Automated tutoring capabilities

In most computer-assisted math problems, the author needs to define a list of correct answers, while the system checks for mathematical equivalence to one of those answers. This approach has a number of limitations, as shown in the table below.

With AlgebraKiT, an author defines math problems through tasks. Based on a single task, AlgebraKiT is able to generate everything that’s needed to offer sub-step evaluation, hints, error feedback, and worked solutions.

Other systems

AlgebraKiT

Evaluation

Accept only inputs that are equivalent to the specified answer.
Accepts inputs that make sense to solve the problem, even if the expression is not mathematically equivalent to the final answer.

Student support

Hints and error feedback must be authored separately for each question. In practice, this implies that most questions offer no or just a few general hints.
Hints and error feedback are generated automatically and do not have to be authored per question. Hints and error feedback are always available, even for unexpected inputs.

Worked solutions

Need to be created by the author.
Generated automatically.

Authoring

Time-consuming and error-prone. You must be sure to include all acceptable final answers for each question.
Efficient and easy. Just specify the task(s).

Example

This question is defined by the task: “Solve the equation 6(p-1)=4p+10 for p.” The step-by-step evaluations, hints, error feedback, and worked-solution are all generated automatically by AlgebraKiT
Click on the live demo to solve the problem and inspect the worked solution.

This image shows a solved question based on the task to find the derivative. Notice how AlgebraKiT accepted a broad range of intermediate steps, including expressions that are not equivalent to the final answer.

Configurable student profiles

All didactic aspects, such as math notation, solution strategies, hints, and error feedback, are configurable through predefined student profiles. Examples of such profiles are: “US grade 8” or “Deutschland Gymnasium.” This guarantees that AlgebraKiT’s responses are tuned to the capabilities of the student.

In this example, you can see the generated solution of the same problem for a French and a Spanish student. See how not only the language but also the solution approach and mathematical notations are different.

Spanish solution

French solution

Extended solution models

A very powerful feature of AlgebraKiT is the ability to combine multiple tasks into a single question. This allows you to define application-oriented problems that involve mathematical modeling.

Example

Possible solution