KNM Math Program Instructions

Disclaimer: This program (actually a set of programs) has many, many options and optional paths of execution. As such it has been impossible to test them all and, therefore, it is possible that errors exist. So, use the program carefully and with thought. The author takes absolutely no responsibility for anything.

The Screen.

The display window for KNM Math program has two sections, on the left is the control button area and on the right is the operating area. Math programs are set up by selecting options from the control buttons in the control area. Math programs are worked by clicking buttons in this control button area and watching the progress of the operation as shown on the right side of the screen.

Operations.

The program handles math problems of six different types: Addition, Subtraction, Multiplication, Division, Modulo Addition and Modulo Subtraction (at least what the author understands to be Modulo Addition and Subtraction, never having seen examples.) When the program begins, the Addition option is selected. Other options can be selected from the “Operation” control box of the left side of the display. Clicking the arrow on the right side of the dropdown box displays the list of six operations and allows the operator to select an operation by clicking on the desired item.

Problem Options.

There are a number of options that can set for each type of problem. Addition problems, for example, can be set up to have from two to six rows of numbers with each number being from one to six digits long. They can also be set up to require the student to enter carry digits or not enter the digits (Carry digits are always used, as is normal. With the “no carry” option the student must remember to add the carry digit but does not need to type it in.) The following table gives all options for the six operations.

Addition
Number of Rows	2 – 6
Number of digits per number	1 – 6
Student enter “carry digits”	Yes/No
Number base	2 – 16
Subtraction
Number of Rows	2
Number of digits per number	1 – 6
Student enter “borrow digits”	Yes/No
Number base	10 (for now)
Multiplication
Size of Multiplier (digits)	1 – 4
Size of Multiplicand (digits)	1 – 6
Student enter “carry digits”	Yes/No
Number base	10 (for now)
Division
Size of Divisor (digits)	1 – 4
Size of Dividend	1 – 6
Number base	10 (for now)
Modulo Addition
Number of Rows	2
Number of digits per number	1
Student enter “carry digits”	No (N.A.)
Number base	2 – 16
Modulo Subtraction
Number of Rows	2
Number of digits per number	1
Student enter “borrow digits”	No (N.A.)
Number base	2 – 16

Base / Modulo Selection.

The Addition, Modulo Addition, and Modulo Subtraction operations allow the use of numeric bases other than 10 (will be extended to the other operations soon.) When these three operations are selected a dropdown box titled “Base” for Addition and “Modulo” for Modulo Addition and Subtraction is displayed and allows the user to select the numeric base (2 – 16) for operations (the current software has an error, “Base” is displayed instead of “Modulo” for Mod Subtract.) With bases greater than 10 for Addition, the computer uses the characters A (for 10), B (for 11), C (for 12), etc.

Response Level.

In addition to the options that can be selected for each mathematical operation, there are four “Response Level” settings that can be selected. These indicate the level of feedback given the student as he or she works the problem. The levels are given in the table given below.

Response Level	Meaning
Immediate	An audio response indicating a correct or incorrect entry is given immediately after the entry is entered. Furthermore, the program will not proceed until the correct entry is typed
Intermediate - With	An audio response indicating a correct or incorrect answer (not just a single entry) is given when the student completes a problem. The “With” part of this option indicates that with any audio response indicating an incorrect answer, red circles will be drawn, by the program, around every incorrect entry. With incorrect answers the student is given the option to start working the problem again.
Intermediate - Without	An audio response indicating a correct or incorrect answer (not just a single entry) is given when the student completes a problem. With incorrect answers the student is given the option to start working the problem again. There is no indication which entries were incorrect.
When Done	A visual response (displayed number) is given the student indicating how many, of an assigned number, of problems were answered correctly. The idea for this option is that the teacher can assign the student a number of problems for “homework”. The student must work the problems but will be given no indication of correctness of work until the assignment is complete.
None	No response is given the student. This option is intended as being a method for helping the teacher give the student an exam. Indication of correctness is only given, by the teacher, after the teacher examines the student’s work.

To fully implement the ideas behind the “Response Level” options, a program has to be written to allow the teacher to set up practice or homework sessions and exams before the student begins work.

Control Panel.

The Control Panel, at the top of the left side of the screen, provides the means of activating a problem once the operation and its options are selected. Clicking on “NEW” generates a new problem and allows the student to begin working on it. “CLEAR” allows the student to “erase” a problem without finishing it. “HELP” isn’t implemented.

Modulo Addition and Subtraction Clock.

Like normal, or traditional, Addition and Subtraction, the Modulo Addition and Subtraction programs display two rows of numbers. Because they are beginning forms of arithmetic, problems are limited to the two numbers of one-digit each (top of figure to the left.) Working these programs can be done in the same manner as the traditional operations. That is, by entering the correct answer digit on the graphic keyboard.

However, to make the problems more interesting, and more instructional, a “clock” graphic is provided (see figure.) Around the outer perimeter of the clock is displayed the numbers in the currently selected numeric modulo. Inside the clock are three clock “hands”. And, below the clock, an in-line equation showing the numbers pointed at by the clock hands. Additionally, as the solution proceeds, a broad, colored arc is displayed showing, like the equation, the solution suggested by the placing of the hands on the clock (see figure below.)

The clock hands and the equation are colored coded to match the numbers in the problem shown above the clock: blue hand for the blue (first) number, red hand for the red (second) number and green hand for the green (answer) number.

The student can move the blue and red hands to help solve the arithmetic problem simply by moving the mouse near the dot of interest and holding down the left mouse button while moving the mouse (the computer picks the dot nearest the mouse when the button is depressed.) The student should rotate the hands to point at clock number corresponding to the number in the problem. As the hands are rotated, the green hand automatically rotates to indicate the sum (for mod addition) or difference (for mod subtraction) of the two numbers. When the hand is rotated to the proper spot, releasing the mouse button keeps it in position. When both blue and red hands have been rotated to their proper position, corresponding to the numbers in the problem, the small green square points to the answer.

Note: Unfortunately, the hands on the clock do not always aligned perfectly with the numbers (as they should.) The student should watch the numbers in the equation below the clock to make sure of which number the hand is aligned with.

Once the student has rotated the blue and red hand he/she should notice the position (number being point at) of the green “answer” hand and use the screen keyboard to enter his/her answer to the problem.