Peter Gottlieb Apps

Most 2nd and 3rd graders struggle withsubtraction problems that require borrowing. Having tostrike-through numbers and then stack new numbers above them is aconfusing process that leads to frustration and under achievement.Here is the answer: let the student step through a promptedsequence and be checked as he/she goes. Let the student concentrateon the essential arithmetic without having to worry about doingneat strike-through's and lining up columns of new numbers. Yourchild/student will appreciate the neat tableau that is generated ashe/she follows the prompts and answers the questions. The promptsconsist of either a yes/no question regarding whether a particularcolumn needs to borrow or question marks where the new numbersshould be in the normal borrowing tableau (“?” if a single digitanswer is expected, and “??” if a 2 digit answer is expected). Thequestion marks are automatically replaced by numbers entered fromthe virtual numeric keypad occupying the lower part of the screen.If the student accidentally presses the wrong numeric key, it canbe erased by the “del” key and re-entered. All numeric entries arecommitted by tapping the “done” virtual key. If the student commitsan incorrect answer, the error count is incremented, and he/she isinstructed to try again. The student cannot proceed to the nextstep until the correct answer (numeric value or yes/no).When the problem is complete both the student and theteacher/parent can see if any errors were made (and corrected)along the way before arriving at the final answer. Doing a sequenceof exercises without errors will demonstrate that the skill hasbeen mastered.Most arithmetic programs follow the “electronic flashcard”paradigm: just present the problems for the student to work andscore the response when the student is finished. This leaves thestudent to struggle through the solution with pencil and paper. Ifthe student finally enters an incorrect answer, and the computertells him so, the student has no idea what went wrong. In contrastsub3 provides prompts that present the student with a sequence ofchallenges and immediate feedback after each step. A tediousexercise is turned into a fascinating game. Another advantage ofsub3 is that the numbers for each problem are generated randomly sothe student will never see the same problem twice.The extensive instructions included with this app providecomprehensive descriptions of all the steps involved in subtractionwith borrowing, which will be a great help for the parent who needsto supplement what the student has learned in the classroom. Thisinitial, free, version of the program uses only 3 digit numbers(hence the name sub3), which should provide sufficient problemvariety to ensure the development of excellent student skills. Ifseveral thousand people install the free app, I will provide anextended version to allow the user to choose a larger number ofdigits, and charge a few dollars.

Here is the best tool for improving a student's skill at factoring.The app presents a target number to be factored, and the studentresponds by entering a prime factor (2, 3, 5, 7, 11) of thatnumber. 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 respondwith the partial factoring 42*5, and the user is prompted to entera factor of the new target, 42. The process repeats until theoriginal number (210 in this case) is completely factored. If, atany step, the user enters a number that is not a prime factor ofthe target number, an error is charged and the user is prompted tore-enter a correct factor. When the factoring is complete the appdisplays the number of errors. This automatic, real-time, scoringsaves the teacher, or tutor, the trouble of correcting theexercises, and provides the student with immediate feedback. A veryefficient process for all concerned. The app can be set up to run aspecified number of problems, and will keep a tally of the numberof errors. This automatic scoring saves the teacher, or tutor, alot of trouble. The other adjustable parameters are the number offactors in the original problem (2 through 5) and the maximum primefactor (5, 7, 11, or 13). The instructions give all the essentialtips to help the student find a factor correctly the first time(avoiding being charged with an error) without the bother of ashort division exercise to test it. Since the app does all thedivision, the student can concentrate on getting the factors. Thiswill sharpen his/her skills, even in the midst of all thedistractions that modern youth is subject to.

Can you read a number that's flashed on the screen for only a fewmilliseconds? This game will start with a few hundred millisecondsand reduce the duration until you can no longer enter the numbercorrectly. You can select the number of digits; 3 is very easy; 5is very hard. Practice and notice the improvement. Find the time ofday when our visual acuity and ability to concentrate is highest.Test your skill against friends and family; it will be rewardingactivity for ages 8 and up. This initial version is free, but notvery slick; if it generates sufficient interest, I will add manyfeatures (such as keeping statistics on scores and for differentplayers) and charge a few dollars.

This app is for anyone who has to calculate formulas: high schooland college students in science, engineering, or business courses,as well as teachers or practitioners in any of these fields whoneed to get quick results when they are not near their computer. Itwill handle a wider variety of formulas than most hand-heldcalculators, particularly formulas for which you want to use namedvariables and change their values frequently. Not only is this appeasier to use than most hand-held calculators (being able to useparentheses rather than the tricky reverse Polish format requiredby most HP machines), it is also easier to use than the formulaediting feature of a spreadsheet. Entering formulas is a snap: allyou have to do is type in characters as you would with a texteditor; the program parser will identify any variables and set up ascreen for you to enter their values. Alphabetic and numericcharacters are entered on different keypads in order to provide youwith larger keys to minimize data entry errors. Close integrationmakes switching between these keypads very fast and easy. Once youhave entered a formula structure, and the initial values for anyvariables it might have, you can name and store it for future use.You can scroll through the list of stored formulas and recognize byname or formula structure any that you want to re-use. Business orfinancial users will find this app a good complement to thecalc_formulas app (by the same author and available for free),which allows the user to select from a list of 27 frequently usedfinancial formulas, but does not have the capability to create newformulas. The only deficiency in “myformulas” is the absence of abuilt-in function library. If more than 1000 people will pay $2.50for this version, I will produce a slightly more expensive versionwith a function library more complete than any spreadsheet.

Here is a drill program that will improve the essential skills forany intermediate algebra student. This is an exercise in thefactoring of quadratic expressions. Such an expression can bewritten as the product of 2 factors, each factor consisting of 2terms: an x to the first power term and a constant term. In theSolvequad app these 4 coefficients are randomly chosen integersfrom 1 to 6. The top/first line of the Solvequad screen presentsthe quadratic expression. The second line shows the skeletons ofthe 2 factors that produce this expression, with 4 blank graybuttons for the 4 unknown coefficients. The user enters the numbersfor these coefficients using the virtual keypad. This keypad hasonly the needed digits, 1 – 6, a minus sign, a delete key and adone key. The small number of keys means that the individual keyscan be nice and large, minimizing entry errors. Accidental errorsthat do occur can be quickly corrected with the delete key. Theselection of the coefficients to enter is made either by tappingthe appropriate gray button, or by tabbing through the 4 buttons.The third line on the screen shows the quadratic expressioncalculated as the coefficients are entered. This automaticcalculation saves the user the trouble, so that he/she canconcentrate on deciding which values to enter for the coefficients.After all 4 coefficients have been entered the student can comparethe calculated quadratic expression in the third line with theproblem quadratic expression in the first line. Any discrepanciescan be corrected by re-entering the any of the coefficients of thefactors. (second line of the screen). The done key is tapped whenthe user is satisfied that the first and third line quadraticexpressions are the same. If the expressions are not the same theuser is charged with an error and is told to re-enter the factorcoefficients until the correct quadratic expression is calculated.This policy makes if easy for the student to avoid errors. The realstrategy is to finish quickly by doing the correct coefficientcalculation mentally so that there is no need to re-enter. Thecurrent version of the program does not track the completion time,but that capability can be added if there is sufficient interest.Factoring a quadratic expression leads directly to solving for the2 roots of the equation made by setting the quadratic expressionequal to zero (values of x that make the quadratic expression equalto zero), hence the app name: Solvequad. The quadratic expressionwill equal zero when either of the 2 factors equals zero, so theroots of the quadratic expression are the 2 values of x that willmake either of the 2 factors equal to zero. To the student ofintermediate algebra this last step (solving a simple linearequation in one unknown) is trivial; it is left out of this app tolimit the app to one process/algorithm and to avoid boring the userwith trivia.

Here is the answer to those tiresome multiplication tableexerciseswith your child. This Android app will flash a sequenceofmultiplication table questions, and you child will entertheanswers to each using a virtual numeric keypad with nicelargekeys. The virtual keypad even has a “delete” key so thathittingthe wrong button can be corrected before getting chargedwith awrong answer. Each question will be selected randomly bytheprogram. You (or your child) can select the total numberofquestions for the sequence before the start. Since a givensequencewill have no repeated questions, there can be up to 28differentquestions in the sequence. Another unique featurethatdistinguishes this app from the countless other flash-cardtypeapps: after each incorrect answer the subject is forced to viewthemultiplication table so that he/she is forced to becomefamiliarwith the table and its relationships. The number of correctandincorrect answers is tallied and displayed at the end ofthesession so that you can verify your child’s progress.Inconstructing the multiplication table questions the numbers 10and2 are omitted because they make the multiplication questiontooeasy, and the child would be annoyed at having to wastetimeanswering trivial questions.

Here is an app that can calculate 27 different formulas usefulinfinancial transactions. This latest version of the app has addedanumeric keypad (with nice large keys) for data entry, asanalternative to the 2 modes of data entry in the originalversion:(1) dragging your finger up or down the screen to increaseordecrease the default value of an input parameter, (2) tapping onablank space on the screen for the same purpose. The 27 formulascanbe divided into 5 categories: (1) interest functions whichrangefrom simple interest to mortgage payments to bond price toyield aspecified interest when the stated rate of the bond(frequentlycalled coupon rate) is specified, (2) notes andpayments, (3)profit and loss (including internal rate of return),(4) inventoryvaluation, (5) depreciation. This app can onlycalculate the 27specified formulas, but it is free. If severalthousand peopledownload it and give me favorable reviews, I will doan enhancedapp (for which I will charge a few dollars) that willallow theuser to specify his/her own formulas, which mayincorporate one ormore of these 27 hard coded formulas.

Here is a game that tests your visual reflex, yourshort-termmemory, and your ability to resolve a rapid sequence ofimages.Randomly selected digits (0-9) are flashed briefly on thescreen ina rapid sequence. You are then asked to recall thesequence andenter the numbers using a virtual keypad. If correct,you canproceed to the next round with a shorter display time foreachdigit. The object is to get to as short a display time aspossible.The challenge is to train your brain to make thepersistence timeof each digit image as short as possible, so thatimages don'tinterfere with each other. If your answer is wrong youget acomment on your capabilities, as demonstrated by yourperformance.You can try again to improve, starting with theoriginal, longerdisplay time. The instructions give some hints thatmay be usefulin this regard. The can select the number of digits inthe sequencefrom 2 through 6, the initial display time from 0.3 to0.7 seconds,and the fraction by which the display time is reducedafter asuccessful round from 0.2 to 0.4.

Here is a division drill that will develop skills in bothbasicdivision and mental arithmetic. Yet it's simple enough to dowhilewatching children's TV. The student can begin with noremainders:dividing integers from 3 to 9 (called divisors) into adividendwhich has been calculated so that the division is even.After thestudent enters the answer (a single digit in the simplestversion)it is scored and, if correct, he/she progresses to thenextproblem. If incorrect, the student is prompted to re-enterthecorrect answer. As each problem is completed the number oferrorsis tallied. At the end of the sequence the student hasevidence ofhis/her progress that can be shown to theteacher/parent. Divisionwith remainder presents slightly morechallenges. The answer isentered in a 2 step process: first thequotient; when that iscorrect the remainder is entered. The numberof cases and problemdifficulty can be selected from a setup menu.The problems arebuilt from factor numbers selected at random, sothe student isunlikely to encounter the same problem twice in asequence, andalmost never for problems with remainder. Thebeginningstudent/user is expected to use pencil and paper forcalculatingremainders (particularly the first few times the app isused).However, he/she should be encouraged to do without pencil andpaperas soon as comfortable. Calculating the remainder withoutresortingto pencil and paper provides a nice drill in simplementalarithmetic.

Here is a painless way for the algebra student todevelopproficiency in solving simultaneous linear equations. Hereis adrill program that leads the student through 8 steps to solve2simultaneous linear equations with 2 unknowns. These 8 stepswouldbe a tedious exercise with pencil and paper. Even worse, asingleerror at one of the steps would not be detected until theproblemwas finished, and the student would be left with theunpleasantexercise of re-doing the whole problem in order to findout whatwent wrong. This app (Linear2) will check each of the8intermediate steps and provide immediate feedback to thestudent.The values of the 2 unknowns and the 4 coefficients intheequations are randomly generated so that there are severalhundredthousand possible combinations, and it is extremely unlikelythatthe student will see the same problem twice. This new version(2.0)is a little more user friendly and prevents crashes fromfaultyuser input.

This app raises the algebra drill program to a whole newlevel.Instead of simply presenting the problem and leaving thestudent towork out the steps on paper, the student is lead throughasuccession of steps, with instant feedback at each step. Inthismanner the student can quickly identify and understandhis/hererrors. The student also avoids the tedium of writing outtheintermediate equations corresponding to these steps andworryingabout keeping the equations neat and having enough space onthepaper. The instructions with this app also provide a nicetutorialon the subject. This app deals with a simple type ofalgebraproblem: one linear equation in one unknown. This type ofequationis a first step in the solution of many word problems; itis alsofundamental to learning the more advanced concepts ofalgebra. Theprogram begins with a single equation with all theconstantsgenerated randomly (so that the student is unlikely toever see thesame problem twice). The form of the equation is fairlygeneral,having one variable term (x multiplied by a constant) andoneconstant term on each side of the equation. The student isleadthrough a 3 step process to solve the equation, to obtain asinglenumeric value for the unknown variable, x. The steps arestructuredso that the student's entry at each step can be checked,andinstant feedback is provided. Each step is completed by enteringanumber using a virtual numeric keypad with large buttonstominimize error. If the number entered is correct thestudentprogresses to the next step. If the number entered is wrongthestudent is notified and prompted to re-enter the number until itiscorrect. The arithmetic for each of the 3 steps (subtraction,ordividing by 2, 4, or 5 to get decimal answers) is simple enoughtobe performed mentally, without resort to pencil and paper.Hencedrill with this app will have the added benefit ofincreasingproficiency in the simple mental arithmetic. The programusuallyruns through a specified number of problems, and the numberoferrors is tallied after the last problem. This is most useful inateacher-student setting, where the number of errors at the endofthe sequence can be used to evaluate the student'sprogress,sparing the teacher the tedium of grading theproblemsindividually. The number of problems in the sequence canbespecified by the user.