Problem solving is the practice of working through the “facts” of a problem or situation to get a solution. Problem solving entails the systematic use of “operations” to measure thinking abilities and skills. Problem solving practices help children to develop cognitive skills.
Polya’s model offers four principles for solving different mathematical problems. The first principle is to “understand the problem”. At this stage, the learner thinks of the best “strategy” to find a solution. The second principle is “devising a conceptual plan”.
The stage helps learners to consider the best strategies to get a solution. The third stage is “carrying out the plan”. This stage entails using the selected plan or choosing a better strategy. The fourth principle is “looking back”. At this stage, the learner examines what he or she has done to obtain the “solution”.
Problem solving in mathematics is vital because it helps learners develop high-order thinking and analytical skills. The learners also become critical thinkers and address the problems encountered in life.
Learners use various strategies to solve mathematical problems. The first one is “model drawing”. The strategy involves the use of visual effects. For example, learners required to add 5 to 2 would draw 5 and 2 cars to get 7. The other strategy is “drawing a picture”.
A learner can draw pictures when adding numbers. For example, a child can draw three and two pens to get five. The third strategy is “making a systematic list”. Systematic “lists” can help learners memorize numerical numbers. For example, a child expected to write numbers 1 to 10 could make a systematic list of items from one to ten.
The fourth strategy is “working backwards” as explained in this example. Jimmy spent five dollars to remain with five dollars. How many dollars did he have in total? The child will work from $5 and add 5 to get $10.
Learner in different grades will use these strategies differently. The first strategy is “drawing a picture”. A second grade science learner can use the method to solve mathematical problems as follows: A carpenter makes four pieces from a wood. How many cuts does she make?
The learner will draw a piece of wood and divide it into four pieces. The child will get three “cuts”. A sixth grade learner can use the strategy as follows: In a party, there were three couples. Every person shook each one’s hand once. What was the total number of handshakes? The learner will draw letters to represent the couples and handshakes made.
The second strategy is “working backwards” as presented below. A child had saved some money. His father gave him 10 dollars. He spent 13 dollars to remain with 7 dollars. How much had he saved? From this problem, the learner will begin with 7 dollars. The next thing is to add 13 to get 20. The learner will then subtract the $10 obtained from the father to get 10 dollars.
A sixth grade learner can work backwards to solve the problem below. Agnes, Ann, and Angel had some coins. Agnes gave Ann 12 coins. Ann gave Angel 10 coins while Angel gave Agnes 4 coins. They all had 20 coins. What is the number of everyone’s coins at the beginning? The learner can work backwards from 20 coins to get the answer.
In conclusion, teachers should incorporate problem-solving activities into instruction because they help sharpen the learners’ skills and competencies. The methods can also make the learning process easier. The learners can use these strategies to achieve mastery and proficiency in mathematics problem solving.
These general heuristics for problem solving are important because they can help people become critical thinkers. Such activities can help learners develop the best interactional and decision-making skills. They also provide skills for dealing with challenges in life.