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.
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, the value of teaching subitizing skills in the classroom is clear. This ability provides a visual tool to young students as they develop a basic understanding of numbers and one to one correspondence, and it establishes a firm foundation for the future skills of addition and subtraction facts. Possessing the knowledge of how and when students develop the cognitive understanding of this concept can drive a teachers instruction so that the students find greater success in the lesson. Knowing that comprehension of number conservation does not occur until age 5 or 6 will definitely have an effect upon early teaching of number sense.
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.
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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).
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.
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.
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.
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.
Ward (2005) explores writing and reading as the major literary mediums for learning mathematics, in order for students to be well equipped for things they may see in the real world. The most recent trends in education have teachers and curriculum writers stressed about finding new ways to tie in current events and real-world situations to the subjects being taught in the classroom. Wohlhuter & Quintero (2003) discuss how simply “listening” to mathematics in the classroom has no effect on success in student academics. It’s important to implement mathematical literacy at a very young age. A case study in the article by authors Wohlhuter & Quintero explores a program where mathematics and literacy were implemented together for children all the way through eight years of age. Preservice teachers entered a one week program where lessons were taught to them as if they were teaching the age group it was directed towards. When asked for a definition of mathematics, preservice teachers gave answers such as: something related to numbers, calculations, and estimations. However, no one emphasized how math is in fact extremely dependable on problem-solving, explanations, and logic. All these things have literacy already incorporated into them. According to Wohlhuter and Quintero (2003), the major takeaways from this program, when tested, were that “sorting blocks, dividing a candy bar equally, drawing pictures, or reading cereal boxes, young children are experienced mathematicians, readers, and writers when they enter kindergarten.” These skills are in fact what they need to succeed in the real-world. These strategies have shown to lead to higher success rates for students even after they graduate
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