Working Backwwards

Assessment format:

The strategy of working backwards essentially means that the student starts with the end results and reverses the steps, in order to figure out the answer to the problem. Such a strategy is used to solve problems that include a number of linked factors or events, where some of the information has not been provided, usually at the beginning of the problem. Such a strategy is also extremely useful in dealing with a situation or a sequence of events. The events occur one after the other and each stage, or piece of information, is affected by what comes next. Students begin at the end, with the final action, and work through the process in reverse order to establish what happened in the original situation.

To solve these problems it is necessary to start working methodically backwards, in a logical step-by-step way, to fill in the missing information. Generally, two types of problems can be solved using this strategy:

1. When the goal is singular and there are a variety of alternative routes to take.  In this situation, the strategy of working backwards allows us to ascertain which of the alternative routes was optimal.

A Simple example of the above: An example of this is when you are trying to figure out the best route to take to get from your house to a store.  You would first look at what neighborhood the store is in and trace the optimal route backwards on a map to your home.

2. When end results are given or known in the problem and you're asked for the initial conditions.

Example: A group of 28 students went to the science museum to see the fossils

exhibit. The museum collected Rs.1000 from the students. How much was the

admission for each student?.

The underlying purpose of this kind of assessment is for the instructor to understand student learning in a step wise manner and then modify the lesson/activity accordingly. The purpose of such an assessment is that students can apply logical reasoning and sequencing to events to solve a problem. The only caution that the instructor should take is that the problem should be properly worded and there should not be an element of ambiguity.

What is an appropriate situation (eg in-class/HW/exam etc) to assign this format of question?

This type of question can be given both in class as well as for homework. Both situations have their respective advantages..if it is given as a classroom task then the students can get realtime feedback from the instructor regarding their progress but time might be a constraint in this setting. Whereas if it is given as a homework activity then, the student gets enough time to logically determine the steps that he would be following. But, in both the cases, this should be an individual activity each student might follow a different approach to the problem and the instructor will get a good idea of the problem solving abilities of each child.

Converting this into a multiple choice question:

In such questions, there can be multiple correct answers..and hence the student is given the flexibility to present his/her answer.

Example: Ratio and Proportions:

The age of the father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The following can be the ratio of their ages:

1. 7:2
2. 5:6
3. 7:3
4. 91:39
5. c but not d
6. Both c and d

In this question we know that both (c) and (d) are the correct answers. Thus, in this way this question can be converted to a multiple choice question.

Another example:

Mom gave me 50 Perks and 125 Cadburys and asked me to make as many jars of candies as were possible with each jar containing 5 Perks and 13 Cadburys. How many jars could I make up? How many Perks and how many Cadburys would be left over?