Let Mentor light the way!
Mentor Products, Inc.
Home
About Us
Math Education
Laws of Algebra
What is Algebra?
The Advisor
A White Paper
Advisor Description
Advisor Features
The Advisor Manual
White Paper
Utilization of the Mentor Mathematics Advisor
I. The Algebra Student at Home
The original concept of the Mentor Mathematics Advisor was to have a computer program that would act like a math teacher looking over the shoulder of the algebra student. The student gains nothing if the teacher simply tells the student everything that needs to be done to solve a problem. Rather, the teacher lets the student work, giving encouragement when the student does something right and stopping the student when a wrong turn is taken.
While nothing is better than a good teacher, the Mentor Mathematics Advisor actually enjoys one advantage a teacher does not. Students are not embarrassed if a computer program tells them that they have made a mistake. That is private, between the student and the computer. No one has to know that the student did something wrong! Mentor has found that many teachers do not fully comprehend how sensitive students are to any appearance of incompetence.
Trends in modern mathematics education emphasize higher order thinking. This is certainly important. Mentor believes that it is also important to be able to perform the traditional algebraic operations on mathematical expressions and equations. After all, to do higher order thinking, one must have certain thinking tools. In algebra, these tools are the Laws of Algebra and the rules of algebraic manipulation that follow from those laws. The Mentor Mathematics Advisor helps with problems of algebraic manipulation: the processes of expansion, simplification, factorization, and solution to equations.
The student, in the privacy of their home, can work problems, step by step, on the computer and have confidence that each step that they make will be correct. If the students makes a mistake, the student is warned and not allowed to continue until the mistake is corrected. When the mistake is corrected, the mistake is no longer displayed unless the students elects to do so, perhaps for review purposes. The Mentor Mathematics Advisor is pedagogically sound. It does not give the student a correct answer. Students must find answers themselves.
The student may work problems from their text book. The student can label a session to reflect a particular assignment such as "Chapter 5, Section 2". Or, Mentor will use the date and time of the start of a session as the session label. Also, each problem can be labeled such as "2-4". Mentor will assign a number to each problem by default. It is noteworthy that the Mentor Mathematics Advisor is not a collection of "canned" problems, for example the problems from a particular book. Rather, Mentor has intelligence to solve a large class of problems and to advise students as students work those problems.
The Mentor Mathematics Advisor also has the capability of presenting problem for the student to solve. The student can select the type of problem and the level of difficulty for the problem. As the level of difficulty increases, problems are presented that are appropriate for even college level students. At the easiest level of difficulty, problems are appropriate for middle school algebra students.
Graphing has traditionally been a useful tool in mathematics education in helping students as well and scientists and engineers, visualize mathematical expressions and relations. The Mentor Graphing Tool makes it easy for students to quickly graph expressions and equations. The Mentor Graphing Tool allows the student to enter equations the way they are typically written, for example
will display as a full ellipse. It is not necessary to put the equation in functional form.
Mentor believes that the Mentor Mathematics Advisor is a unique computer program unlike any other program currently available. Students feel save in using the Advisor. They do not feel threatened by the Advisor. Teachers can be confidant if students use the Advisor that they will receive correct advice and that the Advisor is pedagogically sound and will not give the student the answer. The student must do their own work.
II. In the Classroom
After the Mentor Mathematics Advisor was well into development, a teacher expressed interest in using the program in her classroom. Assuming that the classroom has at least a small cluster of computers available, some suggestions for classroom use of the Advisor are:
| A. | Additional Drill and Practice |
| As the teacher works with one group of students, the rest of the class can be constructively employed on assignment with the Mentor Mathematics Advisor. | |
| B. | Text book assignments |
| Students can be assigned problems from the text book or problems from a teacher handout. A significant power of the Mentor Mathematics Advisor is that it is not restricted to problems from a particular text book. | |
| C. | Random Problem Generation |
| Students can also be assigned to work problems of a certain type and difficulty that the Advisor can generate. It may turn out that Random Problem Generation is one of the most important features of the Mentor Mathematics Advisor. | |
| D. | Random Test Generation |
| Every teacher knows how difficult it is to make out a test with questions that have appropriate characteristics. The Mentor Mathematics Advisor can quickly generate a test with specified problem types and difficulties. The teacher who suddenly needs to keep a part, or all, of the class productively busy can generate an appropriate pop quiz in moments. Of course the teacher can also use this feature for planned test also. |
III. The Classroom where a Computer Lab is Available
If students have access to a computer laboratory where the Mentor Mathematics Advisor is available, the teacher has even more options available for the use of the Advisor.
| A. | The teacher can assign problems from the text book or handouts to be worked using the Advisor. The Mentor Mathematics Advisor can print a session and the student can turn this in to the teacher. Problem of student honesty are the same here as with any other academic assignment. |
| B. | The teacher can generate an assignment and distribute the assignment to the students by floppy disk since sessions can be saved to hard or floppy disk. The students' work can be turned in with pencil and paper, printed by the computer, or by floppy disk. |
| C. | The teacher can generate an assignment and make the assignment available to students by placing the assignment file on a common "read only" location available to the computers in the computer lab. Students can copy the assignment file into the students' work space. |
| D. | If schools set up individual student computer accounts, it is even possible for the students to work their Mentor Mathematics Advisor assignments and for the teacher to access the student work online. |
IV. The Classroom where Library Advisors are Available
A new option for school using the Mentor Mathematics Advisor is to have copies of the Advisor that students can check out for home use just as they would check out library books. These versions of the Mentor Mathematics Advisor are fully functional but require the Mentor CD to be resident in the computer CD drive for the program to operate. Making this available does decrease the sales potential of the Mentor Mathematics Advisor in the home environment and presents some risk of software piracy. However Mentor feels that the overall benefit to students make these risks acceptable.