The Pump Algebra Tutor (PAT) was originally developed by the Pittsburgh Advanced Cognitive Tutor Center at Carnegie Mellon University with support from NSF, Darpa, and foundations in Pittsburgh. It is currently used in some over 75 high schools, middle schools, and colleges around the US and in Europe. Both teachers and students have been enthusiastic about PAT's use as part of the Pump Algebra I curriculum. Field studies have shown dramatic student achievement gains relative to control classes: 15-25% better on standardized tests of basic skills and 50-100% on assessments of problem solving and representation use.
PAT is designed to help students to learn to model real-life problem situations using algebraic representations including tables, graphs, equations, and words. Modern mathematics is less about computing single answers, but more about creating models that can provide answers to multiple questions. The Pump curriculum emphasizes the use of activities that draw on students' common sense and prior informal strategies to help them acquire and make sense of formal mathematical strategies and representations. The goal is to help all students be successful in algebra and see its relevance in both academics and the workplace.'
You may wish to try our experimental, online versions of some of the tutoring systems we developed.
For further information about the tutor, which is now being further developed and offered as part of fully integrated curriculums with various services, please contact Carnegie Learning (TM) at www.carnegielearning.com or by calling (412) 683 - MATH.
The purpose of the PAT Tutor is to help students to develop algebraic skills which they can use in the context of real-life problem situations. For each problem, a textual description of a problem situation and a number of related questions are presented to the student. The student "solves" the word problem by representing information about the problem in various ways, such as tables and graphs, and using those representations to examine the situation and answer the questions. Students must represent and manipulate algebraic expressions and equations to use these tools effectively. Enabling students to understand and use multiple representations of information such as as text, tables, and graphs, is a major focus of the tutor.
The Avis and Hertz Problem Solution shows a sample problem, of a type which students would see towards the end of the year, after they've developed some expertise with developing and using graphs and tables for single linear equations. Two companies, Hertz and Avis, charge different rates for renting out large trucks. The student is given a description of the problem situation, and a number of questions are asked. The student must construct a table and graph showing the different companies and their rates. The student can use these representations to reason about real-world concerns, such as deciding when it becomes better to rent from one company rather than another. Most students spend 20-30 minutes solving a problem of this type on the computer.
During that time, the tutor monitors their activities, and provides feedback on what they are doing. The provision of timely feedback is one way in which the tutor individualizes instruction. If a student makes an error, the tutor can often indicate what is wrong with the answer, or suggest a better alternative. Another way in which the tutor individualizes instruction is by giving help on request. At each step in constructing a solution, the tutor can provide help to the student, suggesting a desirable next activity.
Through feedback and help, the tutors can keep students on-task, and give them a sense of accomplishment and progress towards a successful solution, as well as providing useful information about solving the problem. As well, by monitoring the student's acquisition of problem solving skills, the tutor can identify individual areas of difficulty. As the student progresses through the curriculum, problems can be presented which will target specific skills which that student has not yet mastered.
By individualizing instruction and targetting each student's strengths and weaknesses, intelligent tutors can maximize both the student's and the teacher's use of time in the classroom. Students are shown immediately whether their actions will be successful in constructing a solution. They can more easily focus on correction of errors and development of skills that they find difficult. Teachers are freed to interact with students on an individual basis, targetting and assisting those who have difficulty and can benefit from personal attention.
