Intelligent Tutoring Software and their Effectiveness for Pre-Calculus by Prof. Julian Viera

May 25, 2013

Intelligent tutoring software is becoming more prevalent in hybrid and online courses. Software such as Carnegie Learning Cognitive Tutor and ALEKS (Assessment and Learning in Knowledge Spaces) are software where students must show a mastery of topics or objectives in order to move on to the next objective.

What is the best implementation and learning environment for this type of software?

The software utilized by students taking an online pre-calculus course at UTEP is ALEKS.  ALEKS uses adaptive questioning to accurately determine what a student knows and doesn’t know in a course. ALEKS’ assets are its formative assessments and the knowledge state theory it has as its foundation.  When a student first log into ALEKS he/she is given an initial assessment; this allows the program to gauge where the instruction for this student should begin.

After the initial assessment, students begin practicing concepts from topics ALEKS has determined they are ready to learn.  After fifteen to twenty topics have been practiced, or eight to ten hours of login time has accumulated, the students will be given another assessment.  As students master topics more advanced topics will appear.  Students will practice, assess then repeat this process until they mastered, solved a topic on an assessment correctly, all or most of the topics in a particular course.  Advanced topics will not appear unless the student has practiced or mastered pre-requisite topics.

ALEKS is based on Knowledge Space Theory.  Knowledge Base Theory is the idea that some topics precede other topics.  For example, a set of problems in a linear functions chapter for pre-calculus is given in Table 1 (Falmagne, Doignon, Koppen, Villano, & Johannesen, 1990).  If a student masters problem f, it is highly likely this student has an understanding of all preceding problems.  If a student masters problem e, then she should be able to answer b, c and a.  Hence, the student does not have to learn the material linearly. When a student does master all five problems, it creates a “knowledge state.”

Table 1.

Name of problem type

Example of instance


Word problem on proportions A car travels on the freeway at an average speed of 52 miles per hour.  How many miles does it travel in 5 hours and 30 minutes?


Plotting a point in the coordinate plane Using a pencil, mark the point at the coordinate .


Multiplication of monomials Perform the following multiplication:


Greatest common factor of two monomials Find the greatest common factor of the expression  and .  Simplify your answer as much as possible.


Graphing the line through a given point with a given slope Graph the line with slope  passing through the point


Writing the equation of the line through a given point and perpendicular to a given line. Write an equation for the line that passes through the point  and is perpendicular to the line .

A knowledge state is a set of problems  which are implied by mastering problem e.  Analyzing these problems in Table 1, we see there are 10 learning states.

This type of knowledge structure allows for many learning paths.   A student can master problem b then learn problem a then c, or problem a then c then b.  ALEKS will assess the student to make sure his or her learning has not digressed.  If a student does not show mastery of a certain topic, then the student will have to be re-master those topics.

Although there have been contradictory studies on the effectiveness of ALEKS in student grade and placement test improvement, some studies do suggest a learning environment that may be more beneficial to student outcomes.  Studies that did not show a significant difference with traditional lecture courses (McClendon & McArdle, 2002; Spradlin & Ackerman, 2010) required students to work on ALEKS in addition to traditional homework assignments, in-class work and linear lectures.  Studies that did show an improvement on placement tests or course grades (Barrus et al., 2011; and Reisel, Jablonski, Hosseini, & Munson, 2012) had students work on ALEKS with a teacher available to answer students’ question.  These studies found that students benefitted from working in a computer lab with the availability of immediate help from a teacher.  They also found that having additional homework and in class assignments negatively affected students’ performance on ALEKS.  Finally, they found that a linear lecture was not useful since students were in different knowledge spaces.

The creation of a learning environment that will best utilize the cognitive features of intelligent tutoring software is crucial for the continued success of such software.  I, myself, hope to find a learning environment that will help Latina/o students from the border region to succeed collegiately.


***Prof. Julian Vera is a faculty member in Mathematical Sciences in the College of Science, and a vital member of the Academic Technologies Learning Community!***