The math apps created by iDevBooks can provide good reinforcement for students familiar with standards-based math curricula, such as Everyday Math and Investigations. There are apps for students to practice partial sums, partial differences, partial products, and partial quotients (and even lattice multiplication). While many math apps are formatted to be “games,” these apps present themselves without bells and whistles, gimmicks, and cute creatures to offer students straight-forward practice.
All the apps can be adjusted to an appropriate challenge level. For example, when practicing partial sums students can work with two or three digit numbers and if they make an error, the ‘movement’ simply stops until the correct sum is chosen. There is a logical progression to finding each solution, starting with the largest place value first. Students are given an array of choices from which to choose the correct sum. Scanning the choices takes a moment but the choice is then reinforced with an equation, e.g., 100 + 200 = 300, as the 300 takes its position in the partial sums stack.
In the case of partial products, the app has the students start with the ones. The digits are highlighted to it is clear. The problems have a variety of numbers, including those that often throw students off, such as 50 x 80. The partial quotients app could be improved. While it asks the students to “estimate how many times” the divisor goes into the dividend, for a student just beginning to use partial quotients, it would be better if they were somehow directed to round that dividend before they made that estimate because the beauty of partial quotients is in picking numbers that are easy to work with. For example, in considering how many 3s go into 649, the student is best off first considering how many times 3 goes into 600. Since in this app, there are not choices given, and student must actually type in his or her estimate, it seems the student’s learning is not being supported as well as it could be since many students new to this way of dividing will try to chose numbers they can’t actually multiply in their head. To follow the last example, if the student was somehow prompted to think about how many 3s go into 600, they most naturally would answer 200 and after 600 was subtracted from 649 be prompted again to think about how many times 3 goes into 49. Again, at this point, the students need to be encouraged to choose an “easy number,” that they can multiply in their head, such as 10 or 12. In the end the answer, if it has a remainder as in this example, is presented as a whole number with the remainder written following an upper case R. If the app is to be in keeping with Everyday Math and other standards-based curricula, it would better written as a fraction. This is the natural connection to understanding how those “decimals” appear when dividing on a calculator!
Overall, these are good apps to reinforce classroom work. They don’t teach but they are clear in their presentation and allow students another way to practice on a different medium.