Chapter 12 summarized the different techniques students use when counting. Surprisingly, there is not a definite manner of performing counting techniques. When calculating, students can use various methods such as direct modeling, invited strategies, and standard algorithms. Counting techniques of students evolve when they continue to be exposed to different numbers. At the onset of their studies, students use direct modeling, and when they continue enhancing their counting techniques, they adopted inverted strategies and eventually standard algorithms.
Direct modeling is the most basic technique used by beginners when counting. This method is used to teach students who have a problem seeing ten as a unit. When using this method, students are encouraged to use tools to assist them in counting. Tools such as grouping counters can help the struggling students to make bars of 10 from by connecting cubes. Initially, some students will use base ten to keep track often. However, some students will note down the corresponding numbers for the support of the memory.
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The inverted strategy is a technique that is used by students when they are familiar with direct modeling. This inverted strategy is number oriented since it involves twisting of numbers to find the required solution. Similarly, inverted strategies are left-banded; this method requires a large part of numbers to begin since the whole focus is on numbers. Also, inverted strategy as no definite way to do calculation since this method is flexible. The main advantage of this method is that when doing calculations, it has a few errors compared to other methods. Also, Inverted strategies are important since it helps students to develop a sense of number when conducting calculation such as addition and subtractions. To understand Inventive strategies, it is essential to create a supportive environment, such as mental computation techniques. Also, some models support invented strategies; they include split strategies, jump strategies, shortcut strategies. Split strategies use techniques for separating using visual diagrams, which helps students develop strategies. When using this method, students use arrows and line to display how computation are joined exclusively. Shortcut strategy involves flexibly adjusting the number; numbers are moved to the nearest 10. For instance, 69 can be moved to 70, and then the calculation is conducted after that. Jump strategy is mostly used when subtracting. The number of jumps is counted from one number to another; the number of jumps obtained determines the result of the calculation. For instance, if 60 is subtracted from 20, the number of jumps from 20 to 60 is counted, and it is four, this Implies the result of subtraction is 40.
The standard algorithm is the epitome of all calculations that involved digital-oriented numbers. This method is guided by a set of rules that must be followed when conducting calculations, such as subtraction and addition. The main aim of teaching this method is not to be memorized a series of steps but to ensure students understand the process and procedure. The algorithm must be understood and not memorize; this will help students comprehend calculation and hence find it enjoyable. Cultural differences in the algorithm are crucial in the comprehension of the standard algorithm. Some people presume that mathematics is easier when compared to other fields. This notion is wrong since what is a basic standard algorithm in the USA, for example, is not the same in Sweden. Therefore, as a student, it is crucial to understand the different variants of the standard algorithm to have the notion that algorithms are easier.
