The
strategy of working backwards 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. 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. This strategy is 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. The underlying purpose of this kind of assessment is for
the teacher to understand/gauge student learning in a step wise
manner and then modify the lesson/activity accordingly. It becomes
convenient for the teacher to understand that what the pain areas are
for the students while they work backwards to arrive at the solution.
Finally, it is a systematic approach and can be applied to any
problem of similar type or even more complicated problems. 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.
Since
this kind of assessment is formative in nature, so it is best when
given as an in-class situation so that the instructor can provide
real time feedback, monitor student performance and also modify the
lesson content, if need be. However, incase of paucity of time and
more number of students, it can also be given as homework for the
students to complete and submit their solutions. Giving it as an
individual assignment is preferred because in case some students have
used a different method to solve that problem then the instructor can
discuss and share the alternative methods with the students, which
shall result in increased value-addition and learning.
This
is also a kind of self-assessment wherein once the student has
reached the final answer then he/she can check if they have followed
the given instructions correctly to arrive at an answer. This means
that one can check one’s answer by working forwards through the
problem to see if we reached the correct end point. For example given
the following scenario:
The
present age of a father is 3 years more than three times the age of
the son. Three years hence father’s age will be 10 years more than
twice the age of his son. Find the present age of the father.
Working
with the given details we can say that father’s present age is 33
years and son is 10 years old. If the student has correctly followed
the given information then the students can easily perform their
self-assessment by plugging in the numbers to see if they satisfy the
intermediary equations.
Benefits-
- It leads to discovery based learning
- It is a step wise problem solving technique. Therfore, student’s thinking can be tracked on each step.
- Representing real life problem to the students in an interesting way.
- It encourages students to read the problem carefully a number of times.
- Students should decide how they will solve the problem by thinking about the different strategies that could be used.
- Students should ask themselves ‘what if ’ to link this problem to another.This will take their
- exploration to a deeper level and encourage their use of logical thought processes.
- It gives an opportunity to teachers to show their creativity.
Limitations-
- Sometimes it makes easier problems to complex problems.
How should this kind of question be graded?In working backward problems, you know the end result but you need to find outsomething that happened earlier..In order to do this, the student should be following these steps:1)explore: jot down all the data given in the problem and try to identify the relationship between the variables.2)Plan: Since the problem gives you the end result and asks for something that happenedearlier, start with the end result and work backward. Undo each step.try to break it up into simpler units and then try to link them.3)Solve: depending upon the relationship between the variables, the student should try to calculate/solve/arrive at the answer to the question asked.4)Examine: Once the student arrives at an answer,she should cross check her answer so that she gets back the data given in the problem and finally arrives at the end result stated.This will also confirm that her answer is correct.The teacher should check if the student is following the above steps in answering his problem.The student should work backards,use logical reasoning,make the problem simpler,brainstorm…
Hey...This seems useful.....I was getting stuck at understanding the 2nd planning step...
ReplyDeleteis it that this strategy will work(only) for the problems where we have the end answer in hand?....
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:
ReplyDelete1. 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.
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.
Such Questions can also easily be converted 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:
a) 7:2
b) 5:6
c) 7:3
d) 91:39
e) c but not d
f) 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?