Over the last few weeks, I have been working on problems in tutorial classes and the techniques to follow in order to achieve full credit. One important point to note with problem solving (also known as extended response questions) is to first understand every bit of information given in the question along with what precisely is asked. Having strong comprehension skills helps in order to be successful in obtaining the right solutions to extended response questions. A useful approach to use when solving extended response questions is given below:
1.) Draw a diagram where possible to represent the information given. Remember: a picture tells us 1000 things.
2.) Label the key points of the diagram as per the question.
3.) Label the measurements and assign variables in the diagram that will help answer the question.
4.) Know what theorem or concept to apply and derive appropriate expression/equations. This will come if one has a strong understanding of the theorems and concepts.
5.) Express answer based on what the question has asked us to give it in (including no. of decimal places and units). Including units is very important where appropriate as students will have marks deducted if they fail to do so.
Some extended response questions may contain too much information to process along with several parts to be answered. In this case, it helps to break down the information provided into small bits. Assigning variables and equations where possible will help with lengthy information given. Re-reading the question several times is another useful approach as it helps us identify critical information that we did not spot the first time. Even putting some thoughts on what the question is asking us to do is a good starting point.
To conquer problem solving requires a lot of practice. Especially doing past exam papers with extended response questions will benefit students a lot. Out of tutorial class times, I prepare exercise sheets that contain extended response questions in order to get students to do it under test/exam conditions. Each of the monthly tests I run for a student contains an extended response section that they are to complete.The more one practices, the better. PRACTICE MAKES PERFECT!!!“MATHEMATICS MAY NOT TEACH HOW TO ADD LOVE OR MINUS HATE BUT GIVES ONE EVERY REASON TO BELIEVE THAT EVERY PROBLEM HAS A SOLUTION.”