Overview of the Current Preschool Mathematics Teaching - Dissertation Example

Overview of the Current Preschool Mathematics Teaching Children in the early childhood stage usually get their first taste of math concepts and learn their first known math skills when they step into a day care or nursery program. A special committee of the National Research Council (2009) has concluded that most young children have the ability to learn and be really competent in Math, but there are many constraints that deter them from being so. One is parental attitudes that influence how they regard Math. Another is also the way teachers of early childhood education do not prioritize Math as much as literacy learning. Children who are exposed to negative views of Math at such an early age, are most likely to develop the same negative attitudes towards a subject area that will prove to be very significant in their lives. It is believed that whatever perceptions of what Math is at this early stage will impact their views, attitudes and even performance when they grow older. Hence it is crucial that provision of high quality early childhood Math programs in the foundation stage be ensured (National Council of Teachers of Mathematics, 2000). It is equally important to know how teachers of Math perceive how their young students learn the subject and what particular concepts and skills to teach at that sensitive stage of development. It is a common experience of most people to dread Math and this does not exclude Math teachers who may still nurture some negative emotions for the subject. Good teachers are central to the development of positive attitudes towards a potentially gruelling subject that most people find difficulty in. Enhancing their confidence and competence in their teaching skills goes a long way in implementing an efficient Math program. Schools should be able to provide quality training for teachers that focus both on the relevant content and the development of a positive disposition towards the subject (Tsamir & Tirosh, 2009). This is echoed by the National Association for the Education of Young Children (NAEYC) which calls for the education, experience and expertise of teachers when decisions regarding children’s programs are made (Decker et al, 2009). Platas (2008) came up with the instruments, Knowledge of Mathematical Development (KMD) Survey and the Beliefs Survey that measure the knowledge of early mathematical development and beliefs about mathematics teaching and learning in the preschool classroom of preschool teachers. She found in her study that there was a significant variation in the knowledge and beliefs of early childhood teachers on age-appropriateness of math instruction, classroom locus of generation of mathematical knowledge, math versus socio-emotional development and the comfort level in providing the instruction. Standardizing such knowledge will greatly aid new teachers and old teachers alike in knowing what to teach. Platas’ instrument is very helpful in preparing future Math teachers. Platas’ work has raised many issues and beliefs regarding the developmental knowledge of preschoolers. Such issues include age-appropriateness of mathematical instruction used by teachers in preschools, the extent of learning of such mathematical concepts taught, the purpose of teaching math concepts in preschool and the comfort level of teachers when they introduce such math concepts to preschool children (Clement & Sarama, 2007; Ginsburg & Golbeck, 2004; Platas, 2008). 2. Preschool Teachers' Knowledge of Mathematical Development Platas (2008) defines early mathematical development as “the increasingly complex mathematical constructions and goals that young children develop and pursue in their activities (p.3). It follows the teacher’s knowledge of mathematical development refers to their adeptness in understanding this definition and knowing how to implement developmentally-appropriate programs to help their students achieve these goals. Standardized goals for mathematical development have been developed by several national and state organizations. Forty-six states have comprehensive learning standards for preschool children (Barnett et al., 2008). Furthermore, national organizations such as the National Association for the Education of Young Children (NAEYC) and National Council of Teachers of Mathematics (NCTM) have developed specific recommendations related to high quality mathematics instruction in the early childhood classroom (NAEYC & NCTM, 2006). As the NCTM and NAEYC proclaimed, importance in the learning and development of mathematical skills and knowledge is important in building the foundation of mathematical development of preschool children. However, some early learning programs do not focus on high quality mathematics instruction despite research supporting early mathematics experiences influencing mathematical outcomes later in school and promoting school readiness skills in mathematics (Lopez, Gallimore, Garnier, & Reese, 2007; Slaby, Loucks, & Stelwagon, 2005). Still, other remarkable studies showed that there are many activities involved in teaching mathematics to young children and this would involve knowledge about the subject matter, pedagogical content knowledge, lecturing, introduction of symbolism, and connecting everyday experience to abstract ideas (Ginsburg & Amit, 2008). Wilson (2009) contends that traditionally, teaching of mathematics is associated with computation, memorized rules and rote procedures followed even without understanding the underlying concept. Educational reforms have now emphasized mathematical reasoning, solving problems, connecting mathematical ideas and communicating mathematics to others (Wilson, 2009). The wide spectrum of knowledge of mathematical development keeps growing and this necessitates the effective training of teachers of Math. The National Council of Teachers of Mathematics (NCTM, 2000) standards for early mathematical development (preschool through second grade) include five content standards. The content standards are as follows: Number and operation: includes concepts of one-to-one correspondence, counting, number, place value, operations on whole numbers and fractions. Algebra (Patterns & functions) Patterns – visual, auditory, spatial, numerical or combinations of these Functions – patterns created when certain actions are performed on objects or numbers. Geometry and spatial sense – concepts of how shapes and forms are related to each other. Measurement – experiences must be based on children’s ability to conserve length and area Data Analysis – comparing and analyzing information. The National Research Council (2009) recommends that: Mathematics experiences in early childhood settings should concentrate on (1) number (which includes whole number, operations, and relations) and (2) geometry, spatial relations, and measurement, with more mathematics learning time devoted to number than to other topics. The mathematical process goals should be integrated in these content areas (p.3). These are the two main concepts and skills that young children should first be adept in, as these may be directly applicable to the children’s daily experiences. Number is all around them…their age, their address, their telephone number. They need to find meaning and connections between numbers, as if trying to understand another language. In a sense, Math 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 (National Research Council, 2009). 3. Preschool Teachers' Beliefs about Mathematics Teaching and Learning . Math belief has been defined as what teachers may think as “should and should not be taught, how children will learn the mathematical concepts best and how they will teach each of the objectives” (Jenkins, 2002, p. 2). In 2000, Jenkins investigated pre-service teachers’ beliefs about mathematics. Participants were all early childhood majors who have not yet reached their student-teaching components in their degree requirements. The study asked them to teach math lessons created with NCTM’s 1998 draft of the Standards as the framework, using developmentally-appropriate materials and methods that incorporated the use of play and exploration. Results indicated that the participants experienced significant changes in their beliefs about mathematics teaching, learning and even their future practice as math educators. The teaching experience they had caused a shift in beliefs from the more traditional rote method of mathematics to non-traditional methods integrating play and exploration with NCTM standards (Jenkins, 2001). Similarly, Rosenfeld (2010) conducted a study interviewing pre-service teachers regarding their beliefs about their own mathematics teaching abilities. They also reflected on the experiences and knowledge they needed to increase their comfort and confidence in teaching math. The participants in the study generally felt that they were unprepared to teach Math until they were already in the classroom, tasked to teach young children. Rosenfeld also reported that the other themes that surfaced in the interviews dwelt on the use of external aids such as the planned lesson objectives for judging one’s success in teaching, the value of knowing how to implement effective classroom management strategies, the use of student learning evidences to determine teaching success and finally, but unfortunately, the realization of the lack of consideration of children’s cognitive development and thinking in the evaluation of one’s ability to be an effective math teacher (Rosenfeld, 2010). 4. Current Pre-service Teachers' Mathematics Instruction and Learning It can never be emphasized enough that teachers of young children need to be equipped with the right skills gained from education and experience in order to teach children in their most crucial years. However, the education they gain while in college or university does not seem to be adequate for them to be efficient in their new role as preschool teachers, especially if the subject is Math. Early Childhood Education four-year programs have few or no requirements in Mathematics education (Plata, 2008). This leaves those with lower levels of education with no preparation to teach Math (Baroody, 2004; Ginsburg et al., 2008; Sarama et al., 2004). For example, University of Urbana-Champaign in Illinois, only a 1.5 units of Mathematics education is required for a 4-year Early Childhood Education program. At the San Francisco State University in California, the Child and Adolescent Development Bachelors degree neither requires nor offers a class in children’s mathematical development. Two year ECE programs provide even fewer opportunities to learn about mathematical development. In the state of California, only nine of 109 community colleges offer a course in mathematical development for ECE majors (Chancellor's Office of the California Community Colleges, 2006). These courses are usually just credited for one unit, and are frequently combined with science content, leaving only half of the time devoted to Mathematical content. The California Child Development Permit does not include any requirement for a course in mathematical development. Cox (2011) shares that the requirements for Math courses are better in Texas. Two-year colleges in Bell and Coryell Counties in Texas, require that all degree programs include at least one math course and Early Childhood degrees require at least one math-based course. Degrees for teacher certification require four Math-based courses. However, the sad truth is that most educational systems in the United States leave learning about Mathematical development to general child development courses which do not offer a substantial amount of information on the topic, much less, equip skills in teaching Math to very young children (Plata, 2008). Continuing professional development for faculty and staff should be a priority of schools. However, in most cases, the basic knowledge of teachers may point to a poor foundation in their education way back from undergraduate studies. Colleges and universities produce teachers who are not truly knowledgeable in what young children are capable of learning and the developmentally-appropriate practices to help them learn what they should know. The professional training must begin from the time teachers are students themselves. For practicing teachers, regular in-service training by experts in the field must be invested on, along with attendance in offered seminars and workshops on the teaching-learning paths. The National Research Council (2009) recommends that Coursework and practicum requirements for early childhood educators should be changed to reflect an increased emphasis on children’s mathematics as described in the report. These changes should also be made and enforced by early childhood organizations that oversee credentialing, accreditation, and recognition of teacher professional development programs (p. 4) If reforms in the curriculum of children are to be made, so does reform in the curriculum of teacher education to gear it towards higher standards in all curricular areas, including Mathematics. This is also in recognition of children’s growing capabilities and the value of developing higher thinking skills. 5. Mathematical Training and Education Programs for preschool teachers Regarding in-service ECE professional development, Copley & Padron, 1998) explain that the focus is on an overview of the developmentally-appropriate curriculum, literacy development, classroom management and use of play as a learning strategy. Mathematical development is not given enough stress. Brenneman, Stevenson-Boyd and Frede (2009) lament that among the 50 state-funded preschool programs, 41 require at least 15 hours of in-service training per year which is definitely not enough to equip teachers with enough skills to bring back to the classroom (Barnett et al, 2009). Professional development should be on-going, and should move beyond one day to a week workshops. Training programs should allow teachers to deeply explore the content and pedagogy of Mathematics (NAEYC & NCTM, 2002.; Sarama & diBiase, 2004). Fortunately, developments in in-service programs in the early childhood education field have emerged from 2008. Still in the experimental stage, The Institute of Education Sciences (IES) developed professional development programs for teachers already in the field. These workshops and classroom support contained major mathematics components. Results from the pilot stages indicate that professional development increases teachers’ involvement in the mathematical activities in the classroom and encouraged children’s mathematical skills to flourish (Platas, Klein & Starkey, 2006; Preschool Curriculum Evaluation Research Consortium, 2008). 6. Professional development for Pre-service and In-service Teachers In relation to professional development of early childhood educators, the National Research Council (2009) recommends: the provision of professional development to early childhood in-service teachers that helps them (a) to understand the necessary mathematics, the crucial teaching-learning paths, and the principles of intentional teaching and curriculum and (b) to learn how to implement a curriculum (pp.3-4). Education and specialized training of preschool teachers are associated with young children’s learning and development (Barnett, 2004). Evaluation of the impact of Early Childhood Education teacher preparation programs and professional development conclude that benefits of high-quality preschool education can only be achieved if teachers are professionally prepared and well-compensated (Barnett, 2004). Research shows that a well-prepared early childhood education teacher brings a warm, safe and conducive environment for learning (NAEYC, 2006). Perceptions of teacher on student-teacher quality and of children’s academic abilities proved to influence academic competence among students (Hughes, Gleason, & Zhang, 2005). In addition, it is important to focus on quality of room practices, child characteristics, teachers’ perceptions of school-related climates and teachers’ perceptions of workload stress (Mantzicopoulos, 2005). It was found that the amount of teacher’s math-related teaching was highly associated to children’s mathematical knowledge (Klibanoff, Levine, Huttenlocher, Vasilyeva, & Hedges, 2006). The attitudes of preschool teachers on early mathematics do not change as they acquired knowledge of preschool teachers (Alinsinanoglu, Guven, & Kesicioglu, 2009). Teachers’ elementary education credentials, years of education and years of experience have complex impact to children’s learning (Connor, Son, Hundman, & Morrison, 2005). All of these issues can essentially be addressed by studying further within the context, knowledge and ability of early educators for early childhood education. Teachers should learn to be more reflective of the way they teach and relate to children. French et al. (2008) believe that reflective practice has been recognised to be an important tool for professional development. Rowls and Swick (2000) agree and observed that teachers who regularly reflected enabled them to develop their relationship with children. Focusing on children’s progress facilitates teacher’s understanding of how children learn math and how their curriculum and teaching approaches can further this development (Sarama & diBiase, 2004). A comprehensive and innovative program that teaches pre- and in-service teachers to study and reflect on what they do for children’s mathematical thinking resulted in better attitudes about Math and expanding their repertoire of Math concepts beyond shapes, and counting sequences and yields more positive math learning outcomes for children (Copley & Padron,1999). References Alisinanoglu, F., Guven, G., & Kesicioglu, O. S. (2009). The analysis of preschool teacher candidates’ attitudes about early mathematics education in the views of various variables. Precedia – Social and Behavioral Sciences, 1(1), 2197-2201. Barnett, W. S. (2004). Better Teachers, Better Preschools: Student Achievement Linked to Teacher Qualifications. Preschool Policy Matters, (2): 1-11. Barnett,W.S., Epstein, D.J., Friedman, A.H., Stevenson-Boyd, J., & Hustedt, J.T. (2009). The State of Preschool 2008: State Preschool Yearbook. New Brunswick, NJ: National Institute for Early Education Research. Baroody, A. J. (2004). The developmental bases for early childhood number and operations standards. In D. H. Clements & J. Sarama (Eds.), Engaging Young Children in Mathematics. Mahwah, NJ: Lawrence Erlbaum Associates. Brenneman, K., Stevenson-Boyd, J. & Frede, E.C. (2009) Math and Science in Preschool: Policies and Practice, Preschool Policy Brief, March 2009, Issue 19 Chancellor's Office of the California Community Colleges. (2006). Find a College. Retrieved February 11, 2012, from http://www.ccco.edu/find/alphabetical.htm Clements, D., & Sarama, J. (2007). Early childhood mathematics learning. In F. K. Lester (Ed.), Second Handbook of Research on Mathematics Teaching and Learning. Charlotte, NC: Information Age Pub Inc. Connor, C. M, Son, S. H., Hindman, A. H., & Morrison, F. J. (2005). Teacher qualifications, classroom practices, family characteristics, and preschool experience: Complex effects on first graders’ vocabulary and early reading outcomes. Journal of School Psychology, 43(4), 343-375. Copley, J., & Padron, Y. (1999). Preparing teachers of young learners: Professional development of early childhood teachers in mathematics And science. In Dialogue on early childhood science, mathematics, and technology education.Washington, DC: Project 2061, American Association for the Advancement of Science. Cox, G. (2011) Preschool Caregivers' Mathematical Anxiety: Examining The Relationships Between Mathematical Anxiety, And Knowledge And Beliefs About Mathematics For Young Children. Unpublished Doctor of Philosopy, Texas Woman’s University, May, 2011. Decker, C. Decker,J., Freeman, N. and Knorpf, H. (2009). Planning and administering early childhood programs (9th edition). Upper Saddle River, NJ: Pearson Ginsburg, H. P. & Amit, M. (2008). What is teaching mathematics to young children? A theoretical perspective and case study. Journal of Applied Developmental Psychology, 29(4), 274-285. Ginsburg, H. P. & Golbeck, S. L. (2004). Thoughts on the future of research on mathematics and science learning and education. Early Childhood Research Quarterly, 19(1), 190-200. Hughes, J. N., Gleason, K. A., & Zhang, D. (2005). Relationship influences on teachers’ perceptions of academic competence in academically at risk minority and majority first grade students. Journal of School Psychology, 43(4), 303-320. Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool Children’s Mathematical Knowledge: The Effect of Teacher “Math Talk”. Developmental Psychology, 42(1), 59-69. Jenkins, K.L. (2001) The early childhood field collaborative: a collection of longitudinal case studies revealing pre-service teachers’ beliefs about mathematics”, Unpublished Doctoral Dissertation, University of Houston, May 2001. Mantzicopoulos, P. (2005). Conflictual relationships between kindergarten children and their teachers: Associations with child and classroom context variables. Journal of School Psychology, 43(5), 425-442. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author. Available on- line at: http://standards.nctm.org/. NAEYC. (2006). On standards for programs to prepare early childhood professionals.Retrieved February 10, 2012, from http://www.naeyc.org/shoppingcart/Itemdetail.aspx?Stock_No=256 NAEYC & NCTM. (2002). Early childhood mathematics: Promoting good beginnings. Retrieved February 10, 2012, from http://www.naeyc.org/about/positions/pdf/psmath.pdf NAEYC & NCTM. (2002).; Sarama, J., & diBiase, A. (2004). The professional development challenge in preschool mathematics. In D. Clements, J. Sarama, & A. diBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 415-448). Mahwah, NJ: Erlbaum. National Research Council. (2009). Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Committee on Early Childhood Mathematics, Christopher T. Cross, Taniesha A. Woods, and Heidi Schweingruber, Editors. Center for Education, Division of Behavioral and Social Sciences and Education. Washington, DC: The National Academies Press. Platas, L. M. (2008). Measuring Teachers’ Knowledge of Early Mathematical Development and Their Beliefs about Mathematics Teaching and Learning in the Preschool Classroom. Berkeley, California: ProQuest LLC. Platas, L., Klein, A., & Starkey, P. (2006). How Do Two Years of Professional Development In a Preschool Math Curriculum Affect Teachers' Classroom Practices? Proceedings of Head Start's Eighth National Research Conference. Preschool Curriculum Evaluation Research Consortium. (2008). Effects of Preschool Curriculum Programs on School Readiness (NCER 2008- 2009). Washington, DC: National Center for Education Research, Institute of Education Sciences, U.S. Department of Education. Washington, DC: U.S. Government Printing Office.) Rosenfeld, D. (2010) Increasing perceived efficacy for teaching Mathematics: An exploratory study, Journal of Mathematics Education at Teachers College, Spring-Summer Vol.1 Sarama, J., & diBiase, A. (2004). The professional development challenge in preschool mathematics. In D. Clements, J. Sarama, & A. diBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 415-448).Mahwah, NJ: Erlbaum. Tsamir, P., & Tirosh, D. (2009). Affect, subject matter knowledge and pedagogical content knowledge: The case of a kindergarten teacher. In J. Maass & W. Schloglmann (Eds.), Beliefs and attitudes in mathematics education (pp. 19-32). Rotterdam, Netherlands: Sense Publishers Wilson, J H. (2009) An exploration of early childhood leaders' perceptions regarding their knowledge, skills, and confidence in the areas of mathematical content, child development, pedagogical content, and instructional leadership strategies. Unpublished Doctor of Education Dissertation, University of Houston, May, 2009 Read More