Our program avoids multiple choice questions and instead uses flexible and
easy to use answer input tools that mimic what would be done with paper and
pencil.
We begin by getting certain basic information about each student.
On completing registration, students receive a login name and password enabling them to return to the system at any time. We keep track of the student's progress and always bring the student back to the exact place the student left off at the end of the last session.
Before taking an initial assessment, the new student needs to learn how to provide answers for the questions asked by the system. The system uses no multiple-choice questions. Rather, there is an Answer Editor by means of which the student can enter mathematical expressions of any type and degree of complexity. The Answer Editor was designed to be easy and intuitive for student learners, and the object of the Tutorial is to ensure the student's proficiency with this essential tool. In the course of the Tutorial, the student is guided precisely through the steps necessary to enter a range of mathematical expressions. Throughout the Tutorial immediate feedback is given for all of the student's actions.
Having achieved a basic familiarity with the system and its tools, the student is ready to take an initial assessment. The first question is selected by the system based on the new student's grade level, but each subsequent question is chosen through a computation of all the student's foregoing responses in order to pinpoint as quickly as possible the precise state of the student's knowledge. During the assessment no feedback is provided, and the student does not know whether or not any of the answers given are correct.
Due to the personalized, adaptive nature of the assessment, the number of questions asked may vary for each student, but it is generally between 15 and 25.
At the conclusion of the assessment a report on the student's knowledge state is presented in which, using one or more pie charts, each part of the mathematics curriculum for that student's grade level is evaluated. In a single "pie," each "slice" corresponds to a particular area of the curriculum, such as "integers" or "percentages and proportions"; the degree to which the slice is filled by solid color shows the extent to which the student has mastered that area. One pie might be shown for the knowledge the student is presumed to have before beginning the grade, another for the knowledge the student is expected to gain in the course of the current year, and another for the next year's knowledge. The criteria used to generate these charts are based on published educational standards, and for each section of the curriculum, the pie charts generate a list of specific items that the student is presently able to begin learning.
By clicking on any of the items suggested by the system, the student makes an immediate transition out of the report and into the Learning Mode.
On first entering the Learning Mode, the student is presented with a question representing the particular concept or item just chosen (in the report). Here, the student may proceed to an attempt to solve the problem or may seek further explanation. The following is a typical explanation window:
If the student attempts to solve the problem and is successful, or if the student chooses to read the problem's explanation (containing its answer), a new problem embodying the same concept is generated.
If the student attempts to answer the question and is unsuccessful, the system analyzes the student's answer and gives as precise as possible an evaluation of the nature of the error, with advice for continued work on this item. Among other things, the system's feedback might suggest looking up a definition in the online dictionary of mathematical terms and concepts.
Highlighted words in the question or in the explanation are links to their definitions (or to related terms) in the online dictionary. Clicking on these links opens a new window with the dictionary and an exact definition at hand. The online dictionary can also be searched at any time.
The system provides a variety of kinds of information on the students. You can monitor their progress on different topics and see their pie charts as they go further in their learning sessions. Those graphs, as always, are printable for more convenience.
As an advanced feature, the system grants you access to the whole history of the students' sessions. You can then best follow their strengths and weaknesses from the beginning.
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