Figure 1. Most students performed well throughout. |

Figure 2. Less successful than Figure 1. |

Figure 3. Performed well initially and then went astray. |

Both the "hand-tracking" and "mind-tracking" data are being studied using graph theory. In this article, we will show the analysis of the "mind-tracking" data first. The data were generated by students connecting 6-7 provided molecular concepts between a cause and an effect to compose an explanation. Some of the concepts are irrelevant and used as distractors. For example, increasing the number of molecules has nothing to do with the molecular mass.

Given the fact that there are 65 students and four causality maps, we need a way to quickly visualize student learning. Our solution is to construct graphs based on these data. It becomes immediately obvious that this visual analytics can provide extremely informative graphics that shows student learning on a statistical basis. The three images in this article show that: 1) Most students in Class E performed well throughout Graph 3; 2) Students are less successful in Class B in Graph 1; and 3) Students in Class D performed well in Graph 4 at the beginning and then went astray -- largely because this is a more difficult challenge that involves multiple reasoning paths. (The gray bands in the three images represent the correct reasoning chains in each case. The thickness of an edge represents the number of students who drew the link in the concept map.) These graphs can potentially show the weaknesses of the students at the scale of the whole class. I could not help thinking how useful this would be to the teacher if such informative feedback is provided to her.

**This graph-based analytics is NOT just visual -- It is also interactive**. You can examine all the student data we have collected at this page, programmed in Dart -- the latest Web programming language from Google. The page provides filters for you to examine and compare any number of students' work. You can also drag the nodes around for clarity. This kind of feedback tool is what teachers would want to have and what we should create for them. The world has spent billions of dollars building visual business analytics to assist business executives to make investment decisions day to day. How about spending a bit money to build an infographics system to assist teachers to make instructional decisions day to day?

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Learning Analytics

Theanalysis of datais an important part of almost every research project. This is especially true in social sciences like psychology, sociology, economics and political science. Many have tried to define statistical analysis. For example, Bruce (2007) defined statistical analysis as follows: “the application of statistics to data in order to draw conclusions or make predictions about the population from which the data were drawn” (p. 159). In addition, statistics are used to make these predictions as accurate as possible. This is because statistics are used to reduce the errors that could occur when using other methods.

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