Mathematics was originated as a necessity for the cultural, societal and technological growth or leisure. The principles and procedures of mathematics have always been the predominant building blocks of most of human inventions and discoveries. It is an interdisciplinary human language, developed as a unique tool for modeling and formulating most of the qualitative and the quantitative phenomena as well as the different processes of the world and surroundings (Livio, 2011). Also, Davis, Hersh & Marchisotto (2011) have stated that mathematics is a human activity, which is for everybody. However, everyone is a mathematician. Everyone is able enough to do mathematics operations consciously, for example, trading, measuring, decorating and doing patterns are all parts of mathematics. Livio (2011) has described that mathematics is a universal language with unique syntax, characters, and complex combinations of several rules and principles.
1.1 Background
Unfortunately, school mathematics is a quite difficult and boring subject for many of the students of different grades in school (Zakaria, Chin & Daud, 2010). Most of the time it is considered as difficult and less interesting to the students, and it has been documented in research (Zakaria, Chin &Daud, 2010). Usually it is because of the style of teaching and the style of learning. Several efforts are made in order to reform both the curriculum and instructions of mathematics (Smith, 2000). In addition, Reid et al., (2014) stated that in the past, the educators have been considered that changing of the curriculum could be used as an effective method to change classroom practice and to have an impact on the learning of the students. Also, they pointed out that the curriculum has been called as a change factor for the educational reforms. Furthermore, they have stated that “school mathematics curriculum remains a central issue in our efforts to improve students’ learning”. While it is true that the EQAO results (2017), for both Primary and Junior mathematics assessment of English Language learners’ has dropped between 2013 and 2017 by about 5%. Furthermore, OSSTF (2018) explains that the drop-in students’ level in mathematics since 2012/2013 is not only related to the change in the curriculum but also to the tests. The OECD (2015) also indicates that Canada performs relatively well at Mathematics on the PISA mathematics tests. Canada, nonetheless, has had its results dropping since 2003. Thus, educators should consider the curriculum and teaching methods to develop and reform. In the news GTA (2016), it has been pointed out from an international study that about 70 per cent of the students from grade 4 and 8 in the province are above the average level in mathematics and science.
Teaching and learning of mathematics have always been the focus point of mathematics teachers, mathematics educators, mathematics education researchers, and the other mathematicians. They always strive to redefine and discover instructional and effective teaching approaches to make mathematics more interesting, less intimidating and more accessible to the learners as well as to help the learners achieve more comfort, higher grades, and productive learning skills through mathematics. One of these newly developed approaches is the integration of “Computational Thinking in teaching school mathematics”.
1.2 The Topic
Computational thinking is a recently developed set of skills. Wing (2006) claims that it is going to be one of the basic skills that are used by the students in the middle of the 21st Century. Aho (2012) further states “we consider computational thinking to be the thought processes involved in formulating problems so their solutions can be represented as computational steps and algorithms. An important part of this process is finding appropriate models of computation with which to formulate the problem and derive its solutions” (p. 832). Furthermore, the researchers such as Gadanidis, Minniti & White (2017) are exploring the integration of computational thinking and mathematics thinking in K-8 classrooms. These researchers have observed that computational thinking tools, activities, and processes promises to make the mathematics learning experiences of the students more interesting, helpful, productive and easy to learn more advanced mathematics. Gadanidis (2017) argues that not only is computational thinking similar to mathematics thinking, but also computational thinking offers many affordances such as agency, access, abstraction, automation and audience. Working as a research assistant on computational thinking projects in schools, integrating computational and mathematics thinking is a fresh and new portray of mathematics for both students and their parents. Integrating computational thinking activities in mathematics lessons is not only a novel mathematic learning process but it also offer several affordances such as those noted by Gadanidis (2017). Such an approach can offer a deep actualization and more versatile mathematical thinking to the students (Namukasa, Patel & Miller 2017). Namukasa et al. (2017) also study students and teachers in the context of schools.
Wenglinsky (1998) maintains that using digital technologies, such as computational thinking technologies in teaching methods contributes to changing conventional teaching and learning methods and as a result it promises to lead an improved student achievement, interest and enjoyment in the learning process. Gadanidis (2015) observes that there is a relation in between coding (computational thinking) and mathematics that reforms the mathematics education, and he adds that the children have the ability to learn complex and abstract concepts.
The general research question is:
What is the nature of engagement of learners with their parents on computational and mathematics thinking activities?
The specific research questions are:
1.3 The Purpose
The purpose of this research is to explore the nature of engagement of learners with their parents on computational and mathematics thinking activities, and to investigate the ways in which the students and their parents act and interact during computational and mathematics thinking activities. With the same, it also aims to discover the role of parents when they are interacting with their children during computational and mathematics thinking activities. Furthermore, it will also investigate the benefits and challenges of parent’s engagement with their children during these thinking activities. Finally, several feedbacks are gathered of both students and parents after their engagement during the computational and mathematics thinking activities.
1.4 The Significance of the Study
The core focus of this research is to explore the learning process by using computational thinking in schools in contexts where the children participate with their parents. This research seeks to contribute to this exploration on the integration of computational thinking and mathematics thinking for students and parents at either school or an after-school learning organization. This study is unique as it is going to focus not only on the children but on their parents as well. This research involves conducting workshops for elementary students working with their parents and researching the experiences of the students and their parents. The workshops will be based on computational and mathematics thinking activities designed by Namukasa and Gadanidis.
Conducting mathematics workshops for students and their parents are positively associated with the student achievements and they makes the learning process of mathematics compelling, and more enjoyable (Marshal & Swan, 2010). At the same time, workshops can help the parents to support their children, and thereby increase their abilities and performance in the subject of mathematics (Marshal and Swan, 2010).
In addition, this study will shed light on the need of using computational thinking activities as one of the parts of the theory of teaching mathematics. Weintrop et al., (2016) pointed out about the importance of existence of computation in mathematics. Also, they indicate that in the near future, there will be an urgency of challenge of defining the computational thinking and providing a theoretical foundation for the method that should be used in school for the mathematics classes. This research shall also shed light on how computational thinking tools such as computational modeling environments can have a productive role in endeavouring and benefiting both the students and their parents, as they both are the significant elements of educating young learners. Exposing such aspect of mathematics can increase engagement and contribution of parents to their children learning process.
Theoretical framework
Computational thinking researchers trace back the theory behind computational thinking for the children and youth in the work of Papert (1980). Papert has developed the theory of learning and he referred that to as the constructionism. He considers that the constructionism is based on the idea of “learning by making”. He defines that the learning process is a process of reconstruction instead of a process by which knowledge is transferred, and that the learning is more effective when the learners are able to create a meaningful product as a part of their activities. Constructionism is related to the principles of knowledge, experiences and active learning (Bruner, 2001). In addition, Bruner (2001) theoretical framework is dependent on the theme that learners develop new ideas and concepts depending upon the existing knowledge. Whereby, Bruner is one of the major founding fathers of the constructivist theory. The work of Piaget is regarded as the starting point and the studies point for the work of Brunner. Brunner’s theory of learning is emphasized on knowledge of how this thing has happened. Therefore, the focus will be on different skills, directions and instructions, more than focusing on the information and facts. Thereby, Bruner (2001) indicates that the learning is an active process that includes selection and transformation of information, decision making, generating hypotheses, and making meaning from information and experiences.
This research has adopted the framework of social constructivism. Social constructivism emphasizes learning in social environments. Kotsopoulos et al., (2017) have discussed about constructivism and constructions as CT. They explained that CT includes four pedagogical experiences and they are, “unplugged”, “tinkering”, “making”, and “remixing”. They further explained about these four experiences. They states that Unplugged experiences applies on activities without using the computers, while the tinkering experiences include activities that needs engagements and adjustments to produce the outcomes. On the other hand, the making experiences contain activities to create new objects and, remixing take in multiple experiences that makes uses of other for the purpose. These experiences are necessary for the students to fully experience the CT. In addition, Curzon et al., (2014) states that there are many countries (e.g., they did not mention the names of the countries) that have introduced the computing syllabuses in order to make the computational thinking an essential component.
According to Arvidson (1997), there are many differences in the academic achievement of the students who are in reform programs and the students who belongs to in traditional programs. He stated that “a renewed emphasis on teacher education based on the NCTM standards, time for collaboration among teachers, and a ‘call’ for ongoing professional development in reform practices” (p. 9.) The NCTM or the National Council of Teachers of Mathematics recommends for the K-12curriculum some teaching, and assessment (Hiebert, 1999). Therefore, ICMI Study 24 (2017) is highly recommended in the school mathematics reforms and have taken a large place as a whole in today’s educational system. Also, ICMI Study 24 (2017) indicates that technology has also helped in reforming mathematics curriculum and that have brought calls for the unified standards of mathematics in the school.
Besides, Brennan & Resnick (2012) states that the computational thinking has been considered in the past years as well, but it still lacks strategies to assess the development. Furthermore, Lee et al., (2011) recommended that in order to support the development of CT skills among the children and youth several things are required and they are enriched learning environment, developed teachers’ skills to facilitate using CT in classroom, and more research on computational thinking. In addition, Barr, Harrison and Conery (2011) highly recommends that in the future, all the students are given opportunity to learn about computational thinking skills, and use it in different problems and contexts. Subsequently, the goal of this research is aimed at such aspects of mathematics. The theme of this research is framed around “computational thinking” in schools. It will demonstrate the students and their parents how learning and practicing mathematical computations can be developed in a critical and analytical fashion instead of being a haphazard set of numerical operations.
In addition, the traditional style of teaching makes mathematics boring for the students. They find it difficult, as most of the mathematical concepts are abstract. However, educators cannot consider the old-fashioned of teaching is a bad way, but they should improve teaching style that is called reforming. Reforming mathematics instruction requires changing the materials as well as changing the way of applying them. Marion (2010) explains that the educational reform allows designers of curriculum to create unique curriculum for achieving the requirements they should reach. Nowadays, educators need to skip the time of boredom in mathematics class and the difficulties that students faced in mathematical concepts. Skipping these problems could be ensured by reforming mathematics curriculum and implementing instructions to create new styles of teaching and new styles of learning.
2.1 Integration of computational thinking activities in teaching mathematics.
It is very important for the educators to find a proper environment in order to improve and develop the educational process as well as to lead the students towards the best outcomes by making use of new strategies and methods. Computational thinking contributes to change the old-fashioned teaching and learning methods. In this criterion, this research would like to shed light of the benefits of using computational thinking in mathematics curriculum. Also, to indicate that computational thinking is one of the important strategies that the educators should apply in the curriculum. The literature on integrating computational thinking addresses the following aspects: Definition/frameworks, importance of CT, integration of CT, educational technology, the benefits and activities of computational thinking, and challenge to CT.
Definition/frameworks of CT.
Wing (2006) defines that “Computational Thinking is the processes that is involved in formulating a problem and expressing its solution in a way that a computer—human or machine—can effectively carry out” p7. In addition, Sanford & Naidu (2016) states that “Recent literature discusses the importance of adding ‘computational thinking’ as a core ability that every child must learn”. Also, Sanford & Naidu (2016) adds to the point that nowadays, using the digital computers for mathematical modeling is all related to expanding knowledge boundaries. They also indicated clearly that the” knowledge-based” world needs all of us to understand how to use computational technology for everyday activities.
Importance of CT.
Sanford & Naidu (2016) define this era as the Digital Age, and they believe that the computational thinking concepts should be available in our daily life in order to enrich the quality of our life in modern society. In addition to this, from the grand vision of Wing (2011), he declares that “Computational thinking will be a fundamental skill that is used by everyone in the world from the era of 21st Century”. Thus, Sanford & Naidu (2016) goes beyond the limited applications of computational activities in classrooms and suggested that such activities can be used not only by the students but also by the parents as well. They use these activities for computational needs such as mortgages and handling accounts. Furthermore, Portelance (2015) pointed out how the computing devices that are all structured are based on computations around us. Such integration of computations makes it simple to bring it into learning environment as well. In addition, Wing (2006) labels the computational thinking as a technique that includes solving of problems, design systems, and understand human behavior depending on the concepts that are essential to computer science.
Integration of CT
Farris and Sengupta (2014), described how the computational aspects of mathematics nowadays are becoming integral and core part of presentation for both mathematics and science in K-12 programs. Whereby, they presented a unique aspect of integration of computational techniques with basic principles of physics such velocity, acceleration, energy, etc. for crafting dynamic learning activities. In addition, Bienkowski et al., (2015), rightly pointed out how integrating computational thinking in pre-college curriculum requires an interactive integration of different subjects and concepts in order to construct a grounded approach for computational thinking. Furthermore, Lu and Fletcher (2009) represented the teaching of computational thinking (CT) as an important skill on balance with reading, writing, and mathematics in the category of fundamental knowledge. Therefore, Ortiz, Bos and Smith (2015) have discussed the application of the abstract concepts in real world. They have indicated that use of integrated science, engineering, technology and mathematics helps the students to get engage with the real world.
Educational Technology
Barr and Stephenson (2011) believe that the fundamental changes in traditional instructional setting require thorough dissection of integration of math and computer science, which can lead to generating a reliable teaching technique based on the computational thinking. Also, Hooper and Rieber (1995) distinguished between the concept of educational technology and the concept of technology in education. Technology in education is often apparent of how the computers or technological devices are used to support the traditional classroom activities, but educational technology contains applying ideas from several sources to generate the best learning environments possible for students. In addition, Rieber (1995) adds that the educational technology means that the curriculum also requires changing that is to encounter the opportunities that the technology may offer. Furthermore, Portelance (2015) demonstrates a unique technique for how computational thinking “coding” can be infused into mathematical concepts by examining and activity called “Code and Tell activity” for primary grades students.
The benefits and Activities of Computational Thinking
In Brennan and Resnick (2012) research article, they review and examine various interactive media designed that are based on the computational thinking and concluded that how effectively such interactive media can have enhanced the learning of students comparing to a student that are taught in a conventional instructional setting. Also, Bienkowski et al., (2015) considered that designing interactive models with artefacts is one of the main approaches to computational thinking. Caspersen and Nowack (2013), suggested that based on their experiences with Danish high school system, presenting computational activities using platforms and social media such as Facebook, iTunes, GPS based navigation systems, email, health care systems, etc. makes the activities more relevant to the daily life of student, and consequently such activities are more compelling than the other themes. According to Yadav, Hong and Stephenson (2016), the curriculum in 21st century must focus on the computational thinking concepts for (K-12). Enriching the coding skills would result in having a new generation of real world problem solvers. Moreover, they recommended for infusing computational thinking into the curriculum for every subjects, and they suggested, “Moving students from merely being technology-literate to using computational tools to solve problems”.
Challenges to CT
Bienkowski et al., (2015) explored how generating computational based mathematics knowledge and skill can improve assessment tasks among the students. Atmatzidou and Demetriadis (2016) designed different activities based on computational thinking and they noticed that it was not so easy to connect students’ minds to computational thinking activities. However, as time passed by and students engaged in more diverse activities, they gradually become more comfortable and familiar with the nature of such activities. In fact, Lu and Fletcher (2009) faced some pedagogical challenges. Whereby, the puzzling issue is the role of programming, and whether we can separate it from teaching basic computer science, and how much programming should be required for CT proficiency. They believe that to expand successfully contribution in computer science, efforts should be needed for satisfying the foundations of CT before students apply the first programming language. Recently, Angeli et al (2016) shed light on the challenges that the educators are currently facing when computational thinking is a part of the curriculum. The first, the frame of the curriculum based on a general computational thinking outline. This challenge was debated with a perspective of designing the computational thinking curriculum and focused on real world problems. Second challenge was focused on the teachers. It points out the need of knowledge that the teachers must possess in order to teach computational thinking curriculum by finding a framework of technological pedagogical, and how they apply the ideas of computational thinking in schools. In addition, they indicated that there is a shortage of ample experimental evidences in terms of effectiveness of the context of computational thinking curriculum.
Summary
Overall, Angeli et al (2016) expected that the computational thinking curriculum will be applied all over the school curriculum in the coming years. As the world is changing rapidly, the use of computational thinking got a great attention by the educators all over the world, as it positively changes the educational process by prompting the abstract and concept of the real world. According to Resnick (1995), computational thinking “can significantly influence not only what people do with computers, but also how they think about and make sense of the world”.
2.2 Contribution and Involvement of Parents
“Parents are the real teachers”. The very first teacher a child can have is his parents. Parents educate their children before they enter into the school life. They promote the best early development learning and health of their children by supporting them, encouraging them and engaging with them in their activities. The literature on contribution and involvement of parents addresses various aspects. They include the role of parents to teach their children, the benefits of contribution and involvement of parents, the importance of parent’s involvement, and the workshop models.
The Role of Parents in teaching their Children
According to Civil et al. (2008), parents always teach their children in the manner in which they themselves were learned at their times. They think that this is not good, as they will face new educational strategies that will be unfamiliar to them. This is because, the learning process changes with the change in time. Also, Liang (2013) mentions that the study examines ways in which Chinese immigrant families are involved in mathematics educational process with their children. Liang (2013) mainly focuses on how diverse natures of families’ have an influence on their children’s mathematics education. Therefore, Liang (2013) observes how different types of families use cultural, social and economic capital to influence their children’s mathematics education. Also, Civil et al. (2008) explain that the immigrant families face a gap between their expectations for their children’s education and their experiences, because they have often a cultural difference, social gap and different language. Additionally, Kibasan and Singson (2016) state “education is the process of facilitating learning or the acquisition of knowledge, skills, values, beliefs and habits”. Abusively, most of the values, beliefs and habits for children become from family or parents especially in early years. In addition, in the study of Anisiobi (2014), he has shown that the families of high-achieving students, which are linked in more than one language at home and, they teach their children with high-achievement mindset from early years of their lives. Hence, successful learning process depends on how parents communicate with their children at home.
The Benefits of Contribution and Involvement of Parents
According to Van Voorhis, Maier, Epstein, & Lloyd (2013), the involvement of family are into four categories. They help in various ways. For example, focusing on the Learning tasks for children doing at home with their parents promote math skills outside school. Also, the actions and interactions of parents in the school building promote children awareness. The role of school awareness the engagement of families including the strategies that staff of school are used to encourage engagement of families, and make them feel welcome, and boost the parent’s activities including relationship and home environment, rule-setting, and caring behaviors. As well, they concentrate on parents’ engagement in learning process. Also, Civil et al. (2008) suggested that the engagement of parents with their children in community is promoting the mathematical concepts in house. Furthermore, Liang (2013) argues that the mathematics education can be enhanced without direct connections to schools or teachers. He states parents can provide tutors for their children, but that depends on the incomes of the families. Also, Liang (2013) supposes that teachers can assign additional exercises for students to improve mathematics education, and students can stay long time after school to do more mathematical problems, but that needs double effort or more from students. In addition, he adds parents can use social media to contact with teachers, but educators cannot ignore who does not use social media as a contact way with school. Furthermore, Anisiobi (2014) maintains that engagement with co-ethnic adults at community centers provided support which promoted social-emotional development in the teenagers.
The Importance of Involvement Parents
Epstein (1987) observes that the recent studies of importance of parents’ involvements were shown from research findings that are gathered over two decades that shows that children have an advantage in school, when their parents inspire and support them. In addition, Hartog, Diamantis and Brosnan (1998) declared that there are numerous sources that are provided to parents with games and activities that allow children to involve in mathematical thinking and problem solving, and at the same time, increase the self-confidence of children in mathematics. The sample of this kind of source is the book named, ‘Helping Your Child Learn Math’. Also, the government of Canada, ON, in education declares that when parents engage with their children and support them, the children enjoys exploring the world of mathematics. As well as, the government of Canada, ON, in education mentions that the most support is coming from families, which they offer to increase their children’s learning and do well in school, and parents help their children in educational progress and continue with their education.
Workshop Models
To improve the achievement of children in a better way, educators should seek on the track to improve the design and conduct workshops for children and their parents. Epstein (1987) indicates that the involvement of parents is one of the main standards in educational process. Thus, Xiao, Namukasa, and Zhang (2016) present a workshop model for engaging children and their parents in mathematical activities. Similarly, Paz (2011) conducts a school family night workshops for children and their parents to investigate the rapport between student achievement and parents’ contribution, where that helps students to satisfy a higher academic achievement, when their parents involve that workshops. Also, Xiao, Namukasa, & Zhang (2016) conclude that the parents appreciated workshops because they learned about how mathematics is currently taught in schools, and appreciated the opportunities to interact with their children in the workshops. In the same time, Xiao, Namukasa, & Zhang (2016) observe that the children enjoyed dealing with their parents in workshop session and learning mathematics concept. In addition, Scott (2014) sees that the student mathematics achievement was getting higher when he/ she was conducting workshop in mathematics and involving parents with them. As well, Scott (2014) notices that the students whose parents joined math workshops their level in mathematics became more better than students whose parents did not joined math workshops.
Summary
Van Voorhis et al., (2013) sum up the key findings of involvement of parents with their children. The key findings include, Family participation is an important for young children especially in math skills; Parents with varied experiences can become more engaged with their children and when parents are more engaged, children tend to do well. However, educators can design something systematic and non-profit project. This should do not depend on the income of families, and by this project parents can know the ability of their children, when they work together in workshops. At the same time, they can have fun together. These findings may be useful to direct parent involvement and increase their overall effectiveness.
2.3 Reform in Mathematics Education
Traditionally, the mathematics classrooms were the place where students used to listen quietly to their teacher’s lecture on how to solve the mathematics problems in a proper way. By means of continuous independent practices in recalling and memorizing the basic facts and the word problems, the pedagogical goal was that the students would develop automaticity and proficiency in the skills that are being taught. The Students who were encountered by the difficulties used to receive additional help and practices in order to increase the accuracy and speed of their computations. For reforming the mathematics instructions by changing the mathematics curriculum and the teaching styles, the various literature on reform mathematics education address the following aspects: the beginning of reform, the challenges of reform, the benefits of reform and the reform in mathematics education and its purpose.
The Beginning of Reform
According to Lawson and Suurtamm (2006), in the year 1989, the National Council of Teachers of Mathematics (NCTM) was one of the leaders in pushing the mathematical reforms in response to the research indicating that most of the students were learning the different procedures in mathematics without conceptual understanding. With the same, in the year 1997, the provincial government of Ontario decided to revamp the Kindergarten through Grade 8 (K-8) mathematics program and thus, developing a new curriculum, provincial large-scale assessment and report card. Furthermore, Haeck, Lefebvre and Merrigan (2011) stated that the education of early 2000s reform is implemented in most of schools, both public and private, in some of the provinces in Canada in both primary and secondary schools. They further stated that most of the students of the age of 15 do not possess such skills in order to be successful in the 21st century, and therefore, the educators plans to reform the curriculum. Lawson and Suurtamm (2006) explains that this change will offer a more proper and accurate assessment to the students’ ability in the subject of mathematics, and will support the new curriculum reform such as EQAO. Furthermore, according to Suurtamm, Koch and Arden (2010), over the last decade in Ontario, the teachers were been prompted by the educational policy, the teacher journals as well as the professional development initiatives in order to incorporate the new assessment ideas to implement in their classroom practices. They suggested focusing on the assessment for supporting the learning and the importance of using variety of assessment strategies.
They further said that using a range of assessment strategies is very important in developing the students’ mathematical understanding and for providing teachers with the opportunities to gain the insight into the students’ mathematical thinking. According to them, a great variety of assessment methods are being used to gather a sense of students’ understanding in comparison to the purpose of determining the report card marks. Ross, McDougall and Hogaboam-Gray (2002) explains that assessment in the reform class is very authentic and is integrated into day to day learning versus at the end of the unit. Recently, in the year 2017, Vallera and Bodzin suggested that combining the technology with authentic project based learning challenges using real-world examples can help the students with enhanced understandings of the complex and abstract concepts. With the same, the Project-based learning encourages the students to investigate about the problems and challenges by raising their curiosity for finding out the solutions. Providing them with authentic and project-based performance tasks, which are encountered by the scientists, engineers, technologists or the mathematicians in their lives could inspire the critical thinking, creativity, communication and the collaboration as well as will get the students excited about mathematics learning by making the content-based learning process more interactive.
Reform in Mathematics Education and its Purpose
According to Suurtamm, Koch and Arden (2010), the central aim of the mathematics education reform is to help teachers develop a classroom environment, which can support the development of mathematical reasoning by collaborative problem solving method. Haeck, Lefebvre and Merrigan (2011) further described that the purpose of the reform is to improve the performance of the low-achieving or the average students to bridge the gap in between high achieving students and the low-skilled students as well as to increase the overall performance and reduce the rate of high school dropout.
According to them the reform in the mathematics education value the mathematical inquiry as a method to engage the learners with mathematical ideas and strengthen their understanding of mathematical concepts as well as, encouraging the problem solving approach to teach mathematics to the students.
According to Haeck, Lefebvre and Merrigan (2011), the reform schools have inquiry-based activities such as asking questions, finding alternative solution, discussing to make connections, and involving the hands on learning and active participation. They spend more time by working on the projects, conducting and doing researches and solving problems that are based on their interests and concerns. Lawson and Suurtamm (2006) said that the author of the curriculum suggest that the teachers use problem solving in every strands as the foundation of new curriculum, by which problem solving can be embedded into each lesson. The purpose of curriculum is to help students to think and works like a mathematician for making the new conjectures, justifying their answers as well as evaluating the solutions of others. They further stated that the focus should be on encouraging the students to share their ideas, discuss and debate them rather than just sitting and listening to the class lectures. Furthermore, Ross, McDougall and Hogaboam-Gray (2002) stated that classroom must be organized in a group or pair to encourage the student-student interactions among them. A reform class is more dynamic and ever-changing and not just a fixed body of knowledge.
The Challenges of Reform
According to Ross, McDougall and Hogaboam-Gray (2002), the reform does not entirely relate with the mandated tests, which measure the computational speed as well as accuracy and it does not meet the expectations of the parents about how mathematics should be taught to their children and how it is being tested. Reform makes it more difficult for the students and the teachers to cover the whole curriculum, as it takes longer time.
Suurtamm, Koch & Arden (2010) further declared that the approach emphasizes on using the challenging problem for students to construct various solution methods, discussions and defense of the mathematical ideas. According to them, one of the most challenging implementations is the student discussions on mathematical reasoning, finding out the balance as well as encouraging this construction without leaving them floundering.
With the same, in the comprehensive school reform or the CSR in United States, the students learn and discover the concepts through the process of reasoning and discussions and this provides no explicit opportunities for reviewing or practicing the mathematical concept.
The Benefits of Reform
According to Haeck, Lefebvre and Merrigan (2011), School has moved away from the traditional or academic approaches of drills, memorization, and activity books, to a more comprehensive approach that is focused on learning in contextual setting in which the children are expected to find the answers for themselves. Children should get the opportunity to investigate as well as to explore mathematic problems with their teacher assistance. It is very important to start with what a child already knows, and by activating his prior knowledge.
According to them, reform in mathematics education encourage the problem solving approach to teach mathematics. The teachers who participated in the case studies have used mathematics journals, in-class assignments, homework, performance tasks, observation record sheets, independent study projects, quizzes as well as questioning and listening at the time of problem-solving activities as a part of their classroom practices.
Ross, McDougall and Hogaboam-Gray (2002) further stated that the chief characteristics of math education reform are Broader scope, use manipulatives or mathematical tools to support learning, and use of complex and open-ended problems that are embedded in the real-life contexts. Construction of mathematical ideas through the students discussion, the role of teachers as a co-learner instead of sole knowledge expert are also two of the chief characteristics.
They also stated that from their case studies, they have analyzed that students solves more complex problems, use more advanced strategies when they get confronted with the obstacles and they gain deeper understanding as well. Reform also enables them to describe their thinking, and adapt procedures in response to the problem requirements.
3.1 Data Analysis Method
Data analysis method can be of two types- quantitative and qualitative analysis. This research shall rely on the qualitative data analysis because it is most suitable when a research problem need to be addressed and explored. Through qualitative data analysis, the researchers gets an opportunity to learn more about their participants, and can further gain a deeper understanding and knowledge about the research object and its complexity (Creswell, 2012). Particularly, this research shall use instrumental case study. The case study research helps the researcher to intensively investigate the case in-depth as well as to discover the rich data and to understand its complexity by long-term involvement and with various instructional methods (Yin, 2009). Therefore, case study methods allow the researchers to gain holistic and more meaningful characteristics of the real-life events like international relations, individual life cycles, school performance, etc.
According to Stake (1995), the case study can be classified into three categories and they are instrumental case, intrinsic case, and the collective case study. In case of intrinsic case study, the researchers are guided by their own interest in the case itself, for example, a particular child, clinic or conference or curriculum rather than in the extension of the theory or the generalization across cases. The instrumental case study focuses on a particular issue and develops theory. The case study serves as an important tool for better understanding of the similar situation. In case of collective case study, there are multiple cases that are described and are compared in order to provide an insight to a particular issue (Stake, 1995). According to those differences, the research is planned in order to conduct the instrumental case study for examining the applied computational thinking activities in mathematics workshop with the students and their parents.
In mathematics workshops, the program in computational thinking activities can clearly observe the interaction of students with their parents. Thus, it has documented the impact of mathematics workshops. It can be observed that there is a positive interaction between students and their parents in mathematical activities and this means that they try to improve their attitude towards mathematics, which leads to improve their achievement, understanding, learning, thinking, and confidence of mathematics through mathematics workshops. The case study is about groups of students, parents and teachers. Researchers have observed them as a whole.
Site and participants
In order to conduct this research, data has been gathered from the Al-Tawqa Academy (London, Ontario). Children of grades 3 to 6 along with their parents have participated in a series of coding and mathematical activity workshops (3 to 5 sessions) in Al-Taqwa Academy. Data will be gathered from bservation, photos, videos records, photocopies, reflection forms from students and parents, templates, and interviews. The mathematics program will be designed, implemented and evaluated by the researchers. Research data will be collected about the effects of these activities on the participants, i.e., children and their parents. The data collection methods includs observation from the children and their participating family members. Semi-structured interviews will also be conducted with the children and their family member(s). Moreover, the data will be conducted by focusing on the group of teachers to obtain their feedback.
Research Materials
In computational and mathematics thinking workshops, the research will avoid the traditional teaching style. New styles of teaching will be enabled by integrating the computational thinking activities in teaching style with students and their parents. These styles include making sense for students of the math concepts, and allow for more understanding for students to get in explanation why they are studying math, rather than just following the rulebooks of math. In addition, students will spend easier time they will have in meeting the high social oral and mental hopes and challenges that reform-based instruction presents.
These new styles of teaching contemplate the involvement of parents in their children learning task, and attraction of the parents toward “computational thinking” is inseparable feature of the program. This will allow parents to know about new pedagogical mathematical concepts.
Research Instruments
To conduct the computational activities workshops with students and their parent, some kind of devices such as numerous of Sphero, tablets, chrome, that are connected by internet will be used.
3.2 Data Collection Method
Observations data: Observations of students, parents, and environment in mathematics workshop. I am going to collect data by observation and I am going to fill a form (see Appendix A)- during the workshop or after that depends on the note I have taken during the observation. I am going to concentrate on how students engage with their parent during computational thinking activities by taking notes video records- if I can-, photos. Also, I going to concentrate on parents and hoe they are doing with their children and with computational activities.
Interview Data: I plan to conduct a conversational interview with the students, parents and researchers- if I can-. Also, teacher’s attitude is important to me to give the nature and background of students in normal schooldays. (See Appendix…) by using open-ended questions and yes or no questions. Also, I will conduct interviews for parents with to determine their level of commitment, willingness to participate, etc. I try to do it before workshops and after workshop by two forms (see Appendix …). About students I am going to ask them about their work and personal experiences in computational thinking activities also before and after. After workshop, I have to give both students and parents feedback form to fill (see Appendix…)
Document analysis: The document analysis will focus on the presence of the research questions, and make sure that is data I collected by observations, interviews and feedback for both students and parents are sufficient to cover and answer my research questions.
Participants, such as parents and students, would not be randomly selected, but will give the agreement to be as a volunteer in interviews. A letter will be sent to the principles of Al-Taqwa academy, by email or hand-on, from my supervisor for allowing the researchers to start collecting data in the school. If any picture has taken by accidents, the faces of the participants will be blurred and private information that is related to them. The Audio records shall be free from names and their private information. All data collected will be kept confidential and will be available only to the investigators of the study. The potential risk in this study is really low or non-existent. The students, parents, classroom teacher and principle would not be asked any private information related to them. Confidentiality of the respondents will be maintained throughout the research. Their responses and identity will be kept confidential. This will help in getting a fair and actual responses from the staff members.
The research will point out the benefits of involvement of parents with their children in preview section. It will manifest how these workshops can be beneficial for children and parents together. Children enjoy learning math more when working with their parents, and parents can observe their children’s attitude with their friends, teachers, and so on, and can enhance their parenthood skills as well. Moreover, parents can learn the new teaching styles and can then apply them upon their children. While conducting a research, every researcher faces limitations with regard to the research conducted. In the present research, the limitations are limited period of time and man-power.
This research shall conduct the majority of the data analysis myself. This research is planned to transcribe the interviews data overtime, “optically scanning material, typing up field notes, cataloguing visual material, sorting and arranging the data into different… sources”. Hence, there is no use of lot of transliterating and data analysis in this research.
According to Creswell (2014), there are total of eight strategies for convincing the readers of the study’s validity and reliability like, member checking, triangulation, clarification of any bias (researcher’s), thick descriptive data, present negative or contradictory evidence, external auditor (review entire manuscript), data collected over a prolonged period of time and peer debriefing. The research report will be full of clarity that will keep the evidence and the interpretations separate from each other in the paper to will add credibility to the paper that will clearly present the data with supporting evidence. The research is conducted based on detailed record of the events directly from the field notes, transcribed audio and/or video recordings. Throughout the paper it will refer to the literature and theoretical framework that supports the findings.
As it is mentioned above, the study interested in computational thinking activities in mathematics workshops. It means that workshop depends on activities that they will be applied through workshops. So, teachers need tools, materials, and devises to facilitate the educational process and conduct the workshop’s lessons. In general, workshop needs members to continue and to complete its purpose, so it needs teachers to conduct these kinds of workshops. Also, sometimes parents are not available to attend workshop programs. However, researchers can skip some of these limitations by finding volunteers to conduct the program, and they can encourage students with their parent to attend these workshops by doing fun. In addition, researchers can do the awareness of parents to distinguish the benefits of mathematics workshop in computational thinking activities. In addition, there are Some Logistic Limitation:
However, with all these challenges, the students will enjoy during the lessons, fully engaged and they will try to complete all tasks we need.
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