Welcome to PGSW, applications for smart phones. We now have 9 apps, mostly math drill, but also including productivity tools and games. All are available on the Android market, where they have had over 14000 downloads.

The only crashes users have reported is when they have incorrectly entered numbers. We have upgraded the code so that such input errors are no longer possible. If, however, you encounter a crash or some other problem, please send us an explanatory e-mail at "gottliebpet@gmail.com". We can assure you any such reports will get prompt attention. In order to facilitate the improvement of our product, we would appreciate any comments or suggestions for program modifications.

The following is a list of the apps and their categories. You can rapidly get to more complete description by clicking on any of the links. The description for Multtables also contains a link to run a simplified version as a web-based app in your current browser.

Can you read and remember a number that's flashed on the screen for only a few milliseconds? This game will start with a number flashed on the screen for a few hundred milliseconds; if you can recall correctly you get another try at a reduced duration. You keep playing until you miss (enter the number incorrectly). You can select the number of digits in the number; 3 is very easy; 5 is hard. Practice and notice the improvement. Find the time of day when your visual acuity and ability to concentrate is highest. Test your skill against friends and family; it will be rewarding activity for ages 8 and up. This initial version is free, but not very slick; if it generates sufficient interest, I will add many features (such as using letters instead of numbers, keeping statistics on your scores and the scores of different players) and charge a few dollars.

Here is an app that can calculate 27 different formulas useful in financial transactions. This latest version of the app has added a numeric keypad (with nice large keys) for data entry, as an alternative to the 2 modes of data entry in the original version: (1) dragging your finger up or down the screen to increase or decrease the default value of an input parameter, (2) tapping on a blank space on the screen for the same purpose.

The 27 formulas can be divided into 5 categories: (1) interest functions which range from simple interest to mortgage payments to bond price to yield a specified interest when the stated rate of the bond (frequently called coupon rate) is specified, (2) notes and payments, (3) profit and loss (including internal rate of return), (4) inventory valuation, (5) depreciation.

This app can only calculate the 27 specified formulas, but it is free. If several thousand people download it and give me favorable reviews, I will do an enhanced app (for which I will charge a few dollars) that will allow the user to specify his/her own formulas, which may incorporate one or more of these 27 hard coded formulas.

This app is for anyone who has to calculate formulas: high school and college students in science, engineering, or business courses, as well as teachers or practitioners in any of these fields who need to get quick results when they are not near their computer. It will handle a wider variety of formulas than most hand-held calculators, particularly formulas for which you want to use named variables and change their values frequently. Not only is this app easier to use than most hand-held calculators (being able to use parentheses rather than the tricky reverse Polish format required by most HP machines), it is also easier to use than the formula editing feature of a spreadsheet. Entering formulas is a snap: all you have to do is type in characters as you would with a text editor; the program parser will identify any variables and set up a screen for you to enter their values. Alphabetic and numeric characters are entered on different keypads in order to provide you with larger keys to minimize data entry errors. Close integration makes switching between these keypads very fast and easy.

Once you have entered a formula structure, and the initial values for any variables it might have, you can name and store it for future use. You can scroll through the list of stored formulas and recognize by name or formula structure any that you want to re-use.

Business or financial users will find this app a good complement to the calc_formulas app (by the same author and available for free), which allows the user to select from a list of 27 frequently used financial formulas, but does not have the capability to create new formulas.

The only deficiency in "myformulas" is the absence of a built-in function library. If more than 1000 people will pay $2.50 for this version, I will produce a slightly more expensive version with a function library more complete than any spreadsheet.

Most 2nd and 3rd graders struggle with subtraction problems that require borrowing. Having to strike-through numbers and then stack new numbers above them is a confusing process that leads to frustration and under achievement. Here is the answer: let the student step through a prompted sequence and be checked as he/she goes. Let the student concentrate on the essential arithmetic without having to worry about doing neat strike-through's and lining up columns of new numbers. Your child/student will appreciate the neat tableau that is generated as he/she follows the prompts and answers the questions. The prompts consist of either a yes/no question regarding whether a particular column needs to borrow or question marks where the new numbers should be in the normal borrowing tableau ("?" if a single digit answer is expected, and "??" if a 2 digit answer is expected). The question marks are automatically replaced by numbers entered from the virtual numeric keypad occupying the lower part of the screen. If the student accidentally presses the wrong numeric key, it can be erased by the "del" key and re-entered. All numeric entries are committed by tapping the "done" virtual key. If the student commits an incorrect answer, the error count is incremented, and he/she is instructed to try again. The student cannot proceed to the next step until the correct answer (numeric value or yes/no).

When the problem is complete both the student and the teacher/parent can see if any errors were made (and corrected) along the way before arriving at the final answer. Doing a sequence of exercises without errors will demonstrate that the skill has been mastered.

Most arithmetic programs follow the "electronic flashcard" paradigm: just present the problems for the student to work and score the response when the student is finished. This leaves the student to struggle through the solution with pencil and paper. If the student finally enters an incorrect answer, and the computer tells him so, the student has no idea what went wrong. In contrast sub3 provides prompts that present the student with a sequence of challenges and immediate feedback after each step. A tedious exercise is turned into a fascinating game. Another advantage of sub3 is that the numbers for each problem are generated randomly so the student will never see the same problem twice.

The extensive instructions included with this app provide comprehensive descriptions of all the steps involved in subtraction with borrowing, which will be a great help for the parent who needs to supplement what the student has learned in the classroom. This initial, free, version of the program uses only 3 digit numbers (hence the name sub3), which should provide sufficient problem variety to ensure the development of excellent student skills. If several thousand people install the free app, I will provide an extended version to allow the user to choose a larger number of digits, and charge a few dollars.

Here is the answer to those tiresome multiplication table exercises with your child. This Android app will flash a sequence of multiplication table questions, and your child will enter the answers to each using a virtual numeric keypad with nice large keys. The virtual keypad even has a "delete" key so that hitting the wrong button can be corrected before getting charged with a wrong answer. Each question will be selected randomly by the program. You (or your child) can select the total number of questions for the sequence before the start. Since a given sequence will have no repeated questions, there can be up to 28 different questions in the sequence. Another unique feature that distinguishes this app from the countless other flash-card type apps: after each incorrect answer the subject is forced to view the multiplication table so that he/she is forced to become familiar with the table and its relationships.

The number of correct and incorrect answers is tallied and displayed at the end of the session so that you can verify your child's progress. In constructing the multiplication table questions the numbers 10 and 2 are omitted because they make the multiplication question too easy, and the child would be annoyed at having to waste time answering trivial questions.

A simplified, web-based, version of multtables can be accessed from this link. If you run this web-based version from your computer (instead of a phone or tablet), you will use the actual keyboard instead of a virtual keypad.

Long division need not be the traumatic learning experience for 4th and 5th graders. This app (div2) does all the tedious multiplications and subtractions, leaving the student to learn and practice the basic long division skills of correctly guessing each digit of the quotient (answer) and testing whether it is correct. An additional benefit is the feedback that is provided after each quotient digit.

The long division exercises in this app are carried to 2 decimal places (hence the name div2). The user can specify the number of digits in the dividend (the number divided into) and the divisor. The divisor and dividend are randomly generated integers, so the user will never see any problem more than once. The random numbers of divisor and dividend may sometimes be such that the divisor goes evenly into the dividend, in which case the quotient may end in one, or more zeros.

If long division is done the old fashioned way (with pencil and paper) the student must struggle for each digit of the quotient, multiplying his guess by the divisor and then subtracting the product to test whether his/her guess is correct and to get the difference for determining the next quotient digit. If the student has guessed wrong, the whole step of multiplication and subtraction must be repeated over again. Worse still, the student may fail to detect the error of an incorrect guess, and the error will propagate through the rest of the solution. When the answer is scored (by the teacher, or someone) the hapless student must go back through the entire process to determine what went wrong.

This app will develop proficiency in the key long division skill of guessing the correct quotient digit. When the student is faced with a long division exam problem that must be done with pencil and paper, this proficiency will enable him/her to avoid wasting time multiplying incorrect quotient digits by the divisor, when the correct digit could be guessed to begin with. The instructions in this div2 app provide a set of rules that will guarantee that the user never requires more than 2 guesses for any quotient digit; half the time these rules will even give the correct guess on the first try. If you have a 4th or 5th grader struggling with long division, you will find this app to be a life-saver. Of course, the student who is having trouble with multiplication and subtraction should master these fundamental skills first (see my apps "multables" and "sub3"). Once multiplication and subtraction are mastered, this app will avoid the boring exercise of these skills while trying to master long division.

This app raises the algebra drill program to a whole new level. Instead of simply presenting the problem and leaving the student to work out the steps on paper, the student is lead through a succession of steps, with instant feedback at each step. In this manner the student can quickly identify and understand his/her errors. The student also avoids the tedium of writing out the intermediate equations corresponding to these steps and worrying about keeping the equations neat and having enough space on the paper. The instructions with this app also provide a nice tutorial on the subject.

This app deals with a simple type of algebra problem: one linear equation in one unknown. This type of equation is a first step in the solution of many word problems; it is also fundamental to learning the more advanced concepts of algebra. The program begins with a single equation with all the constants generated randomly (so that the student is unlikely to ever see the same problem twice). The form of the equation is fairly general, having one variable term (x multiplied by a constant) and one constant term on each side of the equation. The student is lead through a 3 step process to solve the equation, to obtain a single numeric value for the unknown variable, x. The steps are structured so that the student's entry at each step can be checked, and instant feedback is provided.

Each step is completed by entering a number using a virtual numeric keypad with large buttons to minimize error. If the number entered is correct the student progresses to the next step. If the number entered is wrong the student is notified and prompted to re-enter the number until it is correct.

The arithmetic for each of the 3 steps (subtraction, or dividing by 2, 4, or 5 to get decimal answers) is simple enough to be performed mentally, without resort to pencil and paper. Hence drill with this app will have the added benefit of increasing proficiency in the simple mental arithmetic.

The program usually runs through a specified number of problems, and the number of errors is tallied after the last problem. This is most useful in a teacher-student setting, where the number of errors at the end of the sequence can be used to evaluate the student's progress, sparing the teacher the tedium of grading the problems individually. The number of problems in the sequence can be specified by the user.

Here is a painless way for the algebra student to develop proficiency in solving simultaneous linear equations. Here is a drill program that leads the student through 8 steps to solve 2 simultaneous linear equations with 2 unknowns. These 8 steps would be a tedious exercise with pencil and paper. Even worse, a single error at one of the steps would not be detected until the problem was finished, and the student would be left with the unpleasant exercise of re-doing the whole problem in order to find out what went wrong. This app (Linear2) will check each of the 8 intermediate steps and provide immediate feedback to the student. The values of the 2 unknowns and the 4 coefficients in the equations are randomly generated so that there are several hundred thousand possible combinations, and it is extremely unlikely that the student will see the same problem twice.

This app is available for both Android (Google Play) and iPhone (iTunes).

Here is a drill program that will improve the essential skills for any intermediate algebra student. This is an exercise in the factoring of quadratic expressions. Such an expression can be written as the product of 2 factors, each factor consisting of 2 terms: an x to the first power term and a constant term. In the Solvequad app these 4 coefficients are randomly chosen integers from 1 to 6. The top/first line of the Solvequad screen presents the quadratic expression. The second line shows the skeletons of the 2 factors that produce this expression, with 4 blank gray buttons for the 4 unknown coefficients. The user enters the numbers for these coefficients using the virtual keypad. This keypad has only the needed digits, 1 - 6, a minus sign, a delete key and a done key. The small number of keys means that the individual keys can be nice and large, minimizing entry errors. Accidental errors that do occur can be quickly corrected with the delete key. The selection of the coefficients to enter is made either by tapping the appropriate gray button, or by tabbing through the 4 buttons. The third line on the screen shows the quadratic expression calculated as the coefficients are entered. This automatic calculation saves the user the trouble, so that he/she can concentrate on deciding which values to enter for the coefficients. After all 4 coefficients have been entered the student can compare the calculated quadratic expression in the third line with the problem quadratic expression in the first line. Any discrepancies can be corrected by re-entering the any of the coefficients of the factors. (second line of the screen).

Here is a division drill that will develop skills in both basic division and mental arithmetic. To make the drill-pill easier to take, the program is simple enough to do while watching children's TV. The student can begin with division problems having no remainders, only one digit quotients. If the student enters the wrong number he gets charged with an error. Division with remainder presents slightly more challenges. The answer is entered in a 2 step process: first the quotient; when that is correct the remainder is entered. The number of cases and problem difficulty can be selected from a setup menu. After completing the selected number of cases, there is a display of the number correct and the number of errors to show the teacher of parent.

Here is the best tool for improving a student's skill at factoring. The app presents a target number to be factored, and the student responds by entering a prime factor (2, 3, 5, 7, 11) of that number. For example, if the initial target number is 210 (2*3*5*7), and the user enters 5, the app will do the division and respond with the partial factoring 42*5, and the user is prompted to enter a factor of the new target, 42. The process repeats until the original number (210 in this case) is completely factored. If, at any step, the user enters a number that is not a prime factor of the target number, an error is charged and the user is prompted to re-enter a correct factor. When the factoring is complete the app displays the number of errors. This automatic, real-time, scoring saves the teacher, or tutor, the trouble of correcting the exercises, and provides the student with immediate feedback. A very efficient process for all concerned. The app can be set up to run a specified number of problems, and will keep a tally of the number of errors. This automatic scoring saves the teacher, or tutor, a lot of trouble. The other adjustable parameters are the number of factors in the original problem (2 through 5) and the maximum prime factor (5, 7, 11, or 13). The instructions give all the essential tips to help the student find a factor correctly the first time (avoiding being charged with an error) without the bother of a short division exercise to test it. Since the app does all the division, the student can concentrate on getting the factors. This will sharpen his/her skills, even in the midst of all the distractions that modern youth is subject to.

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