Destiny Washington Essays (1531 words) - Poetic Form, Stanza

Destiny Washington Professor Hart Eng 380 2 April 2017 Forbidden Fruit: Gwendolyn Brooks's "A song in the front yard" I've stayed in the front yard all my life. I want a peek at the back Where it's rough and untended and hungry weed grow's . A girl gets sick of a rose. I want to go in the back yard now And maybe down the alley, To where the charity children play. I want a good time today. They do some wonderful things. They have some wonderful fun. My mother sneers, but I say it's fine How they don't have to go in at quarter to nine. My mother, she tells me that Johnnie Mae Will grow up to be a bad woman. That George'll be taken to Jail soon or late (On account of last winter he sold our back gate.) But I say it's fine. Honest, I do. And I'd like to be a bad woman, too, And wear the brave stockings of night-black lace And strut down the streets with paint on my face When restricted from something, one naturally becomes fascinated with the very thing, they are restricted from. "A song in the front yard," by Gwendolyn Brooks, creates an analogy of the difference between the poor and wealthy. She ope ns the poem with intensity, making the reader eager to read the next line. The format of the poem is broken into four stanzas. Brooks opens the poem with the metaphor of a luminous life in the backyard and a boring life in the front. There are couplets present at the end of each stanza. Brook's incorporates alliteration, hyperbole and personification and repetition to develop a deeper meaning and purpose of the poem .. In regard to poetic feet, Brook's presents a combination of iambic and anapestic feel. The poem was written in the 1940's at a time when segregation was still legal in specific parts of the United States. This texts connects with social issues that occurred during the time in which it was written. With the black commu nity already having gone through the New negro movement in the 1920's, leading up to new issues with social class, and even the Great depression. Some African Americans were able to relocate and better the lives for themselves and their families, while others weren't able to. Even in the midst of the African American community being less than; inside their own community there was division. The intended audience of the poem is for both the youth and parents. It emphasized in youth nothing is ever enough. Young people always yearn for what they do not have. Brook's comes from an educated background, and displays this with her choice of diction throughout the poem. The words she chooses to vividly describe each action, person, place and thing was carefully crafted. She encourages her readers to dig deep to fully grasp the message. She isn't speaking to the community. She is speaking for and with the community with this poem. She is the voice of the young girls who steadily rema in hungry for more in life, and not allow themselves to be caged off or segregated by social class. Brook's writes the poem for a first person point of view. The narrator appears to be a naive child, who is unaware of the inappropriate actions she eagerly wants to engage in. "Stayed" , implies that she has not been given the opportunity to go elsewhere besides where her feet are already planted. In the first stanza Brook's uses the word "Peek" When a person wants to peek at something, it's something of interest. The female narrator is in desperate need of a small glimpse of the life she's been kept from. This particular word "Peek" hints to the readers, that she has seen the backyard against the better judgment of her mother. Because she has peeked, she is very aware of the forbidden life in the backyard. The stanza does shift to the usage of strong adjectives such as "rough" and "untended". The phraseology of these words is used to describe the backyard. They also suggest that the life in the backyard, that's yearned for, is also not a

Up and Down Phrasal English Verbs

Up and Down Phrasal English Verbs Phrasal verbs formed with up and down are used to indicate increases and decreases in a number of qualities. Each use is indicated by a specific general quality followed by a synonymous verb or short definition. There are two example sentences for each phrasal verb with up or down. Heres an example: Up Increase in ValueDown Decrease in Value to put up (S) to raiseThe supermarket put coffee prices up in January. to bring down (S) to reduceThe recession brought profits down sharply. Remember that phrasal verbs can be either separable or inseparable (review separable inseparable phrasal verbs). Each phrasal verb is also marked as separable (S) or inseparable (I). In the case that verbs are separable, examples will use the separable form of the phrasal verb. For inseparable phrasal verbs, examples keep the phrasal verbs together. Phrasal Verbs With Up Up Increase in Value to put up (S) to raise Well have to put our prices up to compete.Have they put the price of corn up recently? to go up (I) to increase The price of gas went up in March.Our rent went up in January. Up Increase in Size to bring up (S) to raise (usually children) They brought their children up to be responsible adults.Were bringing up two children. to grow up (I) to become older Youve grown up since I last saw you.The children grew up so fast. Up Increase in Speed to speed up (I) to go faster in a vehicle He quickly sped up to sixty miles an hour.His motorcycle can speed up to 100 quickly. to hurry up (I) to do something faster, to get ready faster Could you please hurry up?!Ill hurry up and finish this report. Up Increase in Heat to heat up (S) to make hotter Ill heat the soup up for lunch.What should I heat up for dinner? to warm up (S) to make hotter Ill warm this soup up for lunch.Would you like me to warm your tea up? Up Increase in Happiness, Excitement to cheer up (S) to make someone happier Can you cheer Tim up?I think we need to cheer them up with a song or two. to liven up (S) to make something more fun Lets liven this party up with a game.We need to liven this meeting up. Up Increase Sound to turn up (S) to raise the volume Please turn the radio up.I like to turn the stereo up when nobody is home. to speak up (I) to speak with a stronger voice You need to speak up for people to understand you.Please speak up in this room. Up Increase in Strength to build up (S) to increase over time Its important to build your muscle strength up over time.Theyve built up an impressive stock portfolio. to pick up (I) to improve over time My health has picked up over the past few days.The stock market has picked up recently. Phrasal Verbs With Down Down Decrease in Value to bring down (S) to reduce They bring down prices after Christmas.The summer brought heating oil prices down. to go down (I) to decrease The value of the house went down during the recession.Gas prices have gone down dramatically over the past few months. to cut down (S) to reduce the value of Weve cut our research and development budget down significantly.Theyve cut their investments down to half. Down Decrease in Speed to slow down (I) to reduce your speed Slow down when you drive into town.My car slowed down and stopped at the intersection. Down Decrease in Temperature to cool down (S) to a lower temperature Youll cool down after you stop exercising.This cool towel will cool you down. Down Decrease in Excitement to cool down (S) to relax I need to take a moment to cool down.Tom should cool his friend down so we can continue the meeting. to calm down (S) to make less excited I calmed the children down with a movie.It took him a while to calm down after the meeting. Down Decrease in Volume to turn down (S) to reduce the volume Could you please turn that music down?I think you should turn the volume down on the radio. to keep down (S) to remain soft Please keep your voices down in the library.Id like you to keep it down in this room. to quieten down (S) to encourage someone to become quieter Could you please quieten your children down?Id like you to quieten the class down. Down Reduce Strength to water down (S) to reduce the strength of something (often alcohol) Could you water this martini down?You need to water down your argument.

Course work business law environment Essay Example | Topics and Well Written Essays - 2000 words

Course work business law environment - Essay Example The above legal forms of doing business offer different benefits, rights as well as obligations to the owners of such businesses and as such as one moves from one form of business to another, the extent and nature of the rights and obligations also change. For example, a sole proprietor is personally liable for all the liability of the business running by him and as such the personal property of the sole proprietor is therefore also subject to liquidation if business fails and files for bankruptcy. Similar, in partnership, the partners are subject to personal liability also however as one move up towards formation of a company either a private or a public, the nature and extent of liability start to change. The shareholders of the private and public limited companies are only liable to the extent of their individual shareholding within the business. It is also important to note that in public limited companies, the function of management and ownership are two separate functions i.e. owners and the managers of the business are separate from each other. This paper will prepare a written analysis of a problem which identifies relevant legal principles; identify remedies and obligations appropriate to the circumstances of a legal situation presented in the given question. From the facts provided in the question, it is clear that the apparent form of the business is a sole proprietorship with Ivor being the legal owner of the business and Andrew as the employee of the new business. Sole proprietorship is considered as the oldest and common form of business formation where an individual can form a business without going into too much detail about the legal consequences of the business formation. Typically a Sole Proprietorship is owned and managed by single person and unlike limited company; there is no separation between the ownership as well as the management of the business. This is also the most distinguished character of the

The Responsibility to Protect (R2P) principle is ill suited for the Essay

The Responsibility to Protect (R2P) principle is ill suited for the international legal system and must be abolished - Essay Example The R2P principle required the states to have the first priority in the protection of its citizens but failure to the concerned state to meet to the needs of its citizens, the international community will have the obligation to intervene. The international community would not wait and watch as it had the responsibility to preserve international peace, but not to enforce the laws of the concerned countries.2 However, the mandate of the principle has been exploited through interpretation of its tenets and through the application by humanitarian countries who intrude on the sovereignty of affected states leading to abuse. As such, it is imperative to note that the R2P principle is ill suited for the international legal system and must be abolished. The R2P principle gives consent to the international community to undertake humanitarian intervention with the aim of maintaining peace. However, narrowing down the concept of intervention implies that the international community can get involved in the internal affairs of a country without the consent of the affected country. That is clearly a violation of state sovereignty, which is in most times accompanied by military force.3 Furthermore, such form of intervention results in violations of fundamental human rights. When military forces from outside the boundaries of the country are involved in peace keeping mission without an obligation to enforce the law, the state of lawlessness is likely to result in a huge number of casualties and fatalities in case of combat.4 The UN Charter 2(4) holds ‘protection of human rights’ as its core purpose but then goes ahead to claim that any state can use force â€Å"in any other manner inconsistent with the Purposes of the United Nations†.5 This shows a problem in the interpretation of the mandate of R2P principle given the application of â€Å"force for good† theory. This interpretation is against territorial

Exploring the politics of the Texas Railroad commissions regulation of Research Paper - 1

Exploring the politics of the Texas Railroad commissions regulation of texas oil and gas from 1917-1941 - Research Paper Example In the 1920s, there was a sporadic pattern of cooperation between the state and federal governments. Tensions were high in the coordination of the state activities and those of the federal government over the control of resources. The head quarters of the railroad commission are in the state of Texas in the United States and act as among the most powerful state agencies in the country. The paramount duties and responsibilities of the Texas Railroad Commission were to regulate the entire business of oil and gas exploration and mining in the United States. Most of the oil and gas deposits of the country are in the state of Texas hence the strategic location of the commission’s headquarters in order to ensure proper administration and control of oil and gas exploration activities in the country. In addition to the regulation of gas and oil production in the United States, the Texas railroad commission also monitors and controls major shares of the pipeline safety, uranium mining, gas utilities, liquid petroleum gas safety, and surface coal. All these responsibilities lie under the docket of the commission ever since its inception. The name of the commission is a little confusing to the common citizens who are not aware of the true duties and responsibilities of the company. ... The commission does not have any links or deals with the regulation of railroads in any way at all. The name simply developed out of common utterances. Issues surrounding the commission politics The Texas Railroad Commission had a number of politics surrounding its operations as well as dealing with other factors concerned with their duties and responsibilities. The company had both internal as well as external politics facing its operations and execution of its duties and jurisdictions, especially considering it primary control of the entire industry of oil and gas exploration within the United States of America from the year 1917 to the year 1941. The commission expanded its initial mandate of overseeing petroleum exploration and the regulations of oil pipelines from 1917, to the control of oil and gas production within the entire country in 1919, and finally elevated to the regulation of delivery systems of natural gas in the year 1920. Technically, the Texas Railroad commission g ained control of all the exploration and production activities of oil and gas within the United States, a task that made the commission elevate to become the single most powerful commission in the country, while others argued it had too much power for a single commission. The politics of this commission rose from time to time due to many occurrences in the country. One particular occasion whereby there was high political tension surrounding the activities and duties of the Texas rail road commission was in the 1930s whereby there was an oil boom in the state of Texas. This oil boom led to the escalation of oil prices to 25 cents per barrel. The commission was unable to negotiate a compromise price for the sale of the oil

Nature And Structure Of Mathematics

Nature And Structure Of Mathematics Chapter 2 Literature review In this chapter, literature related to mathematics confidence, reflection and problem- solving are reviewed. The chapter begins with an introduction to mathematics and the occurrence of educational changes and concerns in South Africa. It examines the metacognitive activity reflection and its various facets along with affective issues in mathematics. Then, differentiating between past and current research, the focus will be on how mathematics confidence and reflective thinking relates to the level of achievement and performance in mathematics problem-solving processes. Concluding description will follow, illustrating the relationship between reflection and mathematics confidence during problem-solving processes. 2.1 Mathematics, its nature and structure Mathematics can be seen as a combination of calculation skill and reasoning (Hannula, Maijala Pehkonen, 2004:17) and can further be classified as an individuals mathematical understanding. Mathematics is a process, fixed to a certain person, a topic, an environment or an idea (Hiebert Carpenter, 1992). Mathematics originated as a necessity for societal, technological and cultural growth or leisure (Ebrahim, 2010:1). This desire led to the advancement of concepts and theories in order to meet the needs of various cultures throughout time. With its imprint in nature, architecture, medicine, telecommunications and information technology, the use of mathematics has overcome centuries of problems and continues to fulfil the needs of problem-solvers to solve everyday problems. Although mathematics has changed throughout time, in its progress and influences there are interwoven connections between the cognitive, connotative and affective psychological domains. The increasing demand to process and apply information in a South African society, a society characterised by increasing unemployment and immense demands on schools, still awaits recovery and substance from these cognitive and metacognitive challenges (Maree Crafford, 2010: 84). From a socio-constructivists perspective, developing, adapting and evolving more complex systems should be the aim and goal of mathematics education (Lesh Sriraman, 2005). According to Thijsse (2002:34) mathematics is an emotionally charged subject, evoking feelings of dislike, fear and failure. Mathematics involves cognitive and affective factors that form part of the epistemological assumptions, regarding mathematical learning (Thijsse, 2002:7 that will be discussed in the following section. 2.1.2 Epistemological assumptions regarding mathematics learning English (2007:123-125) lays down powerful ideas for developing mathematics towards the 21st century. Some of these ideas include: 2.1.2.1 A social constructivist view of problem-solving, planning, monitoring and communication; 2.1.2.2 Effective and creative reasoning skills; 2.1.2.3 Analysing and transforming complex data sets; 2.1.2.4 Applying and understanding school Mathematics; and 2.1.2.5 Explaining, manipulating and forecasting complex systems through critical thinking and decision making. With emphasis on the learner, from a constructivist perspective, learning can be viewed as the active process within and influenced by the learner (Yager, 1991:53). Mathematical learning is therefore an interactive consequence of the encountered information and how the learner processes it, based on perceivednotions and existing personal knowledge (Yager, 1991:53). According to DoE (2003:3) competence in mathematics education is aimed at integrating practical, foundational and reflective skills. While altering the paradigms in learning, mathematics education was turned upside down with the shift being towards instructing, administering and applying metacognitive-activity-based learning in schools as claimed by Yager (1991:53) and Leaf (2005:12-18). This change and reform in education and education paradigms is illustrated in Figure 2.1. Early 1900s Early 1900s 1960s 1980s 1980s- 2000s 1980s 2000s The overarching approach with impact on education and therapy focussing on metacognition In Figure 2.1 Leaf (2005:4) states that the intelligence quotient (IQ) is one of the greatest paradigm dilemmas. This approach is designed in the early twentieth century by F. Galton and labelled too many learners as either slow or clever. The IQ-tests did assess logical, mathematical and language preference and dominance in learners but left little or no room for other ways of thinking in mental aptitude (Leaf, 2005:5). In contrast to the IQ-approach is Piagets approach, named after its founder, Jean Piaget, who apposed the IQ-approach. Focussing on cognitive development, he suggests timed stages or learning phases in a childs cognitive development as a prerequisite to the learning process. Piaget exclaims that if a stage is overseen, learning will not take place. A third paradigm, the Information processing age, divided problem-solving into three phases: input, coded storing and output. Designed in an era where technological advances and computers entered schools and the school cur riculum, information processing was seen as comparing the learner with a microchip. Thus, retrieving and storing data and information was seen as a method to practise and learn as being the focus of learning. This learning took place in a hierarchical order, and one phase must be mastered before continuing to a more difficult task. Outcomes Based Education (OBE) was implemented after the 1994 national democratic elections in South Africa. Since 1997 school systems underwent drastic changes from the so called apartheid era. According to the Revised National Curriculum Statement (2003) the curriculum is based on development of the learners full potential in a democratic South Africa. Creating lifelong learners are the focus of this paradigm. After unsuccessfully transforming education in South Africa, a need still exists to challenge some of the shortcomings of the above mentioned paradigms. An Overarching approach is an aided paradigm proposed by Leaf (2005:12). The Overarching approach focuses on learning dynamics or in other words, what makes learning possible. This paradigm utilizes emotions, experiences, backgrounds and cultural aspects in order to facilitate learning and problem-solving (Leaf, 2005:12-15). Above mentioned aspects are also known to associate with performance in mathematics problem-solving (Maree, Prinsloo Claasen, 1997a; Leaf, 2005:12-15). 2.1.3 Some factors associated with performance in mathematics Large scale international studies, focussing on school mathematics, compare countries in terms of learners cognitive performance over time (TIMSS, 2003 PISA, 2003). A clear distinction must be made between mathematics performance factors in these developed and developing countries (Howie, 2005:125). Howie (2005:123) explored data from the TIMSS-R South African study which revealed a relationship between contextual factors and performance in mathematics. School level factors seem to be far less influential (Howie, 2005: 124, Reynolds, 1998:79). According to Maree et al. (2005:85), South African learners perform inadequately due to a number of traditional approaches towards mathematics teaching and learning. Maree (1997b:95) also classifies problems in study orientation as cognitive factors, external factors, internal and intra-psychological factors, and facilitating subject content. One psychological factor in the Study Orientation in Mathematics questionnaire (SOM) by Maree, Prinsloo and Claasen (1997b) is measured as the level of mathematics confidence of grade 7 to 12 learners in a South African context. Sherman and Wither (2003:138) documented a case where a psychological factor, anxiety, causes an impairment of mathematics achievement. A distillation of a study done by Wither (1998) concluded that low mathematics confidence causes underachievement in mathematics. Due to insufficient evidence it could not prove that underachievement results in low mathematics confidence. The study did indicate that a possible third factor (metacognition) could cause both low mathematics confidence and underachievement in mathematics (Sherman Wither, 2003:149). Thereupon, factors manifested by the learner are discussed below. Academic underachievement and performance in mathematics is determined by a number of variables as identified by Lombard (1999:51); Maree, Prinsloo and Claasen (1997); and Lesh and Zawojewski (2007). These variables include factors manifested by the learner, environmental factors and factors during the process of instruction. 2.1.3.1 Some associated factors manifested by the learner Affective issues revolve around an individuals environment within different systems and how that individual matures and interact within the systems (Lombard, 1999:51 Beilock, 2008:339). In these systems it appears that learners have a positive or negative attitude towards mathematics (Maree, Prinsloo Claasen, 1997a). Beliefs about ones own capabilities and that success cannot be linked to effort and hard work is seen as affective factors in problem-solving (Dossel, 1993:6; Thijsse, 2002:18). Distrust in ones own intuition, not knowing how to correct mistakes and the lack of personal effort is regarded as factors that facilitate mathematics anxiety, manifested by the learner (Thijsse, 2002:36; Russel, 1999:15). 2.1.3.2 Some associated environmental factors Timed testing environments such as oral exam/testing situations, where answers must be given quickly and verbally are seen as environmental factors that facilitates underachievement in mathematics. Public contexts where the learner has to express mathematical thought in front of an audience or peers may also be seen as an environmental factor limiting performance. 2.1.3.3 Some associated factors during the process of instruction Knowledge about study methods, implementing different strategies and domain specific knowledge is seen as factors that influence performance in mathematics. It seems as though performance is measured according to the learners ability to apply algorithms dictated by a higher authority figure such as parents or teachers (Russell, 1995:15; Thijsse, 2002:35). Thijsse (2002:19) agrees with Dossel (1993:6) and Maree (1997) that the teachers attention to the right or wrong dichotomy, stresses the fact that mathematics education can also be associate with performance. A brief discussion on mathematics problem-solving will now follow. 2.2 Mathematics problem-solving A mathematics problem can be defined as a mathematical based task indicating realistic contexts in which the learner creates a model for solving the problem in various circumstances (Chalmers, 2009:3). Making decisions within these contexts is only one of the elementary concepts of human behaviour. In a technology based information age, computation; conceptualisation and communication are basic challenges South Africans have to face (Maree, Prinsloo Claasen, 1997; Lesh Zawojewski, 2007). Problem-solving abilities are needed and should be developed for academic success, even beyond school level. According to Kleitman and Stankov (2003:2) managing uncertainty in ones understanding is essential in mathematical problem-solving. Lester and Kehle (2003:510) fear that mathematical problem-solving is currently getting more complex then in previous years. Therefore problem-solving continues to gain consideration in the policy documents of various organisations, internationally (TIMSS, 2003; SACMEQ, 2009; PIRLS, 2009; Moloi Strauss, 2005 NCTM, 1989) and nationally (DoE, 2010; DoE, 2010: 3). As Lesh and Zawojewski (2007:764) states The pendulum of curriculum change again swings back towards an emphasis on problem-solving. Problem-solving is emphasised as a method involving inquiry and decision making (Fortunato, Hecht, Tittle Alvarez, 1991:38). Generally two types of mathematical problems exist: routine problems and non-routine problems. The use and application of non-routine problems, unseen mathematical processes and principles are part of the scope of mathematics education in South Africa (DoE, 2003:10). Keeping track of and on the process of information seeking and decision making, mathematics problem-solving is linked to the content and context of the problem situation (Lesh Zawojewski, 2007:764). It seems as though concept development and development of problem-solving abilities should be part of mathematics education and beliefs, feelings or other affective factors should be taken into account. In the next section a discussion will follow regarding past research done on mathematics problem-solving. 2.2.1 Some research done on mathematics problem-solving in the past Studies on learners performance in mathematics and how their behaviours vary in approaches to perform, was the conduct of research on mathematics problem-solving since the 1930s (Dewey, 1933; Piaget, 1970; Flavell; 1976; Schoenfeld, 1992; Lester Kehle, 2003; Lesh Zawojewski , 2007:764). Good problem solvers were generally compared to poor problem-solvers (Lester Kehle, 2003:507) while Schoenfeld (1992) suggested that the former not only knows more mathematics, but also knows mathematics differently (Lesh and Zawojewski, 2007:767). The nature and development of mathematics problems are also widely researched (Lesh Zawojewski, 2007:768), especially with the focus on how learners seeand approach mathematics and mathematical problems. Polya-style problems involve strategies such as picture drawing, working backwards, looking for a similar problem or identifying necessary information (Lesh Zawojewski, 2007:768). Confirming the use of these strategies Zimmerman (1999:8-10) describe dimensions for academic self-regulation by involving conceptual based questioning using a technique called prompting. Examples of these prompts are questions starting with why; how; what; when and where, in order to provide scaffolding for information processing and decision making. 2.2.2 Working memory, information processing and mathematics problem-solving of the individual learner In the 1970s problems were seen an approach from an initial state towards a goal state (Newell Simon, 1972 in Goldstein, 2008:404) involving search and adapt strategies. 2.2.2.1 Working memory as an aspect of problem-solving The working memory is essential for storing information regarding mathematics problems and problem-solving processes (Sheffield Hunt, 2006:2). Cognitive effects, such as anxiety, disrupt processing in the working memory system and underachievement will follow (Ashcraft; Hopko Gute, 1998:343; Ashcraft, 2002:1). These intrusive thoughts, like worrying, overburden the system. The working memory system consists of three components: the psychological articulatory loop, visual-spatial sketch pad and a central executive (Ashcraft; Hopko Gute, 1998:344; Richardson et al, 1996). 2.2.2.2 Problem-solving persona of the mathematics learner The learner, either an expert or novice-problem-solver is researched on his/her ideas, strategies, representations or habits in mathematical contexts (Ertmer Newby, 1996). Expert learners are found to be organised individuals who have integrated networks of knowledge in order to succeed in mathematics problem-situations (Lesh Zawojewski, 2007:767; Zimmerman, 1994). Clearly learners problem-solving personality affects their achievement. According to Thijsse (2002:33) learners who trust their intuition and perceive that intuition as insight into a rational mind, rather than emotional and irrational feelings, are more confident. The variety of attributes, such as anxiety and confidence, is included in reflective processes either cogitatively or metacognitatively which will be discussed in the next section. 2.3 Cognitive and metacognitive factors Although cognitive and metacognitive processes are compared in literature, Lesh and Zawojewksi (2007:778) argues that mathematics concepts and higher order thinking should be studied correspondingly and interactively. Identifying individual trends and behaviour patterns or feelings, could relate to mathematics problem-solving success (Lesh Zawojewksi, 2007:778). 2.4.1 Cognition processes during mathematics problem-solving Newstead (1999:25) describes the cognitive levels of an individual as being either convergent (knowledge of information) or divergent (explaining, justification and reasoning). 2.3.2 Metacognition 2.3.2.1 Components of metacognition 2.3.2.2 Past research done on metacognition The Polya-style heuristics on problem-solving strategies, mentioned previously, is noted by Lesh and Zawojewski (2007:368) as an after-the-fact of past activities process. This review process between interpreting the problem, and the selection of appropriate strategies, that may or may not have worked in the past, is linked with experiences (negative or positive) which provide a framework for reflective thinking. Reflection is therefore a facet of metacognition. 2.3.3 Reflection as a facet of metacognition Reflection, as defined by Glahn, Specht and Koper (2009:95), is an active reasoning process that confirms experiences in problem-solving and related social interaction. Reflecting can be seen as a transformational process from our experiences and is effected by our way of thinking (Garcia, Sanchez Escudero, 2009:1). 2.3.3.1 Development of reflective thinking Thinking about mathematics problems and reflecting on them is essential for interpreting the given problems provided details about what is needed in order to solve the problem (Lesh Zawojewski, 2007:368). Schoenfeld (1992) mentions an examining of special cases for selecting appropriate strategies from a hierarchical description, but Lesh and Zawojewski (2007:369) argue that this will involve a too long (prescriptive process) or too short conventional list of prescribed strategies. Lesh and Zawojewski (2007:770) rather suggest a descriptive process to reflect on and develop sample experiences. The focus should be on various facets of individual persona and differences, such as prior knowledge and experiences, which differs between individuals. 2.3.3.2 Expansion models for reflectivepractice According to Pletzer et al (1997) applying reflective practice is a powerful and effective way of learning. Three models for reflective practice exist: the reflective cycle of Gibbs (1988), Ertmer and Newby (1996), Johns-model (2000) for structural reflection and Rolfe et als (2001) framework for reflective practice. The first model is that of Gibbs (1988). i Gibbss (1988) model for reflection Gibbs model is mostly applied during reflective writing (Pugalee, 2001). This model for reflection is exercised during problem-solving situations by assessing first and second cognitive levels. A particular situation, such as in Figure 2.2, when the learner has to solve a mathematical problem is described by accompanying feelings and emotions that will be remembered and reflected upon. A conscience cognitive decision will then be made determining whether the experience was a positive (good) otherwise negative (bad) emotion, or feeling. By analysing the sense of the experience a conclusion can be made where other options are considered to reflect upon. (Gibbs, 1988; Ertmer Newby, 1996) iiJohns (2000) model for structural and guided reflection This model provides a framework for analysing and critically reflecting on a general problem or experience. The Johns-model (2000) provides scaffolding or guidance for more complex problems found on cognitive levels three and four. Reflect on and identify factors that influence your actions Figure 2.3Johns model for reflective practice Source:Adapted from John (2000) The model in Figure 2.3 is divided into two phases. Phase 1 refers to the recall of past memories and skills from previous experiences, where the learner identifies goals and achievements by reflecting into their past. This could be easily done using a video recording of a situation where the learner solves a problem. It is in this phase where they take note of their emotions and what strategies were used or not. On the other hand, phase 2 describes the feelings, emotions and surrounding thoughts accompanying their memories. A deeper clarification is given when the learner has to motivate why certain steps were left out or why some strategies were used and others not. They have to explain how they felt and the reason for the identified emotions. At the end the learner should reflect between the in and out components to identify any factor(s) that could have effected their emotions or thoughts in any way. A third model is proposed by Rolfe et al (2001), known as a framework for reflex ive practice. iiiRolfe et als model for reflexive practice. According to Rolfe et al (2001) the questions ‘what? and ‘so what? or ‘now what?, can stimulate reflective thinking. The use of this model is simply descriptive of the cognitive levels and can be seen as a combination of Gibbs (1988) and Johns (2000) model. The learner reflects on a mathematics problem in order to describe it. Then in the second phase, the learner constructs a personal theory and knowledge about the problem in order to learn from it. Finally, the learner reflects on the problem and considers different approaches or strategies in order to understand or make sense of the problem situation. Table 2.1 demonstrates this model of Rolfe et al (2001) in accordance with the models of Gibbs (1988) and Johns (2000) as adapted by the researcher. It shows the movement of thought actions and emotions between different stages of reflection (before, during and after) in problem-solving. Table 2.1Integration of reflective stages and the models for reflective practice Stage 1 Reflection before action Stage 2 Reflection during action Stage 3 Reflection after action Descriptive level of reflection (planning and describing phase) Theory and knowledge building of reflection (decision making phase) Action orientated level (reflecting on implemented strategy-action) Identify the level of difficulty of the problem and possible reasons for feeling, or not feeling, â€Å"stuck†, â€Å"bad† or unable to go to the next step. Pay attention to thought and emotions and identify them. Describe negative attitude towards mathematics problems, if any Observe and notice expectations of self and others: like parents, teachers or peers Evaluate the positive and negative experiences Analyse and understand the problem and plan the next step, approach or strategy Perform the planned action Awareness of ethics, beliefs, personal traits or motivations Recall strategies that worked in the past. Reflect on the solution, reactions and attitudes Source:Adapted from Johns (2000), Gibbs (1988) and Rolfe et al (2001) 2.3.3.3 The reflection process While some research claims, seeing and doing mathematics as useful in the interpretation and decision making of problem-solving processes (Lesh Zawojewski, 2007), a more affective approach would involve feelings or the feelings about mathematics(Sheffield Hunt, 2006), in other words, affective factors. 2.4 Affective factors in mathematics Rapidly changing states of feelings, moderately stable tendencies, internal representations and deeply valued preferences are all categories of affect in mathematics (Schlogmann, 2003:1).Reactions to mathematics are influenced by emotional components of affect. Some of these components include negative reactions to mathematics, such as: stress, nervousness, negative attitude, unconstructive study-orientation, worry, and a lack of confidence (Wigfield Meece, 1988; Maree, Prinsloo Claasen, 1997). Learners self-concept is strongly connected to their self-belief and their success in solving mathematics problems is conceptualised as important (Hannula, Maijala Pehkonen, 2004:17). A study done by Ma and Kishor (1997) confirmed belief, as an affect on mathematics achievement, being weakly correlated with achievement among children from grade 2 to 8. However, Hannula, Maijala and Pehkonen (2004) conducted a study on learners in grade 7 to 12 and concluded that there is a strong correlatio n between their belief and achievement in mathematics. Beliefs and are related to non-cognitive factors and involve feelings. According to Lesh and Zawojewski (2007:775) the self-regulatory process is critically affected by beliefs, attitudes, confidence and other affective factors. 2.4.1Beliefs as an affective factor in mathematics Belief, in a mathematics learner, form part of constructivism and can be defined as an individuals understanding of his/her own feelings and personal concepts formed when the learner engages in mathematical problem-solving (Hannula, Maijala Pehkonen, 2004:3). It plays an important role in attitudes and emotions due to its cognitive nature and, according to Goldin (2001:5), learners attribute a kind of truth to their beliefs as it is formed by a series of background experiences involving perception, thinking and actions (Furinghetti Pehkonen, 2000:8) developed over a long period of time (Mcleod,1992:578-579). Beliefs about mathematics can be seen as a mathematics world view (Schlogmann, 2003:2) and can be divided into four major categories (Hannula, Maijala Pehkonen, 2004:17): beliefs on mathematics (e.g. there can only be one correct answer), beliefs about oneself as a mathematics learner or problem solver (e.g. mathematics is not for everyone), beliefs on teaching mathematics (e. g. mathematics taught in schools has little or nothing to do with the real world) and beliefs on learning mathematics (e.g. mathematics is solitary and must be done in isolation) (Hannula, Maijala Pehkonen, 2004:17). Faulty beliefs about problem-solving allow fewer and fewer learners to take mathematics courses or to pass grade 12 with the necessary requirements for university entrance. Beliefs are known to work against change or act as a consequence of change and also have a predicting nature (Furinghetti Pehkonen, 2000:8). Affective issues, such as beliefs, generally form part of the cognitive domain, anxiety (Wigfield Meece, 1988), which will be dealt with in the next section. 2.4.2 Anxiety Anxiety, an aspect of neuroticism, is often linked with personality traits such as conscientiousness and agreeableness (Morony, 2010:2). This negative emotion manifests in faulty beliefs that causes anxious thoughts and feelings about mathematics problem-solving (Ashcraft; Hopko Gute, 1998:344; Thijsse, 2002:17). Distinction can be made between the different types of anxieties as experienced by learners across all age groups. Some of these anxieties include general anxiety, test or evaluation anxiety, problem-solving anxiety and mathematics anxiety. The widespread phenomenon, mathematics anxiety, threatens performance of learners in mathematics and interferes with conceptual thinking, memory processing and reasoning (Newstead, 1999:2). 2.4.2.1 Mathematics anxiety The pioneers of mathematics anxiety research, Richardson and Suinn (1972), defined mathematics anxiety in terms of the affect on performance in mathematics problem-solving as: Feelings of tension and anxiety that interfere with the manipulation of numbers and the solving of mathematical problems in a wide variety of ordinary life and academic situations This anxious and avoidance-behaviour towards mathematics has far reaching consequences as stressed by a number of researchers (Maree, Prinsloo Claasen, 1997; Newstead, 1999; Sheffield Hunt, 2006 Morony, 2009). Described as a chain reaction, mathematics anxiety consists of stressors, perceptions of threat, emotional responses, cognitive assessments and dealing with these reactions. A number of researchers expand the concept of mathematics anxiety to include facilitative and debilitative anxiety (Newstead, 1998:2). It appears that Ashcraft; Hopko; Gute (1998:343) and Richardson et al (1996) see mathematics anxiety in the same locale as the working memory system. Both areas consist of psychological, cognitive and behavioural components. Although they agree on the same components, Eysenck and Calvo (1999) states that it is not the experience of worry that diverts attention or interrupts the working memory process, but rather ineffective efforts to divert attention away from worrying a nd instead focus on the task at hand. 2.4.2.2 Symptoms for identifying mathematics anxiety Mathematics anxiety is symptomatically described as low (feelings of loss, failure and nervousness) or high (positive and motivated attitude) confidence in Mathematics (Maree, Prinsloo Claasen, 1997a:7). Dossel (1993:6) and Thijsse (2002:18) states that these negative feelings are associated with a lack of control when uncertainty and helplessness is experienced when facing danger. Unable to think rationally, avoidance and the inability to perform adequately causes anxiety and negative self-beliefs Mitchell, 1987:33; Thijsse, 2002:17). Anxious children show signs of nervousness when a teacher comes near. They will stop; cover their work with their arm, hand or book, in an approach to hide their work (May, 1977:205; Maree, Prinsloo Claasen, 1997; Newstead, 1998 Thijsse, 2002:16). Panicking, anxious behaviour and worry manifests in the form of nail biting, crossing out correct answers, habitual excuse from the classroom and difficulty of verbally expressing oneself (Maree, Prinsloo Claasen, 1997a). Mar

Three Cheers for Madness :: Nabokov Heller Montaigne Essays

Three Cheers for Madness Three of Psychology’s Least Wanted sit next to my desk and beckon me closer: A graying Humbert licks the corner of my eye and throws me a pitifully seductive glance; an anxiety-ridden Yossarian repeats over and over that the whole world is trying to kill him, and an almost robotic Montaigne sits as a kind of mediating force between the others, his head snapping back and forth from Humbert to Yossarian while his hands open and close books so quickly one might imagine his purpose is only to get a whiff of each cover’s staling odor. I need no special degree to deem them all nutcases. What I know of Humbert and Yossarian comes by way of Vladimir Nabokov and Joseph Heller, respectively, as they are the creators, surveyors, and closest contacts of the deceivingly fictional characters. Brilliant in their ability to characterize—to sculpt flat words into the kind of real live, dynamic human beings one might well share a cab with—Nabokov and Heller steal a rousing glimpse into the minds of two intensely confusing personalities and succeed in making us forget that the characters are only the brainchildren of the writers, and not the writers themselves. Oddball Michel de Montaigne seems to look on from afar, speculating in an essay entitled â€Å"On Books† about his impatience for a number of acclaimed writers and their works, while confessing his â€Å"particular curiosity to know the mind and natural opinions of [writers].† Knowing well that Nabokov is not the sex offender he appears to have studied so intimately, and that Heller is not the soldier living amidst the confusion he so thoroughly seems to understand, Montaigne would understand that â€Å"from the display of their writings that they make on the world-stage, we may indeed judge their talents, but not their character or themselves† (167). But this is more than I can handle, as my conceptions of these characters as well as the writers who shaped them seem altogether disturbing. While writing out their prescriptions for shock therapy (the paranoid soldier’s frustratingly ambiguous remarks have earned him a bit more of it than the others), Humbert nudges forward his notebook of scattered words and doodles—a notebook containing his deepest thoughts about Dolores Haze (or ‘Lolita’), the twelve-year old girl with whom he has been completely infatuated his entire middle-aged life. I expect to run my eyes over vile passages—perverse diagrams, even—reflecting his disconcertingly base attraction to the pre-teen.