Learning by definition is the process of acquiring skills and knowledge through ways such as classroom teaching, studying and through experience (Schug 2010, pg. 29). Traditionally, studies and research concerning learning have the primary focus on the knowledge acquisition while individuals are in their childhood and adolescent periods mainly through teacher-student interaction. It gives meaning to the traditional classroom which is the traditional learning pedagogy whose belief is that teachers are the sources of knowledge while the students are the recipients. In a traditional learning, the primary characteristics that depict knowledge acquisition as inert include the directive role of the teachers, with teaching materials being mainly workbooks and textbooks (McGill & Beaty 1995, pg. 15). However, there have been series of disapproval of learning from inert to a rather an active, dynamic and interactive process of skills and knowledge acquisition that can lead to a change in behavior as behavioral learning postulate advocate. Theories that are contrary to the traditional learning principle include sociocultural, constructivist and learner-centered models. Koschmann (2011, pg. 119) agrees that all the post-modern learning theories serve as alternative learning models that replace the outmoded teacher-centered style of learning which emphasizes on the transmission of knowledge from teachers to learners. The rationale for the disapproval of the traditional learning model is the recognition through research that it is a continuous procedure that continues throughout the life on an individual. From the constructionist perspective, learning entails the application of personal experience in dealing with novel situations and in developing relationships with others. Furthermore, scholars such as Bonk and Cunningham (1998, pg. 54) contend that constructivist perspective of learning emphasizes on supporting and guiding learners in constructing their comprehension of the issues, new concepts, communities, and culture. Unlike the traditional learning strategy which is unidirectional, constructivist perspective explores learning as an aspect achievable through a combination of teaching practices such as group work and discussions, collaborations.
The constructivist and learner-centered theories have a common feature that they both advocate for the teachers to under the learners' pre-existing conceptions to aid in guiding them in addressing challenging aspects and assist them in building on the understandings (Bonk & Cunningham 1998, pg. 38). The constructivist theory has the other objective of encouraging learners to utilize effective techniques such as experiments for solving problems on real-world. It is in that case that the project takes the constructivist approach as it entails experimenting with the group work for Year 8 students in which they will construct 3D-shape sorters though the applications of 3D-shape nets. The aim of the group project is to utilize collaboration and teamwork in learning how to calculate volumes and surface areas of the shapes. As the learners will work in groups and collaborate with each other, it will serve as the basis of proofing how effective the collaboration and effective in facilitating learning mathematical concepts (Schuman 1996, pg. 41). In applying group work and cooperation, it assists in the creation of more knowledge enabling the learners to reflect and converse about the concepts among each other hence knowing that their comprehension of the subject is changing. Learning mathematics can be achievable through theoretically from the teacher-centered approach, but its effectiveness is uncertain. However, the use of constructivist approaches such as the practical application of 3D shapes in calculating volumes and surface area serve as the discovery of the tools that not only facilitate learning mathematical concepts but also foster learner-centered instructional aspects and social interaction. Therefore, using 3D shapes, collaboration and grouping transform knowledge acquisition from inert teacher-centered practice to an operative and meaning-making procedure that is rich in the interchange, collaborations, and discussion. The suggestion is that constructing 3D shapes in group work is associated with social interaction as a result of debate within the group which is inclusive of the teacher as the facilitator of the lesson. In that way, it endorses Schug (2010, pg. 95) suggestion that learner-centered theory is inclusive of social influence and interaction principles that affect learning. It thus prints an implication that communication and interaction with others, interpersonal relations, and social interactions affect learning.
Motivation and Collaboration
Motivation by definition is the drive within oneself that stimulate one to do actions that lead to the accomplishment of individual objectives (Ross & Erwin 2011, pg. 39). It also has the implication of the creation of willingness in other people to perform actions to the best of their interest and abilities. Motivation occurs in intrinsic and extrinsic forms with the extrinsic motivation originating from external factors which in most cases are tangible. On the other hand, intrinsic motivations arise within oneself that originate from the need for personal satisfactions. In cooperative learning such as the case of facilitating learning through the 3D shapes enhances fundamental type of motivations by making learning engaging and entertaining hence the students become creative and delighted over some activities that might have been difficult when they tackle on their own (Felder & Brent 2013, pg. 1). In the sense of cooperative learning, motivation has social constructs as collaborative learning environment leads to interactions such that motivation conceptualizes the teachers and learners as two mutually constitutive and inseparable elements. Collaboration by definition entail working in groups for the purpose of supporting each other in the realization of a common goal (Thirteen Organization 2016). It is a term applicable in cooperative or collaborative learning environment where students place themselves in small groups to work together towards completing a given structured activity usually set by the teacher. An example of the collaborative learning environment is the case of the calculation of surface are and volume of 3D shapes which is a functional replacement of the theoretical calculation of volume and surface areas of different objects and shapes printed in books. Adding the element of group work and practical part in the mathematical lesson has the aim of testing the efficiency of collaboration and motivation considering that every individual is accountable for the teamwork as the assessment is per the group's overall achievement (Zain 2012, pg. 117).
Gordon (1994, pg. 9)research identify a series of substantial evidence that learners' motive for engaging in learning practices and activities is not only for the purpose of directing their academic performance but also to reflect on the social context in which the students belong. A highlight of the evidence is apparent from the series of social objectives of cooperative learning that literature present such as pro-social, contextual, social status, social relationship, social interaction, social responsibility and social approval objectives that motivate learners to participate in a collaborative learning context. According to Ross and Erwin (2011) study to ascertain the factors that motivate students, the findings indicate that the way learners interpret their interaction and relationship with others in a collaborative learning setting shape their learning goals. Furthermore, Bonk and Cunningham (1998, pg. 71) confirm that the actions, objectives, and morale of the group members participating in the collaborative classroom setting can affect individual motivation negatively or positively. As a result of the dominant view that links social environment as the key factor exerting greater influence on the learners' motivation leads to the justification by Felder and Brent (2013, pg. 2) that type of learning materials and activities in a collaborative environment affect learners' goals. Social interaction is one of the rationales for encouraging scientific investigations by using practical lessons such as of 3D shapes and nets. Mathematical studies through the use of 3D shapes are both engaging and fun in comparison to the traditional teacher-centered mathematical activities. Jaworski (1994, pg. 31) states that the use of practical investigations in mathematics such as the case of 3D shapes for geometry promotes mathematical behavior among learners thus proofing its effectiveness that the traditional diet of classroom teacher-centered exercises and topics. Regarding 3D shapes sorting and affiliated calculations, there is a likelihood of motivations among the learners as it is bound to stimulate the improvement of analytical processes that the students can apply not only shapes sorting and calculating volumes and areas, but also advanced mathematical topics. Therefore, practical mathematical learning is a preferable alternative to the old education setting and an effective approach to engaging students in traditionally theorized mathematical lessons. Group work in mathematics as a way of fostering collaborative learning enable the students to identify and express their problems while tackling mathematical issues at year 8.
The practical use of nets and 3D shapes assist learners in testing their hypothesis and ideas against classwork experience. Collaboration in the group provides students with the rational ways of defending their conclusions, decisions, and plans through the practical submission of ideas to the group for reasoned criticism that contributes to knowledge acquisition. Using 3-D shapes and nets is a type of mathematical investigation where the learners engage their peers in loosely-defined mathematical topics such that after participation, everyone has the chance of giving their questions. Furthermore, since every group member has the opportunity of following individual inclinations and interests, establishing personal goals, doing mathematical research before presenting in the group introduces an element of autonomy and fun in the collaborative learning process. The use of 3D nets and shapes as a practical learning of mathematics is in dissimilar to the classroom chores that the teachers set for the students such as defining mathematical concepts, working mathematical problems while following worked examples and performing teacher-centered projects. The role of the teacher is to ensure reflection and group processing which entail encouraging the individual learner to reflect on personal achievement and the group to process on its experience. Observation and group processing follow Bonk and Cunningham (1998, pg. 52) suggestion that cooperative learning embeds negotiation and collaboration within it are hence providing the learner with the chance to obtain alternative viewpoints regarding diverse issues before giving their personal insights. In the process, the group members engage in knowledge negotiations and meaning making necessary for acquisition of knowledge and skills (Bonk & Cunningham, 1996, pg. 57)
Vygotsky's ZPD and Levels of Control
Vygotsky's ZPD theory explain the primary role that social interaction play in the process by which individuals develop their cognition. According to Vygotsky argument, learning is a universal and mandatory aspect...
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