General Biology Genetic Test - 962 Words

General Biology I Genetic Test Essay Photosynthesis is an important process to living organisms because eliminates Carbon Dioxide and releases Oxygen by the use of a plant. Pigments are color molecules the absorb lights in different color wavelengths of light. The light that the pigments absorb turns into energy (Glucose) in the photosynthesis process. They are different types of pigments like Carotenoids, Anthocyans, Xanthophyll, and Chlorophyll which is the major light absorbing pigment in plants. The more pigments the more food for plants to eat. The pigments absorb energy from different color wavelengths and reflect another like plants which give the color green. The importance of light and pigments don’t only play important role in photosynthesis they also are important to maintain life. In the thylakoid membrane is located the Photosystem consist of three components receiving energy wavelengths in the molecules at P680 and P700. The first component is the reaction center where a Chlorophyll (a) delivers an excited electron to the primary acceptor. The second component is the antenna complex, which are protein and chlorophyll molecules that transfer light energy to Chlorophyll (a). The other component is the primary electron acceptor which receives the lost electron from chlorophyll (a). The importance of non-cyclic electron flow in the light independent phase is a light reaction which helps the excited electron passShow MoreRelatedGenetic Testing : Is We Ready Yet? Essay1740 Words   |  7 Pages GENETIC TESTING- ARE WE READY YET? As exciting as it sounds, genetic testing can give a complete insight of what one’s genetic makeup beholds for his/her future. However this comes with a price that can potentially make or break the life thereafter. Highly accurate genetic testing is a huge step; however, such a success can be fruitful only if the after effects are efficiently managed. Accurate prediction of possible socio-economic and psychological effects and devising efficient management strategiesRead MoreDispositional, Evolutionary And Evolutionary Theory1283 Words   |  6 Pagesdifferences that are among dispositional and evolutionary personality theories, as well as, strengths and limitations of dispositional and evolutionary and biological personality theories their bearing on human behavior. Furthermore, the Big Five personality test and what technique is used to study personality. Difference Facets relating Dispositional, and Evolutionary Theory The premises of dispositional theories fluctuate from those of other theorists because they present the basis of study for personality;Read MoreLab on Thumb Dominance Essay760 Words   |  4 PagesBiology 111 Laboratory #1: MBS Title: Study of the Dominant Thumb and Handedness Abstract: The dominance of the thumb and its relationship to handedness was studied. 50 volunteers were asked to clasp their hands and the thumb dominance and handedness of each subject was noted. The results showed a connection between the handedness of a person and its opposite thumb dominance, though all combinations of handedness and thumb dominance were evidenced. 1. Introduction A. BackgroundRead MoreDispositional Essay example1154 Words   |  5 PagesRoberts, 2013). Comparing dispositional, biological, and evolutionary theories indicates the similarities and differences between the theories; as well as their strengths and weaknesses. The use of these theories has led to research and tests, such as the big five test, that help indicate personality characteristics of individuals (Feist, et al. 2013). Comparison Dispositional personality theory identifies types and traits of characteristics to help determine personality (Feist, Feist, amp; RobertsRead MoreThe Branch Of Biology : An Example Of Multinational Influence1304 Words   |  6 Pageslanguage. The diversity of influences endow spontaneity into art, refining its nature. Art such as the science of biology is an example of multinational influence. Biology helps humans understand themselves and the life surrounding them. As a result, it is a duty for humans worldwide to collaborate as a team, study the topic, and build upon the knowledge of biology. The branch of biology is a complex field, so it requires the assistance of nations globally to make it understandable. The study of lifeRead MoreGenetic Markers : A Genetic Marker1641 Words   |  7 Pagesunattainable without genetic markers. In everyone there are certain markers that can allow a geneticist to determine a person’s medical future, certain medicines work with some genetic markers and not with others. Many genes are linked to certain diseases and allow a geneticist to possibly prevent diseases. A genetic marker is a DNA sequence with a known specific location on the chromosome, they can be a great indicator for genetic disorders and any other hereditary diseases. Genetic markers are alsoRead MorePhenylthiocarbamide Lab Report1612 Words   |  7 Pagespowder (PTC) that was poured into a bottle blew into the air, curiosity began to arise. Dr. C. R. Noller, another individual in the lab, stated that he tasted something bitter, while Fox tasted nothing at all. (Stephen Wooding 2006) Fox then decided to test others to see what they tasted. After several others had tried the PTC powd er, Fox looked at his results. Some reported that they tasted absolutely nothing, while others reported it extremely bitter. Shortly after these results were reported, it wasRead MoreHistorical Discoveries Of Dna And Genetic Material1364 Words   |  6 PagesWhen most people think of DNA, scientists, laboratories, and twisted ladders come to mind. In reality, DNA makes up genetic material, which makes up proteins that form much of the body and perform vital tasks. The study of DNA and genetic material is something more people should be aware of. As a society, knowing how powerful genetic research and technology are holds the possibility to help, or possibly hurt, people now and in the future. The study of deoxyribonucleic acid, better known as DNA,Read MoreHistorical Discoveries Of Dna And Genetic Material1364 Words   |  6 PagesWhen most people think of DNA, scientists, laboratories, and twisted ladders come to mind. In reality, DNA makes up genetic material, which makes up proteins that form much of the body and perform vital tasks. The study of DNA and genetic material is something more people should be aware of. As a society, knowing how powerful genetic research and technology are holds the possibility to help, or possibly hurt, people now and in the future. The study of deoxyribonucleic acid, better known as DNA,Read MoreDispositional Vs Biological Theory Essay990 Words   |  4 Pages405 September 15, 2014 Leslie Binnix Dispositional vs. Biological Theory Dispositional personality theories are quite different from biological personality theories. The two will be compared and dissected in this article. The Big Five Personality Test will also be analyzed and how it is used to study personality will be examined. Dispositional personality theories contend that each person per certain stable, long lasting dispositions. These dispositions make a person display certain emotions, attitudes

Visiting Hour by Norman MacCaig Essay Example For Students

Visiting Hour by Norman MacCaig Essay The poem also contained many metaphors that were very effective. These metaphors were in verse five, when he is in the hospital by his wifes beside. Firstly he says, a white cave of forgetfulness, by this he means that the sheets on her bed are white and contrasting to the black all around her. She was on medicine and maybe that is the reason she was full of forgetfulness. The second describes the frailty of her hands, a withered hand trembles on its stalk, and this describes the frail hand shaking, with a drip attached. I think that this is effective because of the way it says that the hand is withering away comparing it to the stalk of a flower. Next, he writes, into an arm a glass fang is fixed, which is saying the drip is sucking all of her blood out like a vampire. The poet finishes off the verse with a meaningful sentence, the distance of pain that neither she nor I can cross, by this the writer is saying that in no way can he even try and think what his Wife is feeling and there is also no way that his Wife can sense what he is going through. In the last paragraph, MacCaig tries to cross this barrier of pain. He does this by writing the last verse in his wifes perspective. He uses sounds that his wife hears like, in the round swimming waves of a bell, and he also writes about what she is seeing through her eyes, and dizzily goes off, growing fainter, and this shows him trying to break this barrier that he said he couldnt break. As the poems finishes there are two symbolic sentences said. The first one which is, books that will never be read, means that if you are in hospital for a long time then you would expect books. However, if you have been telling someone that they are going to get better and will be out of hospital soon, then books shouldnt be an option as they might get the impression they are here to stay. Also, if the book is not going to be read then that also indicates that they are going to die. The second area of symbolism is,fruitless fruits, and this symbolises that fruit that may be given to someone in hospital, and if it is fruitless it is also lifeless, as fruits are good for you. I conclude that the poet uses good techniques throughout by use of metaphors and symbolism. Throughout the poem he makes me feel empathetic towards him. Although the poem proved confusing at times with his unusual ideas, I still really enjoyed it and I really felt the power of the last two words, which were, Fruitless fruits.

Antz essays

Antz essays In the movie Antz, the producers tied many governmental issues into the story. The colony was led like a communist country, an aristocracy, and had a totalitarianism setup. Communism, for example, was a major part of the story. The government dictated the entire colony and every aspect of the ants lives. Aristocracy was another governmental issue that was part of the movie. The Queen had the final say in all issues in the colony and she had all of the wealth. The ant colony was totalitarianistic, also, for there was a big strong central government, which decided everything for the workers and military ants. General Mandible led the military with an iron fist, and led the army into a coup detat. When the coup began, the soldier ants then became juntas; soldiers involved in a coup, along with Cutter, Mandibles right hand man. The ant colony government strongly disagreed with Z and his individualism because it led other people to think for themselves instead of getting blindly led by the Queen and General Mandible. Zs individualistic views created chaos in the government. This movie showed many of the governments that are throughout the world, including old Great Britain, Russia, China, and even the United States of America. Using ants, they were also able to show how individualism belongs to everyone and that you must fight for your right to do as you please, as long as it is not hindering someone elses freedom. ...

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Contribute to the Blog We are looking for engaging articles aimed at teachers, students, or anyone who just likes to learn. They can be informative or have a sense of humor, but preferably we’re looking for innovative guides to instructing and learning.  Articles could range anywhere from â€Å"Tips on Teaching with the iPad† to â€Å"7 Ways American Idol Can Help You Study.† Be creative! Guest Post Criteria Articles can be up to 1000  words in length ideally, or as long as they need to be to get your message across. If you use sources, please provide links to them. We like posts that are well-written and relatively free of spelling and grammatical errors (articles will be  proofread before publishing, but the fewer errors the better). All content must be original and free of plagiarism. If we do not publish your submission, you are welcome to try again with a different topic. For ideas on what we typically look for, you might want to browse through our most recent posts. Email all submissions to  sburton@  with the subject line â€Å"Guest Blog Post† with a 1-3 sentence bio of yourself to include with the publication along with a headshot photo (optional). Please note We will not link to essay-writing services, nor endorse their products and services.

Debt ceiling Essay Example | Topics and Well Written Essays - 1500 words

Debt ceiling - Essay Example The researcher states that debt ceiling is the limit to which debts can be borrowed. The debt ceiling as perceived in the United States is the maximum amount of debt that can be borrowed by the United States in order to run its operations. The process through which debt is borrowed by the government is by issuing bonds. The government issues bonds in order to raise the debt and the holders of such bonds hold the position of a creditor. The bonds have a date of maturity and a rate of return, and these are held by individuals or organizations as available for sale as well. Due to the application of debt ceiling, there is a limit to the amount borrowed by the United States through such bonds, which means the overall deficit in the federal budget cannot exceed the debt ceiling therefore it can be said the overall spending of the government is limited to the extent of the debt ceiling. The topic of debt ceiling was selected because it holds significant importance in the current economic s ituation of the United States. After the recent debt ceiling crisis and the impacts of this crisis on the overall economy of the United States, the understanding of the concept of debt ceiling holds significant importance. Before the debt ceiling was created in the United States, the President was free to make decisions regarding the overall borrowings by the US. The debt ceiling was created in 1917 in order to ensure the accountability of the debt borrowings by the US. Debt ceiling is important for the economy of the US in a number of ways. Following are some of the important aspects of the debt ceiling.... The debt ceiling does not only keep the overall borrowings in control but there are a number of other economic factors linked with borrowing that also come under control due to the debt ceiling. When the debt ceiling is reached while determining a budget, the regulatory authorities can use ‘extraordinary measures’ to raise the required finances in order to remain under the debt ceiling. Such extraordinary measures are not considered unless there is a genuine need to raise the finances such as for saving a part of the government to shut down. There is a limit to the amount of funds to be raised through such ‘extraordinary measures’ and if the regulatory authorities remain unable to raise the required amount of funds through such measures as well, a rise in the debt ceiling is considered.The debt ceiling also influences the extent of government spending. In the presence of debt ceiling, there would be a control over the government’s decisions regarding spending on its operations. Excess government spending may result in increased deficit in the budget. Since the deficit in the budget and government spending influence the overall economic activity in the country, it may lead to a steep rise in inflation in the country. Thus, debt ceiling is important to keep an active control over the borrowings made by the US and the spending made by the government.The debt ceiling is also important because it keeps the federal budget of the United States under control. The debt ceiling keeps the regulatory authorities from exceeding the borrowing limit and in order to meet the deficits in the budget, other measures are resorted to. In the recent past, the debt ceiling has caused

Chanticleer show ( jazz) Essay Example | Topics and Well Written Essays - 500 words

Chanticleer show ( jazz) - Essay Example However, the group generates substantial incomes from major global events and album sales (Weir, & Alfred Publishing Co. 2008). The following is an intense discussion on Chanticleer Jazz Show, with a reflection of the music genres, advancements, and revenue creation tactics. In the Grammy Awards ceremony, Chanticleer acquired an acknowledgement as the reigning global male chorus ahead of many other groups. Further, the group yields praise from its global audience and the media outlets. Over the past three decades, the group has continually blended the jazz music genre from an earlier and stagnant phase. Chanticleer is renown in San Francisco as an orchestra of voices, a factor that emanates from the combination of twelve members with unique voices. Their sales performances are overwhelming and consequently are leading in San Francisco (Weir, & Alfred Publishing Co. 2008). Opening with the songs, â€Å"The Siren’s Call†, and â€Å"Temptations†, Chanticleer Jazz show attracted a huge audience from all the American states. The countrywide tour in the U.S impacts effective reputation from the fans, and a probability is that the expected turnover at the events shall be overwhelming. As at March of 2013, the group targets to launch the anniversary tour, starting in New York City and spreading to other parts of the world. Chanticleer schedules to travel globally in an effort to complete the planned hundred concerts and performances. The tour will improve on the perceptions held on Jazz music. For example, a reflection of the 2011-2012 tour led to the birth of a music choir –The Louis A. Botto Choir. Therefore, presumptions are that the group serves as a motivating factor to rekindle and improve Jazz music, with a surety that the music genre will successfully pass to future generations. Another aspect that possibly reveals Chanticleer as a promotional choir to ensuring survival of Jazz is the fact that, the group focuses on encourages teenagers

History of Mathematics Teaching in the National Curriculum

History of Mathematics Teaching in the National Curriculum This research paper is to discuss about the nature and history of mathematics, how it has taken its place within the National Curriculum; the framework for teaching Mathematics in Secondary and finally investigation on a series of three lessons designed for Year 7 on Algebra. INTRODUCTION Education has made a difference in my life, the knowledge I have gained has given me the potential to explore, think and make decisions accordingly. In other words, Education is a powerful tool and plays a vital role to shape up a strong economy of a country. As a Mathematics teacher, I clearly understand my key role in imparting knowledge and skills to the younger generation to make full use of their potential. The perception of mathematics has been changed over the years. Hence, it is important to look back at the nature of mathematics, how it has taken its place within the national curriculum; how the teaching and learning of mathematics has been guided by the National Strategies Framework. LITERATURE REVIEW Nature of Mathematics Even though mathematics is one of the many subjects in schools, there is a greater pressure on pupils to succeed in Mathematics other than subjects like History, Geography; why is that so? As part of my investigation into the nature of Mathematics I referred to two sources that gave substantial evidence towards the nature of Mathematics. The Enquiry Committee: A Major Enquiry Committee was set up in 1978 to consider the teaching of Mathematics in Primary and Secondary schools. After 4 years of study and research the committee came out with a report called The Cockcroft Report. It would be very difficult perhaps impossible to live a normal life in very many parts of the world in the twentieth century without making use of mathematics of some kind. (The Cockcroft Report (1982), Mathematics counts) This fact itself for a thought is sufficient to reason out the purpose of importance given in teaching and learning mathematics in Schools. The usefulness of Mathematics can be perceived in different ways; as arithmetic skills needed to use at Home and Office, as basis for development of Science and Technology and usage of Mathematical techniques as management tool in commerce and industry. Therefore, the Enquiry Committee in their report (The Cockcroft Report) concluded that all the perceptions on usefulness of mathematics arise from the fact that mathematics provides a mean of communication which is powerful, concise and unambiguous. Hence, providing a principal reason for teaching mathematics at all stages in the curriculum. According to American Association for the Advancement of Science (AAAS), mathematics is closely related to Science, Technology and being greatly used in real life. The association has launched a program called Project 2061 where they relate mathematics into Science and Technology. Project 2061 is an ongoing project that was launched in 1985 in America, where its main objective is to help all Americans to literate in Science, Mathematics and Technology. As part of the project, it has been clearly defined that mathematics does play an important role in developing Science and Technology in real life. Besides communication, Mathematics can be used to present information by using charts, graphs and diagrams. As what AAAS has mentioned about the Mathematical representation, manipulation and derivation of information based on a mathematical relationship formed; the enquiry committee as well does mention in its report the usage of figures and symbols in mathematics for manipulation and to deduce further information from the situation the mathematics relate to. They gave 3 scenarios; A car that has travelled for 3 hours at an average speed of 20 miles per hour; we can deduce that it has covered a distance of 60 miles. To find the cost of 20 articles each costing 3p, the area of carpet required to cover a corridor 20 metres long and 3 metres wide In the 3 scenarios, we made use of the fact that: 20 x 3 = 60; hence it provides an illustration of the fact that the same mathematical statement can arise from and represent many different situations. This fact has important consequences. Because the same mathematical statement can relate to more than one situation, results which have been obtained in solving a problem arising from one situation can often be seen to apply to a different situation. Thus this characteristic of Mathematics does show its importance in the study of science and Technology as mentioned by both the Enquiry committee and the programme Project 2061 (AAAS). History of Mathematics By looking at the history of Mathematics; it has been further proven how the development of mathematics had impact on development of Science and Technology. The 17th century saw an unprecedented explosion of mathematical and scientific ideas across Europe. Galileo, an Italian, observed the moons of Jupiter in orbit about that planet, using a telescope based on a toy imported from Holland. Tycho Brahe, a Dane, had gathered an enormous quantity of mathematical data describing the positions of the planets in the sky. His student, Johannes Kepler, a German, began to work with this data. In part because he wanted to help Kepler in his calculations, John Napier, in Scotland, was the first to investigate natural logarithms. Kepler succeeded in formulating mathematical laws of planetary motion. This explains the relationship between mathematics and science or another word, how knowledge of mathematics has been used to develop science over the years. The 19th century saw the beginning of a great deal of abstract algebra. Hermann Grassmann in Germany gave a first version of vector spaces, the British mathematician George Boole devised an algebra that soon evolved into what is now called Boolean algebra, in which the only numbers were 0 and 1 and in which, famously, 1  +  1  =  1. Boolean algebra is the starting point of mathematical logic and has important applications in computer science. Abel and Galoiss investigations into the solutions of various polynomial equations laid the groundwork for further developments of group theory, and the associated fields of abstract algebra. In the 20th century physicists and other scientists have seen group theory as the ideal way to study symmetry. The 20th century saw mathematics become a major profession. Every year, thousands of new Ph.D.s in mathematics was awarded, and jobs are available in both teaching and industry. Therefore, from the 20th Century is where importance has been given to teaching of mathematics. National Curriculum of Mathematics This further explains how the national curriculum for Mathematics has been formed in Britain. Lets look at the various views of Mathematics usage in Industry before the Enquiry Committee was set up; From 1973 to 1976 there were a large volume of complaints which seemed to be coming from employers about lack of mathematical competence on the part of some school leavers; In his speech made at Ruskin College, Oxford in October 1976, Mr James Callaghan, at that time Prime Minister, said: I am concerned on my journeys to find complaints from industry that new recruits from the schools sometimes do not have the basic tools to do the job that is required. There is concern about the standards of numeracy of school leavers. Is there not a case for a professional review of the mathematics needed by industry at different levels? To what extent are these deficiencies the result of insufficient coordination between schools and industry? Indeed how much of the criticism about basic skills and attitudes is due to industrys own shortcomings rather than to the educational system? (The Cockcroft Report (1982) In written evidence to the Parliamentary Expenditure Committee, the Confederation of British Industry (CBI) stated: Employers are becoming increasingly concerned that many school leavers, particularly those leaving at the statutory age have not acquired a minimum acceptable standard in the fundamental skills involved in reading, writing, arithmetic and communication. This shows up in the results of nearly every educational enquiry made amongst the CBI membership, and is backed up by continuing evidence from training officers in industry and further education lecturers that young people at 16+ cannot pass simple tests in mathematics and require remedial tuition before training and further education courses can be started. (The Cockcroft Report (1982) In oral evidence to the Expenditure Committee a CBI representative stated: Mathematics, I think or arithmetic, which is really the primary concern rather than mathematics themselves is the one area which is really brought up every time as a problem. It seems that industrys needs are greater in this respect than almost any other. This is the way, certainly, in which shortfall in the education of children makes itself most manifest immediately to an employer. (The Cockcroft Report (1982) Written evidence to the Expenditure Committee from the Engineering Industry Training Board (EITB) stated: The Engineering Industry Training Board, over the last two years, received from its industry increasing criticism, with supporting evidence, of the level of attainment, particularly in arithmetical skills, of school leavers offering themselves for craft and technician training In the view of the Engineering Industry Training Board the industry needs a higher level of attainment in basic mathematics among recruits than it is now getting and believes that, with closer cooperation between school and industry, children can while still at school be motivated to achieve this Mathematics is, however, not simply a question of basic manipulative skills. An understanding of the concepts is also needed and these are better taught by innovative methods, which also appear to enhance the ability to acquire planning and diagnostic skills, of great importance to craft and technician employees. The Cockcroft Report (1982) These are the examples of complaints received and the main reason for the enquiry committee to set up in 1978 to investigate complaints about low levels of numeracy among young entrants to employment and the need for improved liaison between schools and industry. Hence we could deduce that due the mathematical knowledge demand in the work force has brought mathematics an important place in the national curriculum to promote numeracy skills among the young people. Programme of Study (POS) The national curriculum through the Mathematics Programme of Study (POS) aims to develop; Successful learners where pupils should be numerate, creative and able to tackle problems with more than one approach and to solve open-ended problems. Confident Individuals Pupils are given the opportunity to express their ideas using strategies that they are familiar and secure with. Responsible citizens the emphasis on analyzing and justifying conclusions in mathematical situations helps prepare pupils for taking critical and analytical approaches to real-life situations. The framework has set out a number of key concepts that pupils need to know in order to deepen and broaden their knowledge, skills and understanding of Mathematics; Competence should be able to apply a range of mathematical techniques to assess risk, problem solving and decision making Creativity Able to combine understanding, experiences, imagination and reasoning to construct new knowledge and usage of existing mathematical knowledge to create solutions Application and Implication of Mathematics Able to understand that mathematics is used as a tool in a wide range of contexts, such as for Financial issues, Engineering, computer security and so on Critical Understanding Recognizing the limitations and scope of a model or representation. For example, mathematical skills are required to compare different methods of borrowing and paying back of money but the final decision may rely on other factors like comparing the merits of using a credit card that might offer the lowest overall costs. The framework has a set of key processes for both Key Stage 3 and 4 that are essential skills that pupils need to learn to make progress within the Subject. Representing Identify the mathematical aspects of a situation or problem, able to choose between representations to simplify a situation or problem in order to represent it mathematically, using appropriate variables, symbols, diagrams and models to select mathematical information, methods and tools to use. Analysing Use mathematical reasoning, pupils should be able to: make connections within mathematics use knowledge of related problems visualise and work with dynamic images identify and classify patterns; make and begin to justify conjectures and generalisations, considering special cases and counter-examples; explore the effects of varying values and look for invariance and covariance; take account of feedback and learn from mistakes; work logically towards results and solutions, recognising the impact of constraints and assumptions; appreciate that there are a number of different techniques that can be used to analyse a situation; reason inductively and deduce. Use appropriate mathematical procedures Pupils should be able to: make accurate mathematical diagrams, graphs and constructions on paper and on screen; calculate accurately, selecting mental methods or calculating devices  as appropriate ; manipulate numbers, algebraic expressions and equations and apply routine algorithms; use accurate notation, including correct syntax when using ICT; record methods, solutions and conclusions; estimate, approximate and check working. Interpreting and evaluating Pupils should be able to: form convincing arguments based on findings and make general statements; consider the assumptions made and the appropriateness and accuracy of results and conclusions; be aware of the strength of empirical evidence and appreciate the difference between evidence and proof ; look at data to find patterns and exceptions; relate findings to the original context, identifying whether they support or refute conjectures; engage with someone elses mathematical reasoning in the context of a problem or particular situation; consider the effectiveness of alternative strategies. Communicating and reflecting Pupils should be able to: communicate findings effectively; engage in mathematical discussion of results; consider the elegance and efficiency of alternative solutions; look for equivalence in relation to both the different approaches to the problem and different problems with similar structures; make connections between the current situation and outcomes, and situations and outcomes they have already encountered. The framework sets out an outline for teachers to follow in teaching the key concepts and key processes. The range and content for both Key stages are as follow: Key Stage 3: Number and algebra rational numbers, their properties and their different representations rules of arithmetic applied to calculations and manipulations with rational numbers applications of ratio and proportion accuracy and rounding algebra as generalised arithmetic linear equations, formulae, expressions and identities analytical, graphical and numerical methods for solving equations polynomial graphs, sequences and functions Geometry and measures properties of 2D and 3D shapes constructions, loci and bearings Pythagoras theorem transformations similarity, including the use of scale points, lines and shapes in 2D coordinate systems units, compound measures and conversions perimeters, areas, surface areas and volumes Statistics the handling data cycle presentation and analysis of grouped and ungrouped data, including time series and lines of best fit measures of central tendency and spread experimental and theoretical probabilities, including those based on equally likely outcomes.Rules of arithmetic: This includes knowledge of operations and inverse operations and how calculators use precedence. Pupils should understand that not all calculators use algebraic logic and may give different answers for calculations such as 1 + 2 X 3. Calculations and manipulations with rational numbers: This includes using mental and written methods to make sense of everyday situations such as temperature, altitude, financial statements and transactions. Ratio and proportion: This includes percentages and applying concepts of ratio and proportion to contexts such as value for money, scales, plans and maps, cooking and statistical information (eg 9 out of 10 people prefer). Accuracy and rounding: This is particularly important when using calculators and computers. Linear equations: This includes setting up equations, including inequalities and simultaneous equations. Pupils should be able to recognise equations with no solutions or an infinite number of solutions. Polynomial graphs: This includes gradient properties of parallel and perpendicular lines. Sequences and functions: This includes a range of sequences and functions based on simple rules and relationships. 2D and 3D shapes: These include circles and shapes made from cuboids. Constructions, loci and bearings: This includes constructing mathematical figures using both straight edge and compasses, and ICT. Scale: This includes making sense of plans, diagrams and construction kits. Compound measures: This includes making sense of information involving compound measures, for example fuel consumption, speed and acceleration. Surface areas and volumes: This includes 3D shapes based on prisms. The handling data cycle: This is closely linked to the mathematical key processes and consists of: specifying the problem and planning (representing) collecting data (representing and analysing) processing and presenting the data (analysing) interpreting and discussing the results (interpreting and evaluating). Presentation and analysis: This includes the use of ICT. Spread: For example, the range and inter-quartile range. Probabilities: This includes applying ideas of probability and risk to gambling, safety issues, and simulations using ICT to represent a probability experiment, such as rolling two dice and adding the scores. Key Stage 4 Number and algebra real numbers, their properties and their different representations rules of arithmetic applied to calculations and manipulations with real numbers, including standard index form and surds proportional reasoning, direct and inverse proportion, proportional change and exponential growth upper and lower bounds linear, quadratic and other expressions and equations graphs of exponential and trigonometric functions transformation of functions graphs of simple loci Geometry and measures properties and mensuration of 2D and 3D shapes circle theorems trigonometrical relationships properties and combinations of transformations 3D coordinate systems vectors in two dimensions conversions between measures and compound measures Statistics the handling data cycle presentation and analysis of large sets of grouped and ungrouped data, including box plots and histograms, lines of best fit and their interpretation measures of central tendency and spread Experimental and theoretical probabilities of single and combined events. Functional Skills in Mathematics The revised mathematics programme of study has given importance in embedding Functional Maths into teaching. Functional Mathematics requires learners to be able to use mathematics in ways where it make them effective and involve as citizens, able to operate confidently in life and to work in a wider range of contexts. The framework has divided the functional skill into two levels, where level 1 is linked to key stage 3 and level 2 to key stage 4. (Please refer to Appendix 1) The key concept of competence emphasises the need for students to be able to adapt and apply their understanding in a widening range of contexts within the classroom and beyond. This is also at the heart of functional skills. In this way functional skills are much more than a set of technical competencies in mathematics; students have to use mathematics to tackle tasks and problems. All teaching needs to be designed in a way that contributes to the development of functional skills. When planning opportunities for students to develop and understand functional skills you should consider whether you have: provided opportunities for different skills you are focusing on in representing, analysing and interpreting to be developed in combination ensured that students understand that they are learning skills that they will use and apply in a variety of contexts given students the chance to select the skills and tools (including ICT) they need for a particular task provided opportunities for students to apply these skills for real purposes and contexts beyond the classroom. For example, a year 10 project asked students to recommend to school managers a method for electing representatives for the school council. Students explored methods used in politics, including first past the post and different methods of proportional representation. They collected data about different voting methods and carried out simulations, which enabled them to produce a clear recommendation with justification. This project has the potential to be developed in conjunction with ICT, English and citizenship colleagues as it addresses wider curricular issues and also offers opportunities to develop functional skills in ICT and English as well as mathematics. The following are case studies on Functional skills taken from the National Curriculum website (http://curriculum.qcda.gov.uk); Wellacre Technology and Vocational College Objective: To help learners understand the relevance of mathematics in real life Year 9 science project and a Year 7 design and technology project. Both required pupils to solve real-world product design problems; In the year 9 science project, skiing was used as a context for developing learners understanding of pressure, mass, surface area and speed. Pupils had to work out how wide skis would need to be for individual pupils to ensure that their skis did not sink into the snow. This required pupils to rearrange formulae and calculate the surface area of their feet and pressure. For the year 7 design and technology project, pupils were given a budget and challenged to raise as much money as they could for  their partner school in Newcastle, South Africa. Pupils considered a range of products before settling on key fobs. Maximising the amount of profit was the main design criterion and pupils were encouraged to use tessellation to ensure their designs minimised waste. As part of the project they also use formulae to calculate break-even points, profit and loss. In both projects, working with real figures proved both an incentive and a challenge pupils were not able to fall back on a set of answers in a textbook. This generated discussion as pupils collaborated to check their calculations. The nature of the tasks also encouraged learners to think independently and creatively to solve problems. Opened ended mathematical Enquiries- Lancaster Girls Grammar School Objective: to develop pupils functional mathematics and problem-solving skills Introducing open-ended projects that required pupils to use mathematics to solve real-life problems Mobiles and Mathematics in year 8 and Music and Mathematics in year 10. Both projects were based around open-ended problems without a right answer. Pupils were given the broad topic areas and told to devise their own projects. Pupils were given two months to prepare, which encouraged them to make their own choices about how they would work and what they would explore. The range of investigations devised by pupils was broad. Year 8 pupils explored different tariffs, compared costs between pay as you go contracts and investigated different usage patterns of people over and under 30. In year 10 pupils were encouraged to make links between mathematics and music. Some considered what kinds of functions might be used to model sound waves. Others explored the connections between the Fibonacci sequence and the layout of a keyboard. In both projects, pupils defined their own problem, decided on the data to collect and how to collect it, gathered information from a number of sources, including their parents or other pupils, considered how to analyse their data, used and applied mathematics skills and drew conclusions. At the end of the projects, they presented their findings and evaluated how successful they had been. Staff and pupils embraced the new way of working. The head of department acknowledged that it was a considerable risk to introduce this way of teaching but it paid off. Initially, staffs were concerned about setting problems when they didnt know the answers but once the work was underway they enjoyed a different way of teaching. The projects offered opportunities to stretch pupils and encourage them to make connections between different parts of their learning. Many of the pupils were nervous about working on a project when they didnt have an indication of what type of project to make. However they soon began to enjoy the freedom of the approach. At the end of the project, a year 8 pupil reflected: This was a break from everyday work and we can use our imagination as we arent being spoon fed the information. We could decide what we wanted to do I have learnt to make decisions. There were different ways to present information on this project and this made it even more exciting. I could be creative with my choices as I didnt have to do exactly what the teacher said. ASSESSING PUPILS PROGRESS IN MATHEMATICS (APP) Finally, in my literature review, I am going to look into embedding APP guidance into teaching and learning of mathematics. Assessing Pupils Progress (APP) is a structured approach to periodic assessment, enabling teachers to: track pupils progress over a key stage or longer; use diagnostic information about pupils strengths and weaknesses to improve teaching and learning Using APP materials, teachers can make more consistent level-related judgements in National Curriculum The APP focuses on how as mathematics teacher can use AFL (Assessment for learning) strategy in lessons in order to generate evidence pupils learning. The diagram shown below tells how the APP cycle works. Review a range of evidence for periodic assessment (APP) Collect and feedback to pupils evidence of their progress during day to day teaching and learning Plan for progression from learning objectives (Secondary Framework and Planning toolkit) Make level related assessment using APP Criteria Adjust Planning, Teaching and learning by referring to Secondary Framework The focused assessment materials are on the APP assessment criteria and organised in National Curriculum levels. There is a set for each level from 4 to 8. The materials include examples of what pupils should know and able to do and some probing questions for teachers to initiate dialogue as to assist in their assessment judgement. The following is an example from the level 6 focused assessment materials. Add and subtract fractions by writing them with a common denominator, calculate fractions of quantities (fraction answers); multiply and divide an integer by a fraction Examples of what pupils should know and be able to do Probing questions Add and subtract more complex fractions such as 11 Ã¢â‚¬Å¾18 + 7 Ã¢â‚¬Å¾24, including mixed fractions. Solve problems involving fractions, e.g.: In a survey of 24 pupils, 1 Ã¢â‚¬Å¾3 liked football best, 1 Ã¢â‚¬Å¾4 liked basketball, 3 Ã¢â‚¬Å¾8 liked athletics and the rest liked swimming. How many liked swimming? Why are equivalent fractions important when adding or subtracting fractions? What strategies do you use to find a common denominator when adding or subtracting fractions? Is there only one possible common denominator? What happens if you use a different common denominator? Give pupils some examples of adding and subtracting of fractions with common mistakes in them. Ask them to talk you through the mistakes and how they would correct them. How would you justify that 4 à · 1 Ã¢â‚¬Å¾5 = 20? How would you use this to work out 4 à · 2 Ã¢â‚¬Å¾5? Do you expect the answer to be greater or less than 20? Why? Probing questions are an important tool in a lesson as it could be used to confirm pupils understanding in a particular topic or their misconceptions. Before we talked about it I always thought if the shape had three numbers you just times them. But now I know that you split the shape into rectangles and I can find the area of a rectangle. Its so easy. I understand it fully now. (Source: APP: Secondary Mathematics Guidance) That was a comment from a pupil after dialogue about understanding and using the formula for the area of a rectangle using the probing questions. KANGAROO MATHS http://www.kangaroomaths.com/index.html Kangaroo Maths is the home page of Bring on the Maths where interactive activities for teachers can be purchased from Key stage 2 to A level. It has an APP page that provides supporting materials for teachers from Key stage 1 to Key stage 3. The assessment policy from the website (Appendix 5) has been rewritten to reflect the APP and to help with the on going development of APP, it has an evaluation tool (Appendix 6) where it allows teachers to self evaluate themselves in focusing, developing and establishing APP criteria with regards to pupils engagement, lesson planning and evidence gathering. Further more, to understand the assessment criteria on the A3 grid, Kangaroo maths has developed the levelopaedias that provide exemplifications and probing questions for each of the assessment criteria. DISCUSSION/FINDINGS: To add on to my findings, I am going to look into the topic Algebra and analyse how it has developed across the levels using the APP criteria (Appendix 7a) and Kangaroo maths Level Ladders( Appendix 7b). Then, based on level 5 work on Algebra, I am going to design 3 series of lesson plans with the guidance of the level ladders. The word ALGEBRA seems to be a put off to most students when unknown numbers or using formulas to real life context. It is a topic that requires accumulative understanding building on from level 2 onwards as shown below (taken from APP guidelines); Algebra Level 5 Construct, express in symbolic form and use simple formulae involving one or two operations. Level 4 Begin to use simple formulae expressed in words Level 3 Recognise a wider range of sequences Begin to understand