Early childhood education - Essay Example

? Research Proposal Rationale Young children can learn mathematics from anywhere. Number is all around them such as their age, their address and their telephone number and children need to find meaning and connections between numbers, as if trying to understand another language (Cordes et al, 2005). In a sense, math’s is another language in another form that children need to decipher. At a very early age, children can already learn the concepts of numerical operations such as addition, subtraction, multiplication and division, but of course, presented in a developmentally-appropriate manner (Cordes et al, 2005). This research proposal aims to find out how teachers in Key stage 1 approach the teaching of mathematics to their children At this age, it is important that children use a lot of concrete materials to learn math concepts since they still think in more concrete ways. That is why the use of manipulative materials is essential to their learning (Ruthven, 1987). Maths is viewed by some people as being complicated and a number of adults admit that they are not successful in math-related tasks. It is therefore important to study how young children can be helped to make maths more fun and easier to understand so that they will develop a positive disposition towards it. That way, it is assumed that they will be more successful in learning maths. Aim To explore how numeracy skills may be better learned using manipulative materials in key stage 1. Objectives 1. To research related literature on how numeracy skills are developed in KS1 including what strategies teachers use to involve manipulative materials. 2. To establish how teachers encourage the use of manipulative materials in helping their students develop numeracy skills through survey questionnaires. 3. To investigate teacher’s strategies when involving manipulative materials in maths lessons. Approaches of secondary research Secondary research was conducted by searching online libraries and books, journal articles, etc. in the library. The researcher was vigilant for any information that may be relevant to this research by surfing the internet and getting research materials from these sources. For this study, literature already exists that reports data which has been gathered and analyzed by competent researchers in the field. The researcher is in a position to compare existing literature and decide which information will best answer the research aim. A literature search strategy was devised, involving identification of certain keywords. Online libraries were searched for full-text articles with the key topics: Key stage 1 maths, use of manipulatives, maths strategies, numeracy skills, perception of math teachers and the like. Matches that came up were analyzed according to the relevance to the study based on the following inclusion criteria: information was from 2005 or more recent, studies conducted in the UK only, author’s credentials were compared and only sources which referenced their information were included. This inclusion criterion enabled papers relevant to math education, numeracy skills and math teaching to be accessed. Forward and backward citations were also used. The qualitative information was based on the literature search which was specifically relevant to developing numeracy skills with manipulative materials. In addition, research on quantative methods, specifically on survey questionnaires and interviews were also sought. All the references were charted in a literature matrix as shown in the Appendix 1. Literature review Piaget (1969) theorised that intellectual development is influenced by both maturation and experience. “Cognitive development is indicated by a growing ability to plan, to employ strategies for remembering and to seek solutions to problems” (Brewer, 2001, p.26). Piaget describes the cognitive development of children progress in stages. Key stage 1 children belong to the Pre-Operational period (two to seven years) of Piaget’s Stages of Cognitive Development. This period marks the time when a child becomes able to represent objects and knowledge through imitation, symbolic play, drawing, mental images and spoken language. A lack of conservation skills is also characteristic of this stage. “Conservation is defined as the knowledge that the number, mass, area, length, weight and volume of objects are not changed by physically rearranging the objects.” (Brewer, 2001, p.318). That is why it is important to always give concrete materials to young children when teaching a math concept because that is how they understand things better. They need to be able to see things concretely first before they can translate ideas into abstract thinking. Mathematics is a hierarchical discipline where concepts build on previous concepts and more often than not, need full understanding before proceeding to the next, more complicated concept (Ruthven, 1987). For example one cannot just teach multiplication without the student understanding the concept of addition (Hyaloch & Cockburn, 2003). Vygotsky (1978) developed the concept of the Zone of Proximal Development (ZPD). He defined the ZPD as the distance between a child’s independent problem-solving level and that obtained under adult guidance or in collaboration with more capable peers (Wertsch, 1985). Wells (1997) cautioned however, that a ZPD is formed not just within an individual learner, but in the interaction between the learner, co-participants and available tools during involvement in a common activity. ZPDs, therefore, depend on the quality of the total interactive context as well as individual learner capabilities. Children usually find it challenging to learn a slightly more difficult concept to test their knowledge in the skills they have gained. “Such cognitive apprenticeships are, of course, inherently reliant on a mentor or guide who effectively uses “scaffolded instruction” (Bonk & Cunningham, 1998 p.40). As the term implies, scaffolds are temporary supports in the process of learning which are gradually taken away when the children is capable of learning without them. As an example, a teacher helping children to learn a mathematical operation first gives them more concrete materials such as paper shapes or beads and as they master the concept, the materials or “scaffolds” are slowly eased away until they can complete the operations mentally (Bruce & Threlfall, 2004). This method may also be used because children may be at a stage when attention span could be short and supports become necessary to hold the children’s attention long enough for the teacher to introduce mathematical concepts (Cordes & Gelman, 2005). Methodology and Justification This study shall be conducted using mixed methods in gathering and analyzing data to respond to the research question, “How do teachers encourage children to use manipulative materials to develop their numeracy skills?” The study is more qualitative in nature, in that it attempts to go deeper into the issues of the use of manipulative materials to teach numeracy skills in young children. It will evaluate if teachers actually provide their students with opportunities to explore manipulative materials to learn numeracy skills from doing so. It will probe into the teacher’s strategies using survey questionnaires. The quantitative part of analysing the results of the surveys will supplement the qualitative information from the secondary research. Questionnaires will be used because they are a versatile data-gathering method because of its affordability and ease of administration (Campbell et al, 2004). Cohen et al (2004) also praise the use of questionnaires for their efficiency. It allows the researcher to collect a significant amount of information in one attempt, rather than conducting interviews over a period of weeks. Gillham (2000) wrote that questionnaires make efficient use of the respondent’s time, because the survey participant can complete the questionnaire at a time that is suitable, and the survey process does not require the researcher and respondent to match free periods of time to conduct the research. For this study, survey questionnaires shall be conducted with teachers to investigate how they encourage their students to use manipulative materials to develop numeracy skills. It is appropriate to use this research method because the researcher will gain insights directly from the participants. The questionnaire consists of 6 statements that respondents will agree/ disagree with, depending on the degree of agreement relative to their own contexts. The statements were selected to reflect how much the teacher allowed their students the time to explore and work with manipulative materials and how they plan activities for these children to develop numeracy skills. The questions serve as evaluative of the actual conditions in the teachers’ classrooms at the time when they complete the questionnaire. Initially, they can answer the survey questionnaire items and then elaborate on their responses by writing their comments or remarks in the spaces provided for. In the blank spaces, they are given free reign on what they would want to share in relation to the statements. The quantitative aspect of the research design includes the distribution of survey questionnaires that teachers will complete using a Likert scale on questions pertaining to the research. Likert scales are mostly used in survey questionnaires because it gives the respondents choices as to the degree of their agreement/ preferences/ frequency with regards to the items. In this case, the respondents will signify the degree of their agreement with the items, and the responses will be counted per level of agreement per item (ex. How many checked on Strongly Agree out of the total number of respondents). Percentages of responses for each item will be analysed. The qualitative aspect of the research design will be the narrative remarks the participants will write to show how teachers encourage their students to use manipulative materials to learn numeracy skills. Writing their remarks on open spaces in the questionnaires will be useful for exploring strategies they use in the classroom that may not fit within the closed question part of the questionnaire. The questionnaire was piloted with 3 teachers and they commented that it was easy to answer, especially the remarks portion where there were guidelines on how to answer it to provide the answers needed in the research. The quality of the responses were also reviewed and found to be suitable for answering the aims and objectives. Therefore, no changes were made to the Questionnaire. The questionnaires were distributed to 10 KS1 teachers (See Appendix 2) who worked in the school where the researcher was working in placement. They were identified by the researcher as the teachers who taught math and were adept at what they did. The questionnaires were given to the respondents to fill out on their free time and were collected by the researcher when they were ready. In analyzing the completed questionnaires, percentages for each item were computed and the narrative remarks were categorized according to the statements. Since there was only a small number of subjects, inputting the responses into a chart was convenient and made the analysis and comparison easy. Ethical Considerations This study will comply with ethical standards and considerations involved when conducting research with human participants. A letter of consent will be sent to the head teacher of the school requesting permission to question their KS1 teachers (see Appendix 3 for the letter and the reply). Confidentiality of information will be ensured so that the trust of the participants is established. Participation is non-obligatory and participants may withdraw anytime they feel like it. Conclusion This study will explore how teachers encourage their students to use manipulative materials such as blocks, beads, puzzles, counters, etc. in facilitating the development of numeracy skills. The researcher conducted a literature review on the topic as well as planning primary research using survey questionnaires and a focus group interview with KS1 teachers. The information derived from this study will answer the research question, “How do teachers encourage their students to use manipulative materials in developing numeracy skills?” References Bonk, C.J. & Cunningham, D.J. (1998) “Searching for Learner-Centered, Constructivist, and Sociocultural Components of Collaborative Educational Learning Tools Collaborators. www.publicationshare.com/docs/Bon02.pdf. Accessed on 10/05/11 Brewer, J.A. (2001) Introduction to Early Childhood Education. Allyn and Bacon, Boston Bruce, B., & Threlfall, J. (2004). One, two, three and counting. Educational Studies in Mathematics, 55, 3-26. Campbell, A., McNamara, O., & Gilroy, P. (2004). Practitioner research and professional development in education. Paul Chapman London. Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education (5th ed.). Routledge Falmer, London Cordes, S., & Gelman, R. (2005). The Young Numerical Mind: When Does It Count?, Handbook of Mathematical Cognition. New York: Gillham, B. (2000). Developing a questionairre. Continuum. London Haylock, D & Cockburn, A, 2003. Understanding mathematics in the lower primary years: a guide for teachers. Sage publication, London Oppenheim, A. N. (1992). Questionnaire design: Interviewing and attitude measurement. Pinter, England. Piaget, J. & Inhelder, B. (1969) The Psychology of the Child. Basic Books, New York Robson, C. (2002). Real world research (2nd ed.). Blackwell, England: Ruthven, K. (1987). Ability Stereotyping in Mathematics. Educational Studies in Mathematics 18, 243-253. Spodek, B. & Olivia, S. (Eds.), Handbook of research on the education of young children (pp. 187-221).Lawrence Erlbaum Associates, England Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Harvard University Press. Cambridge Wells, G. (1997). “The zone of proximal development and its implications for learning and teaching.” http://www.iose.utoronto.ca/~gwells/zpd.discussion.txt, assessed on 10/05/11 Wertsch, J. V. (1985). Vygotsky and the social formation of the mind. University Press. Cambridge Appendix 1: Literature Matrix Author Year Publication Article Textbook Bonk, C.J. & Cunningham, D.J. 1998 Internet x Brewer, J.A. 2001 Book x Bruce, B., & Threlfall, J. 2004 Article x Campbell, A., McNamara, O., & Gilroy, P. 2004 Book x Cohen, L., Manion, L., & Morrison, K. 2000 Book x Cordes, S., & Gelman, R. 2005 Book x Frey, J. H., & Mertens-Oishi, S. 1995 Book x Gillham, B. 2000 Book x Haylock, D & Cockburn, A 2003 Book x Oppenheim, A. N. 1992 Book x Piaget, J. & Inhelder, B. 1969 Book x Robson, C. 2002 Book x Ruthven, K. 1987 Article x Spodek, B. & Olivia, S Book x Vygotsky, L. S. 1978 Book x Wells, G. 1997 Internet x White, M. D., & Marsh, E. E. 2006 Article x Appendix 2: Survey Questionnaire Dear Teacher, I am conducting research on how KS1 teachers encourage their students to develop numeracy skills. I would appreciate it if you can help me by answering the questionnaire below. Each item is to be rated in accordance to your response, as follows: Legend: SA – Strongly Agree A – Agree NS – Not Sure D – Disagree SD – Strongly Disagree This questionnaire will investigate what teachers of pupils in Key stage 1 do to encourage the use of manipulative materials in order to develop numeracy skills. Check the appropriate response to each item and fill out the remarks portion for each item. Should you need additional space, please fill out the space at the back of the paper. SA A NS D SD 1. My classroom is equipped with teaching aids such as charts and posters about math concepts. Remarks: (enumerate teaching aids in your classroom) 2. My classroom has enough manipulative materials that may facilitate the development of numeracy skills (e.g. blocks, beads, buttons, weighing scale, puzzles, etc.) Remarks: (enumerate materials you have) 3. The children are allowed to explore and manipulate the learning materials in class on their own. Remarks: (when and how?) 4. I prepare some stimulating games/ activities involving the use of manipulative materials to teach numeracy skills. Remarks: (Give examples) 5. I encourage small group activities involving the use of manipulative materials Remarks: (Give examples) 6. I encourage the students to use manipulative materials in order for them to understand more abstract numeracy concepts. Remarks: (How?) Additional Remarks about how you encourage children’s learning: Thank you so much for your participation in this study! Dear Head Teacher I am currently a student at University College Birmingham, studying my Foundation Degree in Early Years Childhood Studies. As part of these studies I will be carrying out a research study within KS 1. Teachers in KS1 classes will be participating as part of my research. I have chosen to explore how numeracy skills may be better learned using manipulative materials in KS1. I will be collecting the data needed by using questionnaires. All information that will be collected will remain strictly confidential and the names of the teachers will not be mentioned in any of the paperwork. Therefore, I am writing to ask permission to conduct my research in your school with KS1 teachers. On completion of the research proposal and completed data collection the school will be presented with a copy of the work which will also be available to the teachers. There will be no involvement of the children, as I will be gathering my data within the normal constraints of the school day. I hope that carrying out this research will meet with your approval. The class teachers in Key stage 1 can withdraw from the study at any point they deem necessary. Please indicate your response by signing and returning this form to inform me if I can carry out the questionnaires in KS1. Please do not hesitate to talk to me if you have any concerns. Yours Sincerely Mrs Khan (Student) ---------------------------------------------------------------------------------------------------------------- CONSENT SLIP I give/do not give my permission for KS1 teachers to take part in the studies. Signed ------------------------------------------------------------------------------------------- Name (print) ------------------------------------------------------------------------------------ Date Read More