Problem Solving as a Process (steps) part 2

As a process, according to George Polya (1957), problem solving originally has 4 steps. The 1^st step is understanding the problem. In this step, students have to carefully read the problem, capable to point out the principal parts of the problem, the unknown, the data, and the condition. George Polya subdivided this step into two stages: 1) getting acquainted and 2) working for better understanding. The 2^nd step is devising a plan where students consider some possible actions or strategies such as drawing a graph, finding a pattern, or making a list. Furthermore, the next step is carrying out the plan in which students implement a particular plan to solve the problem, if necessary, create a new plan.

Finally, students reflect and look back at what they have done, what worked, and what didn't. This is also important for students since by looking back at the completed solution, by reconsidering and reexamining the result and the path that led to it, students could consolidate and develop their ability to solve problems. All these 4 processes should be seen as a dynamic, non-linear and flexible approach. By using these steps, students will deal more effectively and successfully with most types of mathematical problems.

The Antiquity of the Egyptian Mathematics

The History of Mathematics: The Antiquity of the Egyptian Mathematics 

The development of Egyptian civilizations began around 7000 BCE. Many buildings such as pyramids, sphinx, and the temple at Memphis are the proofs of the superiority of the Egyptians on 3100 BCE. These buildings also indicate that at least they knew mathematical concepts in practical. In fact, many evidences like hieratic papyrus and Rhind collections of the British museum indeed shows that the Egyptians knew arithmetic and geometry. This mathematical concepts are crafted in the font of hieratic, hieroglyph, or demotic on papyrus loaves, leather, or clay tablet. 

WHY GIRLS ARE LESS INTERESTED IN SCIENCE

In the recent years, there was a phenomena of declining students’ interest on science. In 1979, Whitfield (1980) conducted a research to analyze students’ favorite subjects. The result indicated that chemistry and physics became the two least preferred subject for 14-year old students. Supporting Whitfield’s findings, the analysis result of the data from the Department for Education of England and Welsh showed that the number of students enrolled in advanced levels science and mathematics only in 1993 had decreased 13% compared to their data at 1980 (Osborne et al, 2003). Furthermore, the UK examination Board and HMSO also claimed that the number of students examined in physics in 2000 were decreased almost 15000 students since 1990. All these findings showed that science is becoming less preferred by the students.

The Importance of Using Contexts in Learning Mathematics

In recent years, many mathematicians argued whether mathematics teaching and learning should begin with contexts or not. In 2007 in California, some people claimed that a mathematical approach that focused on number sense using contexts will be a detrimental to children (Sowder, 2007). Some researchers also showed that abstract examples were more advantageous for students (Kaminski, Sloutsky & Heckler, 2008; Kaminski & Sloutsky, 2012). They stated that concrete instantiations prone to distract students’ concentration in doing transfer task. This lead teachers begin to doubt the importance of involving contexts in teaching learning activity. The role of contexts in the classroom is questioned. How important contexts are in learning mathematics, this paper will discuss this questions.