Program of The National Council of Teachers of Mathematics - Case Study Example

Math in the Early Years Teaching young children can be a very fulfilling career. To be a witness to a child’s curiosity evidently being satisfied with a knowing smile and confident gait is a priceless memory that eggs on a teacher to keep on teaching and touching lives. Math is particularly a tough subject to deal with, especially with its reputation being a difficult one, gauged by many adults. In hearing this, little children might have a distaste for the subject even before they learn it in school. A good early years teacher should be able to set that right and teach that indeed, Math can be fun and interesting. The New South Wales (NSW) Curriculum Framework was created to standardize educational communities in designing curriculum and programs to maximize their students’ potentials in all areas of development. Inclusion of Mathematics in the curriculum is aimed at developing students’ mathematical thinking, understanding, competence and confidence in the application of mathematics, their own creativity, enjoyment and appreciation of the subject and their engagement in lifelong learning (Board of Studies New South Wales, 2002) .Mathematics incorporates the processes of questioning, reflecting, reasoning and proof. It is a powerful tool for solving familiar and unfamiliar problems both within and beyond mathematics. As such, it is integral to scientific and technological advances in many fields of endeavour (Board of Studies New South Wales, 2002). It is heartening to note that “the ultimate reason for mathematics is, after all, not just to solve problems as presented in a text or worksheet but to solve problems that present themselves in many phases of life. The complexity of life today is many times greater than that in earlier centuries, and we are discovering that young children are capable of mathematical thinking that is much deeper and broader than we had ever before realized.” (Krogh, 1995, p.148). The National Council of Teachers of Mathematics (2000) identified high quality mathematics programs for early childhood as having the following characteristics: (Brewer, 2001, pp. 319-320) “They build upon and extend children’s intuitive and informal mathematics knowledge” “They are grounded in knowledge of child development” “They provide environments that encourage children to be active learners, eager for new challenges “They develop a strong conceptual framework that provides the foundation for skills acquisition” They nurture and develop children’s inclination to solve problems.” Vygotsky (1978) believed that children’s intellectual development is influenced more by social context than by individual experiences. His theory places a great deal of emphasis on effective social interaction. Sometimes, the direction of learning is from the teacher to the learner, other times, the learner provides new learning to the teacher. This flow of learning vacillates as teacher and learner interact. Sometimes, learning happens in group interactions, where each member contributes his or her own learning. Such learning gets internalized when the learner is on his own, and does his own individual learning. Vygotsky came up with 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 us, however, that a ZPD is formed not just within an individual learner, but in the interaction between the learner, coparticipants, 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. (Bonk & Cunningham, 1998). With young children there are times when the children were not interested in the lessons, especially if they are repeated on a regular basis. They may find it more challenging to learn a slightly more difficult concept to test their mettle 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 student is already capable of learning without them. The task would not have been completed without the help of scaffolds. As an example, the teacher helping the children to do mathematical operations first give 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 do the operations mentally. This is also done because students are at a stage when attention span could be short and supports are necessary to hold the children’s attention long enough to introduce mathematical concepts. “Examples of this support might include prompts, hints, comments, explanations, questions, counterexamples, and suggestions. A learning scaffold may be embedded in an explicit request to include additional information or a more general question or comment intended to spur new idea linkages or course connections. Of course, these learning aids are faded and removed as the learner assumes control over the activity. Through such assistance, the learner (or a team of learners) solves a problem, generates solutions, and gains insights that would ordinarily rest beyond his or her independent abilities. (Bonk & Cunningham, 1998, p. 40-41) It is essential to strike a balance between giving the pupils sufficient challenge and taking care not to push them into a level they are not yet capable of. Research shows that when children are trained to learn mathematics above their reasoning level, there may be positive results at first but they are “rarely retained unless the child is already in transition from one level to another” (Suydam and Weaver, 1975, p. 47). The teacher should be discerning enough to know when to apply ZPD with her students and know the proper scaffolds to use. According to the behaviorist view, an individual is reinforced (positively or negatively) for responses to various stimuli, hence, the external environment plays a great part in the formation of behaviors. By administering positive reinforcement such as praising or smiling when a desired behavior occurs and administering negative reinforcement such as scolding or correcting when an undesired behavior occurs, one is assumed to encourage the desired behavior and make it more likely that that behavior will recur (Lindfors, 1987). More important than the lessons taught in the sessions are the interests of the children themselves. This is especially true with very young children whose minds are always brimming with ideas. The learning environment must be supportive of children’s ideas and feelings. Being very young, the children must be allowed to express themselves freely. The teacher must allow the children to share their experiences that seem to be all-important to them and the message that comes across is that she is interested in them and their lives. Trafton suggests that individualization must include “acceptance of each child as an individual worthy of adult respect,” and that to this should be added “an acceptance of the child’s ideas, a provision of opportunities for pupil input in developing and selecting learning experiences, a concern for the quality of the child’s intellectual development, and a willingness to take time to know the child as an individual” (1975, p. 39). The experience of working with others and in teams can facilitate learning. Groupwork provides the opportunity for students to communicate mathematically with each other, to make conjectures, to cooperate and to persevere when solving problems and undertaking investigations (Board of Studies New South Wales, 2002). For very young children, ability grouping may work well. “Ability grouping refers to the process of teaching students in groups that are stratified by achievement, skill, or ability levels.” (McCoach, O’connell & Levitt, 2006, p. 339). “Ability grouping refers to the process of teaching students in groups that are stratified by achievement, skill, or ability levels.” (McCoach, O’connell & Levitt, 2006, p. 339). This reflects on the fact that the working world highly values teamwork and cooperation. Grouping puts together students of varying backgrounds and abilities. Teachers need to monitor so that each student is respected and given a fair chance to participate. They need to be reminded that some students need more attention than others. It could also be suggested ability grouping makes better use of time. If children of similar ability were grouped together for example, it would be easier for a teacher to talk and give instructions directly to that group. Paying particular attention to time restrictions, it is worth noting of Moyles’ (1993) suggestion that tasks would be “more efficient and less tedious” for children if they were working collaboratively with children of similar ability. In addition, working in similar ability groups enables the teacher to assess each group needs more effectively and allows children on the same level to have the opportunity to share ideas with each other and support each other in their learning. Ability groups are often viewed to make teaching a class with a wide range of skill levels more convenient for the teaching because she is able to aim their lessons at the middle range of students without being concerned about lower and higher abilities since the specific groups will process the lessons in their own pace. Ability groups are more effective with short-term instruction designed to help students who are experiencing difficulties or who require more extensive instruction in a particular area (Scholz , 2004). The Board of Studies of New South Wales (2002) has identified the values and attitudes developed in the study of Mathematics. In engaging in mathematical inquiry and activities, students appreciate mathematics as an essential and relevant part of life. They show much interest and enjoyment in questioning and feed their curiosity in the pursuit of mathematical knowledge, skills and understanding. Students demonstrate confidence in applying mathematical knowledge, skills and understanding to everyday situations and finding solutions to everyday problems. They get to develop and demonstrate perseverance in undertaking mathematical challenges. Working with various mathematical problems and learning more about how other people use math in their lives helps students recognize that mathematics has been developed in many cultures in response to human needs (Board of Studies of NSW, 2002) . Indeed, it is essential that at a very young age, math should be introduced as fun, interesting and very important in children’s daily living and in their futures as citizens of the world. References Board of Studies New South Wales (2002) Mathematics Syllabus. Sydney: Board of Studies NSW. Bonk, C.J. & Cunningham, D.J. (1998) “Searching for Learner-Centered, Constructivist, and Sociocultural Components of Collaborative Educational Learning Tools” in Electronic Collaborators. Retrieved on February 20, 2008 from: www.publicationshare.com/docs/Bon02.pdf Brewer, J., (2001) Introduction to Early Childhood Education, Allyn & Bacon Krogh, S. (1995) The Integrated Early Childhood Curriculum, McGraw-Hill, Inc. Lindfors, J.W., (1987) Children’s Language and Learning, 2nd Ed. Prentice Hall, Inc. McCoach, D.B., O’Connell, A.A., Levitt, H. (2006) “Ability Grouping Across Kindergarten Using an Early Childhood Longitudinal Study”, The Journal of Educational Research, July/August [Vol. 99(No. 6)] Moyles, J.R., (1993) Organizing for Learning in the Primary Classroom: A Balanced Approach to Classroom Management. McGraw-Hill National Council of Teachers of Mathematics (NCTM) (2000) Standards for Discussion. Available online: www.nctm.org Scholz, S. (2004) “Ability Groups Ineffective or Ineffectively Used?”, Australian Primary Mathematics Classroom, 9 (2) Suydam, M. & Weaver, F. (1975) Research on learning mathematics. In J. Payme (Ed.) Mathematics Learning in Early Childhood. Reston, VA: The National Council of Teachers of Mathematics. Trafton, P. (1975) The Curriculum. Mathematics Learning in Early Childhood Education. Reston, VA: The National Council of Teachers of Mathematics. Vygotsky, L. S. (1978). Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press. Wells, G. (1997). “The zone of proximal development and its implications for learning and teaching.” Retrieved on February 20, 2008 from http://www.iose.utoronto.ca/~gwells/zpd.discussion.txt Wertsch, J. V. (1985). Vygotsky and the social formation of the mind. Cambridge, MA: Harvard University Press. Read More