numbers, subtraction can also be used to separate, combine, or find quantities in other contexts. For example, "Tom has 8 apples. He gives away 3 apples. How many does he have left?" represents separation, while "Tom has 8 apples. Three of the apples are green and the rest are red. How many are red?" represents combination. In some cases, subtraction can also be used to find the total number of objects in a group, as in "Tom had some apples. Jane gave him 3 more apples, so now he has 8 apples. How many did he start with?" There are several methods to accomplish subtraction. The method which in the United States is referred to as traditional mathematics teaches elementary school students to subtract using methods suitable for hand calculation. The particular method used varies from country to country, and within a country, different methods are in fashion at different times. Reform mathematics is distinguished generally by the lack of preference for any specific technique, replaced by guiding 2nd-grade students to invent their own methods of computation, such as using properties of negative numbers in the case of TERC. American schools currently teach a method of subtraction using borrowing and a system of markings called crutches. Although a method of borrowing had been known and published in textbooks prior, apparently the crutches are the invention of William A. Browell, who used them in a study in November 1937. This system caught on rapidly, displacing the other methods of subtraction in use in America at that time. Students in some European countries are taught, and some older Americans employ, a method of subtraction called the Austrian method, also known as the additions method. There is no borrowing in this method. There are also crutches (markings to aid the memory) which vary according to country. In the method of borrowing, a subtraction problem such as 86 - 39 can be solved by borrowing a 10 from the tens place to add to the ones place in order to facilitate the subtraction. For example, to subtract 9 from 6, we can borrow a 10 from the tens place, making the problem into (70 + 16) - 39. This is indicated by crossing out the 8, writing a 7 above it, and writing a 1 above the 6. These markings are called "crutches." The 9 is then subtracted from 16, resulting in a value