The Development Of Children's Thinking Related To Mathematics - Research Paper Example

 The Development Of Children's Thinking Related To Mathematics Introduction Children from economically challenged families appear to have a more difficult time in learning mathematical skills than do children from families with secure finances. While the body of research that exists on the topic has tended to focus on ethnicity as a component to the achievement gaps that are appreciated where learning mathematics is involved, it is more clearly evident that economic disparities create achievement gaps where expectations are not being met. Economic power asserts a certain level of propriety where knowledge is concerned, but this can be used where context is shown to be essential in learning mathematical knowledge. Putting math into context with real-life situations appears to increase the ability to effectively use mathematical knowledge. Socialization appears to be the key to how learning is accomplished and learning math is affected when earlier socialization towards learning intangible concepts has not been established. The effect of economics on the gaps in achievement as observed between low and high-income families is more likely due to the differences in socialization towards learning rather than in a disparity in income. Disparities There is a belief based upon research that children from African American and Latin ethnic origins, as well as those from low socio-economic areas, have lower scores on standardized tests than to those from Caucasian ethnic origins and with a higher level of socioeconomic advantages. According to Flores (2007), "Specifically, data show that African American, Latino, and low-income students are less likely to have access to experienced and qualified teachers, more likely to face low expectations, and less likely to receive equitable per-student funding " (p. 29). This disparity is more likely due to socioeconomic differences than to ethnic issues and evokes the question as to how socioeconomic status affects learning. The focus of this paper is to examine how socioeconomic differences affect learning in mathematics. The data where ethnic issues are concerned is inaccurate because the socio-economic status of students who are used to gather the data is not the primary focus. In the study done by Flores (2007) who also focuses on socio-economic status, the statistics concerned with ethnicity is also considered. Flores (2007) presents data concerning standardized tests still shows a disparity in regard to ethnicity. In African American students, 91% have not met the mathematics proficiencies expected by the eighth grade. For Latino students, that figure is 87%. Asian American students, on the other hand, show that 53% are not meeting mathematical expectations and Caucasian students are at 63%. The first notable information from these statistics is that over half of all students are not meeting mathematical achievement expectations by grade eight. The discussion, when focused on socio-economic backgrounds, shows that while 38% of children from financially secure homes meet expectations in mathematics on standardized tests, only 13% of children from economically insecure families meet those expectations (Flores, 2007). Economic disparities also lead to cultural disparities with families having members with minds that have been trained academically have a much easier time in transferring that type of learning discipline onto their children. As poverty and academic achievement are related, families in lower socioeconomic levels are less likely to have achieved higher education; therefore their children are not taught how to pursue education nor to have an admiration for economic achievement. One of the other misconceptions where research has focused on culture and ethnic issues where learning is concerned is that there has been an association with culture and ethnicity. According to work done by Nasir and Hand (2006), "This body of work assumed that culture was a property of particular racial groups, with some very early work arguing for the heritability of racial characteristics" (p. 451). The disparity involved has not, however, been shown to be related to ethnic or racially grouping, but has been due to the ‘culture of poverty'. Research on the effects of poverty has shown that children in families with financial insecurity "grow in families that are socially ‘disorganized' and lacking in adequate cognitive stimulation" (Nasir & Hand, 2006, p. 451). The culture of poverty leads to adaptations of cultural beliefs that defend against the gaps in achievement that have left them financially vulnerable. Nasir and Hand (2006) note that even as early as 1969, researchers such as Lewis came to understand that “the poor had adapted to their life in a socially stratified society through the perpetuation of a pattern of beliefs and behaviors that include absence of childhood, abandonment of wives and children, predisposition to authoritarianism, and feelings of dependence and inferiority” (p. 451). Power, Knowledge, and Poverty According to work done by Nasir, Hand, and Taylor (2008), “ knowledge is not neutral in respect to power – some types of knowledge are more aligned with communities of practice that have more power, whereas other types of knowledge are more aligned with communities of practice that have less power” (p. 187). Filtering what we know about disparities in mathematical knowledge through this belief allows for an understanding of how the disparities in the acquisition of learning are enhanced by the cultural and community knowledge as it is passed to each subsequent generation. What is important is to understand how context lends itself to learning mathematics, and when math is put into context students from any socio-cultural level find that they can learn. Nasir, Hand, and Taylor (2008) studied the learned mathematics through examining basketball teams. One thing that should be noted is in researching the gaps in achievement through basketball teams at the high school level, the division of gender in middle and high school sports provided for an all-male participant group. The students were asked to solve problems that related to basketball and those that were the simple use of mathematical equations. Where the difficulty was the same in both basketball related questions and equation based problems presented to the students, the students showed a much higher proficiency at solving basketball related problems. The conclusions drawn from this study were that students could use math when it related to a situation at a far higher level of understanding that when it was given as an unrelated mathematical problem (Nasir, Hand, & Taylor, 2008). The conclusion that can be drawn from this is that in relating math to the real world, the context provided purpose to the information and made it easier to calculate. This can be extended so that it is put into context to life in a family that has a higher socio-economic level than one in a lowered socio-economic level. A family with a higher socio-economic level will naturally expose their children to a much wider diversity of uses for mathematics in real life. Banking, large purchases, credit cards, and insurance issues will more than likely be much more extensive in families with more means, thus creating more real-life instances where mathematics are important. As exampled by the basketball teams, math is easier to learn and understand when it has relevance to experiences in life. Culture, Learning, and Mathematics As established, culture has a great deal of influence on the way in which learning is conducted. As Nasir and Hand (2006) have established, cultures will handle learning opportunities and early childhood exposure to education differently depending on how their acculturation has been established. As families socialize either towards or away from education, children follow the examples that they have been given. According to Clements, “Results also support previous studies showing that organized experiences result in greater mathematics knowledge upon entry into kindergarten and that focused early mathematical interventions help young children develop a foundation of informal mathematics knowledge (Clements, 1984), including children living in poverty”. (p. 488). Children who experience introductions to mathematics at an earlier age have a higher possibility of greater achievements in the mathematical area. One of the types of organizational methods that can help children who have not been acculturated into modes of learning is for schools in high-risk areas to provide extra opportunities for learning and growth. An example can be seen through the following example: “In 1994, Congress authorized the 21st Century Community Learning Centers (21st Century) program to open up schools for broader use by their communities. In 1998, the program was refocused on providing academic, enrichment, and recreational activities in public schools during the afterschool hours” (James-Burdumy, Dynarsky, & Dynarski, 2007, p. 296). This form of extension in the use of schools provides for more opportunities for children to discover an academically focused life, which in turn seems to be relevant to how they learn math, rather than influences of poverty that might be associated with at-risk circumstances. Food insecurity, housing insecurity, and safety issues all are a part of the pressures that children face when they come from impoverished circumstances and it is not suggested that these insecurities do not affect the way that children can focus and learn. The large disparity that is observed, however, is more likely due to not having been in organized socialization that was focused towards learning opportunities (Ludvig, 2006). There is a common assumption that private schools will have the better result than will public schools. According to Lubienski and Lubienski (2006), this assumption may be in error. In a study that assessed mathematical performance in both public and private schools while taking into consideration demographic information, private schools did not seem to have higher scores than did public schools and the disparities fell along demographic lines associated with culture rather than location. The conclusion reached by Lubeinski and Lubienski (2006) was that “While public choice theory blames bureaucratic administration of public schooling for mediocre academic performance, our analysis suggests that the sectors more characterized by choice and competition are not necessarily producing better results” (p. 684). One of the problems that are exacerbating the continuation of achievement gaps while the solution may be easily reached through alternative methods of learning approaches in the lowest grade levels. According to Roschelle, Singleton, Sabelli, Pea, and Bransford (2008), old theories of failures on the part of education systems must give way to understand that it is not within the administration end of the system, but through "undervalued integrated methods" which would allow for disparity gaps to begin to close. Specifically addressing the cultural disparities, rather than focusing on elements of irrelevant ethnicity or dismissing merely because of socio-economic issues will help to find solutions for the problem as it is restructured for the reasons that these disparities occur, rather than unrelated assumptions (Bodovski & Farkas, 2007). When specifically researched, the disparities due to ethnic diversities, especially between Caucasians and African Americans, the differences can be measured because of the experiences that African American students have in classrooms where they are treated as if they will not learn the information, leaving them in a position where they are not encouraged, are not given adequate attention, nor expected to achieve (Stinson, 2006). Conclusion The disparities that are observed among children when demographic information is used in regard to ethnicity shows a wide achievement gap between Caucasians and Asians when compared to children who are African American and Latino. However, while these differences historically have been shown to be attributed to ethnicity, the reality is that imposed racial grouping has no real meaning on how children learn. Culture, on the other hand, is far more influential than any other aspect of a child's life on how they will approach their education. Research, it appears, has been focused on the wrong criteria for interpreting the data. New information that has been observed for the reasons why children of different ethnicities have different levels of achievement relies on the experiences that children have within their own cultures in regard to learning in combination with the experiences that they have with learning opportunities within the school systems. Socio-economic diversity appears to be a reason for differences in learning mathematics within the school system. However, it should be noted that culture may have more of an influence than actual poverty levels. The economic status of a family may not have specific reasons as a cause for learning diversity, but rather the causes of a lowered economic status as it relates to the educational levels and achievements of the family may influence the culture towards learning. While it is true that statistics show that children from lower economic classes have a lowered achievement in learning mathematics, it far more likely that the culture that supports that status as it relates to a lack of academic inclination is more influential. References Clements, D. & J. Sarama. (June 2008). Experimental evaluation of the effects of a research-based preschool mathematics curriculum. American Educational Research Journal. 45(2): 443-494. Bodovski, K. & G. Farkas. (November 2007). Mathematics growth in early elementary School: The Roles of Beginning Knowledge, Student Engagement, and Instruction. The Elementary School Journal. 108(2): 115-130. Flores, A. (October-November 2007). Examining disparities in mathematics education. The High School Journal. 91(1): 29-42. James-Burdumy, M. Dynarsky, & Dynarski, J. (December 2007). When elementary schools stay open late: Results from the national evaluation of the 21st-century community learning centers. Educational Evaluation and Policy Analysis. 29(4): 296-318. Lubienski, S. T. & Lubienski, C. (Winter 2006). School sector and academic achievement: A multilevel analysis of NAEP mathematics data. American Educational Research Journal 43(4): 651-698. Ludwig, J. (Autumn 2006). "Culture" and the Intergenerational Transmission of Poverty: The Prevention Paradox. The Future of Children. 16(2): 175-196. Nasir, S. N. & V. M. Hand. (Winter 2006). Exploring sociocultural perspectives on race, culture, and learning. Review of Educational Research. 76(4): 449-475. Nasir, N. S., V. Hand, & E. V. Taylor. (2008). Culture and mathematics in school: Boundaries between "cultural" and "domain" knowledge in the mathematics classroom and beyond. Review of Research in Education. 32: 187-240. Roschelle, J., C. Singleton, N. Sabelli, R. Pea & J. D. Bransford. (December 2008). Mathematics Worth Knowing, Resources Worth Growing, Research Worth Noting: A Response to the National Mathematics Advisory Panel Report. Educational Research. 37(9): 610-617. Stinson, D. W. (Winter 2006). African American male adolescents, schooling (and mathematics): Deficiency, rejection, and achievement. Review of Educational Research. 76(4): 477-506. Read More