The project will explore to what extinct group learning has on the appreciating mathematical discourse and vocabulary.
I would like to simplify what understanding means for me for the purpose of this paper. From my own educational journey and teaching experiences, an educator’s romanticised notion of pedagogy is not always mirrored in their lessons. All of these observations have come to light in my studies this year gone by. The method of repeating long lists of information is a popular method of teaching in this SABIS International School. Perkins (1997) views understanding as a somewhat flexible performance. He views it as a tool which gives the student the ability to think and act on a whim without ever having planned for the necessary course of action.
After careful thought and deliberation, a constructivist style of data collection will be used in this research project. It is the remoulding and reshaping of that knowledge which is of most importance. As the students expand their zone of proximal development, they adjust their preconceived views on the certain concepts (Barnes, 1992).
Students frequently become submissive learners of knowledge. Barnes (1992) discusses the revolutionary notion of learning energetically. By allowing students to actively learn in this way, we are providing them with the ability to construct deeper understandings. Group work learning improves the level of performance within a classroom tenfold (Kuhn, Shaw, and Felton, 1997). Similarily, Colbeck, Campbell and Bjorkland (2000) recommend group work as a social constructivist method of learning.
A particular discourse is used within the mathematics lesson. The students are taught plus and minus linking both to hand signals. Plus means put together, minus means take away. A useful method of evaluating student understanding is by assigned a task whereby they have to draw on specific information (Perkins, 1997). Specific activities are strategically planned to enable observations of the students’ understanding.
The mathematical functions of fact families are of major significance right from this early age of four. Each combination will be either addition or subtraction, e.g. (2, 4, 6). Two plus four will give us an answer of six in the box. Similarly six minus four will result in the answer being two. If the students understand sufficiently, resolving the math problem will not be an issue. On the occasion an equation is presented differently, the student should still be able to decipher the problem.
Each student had to complete a mental math examination containing twenty questions. The students are made to feel relaxed during this very tense moment. The candidates were encouraged to do their best and were guaranteed that they can withdraw from the test at any time if they wish. Of course, this is a very daunting period of their school day so the teacher will be sure to make the kids feel at ease during the five minute CD timer. Through direct observation during the examination, the educator will be able to gage her class and measure understanding (Cohen et al., 2007).
Certain approaches assist significant mathematical understanding. Student input allows young people to develop their confidence. Significant improvement has been seen in the problem solving area along with justifications for their understanding (Cobb, 2000; Martino & Maher, 1999). The educator has quite an important role in managing questioning and listening. If the questions are designing slightly more difficult, it will result in the students expanding their spectrum of learning even further.
The seating arrangement within the class is organised in a deliberate manner where we incorporate a “mentor/buddy” system from the very first days of KG1. This approach fits in very appropriately with Vygotsky’s thoughts on the more knowledgeable other (MKO). It is the teacher’s responsibility to collectively guide the class, however on the other hand there is a strong emphasis placed on this mentor/buddy system. This arrangement involves an advanced student sitting beside a lower level student. The mentor will frequently check the buddy’s work and re-explain a concept if needed. The thinking behind this system is that the MKO assists and aids the learner promoting more understanding than they would have discovered themselves (Morrissey and Brown, 2009).
There are several benefits of using the ZPD and MKO within a KG1 math class. Primarily, it gets each and every child involved in the lesson. Those students who would be regarded as quite advanced for their age will be considered the “mentors”. The lower level students will be the “buddies”. Both have particular functions inside the lesson, for example, the mentor will continuously check up on the buddy. By endowing the mentors/shadow teachers with a key role, it prevents them from becoming bored and uninterested in the lesson while the teacher carries out the scaffold. Instead of becoming passive learners, students are fundamentally involved in the lesson stimulating both creativity and progress within the class.
In relation to ethical issues regarding this project, everything was carried out in alignment with a very strict protocol. Data sheets were provided explaining the purpose of the study to all candidates. Parental approval and authority was received from both the students and parents of students. The students were aware that they could remove themselves from the study at any time. Pseudonyms were used to conceal students’ names and protect identity at all times during this project. I decided to use three kindergarten students for the study. The students are of mixed ability for the completion of this research project.
Ethics are moral ideologies that administer the conducting of research. They play a vital role when conducting any form of research. Pring (2004) states the five key areas of negotiation, the fifth one being the most challenging. It states ”the right of those concerned to offer an alternative interpretation of the evidence’. I believe that it will be difficult for early year’s starters to offer an alternative understanding of the data. If those concerned are given the chance to offer an alternative interpretation of the evidence, the results will not be accurate, and they will not be correct. Involving those concerned to offer an alternate interpretation can affect the results of the data that have been gathered.
I personally feel that early years starters are still young to be offered an alternative interpretation of the evidence because they do not know how to do it and most of the work they do, they do it with adult assistance. I feel this could result in participates to give their opinion however their interpretation of the evidence could be different to the observers opinion. This may hinder the results of an investigation. I feel it is acceptable for all involved to offer an alternative interpretation however, it is essential the results do not change solely on an offer and suggestion made from those concerned
Powell & Steele (1996) suggest the qualitative research method is ideal for this particular age. An open observation method and structured observation method will be incorporated into this study. Hopkins (2008) suggests that this method works best when observing small groups. The students were posed with basic word problems to determine ability. The investigation took place during a fifty minute mathematics lesson on three different days. Throughout the lesson, word problems were asked to the students. The questions were planned with care and caution. By assigning stimulating tasks, student participation is increased dramatically One of the principal aims was creating an environment where collective mathematical understanding could develop.
Throughout the sessions, students were given exercise sheets with a variety of different word problems. These word problems were expressed in a different manner than previously completed word problems. This ensured the children were constantly testing and expanding their zone of proximal development. Mini white boards were distributed among the class to allow illustration of the word problems. The kindergarten class were encouraged to participate and act out the problems within their groups Leng (2008). They would use props and visual aids such as blocks, lollipop sticks and toys to illustrate the mathematical sentence.
Scaffolding was incorporated into a particular lesson where the fundamental objective was to introduce the concept of “addition” or “plus +”. In order to achieve best results in this lesson, a demonstration was performed in front of the class using the pupils themselves as the necessary props. This proved very exciting for the KG class and immediately grasped their full attention. It was imperative to explain, plus ‘+’ signified ‘getting bigger’ or the total number was increasing. As the lesson progressed, the use of many different visual aids and props were used for reinforcement of the new concept. In a short time, the students were completing simple mathematical sentences using lollipop sticks, blocks, coins and so on. Work by (LUI, 2012) confirmed the use of simple encouragement, prompts, facial expressions and physical actions in assisting the students throughout the scaffolding process.
Throughout each assignment student A held a high capacity of understanding. Student A completed all the number sentences correctly without any assistance. Each question was undertaken in a logical manner. Confidence was high and it was clear the student knew exactly what he was applying. This portrayed deep understanding of the concepts taught. A longer period of deliberation was needed for the harder questions which was perfectly normal. More testing questions were used to push students understanding by including a missing addend. The phrase “added” prompted the students to add the two numbers. However, when questioned about what the “number” in question to be added was, student A was quick to discover there was a missing addend to begin with. Once student A had completed the first one or two more advanced questions, the remainder of the examination was not a problem for him.
Unlike student A, student B relied more on illustrations in order to decipher the problems. It took slightly longer for student B to complete the problems but again, this portrays thorough understanding and a clear direction in completion of the task. This particular student took his time to peruse over the questions before making any rash decisions. When posed with the same question about what the ‘number’ to be added was, student B replied with “2 added to 4”. This again sees the student recognising the word ‘added’ and simply adding the numbers in the question. When asked to try again, student B looked to student A for reassurance and was offered guidance in the form of acting it out amongst the group.
Student C looked for guidance from peers more than the other students. It was observed that student C mirrored or imitated the actions or illustrations of student B. Once this was done student C carried out the task successfully. Student C failed to look for leadership and guidance. It was clear to see student C did not totally understand the task at hand. He undoubtedly lacked confidence in his own ability. On observation, student C seemed shy and timid. The students mind appeared to be “drifting’ away when the task should have been completed.
Influenced by the work of Cobb, Wood and Yackel (1992) and Vygotsky the role of the teacher remained as a facilitator. Whilst it is advisable to provide scaffolding within the classroom, it is necessary the teacher knows when to retract the support and allow the students to expand on their own knowledge.
It is clear Vygotsky (1994) truly believed in the power of the social dynamic. He was an advocate of the teacher’s role in the learning process and made the point that assistance was crucial if one was to achieve higher levels of success and development. Vygotsky was the founder of the ZPD (Zone of Proximal Development). This is the term used for the area of the brain demonstrating the difference between the concrete development level and the pending, potential development level of a student. Essentially, Vygotsky created the ZPD to highlight where support is needed to maximise learning. He acknowledges the need for students to actively engage with others who can challenge and develop their zone of actual development. Garcia (2002) mentions the notion of learning incessantly evolving and changing over time. The learning of new information is not something which is solely applicable or only true at that particular moment of learning. Knowledge is rather seen as something in a state of flux, forever changing its cultural values from one cultural paradigm to the next.
Collaborative group work was a huge success in this particular research project. Working with fellow students allowed student B to act out the problems and actively seek the solution. This was completed by linking prerequisite knowledge, adjusting it and applying this knowledge to the current problem (Wood, Bruner & Ross, 1976). Both students were open to sharing ideas to help each other. Although student C didn’t participate in providing scaffolds as such, it was observed that this student benefited immensely from the scaffolds of the more able peers. This coincides with the research of Vygotsky (1978) and Webb (1982).
The primary aim of this investigation was discovering if collaborative learning would assist in the understanding of mathematical language in a kindergarten class. Collaborative group work allowed for higher engagement in tasks. It was heart warming to watch the little kindergarten student’s work collectively to tease out and answer for a mathematical sentence.
Perkins (1997) has authorized me to develop my skills as a facilitator during my lesson planning. This constructivist approach to understanding and knowledge will now be a constant going forward in my teaching career. He states, ‘to understand a topic means no more or less to be able to perform flexibly with the topic- to explain, justify, extrapolate, relate and apply in ways that go beyond knowledge and routine skills’ (Perkins, 1997:42).
It was a joy to witness Student C pick up new information and skills from his peers without ever feeling insecure or let down. Through games, props and imitation, the children shared their knowledge together in order to arrive at the correct answer. There was a real sense of achievement and triumph on completion of the above problem solving equations.
I believe the approaches to teaching need to be adapting continuously in order to provide the best outcomes for future generations. By using alternative teaching methods and including students in constructing what they learn is an approach which I will adapt in my classroom to promote motivation and build positive relationships.
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