Obesity in Texas Research Paper Example | Topics and Well Written Essays - 750 words

Obesity in Texas - Research Paper Example bese children are much more likely to become obese adults, suffering long term health risks such as Type II Diabetes, heart problems, and some cancers (TDSHS 2009). These health care problems affect more than the individual, as the state also faces far-ranging economic and health care system impacts from these trends. Agencies and programs directed at correcting the problems of obesity in the state comprise a significant amount of the Department of State Health Services’ efforts and resources; analysis of the relative and potential successes of these measures likewise presents a valuable area for study. Current state statistics reveal that over 15% of Texas high-schoolers are categorized as overweight, while over 13% were categorized as obese (TDSHS 2010). Furthermore, more than 20% of low income children enrolled in Texas’ Women Infants and Children (WIC) nutrition programs are overweight or obese. Statistics also show much higher rates of obesity for minority groups and those living below the poverty line. The Texas DSHS site also offers some graphs that show overweight and obese statistics by selected grades for overall regions. While these graphs are only for selected age cohorts, only show data by region, and are only available for 2004-5, cumulatively they indicate that the rate of obese and overweight school aged children tends to increase until 8th grade, after which point rates tend to decline. Rates of obese vs. overweight children in different age cohorts, however, seem to vary regionally. Tracking statistical data of this sort over time can reveal some overall trends in childhood obesity in the state. First, while Texas already has higher rates of childhood obesity than the nation in general, these rates have steadily increased over time. Figure 1, compiled from TDSHS data, shows the changing percentages of overweight and obese children in Texas as compared to national averages. While Texas consistently shows higher rates of obesity in

Marketing management exam Essay Example | Topics and Well Written Essays - 2000 words

Marketing management exam - Essay Example However, summed with faulty anticipation of the market trends and too much investment in a particular project to support its aggressive marketing strategies, Tesco also had to face significant challenges in securing the desired return on its investment along with affecting its market reputation to a considerable extent. Illustratively, it was because of the same reason that the launching of Tesco’s fresh and easy store failed in the US market recently. Marketing Plan for the First Year: One of the major problems that Tesco is facing is maintaining accuracy in anticipating the changing needs and wants of the customers. Therefore, in the first year, Tesco should build such product management strategies that could identify the tastes and preferences of the potential customers. Besides ensuring the quality while offering the products to its potential customers, Tesco shall also try to renovate the older products according to the tastes and preferences of the customers to augment t heir demand. Similarly, as a market leader and to make a stronger appeal to its customers, Tesco should note that in the modern world the customers are becoming increasingly quality driven. Therefore, Tesco should reassess its marketing processes concerning certain products in order to attract the customers’ loyalty at a greater degree. To be specific, Tesco should also be concerned regarding its product quality rather than entirely focusing on pricing at a cheaper rate than its competitors. Tesco must also pay due attention on enhancing its customer relationship model to sustain its competitive advantages at stake owing to the rising competition and the various ethical issues surrounding its regular functioning. Accordingly, to maintain transparency and enrich its customer recognition, the company should emphasise taking regular feedbacks from its various stakeholders including customers, employees, suppliers and shareholders. As expected, the feedbacks shall assist Tesco to balance its shareholder-centric objectives and its sustainability goals in a more competent manner and overcome the currently observed challenges. Marketing Plan for the Second Year: In the following year, Tesco should deliver due emphasis on storing and interpreting the feedbacks obtained from the stakeholders. This will certainly assist the company not only to develop a more objective oriented business functioning to reward a better market stance but will also enrich its product/service marketing strategies, contributing to a more competitive advantage to the company. It will be noteworthy for the company to ensure that the feedbacks obtained from the customers and other group of stakeholders are not misinterpreted, which will further assure accuracy in its market anticipation. Likewise, the company can develop different strategies to suffice the market trends and demands in different places. It is very much essential in this context that Tesco aims at taking a competitive advant age of its brand name and keep focusing on its transparency obligations as well as better customer focus in its marketing operations. Besides, in the second year of application of this marketing plan, the company needs to take an assessment of the strategic application effectiveness. Accordingly, Tesco must also shift from its

Causes of and Challenges to Chinas Economic Expansion

Causes of and Challenges to Chinas Economic Expansion As the world adjusts its vision from the Beijing Olympics to a growing Chinese population, the underlying whispers resound with imperialist fears and economic worry. Researchers continue to bolster China’s position as the next superpower, yet remain limited by supposition and faulty conclusions. Regardless of China’s current size or influence, there is a hierarchical foundation within this world which demands economic and military dominance before offering such a broad title of authority. The fundamental definition of a global superpower evolves from hegemony, or an ability to dictate the policies of other nations, according to Britt (2008). As China flexes its economic muscles, the surface level apparition is one of expansive global control. Yet the question remains as to whether such unparalleled growth is sustainable or simply an artificial boost accelerated by a competitive global market. As wary nations anxiously await a Chinese offensive, economic statistics and r esearchers demonstrate conflicting results, challenging China’s superpower status. In actuality, the multitude of pitfalls and fluctuating economic status will continue to offset China’s capacity for ascension beyond its current foothold; and while economists may maintain a wary eye, the future of economic growth is one of stabilization and competition, not domination. Perhaps the greatest hindrance to China’s determined expansion, human variables continue to numerically plague their overtaxed industrial industry. As with historic examples of developing nations, economic fundamentals operating on a strategic and skill based platform in comparison with international competitors are essential to sustaining economic growth. Recognized by Hofman and Zhao (2007) as total factor productivity (TFP), or a measure of how efficiently economies utilize their capital and labor, China’s growth rate over the past decade has been inconsistent. While directly contributing to over 40% of labor productivity, only 5% of such growth is contributed by human capital, thereby asserting the Chinese disparity between educational advance and industry expansion. As Chinese businesses continue to partner with foreign firms, the need for skilled laborers, specifically in the field of management and operations, continues to reduce market effectiveness. If superpow er definition comes through a broadly recognized economic legacy which is influential and market altering, China will fall far short of this goal as their educational system and impoverished rural participants fall short of leveragable human capital. Unfolding challenges to China’s global dominance evolve from the inherent frailties within their vast but immature socio-economic ecology. The continued pollution of China’s urban and rural areas directly influences the health and well-being of the working class, and in spite of industrial projects being placed on hold as environmental goals fall short, current operations further exacerbate the damage (Dollar 2008). As sustainable enterprise rapidly spreads throughout the global community, nations actively pursue carbon reduction schemes and enforce environmental reform legislation. China, represents an at-risk nation given its current sustainability challenges, and as an expanding population is exposed to increasingly harmful conditions substantial overhaul is needed to reduce pollution and improve the health of the Chinese people (Park 2008). Seven of China’s major river systems are now polluted beyond life-bearing limits, intoxifying the nearby residents and r educing the available resources for struggling farmers (â€Å"Poison From the Dragon’s Belly† 2008). Given the aforementioned need for a skilled and healthy workforce, the environmental challenges which accost the Chinese people directly reduce their competitive potential within the global community and diminish a human legacy which could have contributed to additional growth. Perhaps the most widely recognized factor supporting growth in China’s economy since 2000 has been the expansion of the domestic private business, a force once undermined by a capitalist-fearing, overbearing socialist party (Cooke 2005). Such firms demonstrate remarkable adaptability, a trait which continues to sustain economic growth as China diversifies its exports to remain competitive on an international level. Small to medium enterprise has been recognized in countless publications as a method for developing nations to reduce the disparity between impoverished and wealthy classes. Cooke (2008) highlights the improved operational freedom post-socialism, an expanding inexpensive labor force, technological advancement, and a broadening base of Chinese entrepreneurs as the underlying success factors for increasing domestic business growth (p. 32). O’Leary (2007) predicts that by the year 2025, China’s middle class will have expanded to 520 million people represe nting over half their estimated population. As the majority of China’s GDP arises from export revenue, these firms must be provided with resources to actively pursue international commerce, including continued education and government tax reliefs to ensure that expansion is linked with a global partner network. If China has been recognized for one industrial trait over the past decade it has been their pursuit of manufacturing opportunities and capacity to offer low cost, high quality products for foreign firms. Tactically, China’s expanded technological sector has been founded on principles of joint venture and technology transfer, rapidly accelerating growth of a domestic knowledge base and advancing the Chinese reputation as the world’s workshop (Vaidya et al. 2007). Unfortunately, this knowledge capital is not readily transmitted among the working class and is heavily guarded within a hierarchical system. The reality is that unless Chinese corporations actively pursue individualized export operations, the influential nature of a growing Chinese economy is reduced. The fundamentals of expansion are based on innovation and competition; therefore, while the continuation of partnerships is essential to maintaining operations, localized efforts will be needed to increase GDP be yond its current limits. China remains a powerful workshop and should continue to maintain this status; however, expanding their GDP base will rely entirely on more competitive initiatives and a strategic effort which is directly integrated into the world marketplace. There is a substantial dissonance between Chinese operations and their Western partners that arises from operational management practices and the protectionist methods behind distribution of knowledge capital (Meyer 2005). Currently, the limited support for sector based best practices within the Chinese market pushes businesses to innovate and compete without accepting industry standards or expectations. Wang (2004) recognized that there is differentiation between the West and China in terms of knowledge management, specifically highlighted by methods of dissemination and inclusivity. Investing in IT operations and progressive knowledge reform, countries like the US actively pursue broader knowledge exchange among employees. As the Chinese management style integrates an interpersonal cultural relationship, oral communication and inner-circle divulgence become the main forms of knowledge sharing (Wang 2004). Yet such common practices oftentimes limit the ingenuity and innovative poten tial of Chinese corporations, instead placing emphasis on a control system which views knowledge as a guarded commodity (Peng et al. 2007). Regardless of technique, the lack of proficient management candidates for a growing number of industrial firms hinders expansion at a level which could rival other world powers. Cultural influence by Western organizations undermines that of Chinese culture and rejects a longstanding legacy of hierarchical control systems. Homogeneity lingers as the future for Chinese managers, and their limited understanding of Western practices will inevitably act as a hindrance, reducing the available human capital for growing firms. As business practices evolve to integrate a global value chain, corporations such as Microsoft and GE Medical Systems are actively sourcing components for US designed products from Chinese producers (Inkpen and Rmaswamy 2007). Transitioning from a national production formulae which expands domestic jobs, firms are pursuing the wealth of low cost resources available within Chinese borders, stretching the value ideology to include acceptance of international distribution and foreign job creation. Multinational corporations continue to seek out business to business partnerships within Chinese borders, defying conventional operation and expanding a field of vision which redefines strategic business methodology (Inkpen and Ramaswamy 2007). Unfortunately, within a frail and oftentimes frustrating Chinese infrastructure, multinational firms actively pursue third party logistics providers to assist with navigating supply chain challenges including transportation and material availability (Mu lani 2008). Regardless of expanded manufacturing operations, if firms cannot successfully navigate the difficult logistics of the Chinese interior, the cost basis savings from skill-set outsourcing will be lost. Developing nations must enhance their infrastructure, specifically those transport routes which can best interconnect urban areas or commercial centers. China cannot hope to compete with Western powers as their one seaboard and lack of structural integrity continues to reduce capabilities and the expansion of industry to more rural areas. There have been widespread concerns as to the financial influence a growing Chinese economy can wield against global exchanges and competing economies. As the development of high tech industries have encouraged rapid increase in venture capital and foreign direct investment throughout Chinese firms, the limited liquidity of the Shanghai and Shenzhen stock exchanges serve as a hindrance to investment firms, locking in profits and limiting returns (Pukthuanthong and Walker 2007). Humphreys (2007) challenges that regardless of China’s expanding military or dominant technological production, the cultural fundamental of harmony which defined the Chinese people should be recognized as an opportunity for partnership and market based economic principles. Undercutting the potential for rapid Chinese ascension to superpower status, the fluctuations within their capital system, lack of banking liquidity, and unproven financial markets continue to reduce external demand for Chinese sponso red investment opportunities. As current government reform measures seek to develop a more complete structural foundation for the growing economy, rapid advances must be made in the financial markets before foreign investors will pursue returns with confidence. It is the foreign direct investment, however, which will offer Chinese firms the opportunity to rapidly expand, and through such growth, diversify their operations and competitive focus. Capturing the world’s attention during the Beijing Olympic games was a remarkable step for this once guarded nation; however, retention and partnerships which later evolve will demonstrate a sustained international respect and hopeful commitment to Chinese growth. There is a final fundamental frailty within the Chinese economy which mitigates global economic dominance and that lies in the linked nature of their current economic structure. Dollar (2008) recognized the economic inconsistencies which have plagued China throughout their history, demonstrating the substantial effect that the global economic crisis has had on the Chinese GDP, reducing growth to 9%, their first time below 10% in over five years. Export economics are based entirely on a supply and demand structure, and as the world continues to navigate financial catastrophe, China’s reduction in GDP evidences their reliance on external support mechanisms for consistent growth. Regardless of the internal growth which continues to offset international reductions in spending, there is a limited functional infrastructure from which to ensure that citizens can actively support the national economy. Regardless of industrial growth, the repercussions have not been felt throughout the impoverished population which serves as China’s backbone and economic foundation. Long term growth will be leveraged through the inclusion of citizen capital and must be more balanced to allow wealth disparity to realign. Remarkable evolution has contributed to China’s global positioning as the fourth largest economy, generated from an intense industrial focus and the recent allowance of privatized operations. Yet superpower status, while an admirable goal, remains out of reach for this still-developing nation. In spite of concerns from global leaders and theorists, the potential for China to evolve past the US in terms of GDP and begin to dictate policy is simply not realistic. There are currently too many pitfalls which China must over come in the coming decades including infrastructure, environment, and trade imbalance. While Chinese corporations are rapidly pursuing additional modes of differentiation and innovation, their pace cannot match the foundation retained by Western companies who retain countless generations of operating legacy. Similarly, Chinese firms cannot simply operate within their current foundation of manufacturing export. Aggregate growth is a realistic goal over the long term outlook, and founded on a well integrated educational structure, diversified income streams, and active global participation, China will see its status continue to creep towards that ever elusive number one point of power. References Britt, R. R. 2008. Will China Become the No. 1 Superpower? LiveScience, 15th August. Accessed on 11/10/08 From: http://www.livescience.com/culture/080815-china-as-superpower.html. Cooke, F.L. 2005. Human Resource Management, Work and Employment in China. London: Routledge. Cooke, F.L. 2008. Competition and Strategy of Chinese Firms: An Analysis of Top Performing Chinese Private Enterprises. Competitiveness Review: An International Business Journal 18 (1/2): 29-56. Dollar, D. 2008. China’s Growth Surprises on the Downside. World Bank, 20th October. Accessed on 11/10/08 From: http://eapblog.worldbank.org/content/china%E2%80%99s-growth-surprises-on-the-downside. Hofman, B; Zhao, M. 2007. Asian Development Strategies: China and Indonesia Compared. Bulletin of Indonesian Economic Studies 43 (2): 171-99. Humphreys, J. 2007. The Chinese are Coming, and I’m Afraid. Journal of Business Strategy 28 (3): 42-44. Inkpen, A; Ramaswamy, K. 2007. End of the Multinational: Emerging Markets Redraw the Picture. Journal of Business Strategy 28 (5): 4-12. Meyer, M. 2005. The Changing Face of Management in China. Strategic Management, Knowledge@Wharton June. Accessed 11/10/08 From: http://knowledge.wharton.upenn.edu/article.cfm?articleid=1164. Mulani, N. 2008. Gold Medal Solutions to China’s Supply Chain Challenges. Logistics Management September: 23-24. Park, J. 2008. China, Business and Sustainability: Understanding the Strategic Convergence. Management Research News 31 (12): 951-958. Peng, J; Li-Hua, R; Moffett, S. 2007. Trend of Knowledge Management in China: Challenges and Opportunities. Journal of Technology Management in China 2 (3): 198-211. â€Å"Poison from the Dragon’s Belly: Is China Paying Too High a Price for Success?† 2008. Strategic Direction 24 (2): 21-23. Pukthuanthong, K; Walker, T. 2007. Venture Capital in China: A Culture Shock for Western Investors. Management Decision 45 (4): 708-731. Vaidya, K; Bennet, D; Liu, X. 2007. Is China’s Manufacturing Sector Becoming More High-Tech? Evidence on Shifts in Comparative Advantage 1987-2005. Journal of Manufacturing Technology 18 (8): 1000-1021. Wang, G. 2004. Knowledge Management in a Multinational Company. In: Peng, J; Li-Hua, R; Moffett, S. Trend of Knowledge Management in China: Challenges and Opportunities. Journal of Technology Management in China 2 (3): 198-211.

Clubfoot Essay -- essays research papers

CLUBFOOT   Ã‚  Ã‚  Ã‚  Ã‚  Clubfoot is defined as a congenital foot deformity characterized by a kidney shaped foot that turns inward and points down. The forefoot is curved inward, the heel is bent inward, and the ankle is fixed in planter flexion with the toes pointing down. Shortened tendons on the inside of the lower leg, together with abnormally shaped bones that restrict movement outwards cause the foot to turn inwards. A tightened achilles tendon causes the foot to point downwards. The medical term for clubfoot is talipes equinovarus . It is the most common congenital disorder of the lower extremity. There are several variations, but talipes equinovarus being the most common. Clubfeet occurs in approximately 1 in every 800-1000 babies, being twice as common in boys than girls. One or both feet may be affected.   Ã‚  Ã‚  Ã‚  Ã‚  The history of clubfeet began as far back as 400 B.C. Hipocrates was the first to describe it. He used bandages to treat it. As time progressed so did the treatment methods. In about 1743 gentle stretching was recommended. During that same century, a mechanical device resembling a turnbuckle was used to help stretch the tendons. By this time clubfoot was pretty well known around the world, using the typical stretching and splinting methods. In the 1800’s plaster of paris was first introduced, and later that same century, the introduction of aseptic technique and anasthesia diminished, but not eliminated infection. As...

ASEAN Community Essay

ASEAN, â€Å"One vision, one identity, one community† As ASEAN member, I am aware of ASEAN history. It started on August 8, 1967 with 5 countries: Indonesia, Malaysia, Philippines, Singapore and Thailand, but it turned into 10 after years of success: Brunei Darussalam, Cambodia, Indonesia, Laos, Malaysia, Myanmar, Philippines, Singapore, Thailand, and Vietnam. Since then, these 10 countries have been cooperating and collaborating for the benefits of the people and their country. Have you ever thought how important ASEAN is? In 2015, ASEAN COMMUNITY will be launched and I may say that it gives a productive impact on culture, education and tourism of each country member. For example, in Thailand, ASEAN brings cultural diversity. Many nationalities are now staying in Thailand for vacation, business or job, entertainment, education, trade or industry. The good thing is despite the differences, we still live in peace and harmony. Likewise, Thailand has become more open to embrace l earning about culture and language of other countries. ASEAN has a good effect on education. By means of cooperation, students and teachers will develop their skills and they have a chance to further their studies abroad. In school, students will know more about these 10 countries. Language especially English will be widely spoken by the people in ASEAN Community. We will become more globally competitive. ASEAN has a good impact on tourism. People from the southeast Asia have opportunities to travel without hassle. AFTA or Asia Free Trade Area is another good thing to promote tourism. As a result, members of ASEAN will probably enjoy shopping and travelling from one country to another and this leads to a good relationship. Finally, I am proud to be a member of ASEAN. At school I am being built up in my ability on English to be a better and more successful Thai citizen. I thank my teachers for they have done a lot and are still doing much in helping develop my abilities to be a better user of English. May it be a challenge for all students to be serious in learning the English language to become globally competitive.

Principles Of Teaching And Learning In Teaching Math Essay

Students learn mathematics through the experiences that teachers provide. Teachers must know and understand deeply the mathematics they are teaching and understand and be committed to their students as learners of mathematics and as human beings. There is no one â€Å"right way† to teach. Nevertheless, much is known about effective mathematics teaching. Selecting and using suitable curricular materials, using appropriate instructional tools and techniques to support learning, and pursuing continuous self-improvement are actions good teachers take every day. The teacher is responsible for creating an intellectual environment in the classroom where serious engagement in mathematical thinking is the norm. Effective teaching requires deciding what aspects of a task to highlight, how to organize and orchestrate the work of students, what questions to ask students having varied levels of expertise, and how to support students without taking over the process of thinking for them. Effective teaching requires continuing efforts to learn and improve. Teachers need to increase their knowledge about mathematics and pedagogy, learn from their students and colleagues, and engage in professional development and self-reflection. Collaborating with others–pairing an experienced teacher with a new teacher or forming a community of teachers–to observe, analyze, and discuss teaching and students’ thinking is a powerful, yet neglected, form of professional development. Teachers need ample opportunities to engage in this kind of continual learning. The working lives of teachers must be structured to allow and support different models of professional development that benefit them and their students. Mathematics Principles and practice What can learning in mathematics enable children and young people to achieve? Mathematics is important in our everyday life, allowing us to make sense of the world around us and to manage our lives. Using mathematics enables us to model real-life situations and make connections and informed predictions. It equips us with the skills we need to interpret and analyse information,  simplify and solve problems, assess risk and make informed decisions. Mathematics plays an important role in areas such as science or technologies, and is vital to research and development in fields such as engineering, computing science, medicine and finance. Learning mathematics gives children and young people access to the wider curriculum and the opportunity to pursue further studies and interests. Because mathematics is rich and stimulating, it engages and fascinates learners of all ages, interests and abilities. Learning mathematics develops logical reasoning, analysis, problem-solving skills, creativity and the ability to think in abstract ways. It uses a universal language of numbers and symbols which allows us to communicate ideas in a concise, unambiguous and rigorous way. To face the challenges of the 21st century, each young person needs to have confidence in using mathematical skills, and Scotland needs both specialist mathematicians and a highly numerate population. Building the Curriculum 1 Mathematics equips us with many of the skills required for life, learning and work. Understanding the part that mathematics plays in almost all aspects of life is crucial. This reinforces the need for mathematics to play an integral part in lifelong learning and be appreciated for the richness it brings. How is the mathematics framework structured? Within the mathematics framework, some statements of experiences and outcomes are also identified as statements of experiences and outcomes in numeracy. These form an important part of the mathematics education of all children and young people as they include many of the numerical and analytical skills required by each of us to function effectively and successfully in everyday life. All teachers with a responsibility for the development of mathematics will be familiar with the role of numeracy within mathematics and with the means by which numeracy is developed across the range of learning  experiences. The numeracy subset of the mathematics experiences and outcomes is also published separately; further information can be found in the numeracy principles and practice paper. The mathematics experiences and outcomes are structured within three main organisers, each of which contains a number of subdivisions: Number, money and measure Estimation and rounding Number and number processes Multiples, factors and primes Powers and roots Fractions, decimal fractions and percentages Money Time Measurement Mathematics – its impact on the world, past, present and future Patterns and relationships Expressions and equations. Shape, position and movement Properties of 2D shapes and 3D objects Angle, symmetry and transformation. Information handling Data and analysis Ideas of chance and uncertainty. The mathematics framework as a whole includes a strong emphasis on the important part mathematics has played, and will continue to play, in the advancement of society, and the relevance it has for daily life. A key feature of the mathematics framework is the development of algebraic thinking from an early stage. Research shows that the earlier algebraic thinking is introduced, the deeper the mathematical understanding will be  and the greater the confidence in using mathematics. Teachers will use the statements of experiences and outcomes in information handling to emphasise the interpretation of statistical information in the world around us and to emphasise the knowledge and skills required to take account of chance and uncertainty when making decisions. The level of achievement at the fourth level has been designed to approximate to that associated with SCQF level 4. What are the features of effective learning and teaching in mathematics? From the early stages onwards, children and young people should experience success in mathematics and develop the confidence to take risks, ask questions and explore alternative solutions without fear of being wrong. They will enjoy exploring and applying mathematical concepts to understand and solve problems, explaining their thinking and presenting their solutions to others in a variety of ways. At all stages, an emphasis on collaborative learning will encourage children to reason logically and creatively through discussion of mathematical ideas and concepts. Through their use of effective questioning and discussion, teachers will use misconceptions and wrong answers as opportunities to improve and deepen children’s understanding of mathematical concepts. The experiences and outcomes encourage learning and teaching approaches that challenge and stimulate children and young people and promote their enjoyment of mathematics. To achieve this, teachers will use a skilful mix of approaches, including:  planned active learning which provides opportunities to observe, explore, investigate, experiment, play, discuss and reflect modelling and scaffolding the development of mathematical thinking skills learning collaboratively and independently  opportunities for discussion, communication and explanation of thinking developing mental agility  using relevant contexts and experiences, familiar to young people making links across the curriculum to show how mathematical concepts are applied in a wide range of contexts, such as those provided by science and social studies using technology in appropriate and effective ways  building on the principles of Assessment is for Learning, ensuring that young people understand the purpose and relevanc e of what they are learning developing problem-solving capabilities and critical thinking skills. Mathematics is at its most powerful when the knowledge and understanding that have been developed are used to solve problems. Problem solving will be at the heart of all our learning and teaching. We should regularly encourage children and young people to explore different options: ‘what would happen if†¦?’ is the fundamental question for teachers and learners to ask as mathematical thinking develops. How will we ensure progression within and through levels? As children and young people develop concepts within mathematics, these will need continual reinforcement and revisiting in order to maintain progression. Teachers can plan this development and progression through providing children and young people with more challenging contexts in which to use their skills. When the experience or outcome spans two levels within a line of development, this will be all the more important. One case in point would be the third level outcome on displaying information. The expectation is that young people will continue to use and refine the skills developed at second level to display charts, graphs and diagrams. The contexts should ensure progression and there are clear opportunities to use other curriculum areas when extending young people’s understanding. What are broad features of assessment in mathematics? (This section should be read alongside the advice for numeracy.) Assessment in mathematics will focus on children and young people’s abilities to work increasingly skilfully with numbers, data and mathematical concepts and processes and use them in a range of contexts. Teachers can gather evidence of progress as part of day-to-day learning about number, money and measurement, shape, position and movement and information handling. The use of specific assessment tasks will be important in assessing progress at key points of learning including transitions. From the early years through to the senior stages, children and young people will demonstrate progress in their skills in interpreting and analysing information, simplifying and solving problems, assessing risk and making informed choices. They will also show evidence of progress through their skills in collaborating and working independently as they observe, explore, experiment with and investigate mathematical problems. Approaches to assessment should identify the extent to which children and young people can apply their skills in their learning, in their daily lives and in preparing for the world of work. Progress will be seen as children and young people demonstrate their competence and confidence in applying mathematical concepts and skills. For example: Do they relish the challenge of number puzzles, patterns and relationships? Can they explain increasingly more abstract ideas of algebraic thinking? Can they successfully carry out mathematical processes and use their developing range of skills and attributes as set out in the experiences and outcomes? As they apply these to problems, can they draw on skills and concepts learned previously? As they tackle problems in unfamiliar contexts, can they confidently identify which skills and concepts are relevant to the problem? Can they then apply their skills accurately and then evaluate their solutions? Can they explain their thinking and demonstrate their understanding of 2D shapes and 3D objects? Can they evaluate data to make informed decisions? Are they developing the capacity to engage with and complete tasks and  assignments? Assessment should also link with other areas of the curriculum, within and outside the classroom, offering children and young people opportunities to develop and demonstrate their understanding of mathematics through social studies, technologies and science, and cultural and enterprise activities. How can I make connections within and beyond mathematics? Within mathematics there are rich opportunities for links among different concepts: a ready example is provided by investigations into area and perimeter which can involve estimation, patterns and relationships and a variety of numbers. When children and young people investigate number processes, there will be regular opportunities to develop mental strategies and mental agility. Teachers will make use of opportunities to develop algebraic thinking and introduce symbols, such as those opportunities afforded at early stages when reinforcing number bonds or later when investigating the sum of the angles in a triangle. There are many opportunities to develop mathematical concepts in all other areas of the curriculum. Patterns and symmetry are fundamental to art and music; time, money and measure regularly occur in modern languages, home economics, design technology and various aspects of health and wellbeing; graphs and charts are regularly used in science and social studies; scale and proportion can be developed within social studies; formulae are used in areas including health and wellbeing, technologies and sciences; while shape, position and movement can be developed in all areas of the curriculum. The Teaching Principle Effective mathematics teaching requires understanding what students know and need to learn and then challenging and supporting them to learn it well. Students learn mathematics through the experiences that teachers provide. Thus, students’ understanding of mathematics, their ability to  » use it to solve problems, and their confidence in, and disposition toward, mathematics are all shaped by the teaching they encounter in school. The improvement of  mathematics education for all students requires effective mathematics teaching in all classrooms. Teaching mathematics well is a complex endeavor, and there are no easy recipes for helping all students learn or for helping all teachers become effective. Nevertheless, much is known about effective mathematics teaching, and this knowledge should guide professional judgment and activity. To be effective, teachers must know and understand deeply the mathematics they are teaching and be able to draw on that knowledge with flexibilit y in their teaching tasks. They need to understand and be committed to their students as learners of mathematics and as human beings and be skillful in choosing from and using a variety of pedagogical and assessment strategies (National Commission on Teaching and America’s Future 1996). In addition, effective teaching requires reflection and continual efforts to seek improvement. Teachers must have frequent and ample opportunities and resources to enhance and refresh their knowledge. Effective teaching requires knowing and understanding mathematics, students as learners, and pedagogical strategies. Teachers need several different kinds of mathematical knowledge—knowledge about the whole domain; deep, flexible knowledge about curriculum goals and about the important ideas that are central to their grade level; knowledge about the challenges students are likely to encounter in learning these ideas; knowledge about how the ideas can be represented to teach them effectively; and knowledge about how s tudents’ understanding can be assessed. This knowledge helps teachers make curricular judgments, respond to students’ questions, and look ahead to where concepts are leading and plan accordingly. Pedagogical knowledge, much of which is acquired and shaped through the practice of teaching, helps teachers understand how students learn mathematics, become facile with a range of different teaching techniques and instructional materials, and organize and manage the classroom. Teachers need to understand the big ideas of mathematics and be able to represent mathematics as a coherent and connected enterprise (Schifter 1999; Ma 1999). Their decisions and their actions in the classroom—all of which affect how well their students learn mathematics—should be based on this knowledge. This kind of knowledge is beyond what most teachers experience in standard preservice mathematics courses in the United States. For example, that fractions can be understood as parts of a whole, the quotient of two integers, or a numb er on a line is  important for mathematics teachers (Ball and Bass forthcoming). Such understanding might be characterized as â€Å"profound understanding of fundamental mathematics† (Ma 1999). Teachers also need to understand the different representations of an idea, the relative strengths and weaknesses of each, and how they are related to one another (Wilson, Shulman, and Richert 1987). They need to know the ideas with which students often have difficulty and ways to help bridge common misunderstandings.  » Effective mathematics teaching requires a serious commitment to the development of students’ understanding of mathematics. Because students learn by connecting new ideas to prior knowledge, teachers must understand what their students already know. Effective teachers know how to ask questions and plan lessons that reveal students’ prior knowledge; they can then design experiences and lessons that respond to, and build on, this knowledge. Teachers have different styles and strategies for helping students learn particular mathematical ideas, and there is no one â€Å"right way† to teach. However, effective teachers recognize that the decisions they make shape students’ mathematical dispositions and can create rich settings for learning. Selecting and using suitable curricular materials, using appropriate instructional tools and techniques, and engaging in reflective practice and continuous self-improvement are actions good teachers take every day. One of the complexities of mathematics teaching is that it must balance purposeful, planned classroom lessons with the ongoing decision making that inevitably occurs as teachers and students encounter unanticipated discoveries or difficulties that lead them into uncharted territory. Teaching mathematics well involves creating, enriching, maintaining, and adapting instruction to move toward mathematical goals, capture and sustain interest, and engage students in building mathematical understanding. Effective teaching requires a challenging and supportive classroom learning environment. Teachers make many choices each day about how the learning environment will be structured and what mathematics will be emphasized. These decisions determine, to a large extent, what students learn. Effective teaching conveys a belief that each student can and is expected to understand mathematics and that each will be supported in his or her efforts to accomplish this goal. Teachers establish and nurture an environment conducive to learning mathematics through the decisions they make, the conversations they orchestrate, and the  physical setting they create. Teachers’ actions are what encourage students to think, question, solve problems, and discuss their ideas, strategies, and solutions. The teacher is responsible for creating an intellectual environment where serious mathematical thinking is the norm. More than just a physical setting with desks, bulletin boards, and posters, the clas sroom environment communicates subtle messages about what is valued in learning and doing mathematics. Are students’ discussion and collaboration encouraged? Are students expected to justify their thinking? If students are to learn to make conjectures, experiment with various approaches to solving problems, construct mathematical arguments and respond to others’ arguments, then creating an environment that fosters these kinds of activities is essential. In effective teaching, worthwhile mathematical tasks are used to introduce important mathematical ideas and to engage and challenge students intellectually. Well-chosen tasks can pique students’ curiosity and draw them into mathematics. The tasks may be connected to the  » real-world experiences of students, or they may arise in contexts that are purely mathematical. Regardless of the context, worthwhile tasks should be intriguing, with a level of challenge that invites speculation and hard work. Such tasks often can be approached in more than one way, such as using an arithmetic counting approach, drawing a geometric diagram and enumerating possibilities, or using algebraic equations, which makes the tasks accessible to students with varied prior knowledge and experience. Worthwhile tasks alone are not sufficient for effective teaching. Teachers must also decide what aspects of a task to highlight, how to organize and orchestrate the work of the students, what questions to ask to challenge those with varied levels of expertise, and how to support students without taking over the process of thinking for them and thus eliminating the challenge. Opportunities to reflect on and refine instructional practice—during class and outside class, alone and with others—are crucial in the vision of school mathematics outlined in Principles and Standards. To improve their mathematics instruction, teachers must be able to analyze what they and their students are doing and consider how those actions are affecting students’ learning. Using a variety of strategies, teachers should monitor students’ capacity and inclination to analyze situations, frame and solve problems, and make sense of mathematical concepts and procedures. They  can use this information to assess their students’ progress and to appraise how well the mathematical tasks, student discourse, and classroom environment are interacting to foster students’ learning. They then use these appraisals to adapt their instruction. Reflection and analysis are often individual activities, but they can be greatly enhanced by teaming with an experienced and respected colleague, a new teacher, or a community of teachers. Collaborating with colleagues regularly to observe, analyze, and discuss teaching and students’ thinking or to do â€Å"lesson study† is a powerful, yet neglected, form of professional development in American schools (Stigler and Hiebert 1999). The work and time of teachers must be structured to allow and support professional development that will benefit them and their students.