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Chapter Reflection of Error Patterns in Computation

Their argument is that it takes the learning away from understanding the logic behind such mathematical problems and encourages children to solve math problems without really knowing the concept. They claim that calculators take away from children the long-term benefit of learning basic problem solving in math --- a learning that develops logical reasoning. In 2000, the National Council of Teachers of Mathematics (NCTM) states that: Knowing basic number combinations --- the single-digit addition and multiplication pairs and their counterparts for subtraction and division --- is essential. Equally essential is computational fluency --- having and using efficient and accurate methods for computing. (Ashlock , 2002, p. 4) Additionally, NCTM states that: Part of being able to compute fluently means making smart choices about which tools to use and when. Students should have experiences that help them learn to choose among mental computation, paper-and-pencil strategies, estimation, and calculator use. The CHAPTER REFLECTIONS 3 particular context, the question, and the numbers involved all play roles in those choices. (Ashlock, 2002, p. 5) Consequently, the advantages and disadvantages of allowing the use of calculators in lower level math teaching depend on the teacher's methods. Calculator should be considered as mere tools, and students should neither be made dependent on them nor made to avoid them altogether. I believe it is important that teachers understand that while it is good to let children learn other tools for mathematical computations, they should learn the basics as well like paper and pencil and mental calculations. In fact, I believe it is better to let children learn the harder, tougher way of doing calculations before learning the easy, technology-aided ones. The study of mathematics is built on previously founded data. For example, a student who does not understand the principle behind simple division will find it tough to understand the logic of simplifying fractions, factoring, distributive properties, and others. Math concepts are interconnected, and an effective math teacher should understand the importance of letting the students in lower grades learn the hard way of math first before letting them use calculators. A child should learn and understand the basic principles of mathematics --- add, subtract, multiply, and divide numbers --- using papers and pencils. In my experience, this builds number sense among students. Of course, occasional use of calculators for special activities is acceptable, even for students in the lower grade levels. Also, wide use of calculators can even be allowed in higher grade levels of math teaching and learning. But a primary math teacher like me must ensure first that my students are able to do what they do with calculators with pencils and papers. I believe this will prevent the basic error patterns that are common in the four basic computation methods. CHAPTER REFLECTIONS 4 Chapter 2: Diagnosing Misconceptions and Error Patterns in Computation One of the important ideas I have learned in this chapter is the National Council of Teachers of Mathematics Assessment Principle that states: To maximize the instructional value of assessment, teachers need to move beyond a
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