Music Baritone Sax Free Essays

The History of the baritone saxophone was very interesting to research giving that I have played this beautiful instrument for 4 years. Finding a little more about the history of this beautiful instrument was a very interesting time. The baritone saxophone features a low pitch. We will write a custom essay sample on Music Baritone Sax or any similar topic only for you Order Now It is a single reed instrument that is made from brass and has a tapered conical bore. Despite the baritone’s low pitch, its music is written in treble clef instead of bass clef. In modern music, the baritone saxophone is usually the largest sax featured in contemporary ensembles alongside its more common cousins, the alto and the tenor saxophone. The saxophone was invented in 1841 by Belgian manufacturer and instrument maker Adolphe Sax. His intent was to create a new instrument that would fill the gap between the loud woodwinds and the brass instruments. In 1844, Sax introduced his saxophone to the public during the Paris Industrial Exhibition. In February of that year, Berlioz conducted a concert that performed his choral work, â€Å"Chant Sacre,† which featured segments that included the new saxophone. Near the end of 1844, the saxophone enjoyed a successful orchestra debut in Georges Kastner’s opera â€Å"Last King of Juda† at the Paris Conservatory. Adolphe Sax obtained his original patents in 1846 for the baritone variation of the saxophone along with thirteen of its cousins, including the tenor, bass, alto, contrabass and sopranino saxophones. The following year, the first saxophone school was opened at the Gymnase Musical, a military band school. Ten years later, Adolphe Sax wanted to share his love and knowledge of music, so he took on a professorship at the Paris Conservatory. â€Å"Also, in 1866, Sax’s patents expired, leaving the way open for the Millereau Co. o obtain patents for their own variation of the saxophone that featured a forked F sharp key†. In 1881, Adolphe Sax extended his patent for the baritone sax and other variations, and made changes to the design of the instruments. In response to its growing popularity, Gus Buesher was the first person in the United States to build a saxophone in 1885. Over the next few years, the baritone and other variations underwent more design changes, â€Å"such a s the addition of the right hand C trill key and the invention of the single octave key†. Adolphe Sax died in 1894, but his legacy lived on when his son, Adolphe Edouard, continued his life’s work. During the 1900s, the baritone saxophone enjoyed increasing popularity, and was incorporated into Jazz bands and other musical formats. It was also used in classical compositions, but rarely for orchestral music. Notable orchestral exceptions include Richard Strauss’s â€Å"Symphonia Domestica† of 1903 and Charles Ives’s â€Å"Symphony no. 4,† composed from 1910 through 1916. Famous musicians who played the baritone sax include Harry Carney, Pepper Adams, Valentin Alvarez, Bruce Kapler, Lou Marini and LeRoi Moore. † In conclusion the Baritone Sax is a beautiful instrument that should be appreciated. Giving such a beautiful tone. By far the baritone sax is my favourite saxophone giving it shape, color, quality of tone and pitch, and allowing a player to have the control to play with dynamics. I hope you have learned alittle more about my instrument thank you. How to cite Music Baritone Sax, Papers

Human Behavior in Business Model Innovation †MyAssignmenthelp.com

Question: Discuss about the Human Behavior in Business Model Innovation. Answer: Introduction: JET.com is an e-commerce company which specifically deals in a grocery. It was started as a startup in 2014 and eventually grown over a very short span of time (Perez 2014). It is a home for all household grocery items whichever are required by a homemaker. Also, the company has been acquired by WALMART and is officially a subsidiary of it. Being an e-commerce company it provides all of its services online to its customer associated with it. Operating on a very large scale and growing as a grocery company in a short span of this e-commerce website has gained a large number of customers who are dedicatedly associated with it. The business entity is making use of Graphic Clip-boards for making the products available in an innovative manner. In this innovation the customers if searching for a product can search the products by uploading the image on Web-portal of the company. The related options are made available and customer can make choice as per their convenience. Further concerning with its market, so it operates online through the internet so its market is categorized as the virtual market. There is still no existence of its store physically. But its competitors are alibaba.com, amazon.com etc. just like them it operates but it became a subsidiary of Wal-Mart as for now. Business model Canvas A business model is such on which a company operates. Every organization consists of a complete structure upon which its operations are conducted (Roberts, Earnhardt Herron, 2017). The following is the business model canvas in regards to Jet.com: Key Partners It is totally associated with WALMART as its subsidiary but first, it started as a whole eventually it merged under it. Key Activities Key activities are related to an online sale of grocery items to people in the US so as to earn a maximum amount of profit (Fan et al., 2017). Value Proposition The needs and wants of customers are taken care by Jet.com in a very appropriate manner so that there is growth in business as well. So as to do it, it uses a very good pricing algorithm so as to attract and satisfy with the value of money they pay for the products Customer Relationships Maintaining the relationship with customers is as similar as to take care of your belongings (Ng, 2017). After sale services and return policy of Jet.com is very good that customers feel reliable while buying any products from the website. Customer Segments Jet.com have a very defined customer segment as for now as it is an e-commerce website so it is available to many people on a large scale whosoever has access to the internet in the US. People who are being targeted by WALMART are similarly important for Jet.com as it is a subsidiary of it (Zhang, Sun, Lyu 2017). Mainly the females are targeted as they are more concerned about the factor to buy grocery for houses. Eventually, all the other segments such as children men etc. are also targeted. Key Resources The key resources of the company are its products, people, finances it acquires as it is a subsidiary of the giant company WALMART it is in safe hands in the name of resources. Channels There are several channels of communication, products distribution, and sales through which a company sell its products (Remane et al., 2017). Likewise, Jet.com uses online means to reach to its customer and deliver them through courier and various channels of distribution. Cost Structure Costing structure is very much authenticate and expertly driven upon which the customers can rely and totally be in a composition of (Rb, Bahemia, Schleyer 2017). Revenue Streams The company is already working on a very reliable pricing algorithm which returns the company in a very proportionate manner that it supplies satisfaction to a customer as well as the cost of goods is also actualized (Sathananthan et al., 2017). Key relationships across the nine building blocks Each and everything in a business whether it is retail or online operates with integrity. It is considered as a wholesome of the success which a business acquires in a market. It is very obvious that nine block business model activities are also related to each other because to reach on top Jet.com requires a package of all activities in a proper manner. Alone a single activity cannot lead to its success in the market (Tonchev et al., 2017). Hence, all of the activities in nine block model are related to each other. The further key relationship in nine block model is that it is working wholly upon a single firms function and that is Jet.com. Wholly it possesses coordination among function after function which is really important for the company to grow as a whole from each section of it (Dudin et al., 2015). Likewise, there is a relationship between the function that if one will prevail another will be its successor which is shows how much a function is dependent on another in terms of compatibility. The whole company is working upon interconnected functions like these which is a factor for responsiveness and reliability. So, as these functions are really significant for the firm to have proper functioning of its operations. Critical success factors Success factors are those factors which help a firm to reach its mission which has been set by the management. In other world critical analysis of this factor includes two subsections that are key result area (KRA) and key success factor (KSF). Simultaneously for Jet.com the key success factor is to provide and reach a large number of customers as well as the key result area is to perform better as a e-commerce website to reach its goal by targeting the customer through a pricing strategy. This will aid in attracting the customers through the website to maintain long-term relationship with them. In order to gain sustainable success, Jet.com needs to focus on very critical factors such as the area upon which it is trying to target and the success factor it is keeping aside for its strategy. As it is working on the pricing strategy which means its way of targeting its customer is through giving them value for the price they pay. As a subsidiary of WALMART, it has to work very enthusiastically upon these factors as they play a very important role. Plan, process, people, power and contingency strategies, these all are the factors which come under critical analysis and play a very important role in success for a company (Onken, Campeau 2016). Planning is forecasting future which wholly means setting up the goal, mission and vision for the company and also the norms upon which the company will operate on long-term basis. Downside risk The downside risk is a risk associated with the losses which might incur while a company is working. In regards with Jet.com contribution to downside risk will be done through various strategies where it works upon the best pricing strategy also it has the best parent company under which it is working as a subsidiary (Muzellec, Ronteau Lambkin, 2015). Hence, the chances where loss may incur would be dealt in such a way that the company will not face any downfall in operations. Likewise, maintenance of provident funds and reserves is a must. The actualization of the financial resources in such a way that if any downside situation occurs it can be faced properly. Changes to the business model In case of Jet.com there are various changes that can be introduced and which will make the company grow worldwide. First, renovation of the website from time to time and making it more attractive those customers get attracted towards it. Second, user-friendly website so that no one faces any kind of problem while operating it. Also the after sale services of the company must be at a very high level those customers are satisfied fully. In order to maintain the decorum of the company, all the engineers and workers who are working for it must be very much appropriate and they must also be satisfied because a good team always leads to success. I would like to keep the algorithm strategy of pricing as it is very fascinating and attractive (Sathananthan, 2017). Also, the company might work on factors such as building its physical stores as well as the Amazon is doing which will be really beneficial for it. Despite being wholly relying on the pricing strategy it will also work upon various other sections where there is required like- development of business in various other countries, targeting every age group, planning to expand the section in which the company is operating, can also launch something new in association with it etc. A business model of Jet.com is consistent and it is up to date and the concentration must be more on maintaining it as the environment upon which it is working is very dynamic and ever-changing and as each one of us knows that change is inevitable when it is concerned with business entities. There may come situations where a company might face any kind of problem so my preferably focus would be on planning and forecasting the future at an urge so that there is no problem arises which is unable to handle by the e-commerce website. The secondary focus would be upon the competitive strategy as the rivals are more in this field. And hence to maintain the long-term operations it is very necessary for it to have better strategies as compared to rivals. References Brea, E. (2018). A developmental perspective on business model innovation: exploring sequences of change in high-performing IT firms. Dudin, M. N., Lyasnikov, N. V. E., Leonteva, L. S., Reshetov, K. J. E., Sidorenko, V. N. (2015). Business model canvas as a basis for the competitive advantage of enterprise structures in the industrial agriculture. Biosciences Biotechnology Research Asia, 12(1), 887-894. Fan, Y., Pei, G., Mengnuo, D., Yingying, L., Xiao, W., Zhang, Z. (2017). Key technologies and development prospect of urban energy internet. InEnergy Internet and Energy System Integration (EI2), 2017 IEEE Conference on(pp. 1-6). IEEE. Muzellec, L., Ronteau, S., Lambkin, M. (2015). Two-sided Internet platforms: A business model lifecycle perspective. Industrial Marketing Management, 45, 139-150. Ng, H. Y. (2017). Categorization of business model patterns and mapping of their relations with business model building blocks. InIndustrial Engineering and Engineering Management (IEEM), 2017 IEEE International Conference on(pp. 1767-1771). IEEE. Onken, M., Campeau, D. (2016). Lean Startups: Using the Business Model Canvas. Journal of Case Studies, 34(1), 95-101. Perez, S, (2014). Quidsi co-founder raises an additional $20m for his new e-commerce biz, Assessed on 23rd March 2018, https://techcrunch.com/2014/09/16/quidsi-co-founder-raises-an-additional-20m-for-a-new-e-commerce-biz/. Remane, G., Hanelt, A., Nickerson, R. C., Kolbe, L. M. (2017). Discovering digital business models in traditional industries.Journal of Business Strategy,38(2), 41-51. Roberts, R. A., Earnhardt, M. P., Herron, R. (2017). Human Energy Maximization in a Customized Leadership Program.Global Journal of Business Pedagogy.1(3). 64. Rb, J., Bahemia, H., Schleyer, C. (2017). An examination of barriers to business model innovation. InEngineering, Technology and Innovation (ICE/ITMC), 2017 International Conference on(pp. 335-350). IEEE. Sathananthan, S., Hoetker, P., Gamrad, D., Katterbach, D., Myrzik, J. (2017). Realizing digital transformation through a digital business model design process. InInternet of Things Business Models, Users, and Networks, 2017(pp. 1-8). IEEE. Tonchev, K., Lindgren, P., Manolova, A., Neshov, N., Poulkov, V. (2017). Digitizing human behavior in business model innovation. InWireless Summit (GWS), 2017 Global(pp. 97-101). IEEE. Zhang, H., Sun, X., Lyu, C. (2017). Exploratory Orientation, Business Model Innovation and New Venture Growth.Sustainability.10(1). 56.

COMPARACION DE LA S DOCTRINA S DE LAS OPERACIONES Essays

COMPARACION DE LA S DOCTRINA S DE LAS OPERACIONES DE DEFENSA MOVIL ENTRE LOS EJERCITO S DE PERU Y DE BRASIL. INTRODUCCION . Resumen del trabajo . El presente trabajo tiene por finalidad hacer un breve estudio de las doctrinas militares para operaciones defensivas de los ejercitos del Peru y Brasil, particularmente la defensa movil; asimismo realizar una comparacion entre ambas para determinar ciertas ventas y desventajas de cada un a de ellas . Finalmente presentar algunas conclusiones y recomendaciones que pueden ser consideradas en ambas doctrinas. La doctrina militar de los ejercitos obedece a la situacion estrategica que vive su pais. En el caso de Peru y Brasil sus situaciones estrategicas difieren particularmente en virtud de las amenazas que e nfrentan en el contexto mundial (externo) e interno, asi como de sus aspiraciones nacionales que son productos de esa realidad; sin embargo, compartimos situaciones problematicas similares y que podemos enfrentarl as juntos como es el caso de la proteccion y soberania de la amazonia, el trafico de ilicitos a traves del Amazonas y sus afluentes, asi como a lo largo de nuestra extensa frontera. Tambien compartimos intereses estrategicos comerciales al formar juntos, el eje de desarrollo Atlantico - Pacifico. Todos estos aspectos han motivado la iniciativa de ambos paises de integrar lazos politicos y comerciales la cual involucra la integracion de nuestros ejercitos a un nivel de intercambio doctrinario y academico, es asi que desde el ano 2003 tenemos en el Peru oficiales del ejercito brasilero como profesores y alumnos en nuestras escuelas de perfeccionamiento, tambien, nosotros tenemos oficiales alumnos en el ejercito brasilero. Situacion estrategica de Peru . El Peru atraviesa hoy una bonanza economica y relativa estabilidad social (producto de la misma) sin embargo, aun enfrentamos el descontento social fruto de la desigualdad y la desconfianza en los gobernantes, el poder judicial y otras instituciones del estado. La seguridad nacional se ve seriamente afectada debido a que aun enfrentamos el problema del terrorismo en el VRAEM , el TID y el crimen organizado; en lo referente a l a Integridad Territorial (que en un sentido amplio implica tanto la integridad territorial interna como la externa: fronteras) el Peru ha descuidado la participacion constitucional de la FFAA en este pilar, la explotacion de recursos minerales a traves de contratos oficiados por el gobierno carecen la evaluacion o aprobacion de "quien es responsable de la integridad territorial", lo que ha ocasionado grandes protestas de descontento popular. Asimismo, el problema de la mineria ilegal y tala ilegal proyectan problemas mayores que aun no asume frontalmente el gobierno y en donde tiene competencia las FFAA. En el ambiente externo, es conocido la estrategia (a gran escala y que ya esta en curso: brazo economico) e intencion de Chile por poseer nuestros patrimonios directa o indirectamente, sabemos asimismo la crisis energetica e hidrica que afronta y afrontara en un futuro cercano lo que le obligara a tomar medidas drasticas. Todos estos aspectos configuran un escenario inestable para lo cual, ademas de ser conscientes, debemos estar preparados. Situacion estrategica de Brasil . Brasil comparte muchos de nuestros problemas internos (a excepcion del terrorismo) los estan representados por la inestabilidad social fruto del descontento frente a sus gobernantes y la falta de seguridad interna (alto nivel de crimen organizado). Asimismo, la mala reparticion de riquezas que establece picos elevados de poblacion rica, asi como valles extremos de pobreza (mayores al Peru). En la parte externa, Brasil nos adelanta en su preocupacion de "ser permanentemente conscientes" de la problematica que enfrentan, particularmente en la soberania exclusiva, proteccion y conservacion de la selva amazonica. Este problema ocupa seriamente su preocupacion debido a la amenaza constante de paises, organismos e organizaciones internacionales que utilizan como mascaras ciertos personajes y circulos de poder; ellos pretenden aduenarse de su gran valor para obtener sus frutos so pretexto de su cuidado en calidad de bio -reserva mundial. Es por ello que Brasil, ha asumido el papel de "padre protector" que busca "hermanos e hijos aliados" pues comprende que esta labor no podra realizarla solo, razon suficiente para justificar nuestra integracion reciente. ANALISIS Resumen de la doctrina en operaciones defensivas del ejercito del Peru. La doctrina de defensa del Ejercito del Peru,

Innovation Case Essay Example

Innovation Case Essay Example Innovation Case Essay Innovation Case Essay Technische Universitat Berlin Faculty of Economics and Management Chair for Technology and Innovationmanagement Case 1: From Imitation to Innovation: Zongshen Industrial Gr. By Willy Shih Nancy Hua Dai Case Seminar on Strategic Innovation Management Summer Term 2011 Name: Simon Delcourt Marc Esslinger Dennis Fakner Matriculation Number 337929 337772 331557 #Words: 399 Question 1: Originally, Zongshen sold engines for motorcycles which were mainly knock-offs Japanese motorcycle engines. As the Chinese government lowered its restrictions Zongshen also began to sell actual motorcycles. Since the produced motorcycles were low quality copies of the Japanese ones, most of the Chinese manufacturers were also able to make them. The lack of product differentiation encouraged Zongshen to follow a low price strategy. However, after Zuo Zongshen the chairman and CEO of the company read the â€Å"Blue Ocean Strategy†, he figured out the company should not only be selling low margin products on â€Å"red ocean† markets. Zuo Zongshen therefore made the decision to stop the launching of Japanese-like low quality motorcycles and to develop a whole new motorcycle, thus following the path of differentiation. Imitation Imitation products are quite often Me-Too products, meaning that the producing company is trying to copy a specific good which is already on the market. In this case, the Chinese motorcycle manufacturers are trying to do so with Japanese motorcycles. For imitators it is quite essential that the production costs drop to a minimum so that they can sell their products following a low price strategy. They usually have low RD expenditures due to specific measures such as reverse engineering. Furthermore they have an advantage over innovators: information about the market structure and the customer needs is already available. Since the market need for a product is established when an imitator launches his lines, it is easier for the latter to sell its product since there already is a demand for it. Innovation The Innovator with e. g. a product innovation follows usually a first to market strategy which means that he undertakes high RD efforts and also has to take a high risk, since he doesn’t know how the market will react. Risks must however be put into perspective since they are different according to the degree of innovation: a higher risk is often associated with radical innovation. The risk can shatter a company’s image as well as generate substantial losses. A product innovation is usually characterized by a high technological standard or a technical advance. Thereby, the innovator with a first to market strategy can get a temporary monopoly notably thanks to barriers set by the product characteristics. Another advantage of the innovation over the imitation is the usually longer product lifecycle and the learning process impacting the general experience curve.

Compare three companies Essay Example | Topics and Well Written Essays - 1250 words

Compare three companies - Essay Example This used to happen only with Sony and Apple products before. Samsung is not only one of the greatest businesses today, but the company tends to have a great goodwill as a responsible global entrepreneurship. The objective of this paper is to explore the tactics and strategies that were employed by Samsun to climb up and reach the top of the success ladder at such lightning speed. It is important to review the success story of Samsung before analyzing the strategies it has utilized for achieving the numero uno spot in corporate world. Samsung came into being in 1938, as a small trading company and transformed into a business group. And from its branch in Tokyo it started to expand its business first by entering in the textile business, then started establishing electronics, introduced the company in heavy industry by affiliating in shipbuilding. Samsung itself had built huge companies based on sugar and seasonings and textiles; and LG on chemicals for household and industrial consump tion (Michell, 13). It also expanded the business by acquiring Hankook Semiconductor. Later on it also introduced first 10 – million seller cell phones, became world’s best TV manufacturer. And today Samsung claims to have the largest share in the global smartphone market, which is because of the Galaxy smartphones of Samsung. In 2012 it was awarded as world’s ninth best brand (Tek, n.p). Samsung now stands among the top tier global corporations, possesses good ranking in the superior management, and provides innovation in design along with improving its sales and earnings (Lee, 9). The competition between the two famous smartphones brands Samsung and Apple started in 2008, when Samsung targeted the smartphone market by investing on large scale in it. Apple is a multinational company, which provides phones, personal computers, iPads, iPods and much more. In 2008, the most valuable company of the world was Apple because it had the shares with prices up to $ 373 ( Zylla-Woellner, n.p). Samsung and Apple without any doubt were leading the cellular especially the smartphone industry, however, Samsung suddenly shifted gear and turned the entire game in its favor. Apparently, Samsung’s most significant tactic is that the company never ceased to introduce variety in their products and in their strategies of selling the products too. Samsung Corporation has successfully blended speediness, imagination and affordability in their offerings to capture the consumers’ attention. While Samsung was busy investing huge sums on extensive research and development to gain the market share, Apple was stagnant using only 2.4 percent of its revenues on innovation (Roll 154). Samsung spent around US$ 2.3 billion on research and development (Roll, 154). The major competitors Sony and Apple were badly defeated by Samsung. The reason is that whenever these companies introduced a new product Samsung copied the concept and followed their path to introduc e similar product but with a definite edge and innovation from its predecessors. In order to learn latest designs in trend, Samsung even started comprehensive training sessions for all employees. Apple only introduced several versions of iPhone whereas in the meantime Samsung not only introduced Samsung galaxy, note book, smart TV and other economical smart phones but has been regularly updating its products’

Otto von Bismarck as a statesman Term Paper Example | Topics and Well Written Essays - 3250 words

Otto von Bismarck as a statesman - Term Paper Example In 1838, he resigned from his job because of boredom. In 1847, he got married to Johanna von Puttkamer; this was a turning point in his life because of the enormous support he received from Puttkamer. During the same period he embraced Christian tradition of the Lutheranism and began his service in the Prussian legislature; in 1847, he was elected into the Prussian parliament. In his tenure in the parliament, he opposed the liberal movement and campaigned for the unification of Germany under the support of Prussia. He also protected the rights of the Junkers (his elite social class). He served as a Prussian minister in the German government at Frankfurt between 1851 and 1859. He also served as an ambassador to Paris in 1862 and to St. Petersburg between 1859 and 1862. In both services he acquired more insight and experience that would partially establish his subsequent policies (The Questia.com 1).it is up to today debated whether Bismarck had a master plan to expand the north German confederation of 1866 to include the remaining independent German states into one country or maybe he just wanted to expand the power of the kingdom of Prussia .many reaction to Danish and other neighboring country provided foci for German unity Bismarck was an opportunist and good diplomat than a master planner. Political discontent and democratic liberalism were spreading through the parliaments and streets of Europe and people like Bismarck staunchly opposed to democratic liberalism were staunchly opposed to democratic liberalism were to work very hard to stay afloat. Bismarck did it by being pragmatist instead of idealist. He opposed any concession to the liberals and expressed contempt for the king’s willingness to bargain with revolutionaries. He was the best into taking advantage of his opportunities and leading them in the right way always. He was the main factor in unification of Germany. Otto von Bismarck was a very conservative political leader Germany has ever ha d. Wars with Austria and France He was appointed as a premier in 1862 by William I in order to securely adopt the Prussian program for the king’s army; the program was overwhelmingly rejected in the parliament. Bismarck’s main purpose was to drive out Austria from the German Confederation. He provoked the Austro-Prussian War of 1866 by accusing Austria of violation of the Gastein treaty. Austria was defeated and Germany reorganized into the North German Confederation under the Prussian leadership; Austria was not included. He also provoked the Franco-Prussian War (1870-1871) and he was able to obtain Lorraine and Alsace from France (The Questia.com 1). Alignments and Alliances Bismarck had full control of the domestic and foreign affairs. For the consolidation of the empire, he aimed at gaining the friendship of Austria, maintain British friendship by avoiding colonial or naval rivalry and isolate France through diplomacy. Thus, in 1872, he created the Three Emperorâ⠂¬â„¢s League (Austria-Hungary, Russia, and Germany). A rift in the Russo-German relations led to a Dual Alliance with Austria and the Dual Alliance became a Triple Alliance when Italy joined in 1882. The Reinsurance Treaty of 1887 revived Germany relationship with Russia (The Questia.com 1) how strong the nationalism. Bismarck knew very well that the alliances that war could accomplish his goals. How Bismarck dealt with Austria shows his commitment to maintaining boundaries based on political and

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