Intelligent Tutor for Basic Algebra

• The study focuses on an intelligent tutor for basic algebra.
• The project aims to develop a computer system with skills and knowledge similar to a high-quality human tutor.
• The study explores novel learning opportunities using the reactive capabilities of intelligent tutors.
• The focus is on the role of an algebra expert system within the tutor.
• Discusses how this system can help students acquire skills and knowledge, including reasoning and debugging techniques.
• The goal is to provide a computer tutor that mirrors the abilities of a skilled human tutor.
• Existing computer-aided instruction programs lack real subject matter knowledge, making it important for the tutor to embed several types of knowledge.

Types of Knowledge Embedded in Tutor:

• Knowledge of the subject: Expert problem-solving abilities in basic algebra. Tutor has an inspectable algebra expert system able to solve algebra problems and give reasoning steps like an "ideal" student.
• Knowledge of the student: Tutor being built to understand difficult concepts for students and address their misconceptions, handled by the student diagnosis module.
• Knowledge of teaching: Incorporating pedagogical techniques that simplify concepts, determining when to provide information and start learning.
• Identifying specific skills for algebra students and designing learning tools to support cognitive processes to learn these skills is important.

Knowledge Goals for Basic Algebra

• Identify skills and knowledge to communicate.
• Design computer-based learning tools to aid in the processes through practice.
• Students should learn the "laws" of algebra, like the distributive property, referred to as axiom-level knowledge.
• Students need to understand algorithms or procedures for various classes of problems.
• The focus shifts to computer-based systems alongside learning theory, where computers create new learning opportunities.

Students Should Learn

• Goal-directed reasoning skills: the ability to break down problems into smaller subproblems and identify the right knowledge.
• Debugging and self-diagnosis skills: to learn from errors, locate the source of errors, and find ways to correct them.
• Reasoning skills are critical and can make the difference between practice and learning.
• Historically, teaching has focused on more known and understood concepts
• Research, cognitive psychology, and AI now allow the creation of expert systems to benefit students.

Overview of An Intelligent Computer Tutor For Basic Algebra

• The algebra tutor is being developed and tested in various versions.
• The first tutor version operates on the Symbolics 3600 Lisp machine and Sun Microsystems workstations, tested at The RAND Corporation with high school students.
• Six Sun 3/50s are being installed in Santa Monica High School to develop this tutor.
• Version 1.0 lacks complete student knowledge and intelligent teaching to present concepts with feedback.
• The focus is on building an "inspectable" algebra expert system to teach problem-solving skills.
• Standard misconceptions of students are cataloged to create a knowledge base and the module for student diagnosis.
• Interviews with tutors and cognitive modules were conducted to enhance student learning.

Student Interface

• The tutor is seen as a collection of windows and menus.
• Reasoning is recorded and queried in the DisplaySpace in a large-scale data structure
• Problem-solving is presented as a reasoning tree showing solution branches.
• A boxed equation highlights the student's focus.
• Menus left of the DisplaySpace allow users to manage reasoning and get assistance.
• The CommentSpace sends tutor feedback.
• The WorkSpace allows new solution lines to be created.
• Students create solution lines in two ways: typing equations using a keyboard or writing on an electronic tablet that reads the strokes and characters to send to the tutor.

The Inspectable Algebra Expert System

• Menu items allow discussion about reasoning steps for students.
• The algebra expert system responds to the menu requests and needs to support student's learning of problem-solving knowledge.
• The goal is to mimic the behavior of an "ideal" algebra student with several constraints: give the right answer, produce comprehensible reasoning steps, be flexible, and be inspectable.
• The system solves first-semester equations in a flexible manner.
• Axiom-level knowledge: the lowest-level knowledge with primitive axioms for legal transformations.

Cognitive Axioms / Strategy-Level Knowledge Needed

• Cognitive axioms are based on pattern recognition abilities.
• Algebraists need tools because they operate naturally with the ability to recognize repeating algebraic patterns.
• Strategic Rules: advice about axioms to use under different conditions. A good rule for isolating the unknown is, with an equation, to move terms without the variable to the equation's other side.
• Algebraists have rules of thumb for steps to take, as well as conditions
• Strategic rules are also known as cognitive axioms

Axioms

• Compound strategic rules encode conjunctions of strategic rules, where each rule on its own can be less effective.
• The goal is to automatically apply the most relevant code or action.
• For instance, collecting like terms involves the actions like evaluation, rearranging, and coefficient addition.
• Rule types aggregate strategic rules, allowing the problem solver to reason at a higher level and decide which processes act first based on abstraction.
• Plans are lists of rule types with information on how rules are used.
• The plan example presented is to first remove parens, attract variables, collect them, and then isolate the variables and create solutions.
• Using different patterns and rules enables the solver to create new solutions or find multiple possible avenues of operation and solution.

Tools For Helping Students Learn Problem-Solving Skills

• Debugging skills allows students to remedy and understand mistakes.
• Students should be given credit for finding and fixing mistakes.
• Encouraging mistakes and not penalizing them is of importance.
• The tutor can aid in debugging to determine whether an answer is acceptable using feedback, and answers are distinguished as wholly wrong versus correct as is to this point.
• The Go Back menu is for the student to backtrack and retry when told the answer is incorrect.
• The student can also go back even if they are not aware of an error.

Support For Component Subskills

• GO Back aids strategic solutions to try problem solutions.
• Isolate the bug by determining the algebra knowledge needed in its step.
• A menu simplifies the search through STEPOK for a mathematical transformation.
• Additional menu items provide insight. Step Ok allows for steps in reasoning to be checked.
• A correct solution is not always logical. The tutor determines steps invalid in algebra or inappropriate.
• There are also methods like checking rules and axioms for misconceptions.
• The student can use STEP OK. operation anytime - in careful mode or reckless mode where they must go through the tree to locate the issue.
• Do Next Step shares the correct next step for students
• Both options point to the part of learning cognitive skills by way of examining processes; only slight modifications can change performance.

Tools for Learning Goal-Directed Reasoning Skills.

• The goal-directed process creates solutions, while the computer exposes process aspects to show students algebra problems are solved through reasoning
• Menu items open up to a degree suited to needs; otherwise, seeing algebra would be uninformative.
• Several aspects of reasoning reveal "Elaboration Step", for instance.

Specific Examples Of How AI Can Guide a Student

• The student may not understand going from expressions, so he or she can more clearly see steps using the Expert's reasoning.
• "Explain step" provides justifications for steps taken, as AI's abilities create multi-leveled explanations, and the capacity to manipulate the tutor further helps students learn special cases.
• The tutor explains what it's doing with an explanation menu Explain Steps show the steps for students to explore what they are doing

Hints

• Hints are another tool that students can engage
• One option from the tutor is to suggest the following general goals (the most common one is to isolate the variable)
• The student controls, however, the specificity of the hints received
• Two roles in this process, like explanations; the chance exists to better acquire general knowledge, and those skills become more easily implemented.
• AI lets students break down large, unfamiliar tasks.
• A skilled tutor supports student goals, so students learn to recognize and systematically approach problems to identify solutions.

An intelligent tutoring system for basic algebra is explored. The computer system has skills and knowledge similar to a human tutor. It explores novel learning opportunities using the reactive capabilities of intelligent tutors, focusing on the role of an algebra expert system.