As a student, I always enjoyed math. In high school I took all math classes offered, including Calculus. The first math class I took in college was a breeze, and I thought that this one would be no different. What could I learn about elementary school math that I didn’t already know? The first day of class showed me what a ridiculous question that was and I went on to learn things about math that had never before been brought to my attention. This paper will discuss what I’ve learned about subtraction, about students, about the Common Core State Standards, and how my concept map has changed since my first draft.
Cardinality and Subitizing
Cardinality and subitizing are not topics encountered in everyday life, unless you happen to be a math education specialist. Both were labels I had not heard before for concepts that hadn’t previously occurred to me. They were the beginning of my math vocabulary—an important asset when expected to talk freely about math. Van de Walle, Karp, and Bay-Williams explain that understanding the concept of cardinality means knowing that “the last count word indicates the amount of the set” (p. 127). Those who understand this concept—that the last number counted has value—“are said to have the cardinality principle” (Van de Walle, et. al, 2010, p. 127). The concept of cardinality initially perplexed me—I took for granted that counting had meaning. However, putting a name to the concept helped to solidify my understanding of numbers and provided me with a vital piece of vocabulary when discussing mathematics. The same was true for subitizing. Clements describes subitizing as “the direct perceptual apprehension of the numberosity of a group” or “instantly seeing how many” (1999, p. 400). I ...
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...nship between addition. The difference between kindergarten and fifth grade is only the numbers within which these computations should be done.
Works Cited
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Gelernter disagrees with the comment made by a school principal, “Drilling addition and subtraction in an age of calculators is a waste of time” (279). He reveals the bitter truth that American students are not fully prepared for college because they have poorly developed basic skills. In contrast, he comments, “No wonder Japanese kids blow the pants off American kids in math” (280). He provides information from a Japanese educator that in Japan, kids are not allowed to use calculators until high school. Due to this, Japanese kids build a strong foundation of basic math skills, which makes them perform well in mathematics.
The second part of this memo contains a rhetorical analysis of a journal article written by Linda Darling-Hammond. Interview The following information was conducted in an interview with Diana Regalado De Santiago, who works at Montwood High School as a mathematics teacher. In the interview, Regalado De Santiago discusses how presenting material to her students in a manner where the student actually learns is a pivotal form of communication in the field (Personal Communication, September 8, 2016).
Van de Walle, J., , F., Karp, K. S., & Bay-Williams, J. M. (2010). Elementary and middle school mathematics, teaching developmentally. (Seventh ed.). New York, NY: Allyn & Bacon.
In the early part of the century researchers believed that subitizing represented a true understanding of a number, acting as a developmental prerequisite to counting. Research had supported the idea through the findings that young infants are skilled at using subitizing to represent small numbers contained in sets. This skill emerged well before the skill of counting.
Steen, Lynn Arthur . "Integrating School Science and Mathematics: Fad or Folly?." St. Olaf College. (1999): n. page. Web. 12 Dec. 2013..
middle of paper ... ... Barr, C., Doyle, M., Clifford, J., De Leo, T., Dubeau, C. (2003). "There is More to Math: A Framework for Learning and Math Instruction” Waterloo Catholic District School Board Burris, A.C. "How Children Learn Mathematics." Education.com.
To investigate the notion of numeracy, I approach seven people to give their view of numeracy and how it relates to mathematics. The following is a discussion of two responses I receive from this short survey. I shall briefly discuss their views of numeracy and how it relates to mathematics in the light of the Australian Curriculum as well as the 21st Century Numeracy Model (Goos 2007). Note: see appendix 1 for their responses.
Children can enhance their understanding of difficult addition and subtraction problems, when they learn to recognize how the combination of two or more numbers demonstrate a total (Fuson, Clements, & Beckmann, 2011). As students advance from Kindergarten through second grade they learn various strategies to solve addition and subtraction problems. The methods can be summarize into three distinctive categories called count all, count on, and recompose (Fuson, Clements, & Beckmann, 2011). The strategies vary faintly in simplicity and application. I will demonstrate how students can apply the count all, count on, and recompose strategies to solve addition and subtraction problems involving many levels of difficulty.
Countless time teachers encounter students that struggle with mathematical concepts trough elementary grades. Often, the struggle stems from the inability to comprehend the mathematical concept of place value. “Understanding our place value system is an essential foundation for all computations with whole numbers” (Burns, 2010, p. 20). Students that recognize the composition of the numbers have more flexibility in mathematical computation. “Not only does the base-ten system allow us to express arbitrarily large numbers and arbitrarily small numbers, but it also enables us to quickly compare numbers and assess the ballpark size of a number” (Beckmann, 2014a, p. 1). Addressing student misconceptions should be part of every lesson. If a student perpetuates place value misconceptions they will not be able to fully recognize and explain other mathematical ideas. In this paper, I will analyze some misconceptions relating place value and suggest some strategies to help students understand the concept of place value.
...ett, S. (2008) . Young children’s access to powerful mathematical ideas, in English, Lyn D (ed), Handbook of international research in mathematics education, 2nd edn, New York, NY: Routledge, pp. 75-108.
With this promise came serious concerns over education taught students ranked 28th in the United States out of 40 other countries in Mathematics and Sciences. 80% of occupations depend on knowledge of Mathematics and Science (Week and Obama 2009). In order to ensure that educators have enough money to fund the endeavor to be more competitive with the rest of the world in Mathematics and Science, President Obama will increase federal spending in education with an additional 18 billion dollars in k-12 classrooms, guaranteeing educators have the teachers, technology, and professional development to attain highly quali...
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Towers, J., Martin, L., & Pirie, S. (2000). Growing mathematical understanding: Layered observations. In M.L. Fernandez (Ed.), Proceedings of the Annual Meetings of North American Chapter of the International Group for the Psychology of Mathematics Education, Tucson, AZ, 225-230.
Throughout out this semester, I’ve had the opportunity to gain a better understanding when it comes to teaching Mathematics in the classroom. During the course of this semester, EDEL 440 has showed my classmates and myself the appropriate ways mathematics can be taught in an elementary classroom and how the students in the classroom may retrieve the information. During my years of school, mathematics has been my favorite subject. Over the years, math has challenged me on so many different levels. Having the opportunity to see the appropriate ways math should be taught in an Elementary classroom has giving me a