Principles Of Teaching And Learning In Teaching Math Essay

Students tick math by means of the experiences that t on the whole(prenominal)ers provide. T to each oneers moldiness(prenominal)(prenominal) see and visualize deeply the maths they ar teach and take c be and be committed to their students as learners of math and as humanity beings. at that place is no one right office to teach. Nevertheless, much is get laidn almost effective math inform. Selecting and prevail suit qualified curricular materials, utilize eliminate instructional tools and techniques to acquit reading, and pursuing continuous self-improvement be actions life-threatening teachers take every day. The teacher is responsible for creating an intellectual environment in the classroom where serious necessitatement in numeric view is the norm. good teaching requires deciding what aspects of a t occupy to highlight, how to organize and orchestrate the treat of students, what questions to ask students having alter take aims of expertise, and h ow to support students without taking over the process of sentiment for them. Effective teaching requires continuing efforts to learn and improve.Teachers assume to increase their familiarity about maths and pedagogy, learn from their students and colleagues, and engage in professional discipline and self- jobion. Collaborating with new(prenominal)spairing an experienced teacher with a new teacher or forming a community of teachersto observe, give way, and talk over teaching and students thought process is a powerful, only neglected, form of professional phylogenesis. Teachers need ample opportunities to engage in this winsome of continual learning. The working lives of teachers must be organize to wholeow and support diametrical models of professional development that benefit them and their students. mathPrinciples and behaveWhat coffin nail learning in maths enable children and teen stack to obtain? math is important in our everyday life, each(prenominal)owing us to run genius of the world around us and to manage our lives. Using mathematics enables us to model real-life situations and ground connections and informed predictions. It equips us with the skills we need to interpret and kindlevas information,simplify and solve problems, assess risk and make informed decisions.Mathematics plays an important role in aras such as experience 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 irritate to the wider curriculum and the opportunity to pursue further studies and interests.Beca manipulation mathematics is rich and stimulating, it engages and fascinates learners of tout ensemble ages, interests and abilities. Learning mathematics develops logical reasoning, analysis, problem-solving skills, creativity and the cogency to think in abstract shipway. It expenditures a universal language of arrives and symbols which wholeows us to state ideas in a concise, unam liberaluous and rigorous way.To face the contends of the 21st century, each young person needs to have self-confidence in using numerical skills, and Scotland needs both specialist mathematicians and a highly numerate population.Building the Curriculum 1Mathematics equips us with many of the skills mandatory for life, learning and work. Understanding the piece that mathematics plays in almost all aspects of life is crucial. This reinforces the need for mathematics to play an integral p machination in lifelong learning and be appreciated for the richness it brings.How is the mathematics poser structured?Within the mathematics framework, some statements of experiences and outcomes atomic number 18 also set as statements of experiences and outcomes in numeracy. These form an important part of the mathematics tuition of all children and young people as they include many of the quantitative and analytical skills r equired by each of us to function effectively and successfully in everyday life. All teachers with a responsibility for the development of mathematics give be familiar with the role of numeracy in spite of appearance mathematics and with the means by which numeracy is unquestionable across the range of learningexperiences. The numeracy subset of the mathematics experiences and outcomes is also published separately further information whoremaster be found in the numeracy principles and practice paper.The mathematics experiences and outcomes ar structured deep down three main organisers, each of which contains a number of subdivisionsNumber, money and strideEstimation and roundingNumber and number processesMultiples, factors and primesPowers and rootsFractions, decimal fractions and percentages bullionTimeMeasurementMathematics its impact on the world, past, present and approachingPatterns and relationshipsExpressions and equations.Shape, aspect and movementProperties of 2D shapes and 3D objectsAngle, symmetry and transformation.Information discourseData and analysisIdeas of chance and uncertainty.The mathematics framework as a whole includes a strong emphasis on the important part mathematics has played, and exit fall out to play, in the advancement of society, and the relevance it has for day-after-day life.A key feature of the mathematics framework is the development of algebraicalal idea from an first stage. Research shows that the earlier algebraic opinion is introduced, the deeper the mathematical arrest result beand the greater the confidence in using mathematics.Teachers will use the statements of experiences and outcomes in information handling to stress the adaptation of statistical information in the world around us and to emphasise the knowledge and skills required to take account of chance and uncertainty when do decisions.The level of achievement at the fourth level has been designed to near(a) to that associated with SCQF level 4.What argon 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 consternation of being wrong. They will enjoy exploring and wearing mathematical concepts to understand and solve problems, explaining their thinking and presenting their solutions to others in a conversion of ways. At all stages, an emphasis on collaborative learning will encourage children to reason logically and creatively through questionion of mathematical ideas and concepts.Through their use of effective call into question and discussion, teachers will use misconceptions and wrong answers as opportunities to improve and deepen childrens understanding of mathematical concepts.The experiences and outcomes encourage learning and teaching approaches that challenge and baffle children and young people and promote their enjoyment of mathematics. To achieve this, teachers will use a skilful mix of approaches, includingplanned 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 independentlyopportunities for discussion, communication and explanation of thinking exploitation mental elationusing relevant contexts and experiences, familiar to young people devising tie in across the curriculum to show how mathematical concepts argon applied in a wide range of contexts, such as those provided by science and social studies using technology in appropriate and effective waysbuilding on the principles of estimate is for Learning, ensuring that young people understand the map and relevance of what they are learning evolution problem-solving capabilities and critical thinking skills.Mathematics is at its most powerful whe n the knowledge and understanding that have been developed are use 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 divergent options what would happen if? is the fundamental question for teachers and learners to ask as mathematical thinking develops.How will we ensure keepion within and through levels?As children and young people develop concepts within mathematics, these will need continual reinforcement and revisiting in order to maintain boardion. Teachers can plan this development and progression through providing children and young people with more(prenominal) intriguing contexts in which to use their skills. When the experience or outcome spans both levels within a line of development, this will be all the more important.One case in point would be the third level outcome on discloseing information. The expectation is that young people will continue to use and re fine 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 peoples understanding.What are broad features of judgment in mathematics?(This section should be read alongside the advice for numeracy.)Assessment in mathematics will focus on children and young peoples 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 take the stand progress in their skills in interpreting and analysing informa tion, 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 parade their competence and confidence in applying mathematical concepts and skills. For exampleDo 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 previous ly? As they adopt problems in unfamiliar contexts, can they confidently identify which skills and concepts are relevant to the problem? Can they hence apply their skills accurately and then appraise 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? atomic number 18 they developing the capacity to engage with and complete tasks andassignments? 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 set example is provided by investigations into area and perimeter which can involve estimatio n, 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 snapper 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 fresh 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 harmonise 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 de veloped in all areas of the curriculum.The instruction PrincipleEffective 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 reckon in school. The improvement ofmathematics 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 dowry 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 flexibility 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 Americas proximo 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 knowledgeknowledge about the whole domain deep, pliable knowledge about curriculum goals and about the important ideas that are commutation to their grade level knowledge about the challenges students are likely to encounter in learning these ideas knowledge about how the ideas can be del ineate to teach them effectively and knowledge about how students 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 classroomall of which affect how well their students learn mathematicsshould be based on this knowledge. This kind of knowledge is beyond what most teachers experience in sample 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 number on a line isimportant for mathematics teachers (Ball and Bass forthcoming). Such understanding might be characterized as 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 associate to one another (Wilson, Shulman, and Richert 1987). They need to know the ideas with which students often have difficultness 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 bu ild on, this knowledge.Teachers have different styles and strategies for helping students learn particular mathematical ideas, and there is no one right way to teach. However, effective teachers recognize that the decisions they make shape students mathematical dispositions and can lay down 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 necessarily 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 flummox interest, and engage stud ents 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 thephysical 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, bulle tin boards, and posters, the classroom 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, score mathematical arguments and respond to others arguments, then creating an environment that fosters these kinds of activities is essential. In effective teaching, worthy 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 number 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 totally 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 practiceduring class and outside class, alone and with othersare crucial in the vision of school mathematics defined 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 affe cting 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. Theycan 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 heighten 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 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 depart and support professional develo pment that will benefit them and their students.