# Paper Feedback
[A Context Sensitive Model for Concept Understanding (Proceedings of ITALLC, 1998)](http://iasl.iis.sinica.edu.tw/webpdf/Paper-1998-A_Context_Sensitive_Model_for_Concept_.pdf)
### Section 6. Application to the Elementary Mathematics Agent System
Given an elementary school mathematics word problem, we designed an Elementary Mathematics Agent (EMMA) system [5] that can automatically solve the problem, explain the solution procedure and the answer in natural language. We found that the most difficult part about elementary mathematics for kids is that, within the question, there are a lot of omissions or implications (more formally, ellipsis and anaphora) that maybe quite stylish for adults but confusing for kids. Thus, EMMA tries to discover and fill in those omissions and implications, derive the corresponding mathematical formulas and obtain an answer.

One important component of EMMA is that it needs to acquire enough common sense knowledge to deal with ellipsis and anaphora in the given problem. To achieve that we need to:
1. create event representation for natural language sentences. This part is related to natural language understanding.
2. generate event association such as **expected events(?)** and `causal events` that can be used for inference. This would provide the candidate choices to many queries.

Another feature of the EMMA is that its understanding mechanism is not restricted to natural language understanding. For specific types of mathematics problems we need to create a script in which several current events and expected events are listed, the relationships among them are then inspected to make inference. Examples of such problems are:
1. ***The clock problems***
when do the minute and second of a clock overlap with each other, say, after 9 a.m.?
2. ***The cage problems***
how many chickens and rabbits are there in a cage if we know that there are 10 heads and 24 legs (note that the use of variables is disallowed in elementary school math.)?

Furthermore, instead of presenting the correct solution procedure to the student
directly we can change EMMA to a system that asks the student to take step-by-step
actions. At each step the student is asked to select an answer in a MCQ(multi-choice query), where some of the candidate answers will indicate misconceptions on the part of the student. Thus, by taking a series of test questions, our modified EMMA can find out the potential problem with the student and provide needed help automatically. Naturally, this is a
task requiring the collaboration with researchers in education methodology. The above procedures are not much different from that used in an MT translation. What we did in EMMA is to translate a word problem into mathematical formulas that can be readily used to solve the problem. It is quite natural for our **MCQ representation(?)** to define different levels of mathematical understanding through appropriate **query set selection(?)**.