Mathematical problem solving related to counting and daily transactions of commerce has been present from the earliest days of human experience.
Geometry was also widely used in land measurement .
Mathematical problem solving is a process that involves a set of factors and tasks to achieve a defined goal.
It depends on many skills and factors which therefore makes it challenging both to learn and to teach.
Students learning is limited if only routine problems are solved.
The problems used to create genuine learning opportunities should be of the challenging type and not only those similar to ones already solved in the past.Mathematics educators have accepted the idea that that the development of problem solving ability deserves special attention [2 ] and that one of the most important components in any mathematics curriculum or program is genuine mathematical problem solving .If well facilitated, mathematical problem solving may help students Most of the mathematics textbooks suggest few types of problems as examples with detailed solutions and then suggest similar problems as exercises.First, the student is taught a 7-step process for attacking a math word problem (cognitive strategy).Second, the instructor trains the student to use a three-part self-coaching routine for each of the seven problem-solving steps (metacognitive strategy). I will reread the problem if I don’t understand it.” Ask: “Now that I have read the problem, do I fully understand it” Check: “I understand the problem and will move forward.”Say: “I will highlight key words and phrases that relate to the problem question.” “I will restate the problem in my own words.” Ask: “Did I highlight the most important words or phrases in the problem” Check: “I found the key words or phrases that will help to solve the problem.”Say: “I will compute the answer to the problem.” Ask: “Does my answer sound right” “Is my answer close to my estimate” Check: “I carried out all of the operations in the correct order to solve this problem.”Students will benefit from close teacher support when learning to combine the 7-step cognitive strategy to attack math word problems with the iterative 3-step metacognitive Say-Ask-Check sequence.To balance the equation, they can then subtract 7 from 89.Suppose students must find the difference of 567 and 153.If the instructors understanding of the process is limited, difficulties in teaching mathematical problem solving, will arise.Hence the great need to understand these factors and skills if we want to help our students acquire this important process.Problem solving can also be used, as a teaching method, for a deeper understanding of concepts.Successful mathematical problem solving depends upon many factors and skills with different characteristics.