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The definition essay seeks to test a student’s ability to put abstract theories into words, and to see if they are able to passionately present their opinions on abstract theories.
If we take love as an example, there are lots of different ways this could be described (it’s a good job you can buy definition essay because this can get complicated). You could talk about platonic love, romantic love, the love someone has for an object, or self love. You could talk about how love can change the world or how love can break a person.
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The level of depth you will need to include in your essay depends on your academic level – for examples, a definition essay for a master’s degree will need a lot more expansion than a definition essay for a high school student or an undergraduate. A graduate level will fall somewhere in the centre. And although it’s unlikely that any university will require this specifically for a doctoral candidate, it’s an excellent way to introduce parts of your thesis if they fall into an abstract category.
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The definition essay is an often short piece of writing that aims to define a word. Although this sounds simple, students should bear in mind that the word they will be defining in unlikely to be a straight forward word like towel. Usually the word will be an abstract word like love, honour, bravery etc.
Math anxiety is the feeling of nervousness and apprehension toward math problems, classes, or exams. It generally begins when a child is in fourth grade and escalates throughout high school. Math anxiety is not just a psychological problem as it can cause students to discontinue taking math classes beyond high school requirements, limiting their choices with regard to college or career opportunities. Teachers and parents have been shown to influence math anxiety, and both can assist in easing the psychological and physical symptoms children experience. Practice with various math problems, having no time limit for exams, and being encouraged through errors have been shown to ease math anxiety.
Keywords Math Anxiety; Mathematics; Phobia; Psychology; Short-Term Memory; Working Memory
Math anxiety is the feeling of worry, frustration, agitation, and a fear of failure with regard to taking a math class, completing math problems, and/or taking a math exam. Being anxious about math can begin when a child is in fourth grade and generally increases when students are in middle and high school. Some studies have focused on students as young as first grade experiencing math anxiety (Harari, Vukovic & Bailey, 2013). In addition to past experiences with math, teachers and parents can influence the anxiety a child feels when presented with math problems. A person suffering from math anxiety usually experiences the physical signs of having a phobia or anxiousness: increased heart rate, stomach discomfort, sweating, trembling, and weakness within the body. Anyone who has experienced extreme discomfort being in a crowded elevator (claustrophobia) or looking out a window on the top floor of a building (vertigo) can relate to the sense of panic when a math test is placed in front of a person suffering from math anxiety.
Math anxiety is so pervasive that it has been researched for over fifty years, and more than 167,000 websites are devoted to math anxiety on any given day to explain the causes and the remedies for the disorder. According to Ashcraft and Kirk (2001), math anxiety has been shown to actually "disrupt mental processes needed for doing arithmetic and [to] drag down math competence" (p. 224). Other kinds of anxiety or phobias can inhibit a person's activities; for example, a person suffering from claustrophobia can take several flights of stairs rather than getting on an elevator, and a person experiencing vertigo can choose not to go to the top of the Empire State Building. However, math anxious people suffer from an actual dysfunction in brain activity; more specifically, working memory is affected. Working memory holds "the capacity to retain a limited amount of information while working on a task and [to] block out distractions and irrelevant information" (Cavanaugh, 2007a). Furthermore, Gardner (1983) asserts that "the most central and least replaceable feature of the mathematician's gift is the ability to handle skillfully long chains of reasoning" (Gardner, 1983, p. 139). If the capability to work with long strings of numbers is affected due to math anxiety, solving such problems can be impossible.
How Does Math Anxiety Affect Children?
Unfortunately, when faced with a math problem that he doesn't understand, the child suffering from math anxiety fills his head with negativism and focuses on that, distracting himself from attempting to work through the problem in front of him. Furthermore, this distraction can start a negative cycle in which the same child rushes though the problem and makes a mistake because he's not focusing on the problem itself. The mistake then reinforces the negativism and increases the need to rush through homework or an exam (Math Anxiety, 2007). And, unlike the people who avoid the situations that make them anxious, a student doesn't have the option of avoiding math during the school day - or afterward, for that matter, when faced with assigned homework.
Ashcraft and Kirk (2001) note that there are specific types of math problems that tend to give students the most anxiety. Those problems are the ones that deal with large numbers and require several steps like carrying and borrowing numbers and long division - tasks that require working memory. Amanda McMahon, a ten-year-old fifth grader, is currently working on algebra in her elementary class. She identifies confusion as a feeling she gets when working on her assignments because "letters divided by other letters are somehow supposed to equal a different set of letters multiplied by other letters" (personal communication, October 24, 2007). At the end of this school year, McMahon will take a comprehensive New York State standardized exam in mathematics in addition to culminating math exams required by her school district. Her view of math is not a positive one.
However, it could be a very costly one. The issue with students like McMahon - those who complete their homework and pass tests but fear doing either - is not simply a psychological concern; it is a lifetime concern. Students who feel anxious when faced with math problems or who perform poorly on math exams tend to stop taking math classes beyond the point at which they are required. By not taking higher-level classes, students greatly limit their options regarding higher education and employment possibilities. While it is commonly believed that boys outperform girls on math achievement, there is evidence that whenever such a divide is noted, the divide is not permanent. Woolfolk (1998), points out that the difference in gender and math performance can "decrease substantially or disappear altogether when the actual number of previous math courses taken by each student is considered" (Fennema & Sherman, 1977; Oakes, 1990; Pallas & Alexander, 1983, as cited in Woolfolk, 1998, p. 183). The more classes a student takes, the more familiar with the material she will become, and the more comfortable manipulating math problems she will be. However, when faced with the option of feeling frustrated and anxious much of the time, it is easy to see why boys and girls cease taking math classes rather than adding to their frustration with additional courses in their not so favorite subject.
When looking toward higher education, a lack of math experience can cause the need for non-credit bearing courses in college, in addition to the required math courses for any specific field. This adds to tuition bills and the time it takes to complete a degree, and, when in conjunction with math anxiety, can cause psychological problems as well. Karin Killough, Director of the Learning Center at the State University of New York College at Plattsburgh, notes that in the 2006-2007 academic year, her tutors accumulated 10,000 contact hours assisting students in various subjects. Math courses, including statistics and calculus, total almost one quarter of those contacts (personal communication, October 24, 2007).
Sarah Taylor, a math tutor in the Learning Center, indicates that when having to break down the number of contacts she has with students who have trouble with math problems versus those with math anxiety, the breakdown differs depending on the time of the semester. During mid-terms and final exams more than three-quarters of the students she assists have anxiety issues; on the other hand, during the less stressful times of the semester, almost the same amount comes to her for assistance with math problems. Taylor, a math and accounting major, attributes this discrepancy to the high stakes of exams and students' lack of confidence in their math ability when those stakes are higher (personal communication, October 24, 2007). When a final grade is at stake, it is likely that college students who experience math anxiety will not continue taking math courses beyond what is required of them.
It is important that teachers understand when the introduction to mathematics takes place in the life of a child. According to Gardner, introduction to the concept of math begins when infants first learn "the world of objects" (Gardner, 1983, p. 129).
For it is in confronting objects, in ordering and reordering them, and in assessing their quantity, that the young child gains his or her initial and most fundamental knowledge about the logical-mathematical realm. From this preliminary point, logical-mathematical intelligence rapidly becomes remote from the world of material objects … the individual becomes more able to appreciate the actions that one can perform upon objects … Over the course of development, one proceeds from objects to statements, from actions to the relations among actions, from the realm of the sensory-motor to the realm of pure abstraction-ultimately, to the heights of logic and science (Gardner, 1983, p. 129).
Math anxiety develops shortly after children enter the world of structured education. If left on their own, Gardner asserts, children will manipulate objects and utilize them in a way that best fits their needs (p. 129). Once they enter into a school system, however, fitting their needs loses priority to goals, objectives, and standardized tests outside their control. Furthermore, there is research that points to teachers being the possible culprits of the math anxiety their students experience. In a study conducted in 1999 by Jackson and Leffingwell, the researchers identified several teacher behaviors that cause math anxiety in students:
• Being hostile
• Exhibiting gender bias
• Having an uncaring attitude
• Expressing anger
• Having unrealistic expectations and
• Embarrassing students in front of their peers (as cited in Furner & Duffy, 2002).
In addition, Oberlin (1982) found that teaching techniques also cause math anxiety. "Assigning the same work for everyone, teaching the textbook problem by problem, and insisting on only one correct way to complete a problem" increase a student's anxiousness (as cited in Furner & Duffy, 2002, p. 69). Furthermore, Woolfolk (1998) notes that
some elementary-school teachers spend more academic time with boys in math and with girls in reading. In one study, high school geometry teachers directed most of their questions to boys, even though the girls asked questions and volunteered answers more often (p. 183).
It is plausible to expect that if teachers have positive attitudes, treat students respectfully - and individually - and treat girls and boys as if both genders have the same potential for success in math, the instance of math anxiety would decline. Furthermore, there are more specific changes teachers can make in the experiences of their students.
Researchers have also indicated that the use of breathing exercises before exams may greatly impact math anxiety in students. This may be a possible area for teachers or other school staff to explore (Brunyé, Mahoney, Giles, Rapp, Taylor & Kanarek, 2013)....