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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Maths is a tool needed for everyday life and it is a way of helping children to understand the concepts of the world around them. Using the programmes of study from the National curriculum and the EYFS curriculum for numeracy, Washingwell Community Primary school aim:-
Restivo, Sal, Jean Paul Van Bendegen, and Roland Fischer. Math Works: Philosophical and Social Studies of Mathematics and Mathematics Education. Albany, New York: State University of New York Press, 1993.
Teachers and textbooks present math as a settled notion, but mathematics is the exact opposite for it is continually discovered. “School mathematics is largely made up of a sequence of facts and rules, facts which are certain rules which come from a higher authority and cannot be questioned. It treats mathematical matters as completely settled. Mathematics is not settled”, exclaims Jordan Ellenberg. For this reason, students view math as a set of regulations rather than the structure of their entire lives. Jordan Ellenberg speaks of the dangers of modern math saying, “If we settle on a vision of mathematics that consists of getting the answer right and no more, and test for that, we run the risk of creating students who test very well but know no mathematics at all.” Apparently, Common Core Standards does not require teachers to instruct students mathematics with meaning, but rather let the teacher choose their strategies which will ultimately lead to a complex idea of
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.
Mathematics education has undergone many changes over the last several years. Some of these changes include the key concepts all students must master and how they are taught. According to Jacob Vigdor, the concerns about students’ math achievements have always been apparent. A few reasons that are negatively impacting the productivity of students’ math achievements are historical events that influenced mathematics, how math is being taught, and differentiation of curriculum.
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.
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
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...
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
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.
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The prominence of numeracy is extremely evident in daily life and as teachers it is important to provide quality assistance to students with regards to the development of a child's numeracy skills. High-level numeracy ability does not exclusively signify an extensive view of complex mathematics, its meaning refers to using constructive mathematical ideas to “...make sense of the world.” (NSW Government, 2011). A high-level of numeracy is evident in our abilities to effectively draw upon mathematical ideas and critically evaluate it's use in real-life situations, such as finances, time management, building construction and food preparation, just to name a few (NSW Government, 2011). Effective teachings of numeracy in the 21st century has become a major topic of debate in recent years. The debate usually streams from parents desires for their child to succeed in school and not fall behind. Regardless of socio-economic background, parents want success for their children to prepare them for life in society and work (Groundwater-Smith, 2009). A student who only presents an extremely basic understanding of numeracy, such as small number counting and limited spatial and time awareness, is at risk of falling behind in the increasingly competitive and technologically focused job market of the 21st Century (Huetinck & Munshin, 2008). In the last decade, the Australian curriculum has witness an influx of new digital tools to assist mathematical teaching and learning. The common calculator, which is becoming increasing cheap and readily available, and its usage within the primary school curriculum is often put at the forefront of this debate (Groves, 1994). The argument against the usage of the calculator suggests that it makes students lazy ...
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