Two Digit Subtraction with Regrouping Two Digit Subtraction with Regrouping Subtraction is a major mathematical concept that is introduced as early as Kindergarten. Subtraction with regrouping is part of the second grade Mathematics Standard for the state of California. By the end of second grade, students are required to know how to find the difference of two whole numbers up to three digits long, and use mental arithmetic to find the difference between two two-digit numbers (Number Sense 2.2, 2.3).Subtraction with regrouping requires students to keep track of mathematical processes mentally and to move and manipulate numbers across place value. Learning regrouping conceptually requires twice as much effort for students to learn (Ohlsson, S., et al, 1992, p. 443). Students are often confused about their understanding in regrouping with subtraction. The academic language addressed in learning the concept of regrouping is conceptually misleading.The term “regroup” has little meaning for students. An easier term teachers might want to substitute for regroup is “trade”. Using the term trade has more significant meaning to students. For example, saying ten ones are traded for a ten conceptually makes more sense to young students. Research has also shown that when given directions from teachers, students can successfully understand the procedure of using tens and ones places and place values. However, students fail to understand this procedure when asked to work independently. (Van de Walle, 2004). There is a large emphasis on teaching students to correct methods of subtraction with regrouping. Know More About :- Kite Geometry
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Students need to understand and be able to demonstrate certain strategies that involve place value and meanings of numbers (Fuson, K. C., el at., 1997, p. 131). According to Haylock and Cockburn (1987), learning math requires a connective model in addressing symbols, language, pictures/images, and context/concrete experience. Each category is related and intertwined. It is important for the teacher to address the appropriate mathematical language and have students be able to concretely visualize the concept with manipulatives or images, and then have them relate it to their own experiences. Without addressing one component, the student will not be able to conceptualize the mathematical concept. Therefore, teachers need to plan strategically and incorporate all components so that the students can explore, analyze and understand the mathematical concept as it relates to them. Subtraction with regrouping requires the student to learn the language of regrouping by using manipulatives to visually demonstrate place values and then having them manipulate the manipulatives in borrowing tens and adding ones. From there, students will learn and use inventive ways in solving problems as they relate it to their own experiences. In the book, Teaching Children Mathematics, the authors present a case study in which a 2nd grade teacher, shows her student how to use ones and tens interchangeable to develop mathematical reasoning by using a real life example of her Aunt Mary’s candy business. The students were able to understand the flexibility of addition and subtraction by coming up with inventive ways of packing and distributing the candy (Whitenack et al, 2001). Initially, students have learned major mathematical concepts through the use of manipulatives (i.e. base ten blocks, unifix cubes, number lines, etc.). Ideally, the overall goal for students is to eventually be able to recognize place value without counting and recognize or construct two digit quantities using tens and ones (Fuson, K. C., et al., 1997, p. 134). In some Asian countries such as China, students are taught to focus on making “tens” with numbers as a support for learning mathematical concepts such as addition and subtraction. For example, when saying the number 53, students in China say “five then three”. Slight irregularities fall for digits that begin with the number 1. They do not say the one. For instance, the number 12 is said “ten two” (Fuson, K. C., el at., 1997, p. 141).A common misconception students have when regrouping with subtraction is that they subtract the smaller number from the larger number. Due to the nature of subtraction, students “add one column and subtract the others” or try to use another incorrect strategy, resulting in a violation of some mathematical solution (Leinhardt, G., 1987, p. 227). Read More About :- Definition of Real Numbers
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