Integrating Computational Thinking In Mathematics Education

The Importance of Computational Thinking in Mathematics Education

Explain On Computers In Mathematics Science Teaching.

Computational thinking (CT) is a recently developed set of skills. Wing (2006) claims that Computation Thinking will 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 (CT) to be the thought processes involved in formulating problems, so their solutions can be represented as computational steps and algorithms. Finding appropriate models of computation with which to formulate the problem and derive its solutions is an important part of computational thinking.” (p. 832). Researchers such as Curzon (2014), Gadanidis et al. (2017), Farris and Sengupta (2014),  Kotsopoulos et al. (2017), and Namukasa et al. (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 promise to make the mathematics learning experiences of the students more interesting, more productive and easier to learn more advanced mathematics. Gadanidis (2015) observes that there is a correlation between coding (computational thinking) and mathematics, and he adds that the children have the ability to learn complex and abstract concepts. 

Working as a research assistant on computational thinking projects in schools, I noticed that the integration of computational and mathematics thinking is a fresh and new portray of mathematics for students. Integrating computational thinking activities in mathematics lessons is not only a novel pedagogical strategy in mathematics learning, but it also offers several affordances such as those noted by Gadanidis (2017). 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 create possibilities for improved student achievement, interest, and enjoyment in the learning process.

Weintrop et al. (2016) indicate that there is an urgency of defining computational thinking, providing a theoretical foundation for the method that should be used in school when integrating computational thinking in mathematics classes. Certain research is addressing this gap. This research seeks to explore the ways in which computational thinking tools such as computational modeling, computational designing, and computational programming environments may be used in workshops for both the students and their parents.

Many students find school mathematics to be quite difficult, less interesting, and less relevant (Zakaria, Chin, & Daud, 2010). Also, in my experience as a middle school teacher and parent of children Grade K-9 this challenge for mathematics education appears to be due to the style of teaching and the nature of the content. In addition to teachers, parents have been noted to play some major roles in supporting (or, not supporting) students in learning mathematics (Marshal, Swan, & others, 2010). With changing curriculum and instruction there is a growing need to build capacity among parents to support their children when teachers are teaching students through new ways or teaching more advanced content.

Benefits of Integrating Computational and Mathematics Thinking

The purpose of this research is to explore the nature of engagement of learners with their parents on computational and mathematics thinking activities. The study specifically purposes to investigate: the ways in which the students and their parents act and interact during computational and mathematics thinking activities; the benefits and challenges of parents’ engagement with their children during these thinking activities; the views of both students and parents on their engagement in the computational and mathematics thinking activities.

The core focus of this research is to explore the learning process, the supports, and challenges, as well as the experiences involved in using computational thinking in schools in mathematics learning contexts where the children participate with their parents. This research involves conducting workshops for elementary students working with their parents. This research seeks to contribute to two areas: the exploration of the integration of computational thinking and mathematics thinking, and the role of parents in supporting students in learning mathematics. The students and parents will participate at either school or at an after-school learning organization. This study is unique as it is going to focus not only on the children in a classroom setting but on the role of parents as well. The workshops will be based on computational and mathematics thinking activities designed by Namukasa (2017) and Gadanidis (2017). Grover and Pea (2013) see the integration of “computational thinking in teaching school mathematics” as a promising way to teach mathematics in ways that make mathematics more interesting, less intimidating and more accessible to learners.

Researchers in the field of computational thinking trace the engagement of students in computational thinking activities back to Papert’s work exploring Logo Programming environments for children and youth. Papert (1980) developed the theory of learning that he referred to as constructionism. He considered that constructionism is based on the idea of "learning by making". He defined that the learning process is a process of reconstruction instead of a process by which knowledge is transferred and that 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 by Bruner (2009) who states that students construct new ideas based on their knowledge and experiences. Bruner (2009) points out to the theoretical framework as based on the theme that learners construct new ideas or concepts depending on the existing knowledge. 

Exploring the Learning Process of Computational Thinking in Mathematics Education

In addition to constructionism, this research adopts the framework of social constructivism. Social constructivism emphasizes learning in social environments. Burke (2004) states that social constructivism created with a movement in psychology that was a shift from behaviorism.   Vygotsky (1980) maintained that the intellectual growth is also of a society in addition to a biological nature, and the intellectual activity of the individual may not be separated from the intellectual activity of the group in which the individual belongs. Therefore, social constructivism is more interested in learning with other children and adults. Kotsopoulos et al. (2017) adopts social constructivism in their exploration of the four pedagogical experiences of computational thinking activities, which include the "unplugged", "tinkering", "making", and "remixing". They further explained about these four experiences. Kotsopoulos et al.   state that unplugged experiences apply to activities without using the computers, while the tinkering experiences include activities that need engagements and adjustments. On the other hand, the making experiences contain activities to create new objects and, remixing takes in multiple experiences that makes uses of old objects for the new purpose. The authors argue that these experiences are necessary for the students to have a full experience of the computational thinking activities.

Namukasa et al. (2017) observe that students are not just users of CT tools; they can create their own projects. 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 in the teaching of mathematics. Also, Gadanidis et al. (2017) have observed that computational thinking tools, activities, and processes make the mathematics learning experiences of the students more productive and easier to learn more advanced mathematics.

During computational thinking activities, as Bruner (2009) states, students are offered opportunities to experience learning as an active process, and as Papert (1980) states students experience “learning by making”. Computational activities allow students to learn concepts when they are playing in coding (CT).

Thus, this study proposes a computational thinking pedagogical framework established in a constructionism (Papert, 1980) and social constructivism theories (Vygotsky, 1980).  The study draws from (Kotsopoulos et al., 2017) computational thinking pedagogical framework of four pedagogical experiences: (a) unplugged, (b) tinkering, (c) making, and (d) remixing, as well as from Gadanidis (2017) computational thinking offers many affordances in the teaching of mathematics that include (e) agency, (f) access, (g) abstraction, (h) automation and (g) audience.

Engaging Parents in Computational and Mathematics Thinking Activities

To situate my study, I reviewed the following literature:

• Integration of computational thinking activities in teaching mathematics
• Involvement of parents in students’ learning of mathematics
• Reform in mathematics teaching and learning

Sanford and Naidu (2016) state that "recent literature discusses the importance of adding ‘computational thinking' as a core ability that every child must learn" (p. 23). Gadanidis (2015) has noted that computational thinking contributes to change in the traditional teaching and learning methods. In addition, Curzon et al. (2014) state that there are many countries that have introduced the computing syllabuses in order to make the computational thinking an essential component of the curriculum. A few studies exist on integrating computational thinking in teaching and learning as well as in the curriculum. The literature on integrating computational thinking addresses the following aspects: Definition/frameworks, the importance of CT, the benefits and activities of computational thinking, and challenge to CT.

According to Farris and Sengupta (2014), computational aspects of mathematics nowadays are becoming integral and core part of a presentation for both mathematics and science in K-12 programs. Bienkowski et al. (2015), rightly point 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 to computational thinking. Furthermore, Lu and Fletcher (2009) represent the teaching of computational thinking (CT) as an important skill to balance with reading, writing, and mathematics (arithmetic) in the category of fundamental knowledge. According to Ortiz, Bos, and Smith, (2015), the use of integrated science, technology, engineering and mathematics (STEM) helps students, through the application of abstract concepts in the real world, to engage with the real world. Furthermore, Barr and Stephenson (2011) believe that the fundamental changes in traditional instructional setting require integration of math and computer science, which can lead to generating a reliable teaching technique based on the computational thinking. Furthermore, Yadav, Hong, and Stephenson (2016) recommended infusing computational thinking into the curriculum for all subjects, and they suggested, "Moving students from merely being technology-literate to using computational tools to solve problems" (p. 565). In addition, Barr, Harrison, and Conery (2011) highly recommend that in the future, all the students are given the opportunity to learn about computational thinking skills and use it in different problems and contexts.

Wing (2006) defines that "Computational Thinking as the processes that are involved in formulating a problem and expressing its solution in a way that a computer-human or machine—can effectively carry out” (p.7). Also, Aho (2012) considers that computational thinking is a thought process and includes formulating problems so the solutions of problems can be embodied as computational steps and algorithms, and Aho (2012) indicates that the important part of thought process is to find appropriate models to formulate the problem and find its solutions. In addition, Sanford and Naidu (2016) add to the point that nowadays, using the digital computers for mathematical modeling is all related to expanding knowledge boundaries in varied disciplines.

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” (p. 31). When students learn through computational thinking, they can understand deeply the abstract concepts by promoting the reality to students’ thinking. Sanford and 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 lives in modern society. In addition to this, from the grand vision for computational thinking of Wing (2006), she declares that “Computational thinking will be a fundamental skill that is used by everyone in the world from the era of 21st Century” (p. 2). Thus, Sanford and Naidu (2016) go beyond the limited applications of computational activities in classrooms and suggest that such activities can be used not only by the students but also by the parents as well.

Lee et al. (2011) recommend that in order to support the development of CT skills among the children and youth in classrooms several challenges need to be addressed including enriched learning environment, developed teachers' skills to facilitate using CT in the classroom, and more research on computational thinking. Atmatzidou and Demetriadis (2016) designed different activities based on computational thinking and they noticed that it was not so easy to engage students in computational thinking activities. However, as time passed by and students engaged in more diverse activities, students gradually became more comfortable and familiar with the nature of such activities. Lu and Fletcher (2009) noted some pedagogical challenges, including the role of computer programming, and whether this role can be separated from teaching basic computational thinking concepts.

Recently, Angeli et al. (2016) highlight the challenges that the educators are facing when the computational thinking is made a part of the curriculum: The first is the design of the curriculum framework for computational thinking, specifically, whether computational thinking curriculum designs should focus on real-world problems. The second challenge is focused on the teachers, as teachers need knowledge, both technological and pedagogical, in order to teach computational thinking curriculum and apply the ideas of computational thinking in schools.

 In addition, Angeli et al. (2016) indicate that there is a lack of ample experimental pieces of evidence in terms of effectiveness of the context of computational thinking curriculum. Besides, Brennan and Resnick (2012) state that the computational thinking has been considered in the past years as well, but it still lacks strategies to assess students’ learning.

According to Gadanidis et al. (2017) and Namukasa et al. (2017), varied CT tools and activities are used in mathematics. Namukasa et al. (2017) observe that students have the abilities to represent and simulate abstract, advanced and complex concepts. The abstract concepts might be understood by computational thinking activities such as coding that involves students’ exploration of mathematics concepts through robots and apps.

Overall, given the benefits of computational thinking curriculum, its integration in the curriculum and research on its teaching and assessment, Angeli et al. (2016) forecasts that computational thinking curriculum will be adopted in the school curriculum in the coming years.

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 models of involving parents.

According to Civil et al. ( 2008), parents always teach their children in the manner in which they themselves learned during the time when they were children. Many parents find it challenging to support students when learning in ways that are unfamiliar to them and or with content that is more advanced. With changing curriculum and instruction there is a growing need to build capacity among parents. This is evident in the increased availability of parent guides such as “Doing Mathematics with Your Child, Kindergarten to Grade 6. (2014)” provided by the ministries and school board offices to parents. In mathematics education, it has been noted that parents pass on fear of mathematics to their children when for example they profess that they were never good at mathematics or that mathematics is difficult or not useful in life ( Ontario Ministry of Education, 2014).

Epstein (1987) observes that the recent studies on parental involvement in school work over two decades show that children have an advantage in school when their parents inspire and support them. Support provided by parents to their children varies with culture, social economic status and other background characteristics of the family. Families of high-achieving students, for example, would have taught their children a high-achievement mindset from early years of their lives. Liang (2013) mainly focuses on how diverse natures of families have an influence on their children's mathematics education. Liang (2013), for instance, examined the ways in which Chinese immigrant families are involved in mathematics educational process of their children. The results of Liang (2013) suggest that families can be involved in children’s mathematics, with or without direct connections to schools and interaction with teachers: Teachers can assign additional exercise for students, who may need to improve, and students can stay a long time after school to do more mathematical problems, but that needs more effort from students. Parents may provide tutoring activities for their children, but that depends on the income of families and, in my view, that encroaches on the time students would be spending on other activities at home. In addition, parents and teachers may use social media to communicate regularly about the children’s learning at school and at home, but some parents may not find social media convenient to use. 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 often do not consider the opportunities and challenges that their students face due to cultural differences, social gap, and different languages.

As Hoover-Dempsey, Walker, Jones, and Reed (2002) state “Parental involvement has been associated with stronger academic achievement by children and adolescents” (p.843). According to Van Voorhis et al. (2013), the involvement of family in supporting students at learning mathematics fits into four categories: Family engagement in school activities, family engagement in the school activities students bring at home, support of parent on home activities for their children, and family engagement at home without contact with the school.  For example, focusing on the learning tasks for children doing at home with their parents promote mathematics skills and the understanding of mathematical concepts (Civil et al., 2008).  Also, the role of the school to facilitate the engagement of families by encouraging families, and make them feel welcome, as well as boost the parent's activities including relationship and home environment, rule-setting, and caring behaviors. As well, they concentrate on parents' engagement in the learning process. Liang (2013) states that parents can provide tutors for their children.

Epstein (1987) indicates that the involvement of parents is one of the main standards in the educational process.  Xiao, Namukasa, and Zhang (2016) present a workshop model for engaging children and their parents in mathematical activities. Similarly, Nohemy (2011) conducts a school family night workshop for children and their parents to investigate the rapport between student achievement and parents’ contribution. Xiao et al. (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. At the same time, Xiao et al. (2016) observe that the children enjoyed when they were learning mathematics concept with their parents in a workshop session. In addition, Scott (2015) sees that the student mathematics achievement was getting higher when he/she was conducting workshops in mathematics and involving parents with them. As well, Scott (2015) notices that the students whose parents joined math workshops had their level of mathematics performance improve better than students whose parents did not join math workshops.

Parents play a major role in supporting their children at what they learn at schools. The engagement of students with their parents in school or community setting may be useful to provide support parental/guardian involvement in their children's learning and study and inform productive learning interactions among parents and children.

Traditionally, in many countries, mathematics classrooms were the places where students used to listen quietly to their teacher’s lectures on how to solve the mathematics problems. 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. In other countries, students learned quietly from practicing with textbook exercises at their desks. The students who encountered the difficulties used to receive additional help and practices in order to increase the accuracy and speed of their computations. Many students find this traditional style of teaching that many teachers and parents experienced at school makes boring and difficult.

Mathematics education researchers strive to redefine instructional and teaching approaches to make mathematics more interesting, less intimidating and more accessible to learners as well as to support the learners to achieve more comfort, higher grades, and productive learning skills in mathematics. Reforming mathematics instruction requires changing the teaching practices, curriculum frameworks, and learning resources. Marion (2010) explains that the educational reform allows designers of curriculum to create a unique curriculum for achieving the requirements of reforming of the curriculum. The various literature on reforming mathematics teaching address the following aspects:  the beginning of reform, the challenges of reform, the benefits of reform and reform in mathematics education and its purpose.

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 then current mathematical reforms in response to the research indicating that most of the students were learning the procedures in mathematics without conceptual understanding. Also, Lawson and Suurtamm (2006) indicate that, in  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) state that the education of early 2000s reform is implemented in most of the schools, both public and private, in some of the provinces in Canada in both primary and secondary schools.  

According to Suurtamm et al. (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 the collaborative problem-solving method. Haeck et al. (2011) further describe 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 values 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.  Recently, Vallera and Bodzin (2017) suggest 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. 

According to Haeck et al. (2011), the reform schools have inquiry-based activities such as asking questions, finding an 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. The Ontario revised curriculum suggests that the teachers use problem-solving in every strand as the foundation of the curriculum that problem-solving can be embedded into each lesson (Lawson & Suurtamm, 2006). The purpose of the curriculum is to help students to think and work 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 et al. (2002) state 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 environment.

According to Ross et al. (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. Reformed ways of teaching make it more difficult for the students and the teachers to cover the whole curriculum, as it takes longer time.

Suurtamm et al. (2010)  state that the approach emphasizes on using the challenging problem for students to construct various solution methods, discussions and defend their mathematical ideas. According to Suurtamm et al., one of the most challenging implementations is the student discussions involving mathematical reasoning, finding out the balance between learning procedures, process and understanding concepts as well as encouraging the construction of new knowledge without leaving students floundering.

Also, Haeck et al. (2011) mention that in the comprehensive school reform (CSR) in the 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. 

According to Haeck et al. (2011), the 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 a 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 mathematics problems with their teacher assistance. It is very important to start with what a child already knows and activate his prior knowledge. According to Haeck et al. (2011), reform in mathematics education encourages the problem-solving approach to teach mathematics. The teachers who participated in Haeck et al.’s case studies used mathematics student 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 et al. (2002) further state that the main characteristics of math education reform are broader scope, use manipulations 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. Ross et al. (2002) observed in their case studies that when students solve more complex problems, use more advanced strategies when they get confronted with the obstacles they gain a deeper understanding as well. Reform curriculum also enables students to describe their thinking and adopt procedures in response to the problem requirements.

According to Arvidson (1998), there are many differences in the academic achievement of the students who are in reform programs and the students who belong to 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.). Also, ICMI (2017) in Study 24, indicates that technology has also helped in reforming mathematics curriculum.

The teachers along with the parents need to assist the children in speaking about their mathematical ideas and knowledge as well as they must encourage them to explain how they have arrived at their answers. The more practice the students do in explaining why they are doing mathematics, on top if following the rules of mathematics, the easier time they will have in meeting the high verbal, social, and cognitive expectations as proposed in reform-based instruction presents.

This research shall rely on a qualitative research method because the research problem in this study needs to be explored in depth. Through qualitative research method, the researchers get an opportunity to learn more about their participants, and can further gain a deeper understanding and knowledge of the research object and its complexity (Creswell, 2015). Particularly, this research uses case study. The case study research helps the researcher to intensively investigate the case in-depth as well as to discover the rich data by long-term involvement and use of various data collection methods (i.e., triangulation) (Yin, 2009). Therefore, case study methods allow the researchers to gain holistic and more meaningful characteristics of the real-life events (Yin, 2009).

According to Stake (1995), the case study can be classified into three categories and they are the instrumental case, intrinsic case, and the collective case study. In case of an 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 the collective case study, there are multiple cases that are described and are compared in order to provide an insight into a particular issue (Stake (1995). A collective case study is conducted by a researcher who can select more than one case to provide a representative sample (Cousin, 2005). The researcher in collective case study makes more generalizations and exploration of the concept in further depth (Cousin, 2005).

This research uses an instrumental case study to examine the integration of computational thinking activities in mathematics workshop for both students and their parents.

 In order to conduct this research, data would be gathered from computational thinking and mathematics thinking parent-child workshops conducted at a religious-based private school or at a community organization in South Western Ontario. Children of grades 4 to 6 along with their parents will be invited to participate in a series of computational and mathematics thinking activity workshops (3 to 5 sessions). I have spoken to the school principal and he has offered me to conduct the workshops as part of their evening workshops for parent nights. Research data will be collected to answer questions on, generally, the nature of engagement of learners with their parents on computational and mathematics thinking activities, and specific questions on the ways students and their parents act and interact during computational and mathematics thinking activities, and the benefits and challenges of parent’s engagement with their children during computational and mathematics thinking activities. And, the views and   the feedback of both students and parents after engagement during computational and mathematics thinking activities

Data will be gathered from observation, photos, videos records, audio records, photocopies, reflection forms from students and parents, and from interviews of the children and their participating family members. The interviews will also be conducted with the children and their family member(s). As well, the interviews will be conducted with a group of participating teachers to obtain their feedback.

The workshops design is going to be based on Xiao et al. (2016) and the workshop activities are going to be based on computational and mathematics thinking activity workshops, designed by Namukasa (2017) and Gadanidis (2017). Namukasa (2017) offers CT activities in exploration centers based on CT tools; Gadanidis (2017) designs CT and mathematics activities for students centered on specific mathematics content. The research is going to adopt selected activities and implement them in the research.

Data will be gathered from observation, photos, videos records, audio records, photocopies, reflection forms from students and parents, and from group interviews with children, parents, and teachers.

On the question of the ways students and their parents act and interact during computational and mathematics thinking activities, the researcher will make observations and complete an observation form and take fields notes. The researchers will particularly be interested in: the role of parents when they are interacting with their children during computational and mathematics thinking activities, the role of children during integration with their parents, and the action of the computational and mathematics thinking activities with children and parents and their interactions.

On the question of the benefits and challenges of parent’s engagement with their children during computational and mathematics thinking activities, the research will interview students, parents and teachers to share about what they see as the benefits and challenges. The researcher will also make observations and take field notes. The researcher will be particularly interested in: the math and computation thinking that students conducted how the students experienced the activities, the views of parents.

On the question of the views and the feedback of both students and parents, the researchers would interview the students as well as make observations and take field notes. The researcher will particularly be interested in the feedback on the interactions among the students and parents, what surprised them, what the difficulties they faced, and what they suggest being more helpful.

Observations data: Cohen, Manion, and Morrison (2013) state that “observation is highly flexible form of data collection that can enable the researcher to have access to interactions in a social context and yield systematic records of these in many forms and contexts, to complement other kinds of data” (p. 457). Cohen, Manion, and Morrison (2013) label that observation allows researchers to collect data on physical setting, human setting, interactional setting, program setting. Also, Cohen, Manion, and Morrison (2013) mention that “observation data may be beneficial for recording non-verbal behavior, behavior in natural or contrived setting, and longitudinal analysis” (p. 457). Hence, observation data would permit researchers to enter and realize the case that is described.

I am going to collect data by observation data in a human and interactional setting, and I am going to complete an observation template (see Appendix B) during the workshop or after the workshop that depends on the notes I have taken during the observation.

Interview Data: As Cohen, Manion, and Morrison (2013) mention “ interviews are widely used instrument for data collection” (p. 409).  I am going to conduct a conversational interview. Student participants will be interviewed to know about the benefits and challenges of computational and mathematics thinking activity workshop (see Appendix C). Also, teacher’s views about the nature and background of students’ engagement in the workshop activities in relation to their engagement in normal schooldays and his/ her notes about the workshop (see Appendix C). Also, parent participants will be interviewed to determine their level of commitment, willingness to participate. (see Appendix C). Student participants will be asked about their work and personal experiences in computational thinking activities (see Appendix C). After conducting the workshop, student participants and parent participants will be asked to complete a feedback form (see Appendix D).

This research is included under the Western NMREB ethics review protocol of Dr. Namukasa file number 109494 entitled, tool-based innovative learning and teaching practices and Approved on August 17, 2017. Participants would include parents, students and teachers in the workshops who consent to participate in the research activities. Letters of information and consent forms for teachers and parents as well as assent letters for students and recruitment emails as well as research instruments for the file number 109494 protocol are going to be used in this research. A letter will be sent to the school principal or to the director of the community organization, by email or in person seeking for permission from the researcher and her supervisor to carry out the study in the school or the organization. Once the permission is given, letters of information and consent forms are going to be distributed to the teachers and the teachers asked to send the parent and student letters of information and consent forms and assent forms home with the students. During the workshops, data is going to be collected from only the consenting participants. If any data is inadvertently taken from the non-consenting participant, it is going to be deleted from the study data set. Photocopies, photographs and video records of students’ work, which in error, show identifying information of participants will have this identifying information blurred or deleted. 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, and classroom teacher 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.

 I am going to use NVivo software to carry out the data organization and analysis. The analysis will focus on the research questions, and make sure that the data I have to collect by observations, interviews, and feedback for students, parents, and teacher is sufficient to cover and answer my research questions. The researcher plans to transcribe the interviews data overtime, optically scanning material, typing up field notes, cataloging visual material, sorting and arranging the data into different sources then this research thesis is started to write its finding.

While conducting a research, every researcher faces limitations with regard to the research conducted. The study is interested in computational thinking activities in mathematics workshops for students with their parents. It means that findings from this study will be based on activities that will be applied in the workshops and the nature of children and their parents who participate. The study's findings might not be generalizable to other contexts and populations.

The following are some logistic limitation such as a limited number of devices, connectivity challenges with the web, and the devices are sensitive may be broken or stop working suddenly.

The student researcher shall conduct the majority of the data analysis under the guidance of her supervisory committee and without the help of trained assistants.

According to Cohen, Manion, and Morrison (2013) “more recently, validity has taken many forms. For example, in qualitative data validity might be addressed through the honesty, depth, richness, and scope of the data achieved, the participants approached, the extent of triangulation and the disinterestedness or objectivity of the researcher" (p. 179). In this study, observation, photos, videos records, audio records, photocopies, reflection forms and interview data from students, parent, and teachers participating in the workshop will be analyzed.  The research is conducted based on the detailed record of the events directly from the field notes, transcribed audio and/or video recordings. In the research report, the evidence and the interpretations will be kept separate from each other in the study report to add credibility to the study. Also, to achieve the accuracy of the data, transcripts will be checked for any errors and allowing of adult participants to make sure and review their responses, to ensure that the responses of members are correct and reality. When interpreting the findings, the researcher is going to refer to the literature on integration of computational thinking in teaching, and on parental involvement and on mathematics reform.

In conclusion, several researchers and educators maintain that using computational thinking tools and activities in teaching school curricular contributes to learning in creative and imaginative ways and as a result, it promises to lead an improved student achievement, interest, and enjoyment in learning content that several students experience as difficult, boring, and less relevant. Because computational thinking tools and activities are new, little is known about how to use them well and fewer resources are available to support teachers who choose to use them. Drawing from computational and mathematics thinking activities designed by Namukasa (2017) and Gadanidis (2017) for use in elementary schools, in my study I research the nature of engagement of learners with their parents in a school setting on computational thinking activities when they are integrated with mathematics activities. 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. 

This qualitative case study research seeks to contribute to the exploration of 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 on children learning with their parents. Conducting mathematics workshops for students and their parents can help the parents to support their children, especially with changed and difficult curriculum, as well as with new ways and tools for learning.

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