference of Two Squares
To teach students the perfect square and the difference of two squares.
As shown in the table above, the participants prepared 18 "Discovery" activities dealing with different subjects.As shown in the table above, the participants prepared 9 "Computer-assisted Mathematics" activities dealing with different subjects.
The participants were given three weeks to determine activity types, content and their group mates.At the end of three weeks, the participants presented their activities in the classroom.The names of the activities were determined as a result of cooperative work of each group.The participants were asked to form groups consisting of at least two and at most four members.Groups were created in the study since it is stated in the literature that activities should be designed in a way that they will allow students work in groups (Kayaaslan, 2006) and should also involve situations requiring both group and individual work (Baki and Gokcek, 2005;Baki, 2008).The participants were asked to take photos during the performance of activities and complete the activities two weeks prior to the end of the semester.The participants were interviewed during class hours each week and asked to prepare reports for each activity.The reports prepared by the participants were examined and feedback was given on how to perform the activity in the next class.Once the activities were completed, groups made presentations about their activities in the last class of the semester.As an example, the application processes of four different activities (history of mathematics, theory of multiple intelligences, teaching rules and problem-solving activities) are presented below:

History of Mathematics Activity
Figure 1 shows reflections from the activity "Napier's Bones".The aim of this activity was to show students how mathematics was transfered from the past to this day and how mathematical operations were performed in the past.The students were also explained that mathematics is man-made and not sent from heavens.Before the application, the appropriate ones were selected among worksheets on "History of Mathematics" prepared for 5th graders depending on the gains desired and the subject.After consulting with the responsible teacher of the school providing the internship program, the students were explained the purposes of the worksheets.The activities were distributed to 18 students.After wishes of good luck, the students were told that they could ask for help from the participants should they have any difficulties.The application was carried out on an individual basis by 14 students due to the low classroom size.The students were asked to read the text at the beginning of the worksheet involving two activities each having seven questions.The students were told to answer the questions in accordance with instructions.In a nutshell, the text involved a story about how to multiply numbers using the Napier's bones method.It was observed that three students answered all of the questions correctly, however the students generally had difficulty in answering the questions in the activities.

Theory of Multiple Intelligences Activity
Figure 2 shows reflections from the "Discovering Ourselves" activity.The purpose of this activity was to adopt an approach which considers individual differences of students and regulates the teaching process according to these individual differences and to help students realize these differences and value mathematics and also themselves.
Prior to the application, the participants prepared a worksheet for 8th graders about the "Theory of Multiple Intelligences".
After consulting with the responsible teacher of the school providing the internship program, the students were explained the purposes of the worksheets.The application was carried out in groups of two with the participation of 18 eighth grade students.In the beginning, the students showed a prejudiced attitude toward the activity and thought that they could not answer the questions.It was observed that these prejudices diminished once the students reviewed the worksheet.As stated in Gardner's "Theory of Multiple Intelligences", worksheets were prepared to consider individual differences of students and regulate the teaching process according to these individual differences.The students stated that they found the activity to be fun and it was observed that they had a good time because they were offered learning experiences appealing to all senses and given the opportunity to play an active role in learning (Baki, Gurbuz, Unal & Atasoy, 2009).
It was found as a result of the activity that the students identified the intelligence domain which suited them the best and drew pictures and wrote stories and poems accordingly.The students realized their capacity to create a product, their ability to come up with effective and efficient solutions for real life problems, their ability to solve new and complex problems which need to be addressed and thus discovered themselves.Moreover, the activity attracted the attention of middle school students since it helped them get to know themselves and the students expressed that they discovered their intelligence type at the end of the application.

Rule Teaching Activity
Figure 7 shows reflections from the "How About Working with Cylinders?"activity.The prospective teachers who supervised the activity aimed to have students calculate the volume of the cylinder and find the pattern between volumes of two cylinders whose diameters were doubled.Prior to the application, the students were reminded how to calculate the volume of the cylinder.The students found the subject to be fun and enjoyable.The participants guided them in cases where students had difficulties in understanding the subject.In spite of the guidance provided by the participants regarding the performance of the activity, 14 students asked for help from the prospective teachers on how to perform the activity.The reason why the students had difficulties might be because they could not discover the relation over the pattern.After the application, the worksheets completed by the students were evaluated and it was detected that they had difficulties in finding the rules and relations using the operational steps.

Figure 7. Reflections from the "How About Working with Cylinders?" activity
European Journal of Educational Research 167

Problem-solving Activity
The aim of the "Whole Numbers/All Numbers" activity was to identify the problem situation and look for solutions.Prior to the application, the participants prepared a worksheet for 8th graders about problem-solving.The group work method was used when performing the problem-solving activity.The application was performed with 16 eight grade students assigned to 8 groups of two.The worksheet related to whole numbers was introduced to the students prior to the application.After necessary explanations, the students were handed the worksheet consisting of 8 questions and asked to read the instruction at the beginning of the worksheet.The students were asked to solves the given problem in the first activity, to write down problem steps in the second activity and form a problem in the third activity.The worksheets completed by the students were evaluated after the application and it was found that most groups participating in the activity answered all of the questions correctly, whereas the group with the least number of correct answers had 3 correct answers.At the end of the application process, it was seen that almost all of the students answered problems in the activities successfully without difficulty.

Findings / Results
The findings obtained according to sub-problems of the study are given below in tables.It is difficult to find a school to perform the activity.4

Findings Related to The Difficulties Encountered by Prospective Mathematics Teachers During The "STM-II" Course
Some of the participant opinions regarding codes derived from "Prospective Teacher", "Student" and "Time" themes given in Table 8 can be found below.
"The students... did not want to participate in the application process and made a fuss about it… (K19)" "It took me more time than I expected to prepare the worksheet.(P3)" "We encountered problems while arranging a class in the school which we visited to perform the activity.There where teachers who did not want to give their course hour because they did not want to fall behind in their schedule.But we were able to perform the activity in a fifth grade class in the end by asking one of the teachers.(P11)"

Findings Related to The Opinions of The Participants About Gains Provided by Activities Developed in The "STM-II" Course for Middle School Students
Table 9.The gains provided by activities developed in the "STM-II" course according to prospective teachers  "We have also decided to review our class management and focus on our shortcomings.(P1)"

Discussion and Conclusion
This study focused on the difficulties encountered by prospective mathematics teachers while carrying out activities, the opinions of prospective teachers about what middle school students gained from the activities and about what participants gained from the activities.Thus, an attempt was made to reveal the opinions of prospective teachers regarding the benefits achieved through and problems countered during the application of activities related to multiple intelligences, discovery, group work, problem-solving, the history of mathematics, mathematical rules and computerassisted teaching.
Regarding difficulties encountered by the participants during the application process of mathematical activities, the participants mostly mentioned that it was time-consuming to prepare worksheets, it was difficult to find a school to perform the activity and students were reluctant toward the activity.Some of the findings obtained from "Prospective Teacher", "Student", "Time" and "School" themes show similarities with some studies in the literature (Bal, 2008;Ozpolat, Sezer, Isgor & Sezer, 2007).This shows that students and teachers are not accustomed to carry out mathematics classes with activities.
Regarding gains of "Discovery-Group Work-Multiple Intelligences-Problem-solving-Rule Teaching-Computer-assisted Mathematics" activities for students, the participants expressed that students had increased interest and curiosity in mathematics, classes became more enjoyable, prejudices toward mathematics were eliminated, participation in class increased, students helped each other more and permanent and meaningful learning was ensured.These findings are consistent with those of Elbers (2003) who reported that activities encouraged students to study and discover mathematical learning processes, allowed them to gain experience and develop new strategies.In addition, these findings show parallelism with those obtained by Yildiz andBaki (2016a, 2016b) in their study on the history of mathematics education.This leads to the idea that the activities developed greatly contributed to both cognitive and affective skills of the prospective teachers.
Regarding gains of the participants related to "Professional and Personal Development", it was revealed that the prospective teachers learned how to make mathematics classes more interesting, gained experience about how to manage the class and realized their lack of knowledge about certain subjects.In this context, Bozkurt (2012) found how perceptions of participants regarding the activity are reflected on the application to be a remarkable situation.These findings are consistent with the findings of the study.From this point, we can say that the activities allowed the prospective teachers to gain preliminary experience related to teaching.
Almost all of the participants included in the study expressed that the activities which they developed in the "STM-II" course and applied to middle school students improved their beliefs and confidence in their ability to teach mathematics.Thanks to this course, the prospective teachers found the opportunity to come out to the field outside the faculty environment and perform the activities.The prospective teachers stated that they believed these activities which they performed with students contributed a lot to their social-emotional and professional skills as well as their cognitive skills.The participants better understood the importance of the teaching profession thanks to beneficial learning processes which took place as a result of the activities.From this, we may conclude that the course helped the participants become prospective teachers who experienced the excitement and joy of teaching students mathematics through various activities.A literature review reveals that there are numerous studies conducted with the idea that developing activities will contribute to mathematics education and therefore teacher education (Herbst, 2008;Kerpic, 2011;Ozmantar, Bozkurt, Demir, Bingolbali & Acil, 2010;Ugurel, Bukova-Guzel, 2010).Therefore, the findings of the study show that the activities have positive reflections on teacher training.
The participants made the necessary research using the curriculum, textbooks and various studies in the literature under the guidance of the researcher in the activity development stage and therefore were well-prepared and placed the necessary importance and value to the activities, which ensured that the activities were beneficial and effective.Similarly, Ersoy (2006) found that teachers' high level of knowledge, increased awareness and sensitivity toward their duties allowed activities to be beneficial and effective.
Considering the importance of guidance offered by the teachers and clues provided on how to learn in activities performed with primary school students, the importance of in-class activities is better understood (Ozmantar et al., 2010).In this context, students who perform or are encouraged to perform activities within the scope of in-class applications will become individuals who are accustomed to activities, able to understand the purpose of activities (Saglik, 2007;Yalvac, 2010) and eager to perform activities.Therefore, students will see that mathematics is actually an engaging course and it is possible to enjoy mathematics if they crack the secret of it as they perform activities.From this point, it seems that activities are effective in enabling students to view mathematics as an engaging course rather than a scary one and like mathematics better, understand the importance of cooperation and collaboration in group works (Baki et al., 2010), understand mathematics better and enhance their cognitive and social-emotional development.In this context, students should be encouraged to find their own solutions and make generalizations from their solutions while performing activities (Olkun & Toluk, 2003).
Researchers concluded that activities in almost all mathematics textbooks undervalued efficient use of time and preconditioned behaviors of students and did not include activities related to use of computer technologies other than the calculator (Arslan & Ozpinar, 2009;Kerpic & Bozkurt, 2011).Similarly, the results of the trends in international mathematics and science study indicate that activities developed and performed in the process are not implemented efficiently (Sisman, Acat, Aypay & Karadag, 2011).These results contrast with the findings of the study.Because the results of the study show that the activities were quite effective.
It was concluded that the "STM-II" course allowed prospective teachers to think mathematically (Arslan & Yildiz, 2010;Yildiz, 2016), solve problems (Taskin, Yildiz, Kanbolat & Baki, 2013), learn by doing and experiencing, reason, make connections and achieve permanent learning when learning concepts through activities developed and performed within the scope of the course.In addition to the cognitive dimension mentioned above, considering the affective dimension; the activities improved prospective teachers' belief and self-confidence, their ability to communicate with students and teachers at the school, their class management skills, their ability to cooperate with students and their sense of responsibility and allowed them to feel themselves as teachers.
The following recommendations are presented considering the results of the study: 1.The participants stated that they had difficulties in finding a school to perform the activities.Teachers and administrators serving in middle schools may try to help prospective teachers who will soon be in service to solve this problem.Also, considering that activities have an important place in student achievement in mathematics, the awareness level of teachers may be increased on this matter.
2. Some participants expressed that students were reluctant to perform the activities.It may be beneficial that teachers perform activities, especially those included in the 2009 curriculum and textbooks, more frequently in their classes and ensure students get accustomed to perform activities to overcome or reduce this problem.Also, learning-teaching activities in the 2013 curriculum may be enriched.In-service trainings may be organized to provide teachers with adequate knowledge and skills regarding activities included in the middle school mathematics curriculum in order to improve the situation.
3. The participants expressed that students had increased interest and curiosity in mathematics, classes became more enjoyable, prejudices toward mathematics were eliminated, participation in class increased, students helped each other more and permanent and meaningful learning was ensured.Considering the interest of students in the activities, teachers and prospective teachers may be informed about mathematics teaching through activities.Thus, the increase in the interest of students in mathematics will be sustainable.
4. Almost all of the participants included in the study expressed that the activities which they developed in the "STM-II" course and applied to middle school students improved their beliefs and confidence in their ability to teach mathematics.In all major field courses received by prospective teachers at undergraduate level, prospective teachers may be given the opportunity to develop activities with more tangible, clear and rich material support in order to achieve goals specified in the curriculum.
5. Interviews may be held with prospective teachers to investigate participant opinions about how to improve and apply activities in more depth.Also, observations may be conducted in order to examine how teachers develop activities and perform them in their classes and reveal difficulties which they encounter.
To summarize, it is recommended that mathematical activities are given more weight in schools, students are familiarized with activities and raise the awareness of teachers and prospective teachers regarding mathematical activities.Activities in the updated curriculum and textbooks may be enriched in a way that all mathematical gains from primary education level to secondary education level are emphasized.

Figure 8 .
Figure 8. Reflections from the "Whole Numbers/All Numbers" activity communication between students To improve students' motivation To improve students' self-confidence To teach how to work in cooperation To create a sense of responsibility To enable students see their deficiencies Discovery To create an interest and curiosity toward mathematics 31 To ensure permanent and meaningful learning 10 To enhance the communication between students To improve students' self-confidence To have students discover mathematical concepts To allow students learn through brainstorming To offer different perspectives To raise a generation which produces information

Table 1 .
Multiple Intelligences Activity To improve communication skills and use problem-solving, reasoning and logical thinking skills efficiently.10Let'sDoIt TogetherTo name and classify polygons.11Brand New Ideas To help students suggest new mathematical ideas.

Table 3 .
Problem-solving Activity Time to Solve ProblemsTo interpret the time chart given and understand the concept of time by solving problems.14Get The Frog out of The Well To solve problems using Polya's problem-solving steps.

Table 4 .
ContinuedAs shown in the table above, the participants prepared 18 "History of Mathematics" activities dealing with different subjects.
4 De Moivre's Calculation To help students realize the ability to measure time.

Table 6 .
Discovery Activity

Table 7 .
Computer-assisted Mathematics Activity

Table 8 .
Difficulties encountered by prospective teachers

Table 9 .
ContinuedSome of the participant opinions regarding "Discovery-Group Work-Multiple Intelligences-Problem-solving-Rule Teaching-Computer-assisted Mathematics" themes given in Table9can be found below.Findings Related to The Gains Provided by Activities Developed in The "STM-II" Course for Prospective Teachers

Table 10 .
The gains provided by activities developed in the "STM-II" course for the participants Some of the participant opinions regarding codes derived from "Professional Development" and "Personal Development" themes given in Table10can be found below.