Mathematics is either loved or hated by those who are charged with mastering it. In a world that has such strong feelings about mathematics, negative and complex numbers have been considered erroneous throughout most of history. It is understandable that many young students have dread in their hearts about new and unknown topics like negative and complex numbers, especially when mathematicians for thousands of years have had those same feelings. In Tennessee, according to state standards, negative numbers are introduced in sixth grade as an extension of the rational number system and complex numbers are introduced in high school Algebra. Some middle and high school teachers look back on their years as math students with dislike for such topics and create more anxiety than is necessary for their own learners. Historically speaking, these students and teachers are actually in the company of many great mathematicians who had strong feelings about or denied the existence of negative and imaginary numbers altogether. These numbers were largely a stepchild of mathematics until modern times. Even the etymology is, for lack of a better word, negative. Words like false, fictitious, sophistic, and absurd have been traditionally common descriptors, but the modern terminology does not put one’s mind at ease. The word imaginary might cause a person to think of unicorns and fairies rather than numbers and the term complex just makes the concept seem more difficult. The influence of history could be related to the way this mathematical topic has caused and is still causing anxiety in classrooms. Negative and complex numbers have always existed even though they may not have been accepted, and because of the work of the nineteenth centu...
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... normal rules of arithmetic and building rules for the imaginary numbers. (Berlinghoff and Gouvea 81-86, 141-146, Katz 360)
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Abstract: This paper gives an insight into the Mathematics used by the American Indians. The history of American Indians and how they incorporated mathematics into their lives is scarce. However from the information retrieved by Archeologists, we have an idea of the type of mathematics that was used by American Indians.
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Michael Guillen, the author of Five Equations that Changed the World, choose five famous mathematician to describe. Each of these mathematicians came up with a significant formula that deals with Physics. One could argue that others could be added to the list but there is no question that these are certainly all contenders for the top five. The book is divided into five sections, one for each of the mathematicians. Each section then has five parts, the prologue, the Veni, the Vidi, the Vici, and the epilogue. The Veni talks about the scientists as a person and their personal life. The Vidi talks about the history of the subject that the scientist talks about. The Vici talks about how the mathematician came up with their most famous formula.
Over the course of these past few weeks we have learned all sorts of math that we will utilize in our everyday lives. They have all been very interesting; my favorite subjects were learning about how voting works and how to calculate owning a home. For our final math project in our math modeling class, we had to choose a topic that interested us yet had something to do with mathematics. For this presentation, I decided to research the history of math and art and how the two have been used together to create amazing artwork.
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.
Leonhard was sent to school in Basel and during this time he lived with his maternal grandmother. The school was a rather poor one, and Euler learned no mathematics at all from there. However, his father’s teaching had sparked his interest in mathematics. He read mathematics books and papers on his own and took some private lessons (Leonhard Euler).
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.
...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.
In conclusion, it is clear that while their ancient civilization perished long ago, the contributions that the Egyptians made to mathematics have lived on. The Egyptians were practical in their approach to mathematics, and developed arithmetic and geometry in response to transactions they carried out in business and agriculture on a daily basis. Therefore, as a civilization that created hieroglyphs, the decimal system, and hieratic writing and numerals, the contributions of the Egyptians to the study of mathematics cannot and should not be overlooked.
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.
Prime numbers have been of interest to mathematicians for centuries, and we owe much of our existing knowledge on the subject to thinkers who lived well before the Common Era––such as Euclid who demonstrated that there are infinitely many prime numbers around 300 BCE. Yet, for as long as primes have been an element of the mathematician’s lexicon, many questions about prime numbers remain unreso...
[4] Nolan, Deborah. Women in Mathematics: Scaling the Heights. The Mathematical Association of America, 1997
Irrational numbers are real numbers that cannot be written as a simple fraction or a whole number. For example, irrational numbers can be included in the category of √2, e, Π, Φ, and many more. The √2 is equal to 1.4142. e is equal to 2.718. Π is equal to 3.1415. Φ is equal to 1.6180. None of these numbers are “pretty” numbers. Their decimal places keep going and do not end. There is no pattern to the numbers of the decimal places. They are all random numbers that make up the one irrational number. The concept of irrational numbers took many years and many people to discover and prove (I.P., 1997).
Melville, Duncan J, Tokens: the origin of mathematics, St Lawrence University IT Retrieved January 19th 2014, from St Lawrence University: http://it.stlawu.edu/~dmelvill/mesomath/tokens.html
The history of math has become an important study, from ancient to modern times it has been fundamental to advances in science, engineering, and philosophy. Mathematics started with counting. In Babylonia mathematics developed from 2000B.C. A place value notation system had evolved over a lengthy time with a number base of 60. Number problems were studied from at least 1700B.C. Systems of linear equations were studied in the context of solving number problems.