#### Тема: A critical look at - ASCD: Professional Learning.

Abc General Certificate of Secondary Education Additional Mathematics 9306 Pilot Specification 2008 PROBLEM-SOLVING QUESTIONS version 1.0

AQA is hard.check thier website it should be there or a revision guide @robertMa i need help with maths for my exam..

Problem solving method can be an effective method for teaching mathematics in the hands of an able and. Module 9: Problem Solving Method;.

Order essay here problem solving method of teaching mathematics

Abc General Certificate of Secondary Education Additional Mathematics 9306 Pilot Specification 2008 PROBLEM-SOLVING QUESTIONS version 1.0

Explicit modeling involves well-prepared teachers employing a variety of instructional techniques to illuminate the key attributes of any given mathematics concept/skill. In a sense, you serve as a bridge of learning for your student, an accessible bridge between the student and the particular mathematics concept/skill they are learning:

The level of teacher support you provide your students depends on how much of a learning bridge they need. In particular, students with learning problems need a well-established learning bridge (teacher model). They learn most effectively when their teacher provides clear and multi-sensory models of a mathematics concept/skill during math instruction.

The problem-solving process can be described as a journey from meeting a problem for the first time to finding a solution, communicating it and evaluating the route. There are many models of the problem-solving process but they all have a similar structure. One model is given below. Although implying a linear process from comprehension through to evaluation, the model is more of a flow backward and forward, revisiting and revising on the problem-solving journey.

Having understood what the problem is about and established what needs finding, this stage is about planning a pathway to the solution. It is within this process that you might encourage pupils to think about whether they have seen something similar before and what strategies they adopted then. This will help them to identify appropriate methods and tools. Particular knowledge and skills gaps that need addressing may become evident at this stage.

An important goal of education is helping students learn how to think more productively while solving problems, by combining creative thinking (to generate ideas) and critical thinking (to evaluate ideas). Both modes of thinking are essential for a well-rounded productive thinker, according to scholars in both fields:

Richard Paul (a prominent advocate of CRITICAL THINKING ) says, Alternative solutions are often not given, they must be generated or thought-up. Critical thinkers must be creative thinkers as well, generating possible solutions in order to find the best one. Very often a problem persists, not because we can't tell which available solution is best, but because the best solution has not yet been made available no one has thought of it yet. { source }

The importance of mathematics The everyday use of arithmetic and the display of information by means of graphs, are an everyday commonplace. These are the elementary aspects of mathematics. Advanced mathematics is widely used, but often in an unseen and unadvertised way. The mathematics of error-correcting codes is applied to CD players and to computers. The stunning pictures of far away planets sent by Voyager II could not have had their crispness and quality without such mathematics. Voyager s journey to the planets could not have been calculated without the mathematics of differential equations. Whenever it is said that advances are made with supercomputers, there has to be a mathematical theory which instructs the computer what is to be done, so allowing it to apply its capacity for speed and accuracy. The development of computers was initiated in this country by mathematicians and logicians, who continue to make important contributions to the theory of computer science. The next generation of software requires the latest methods from what is called category theory, a theory of mathematical structures which has given new perspectives on the foundations of mathematics and on logic. The physical sciences (chemistry, physics, oceanography, astronomy) require mathematics for the development of their theories. In ecology, mathematics is used when studying the laws of population change. Statistics provides the theory and methodology for the analysis of wide varieties of data. Statistics is also essential in medicine, for analysing data on the causes of illness and on the utility of new drugs.. Travel by aeroplane would not be possible without the mathematics of airflow and of control systems. Body scanners are the expression of subtle mathematics, discovered in the 19th century, which makes it possible to construct an image of the inside of an object from information on a number of single X-ray views of it. Thus mathematics is often involved in matters of life and death. These applications have often developed from the study of general ideas for their own sake: numbers, symmetry, area and volume, rate of change, shape, dimension, randomness and many others. Mathematics makes an especial contribution to the study of these ideas, namely the methods of precise definitions; careful and rigorous argument; representation of ideas by many methods, including symbols and formulae, pictures and graphics; means of calculation; and the obtaining of precise solutions to clearly stated problems, or clear statements of the limits of knowledge. http://www.popmath.org.uk/centre/pagescpm/imahob95.html