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Development and Implementation of Mathematics Instruction Programs Based on Students' Individual Cognitive and Developmental Abilities

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Identifier	SPEC 8
Author	Keithan, Amy E.
Title	Development and Implementation of Mathematics Instruction Programs Based on Students' Individual Cognitive and Developmental Abilities
Publisher	Central Connecticut State University
Date	2009
Resource Type	Special Project
Notes	The purpose of this project is to develop and implement instructional, mathematics programs that are based on the students' individual developmental and cognitive levels of functioning. The goal is to teach students with meaning so that they gain a deep understanding of mathematical concepts such as addition, subtraction, regrouping, renaming, and place value. Students will gain a strong foundation of arithmetic in order to continue to learn mathematics concepts and knowledge so that they can solve problems in their future experiences. The subjects for this project are eight third grade students who are eight and nine years old. They attend a private, Catholic school located in an urban environment. In this particular school, there is no standard curriculum and students do not take the Connecticut Mastery Test. The textbook serves as the basis for mathematics instruction. Since each student has different strengths and weaknesses, each learns in different ways. This creates an environment in which the students are functioning on different levels of developmental and cognitive abilities. In order to assess a student's developmental and cognitive levels of functioning two diagnostic tests were administered. The developmental test consists of three parts which is based on Piaget's theory of conservation of number, length, and area. Each student was interviewed individually and was continually asked to explain their thinking by answering the question "Why?" The implications for instruction are that conservers of number are able to understand place value, conservers of length are able to understand the comparison notion of subtraction and the missing addend notion of subtraction, and conservers of area are able to understand the repeated addition of equal measures or array notion of multiplication. The developmental level demonstrates the concepts that a student is capable of learning and understanding. The second assessment task is to determine the student's cognitive level of functioning through observation and questioning. The functioning level of cognitive development is assessed through the modeling with manipulatives, verbal explanations, and symbolic representations of the arithmetic operations of addition, subtraction, multiplication and division that were presented as word problems in a real world context. The cognitive assessment tasks indicate prior knowledge as to what a student has already learned about mathematics both correctly and incorrectly. Meaningful instruction occurs when a student is taught based on these two levels of functioning. The analysis of the developmental assessments indicated that 7 students or 87.5 % are conservers of number, 4 students or 50 % are conservers of length, and 3 students or 37.5 % are conservers of area. The cognitive assessment consisted of twelve word problems each illustrating one of the twelve notions.There were 2 addition, 4 subtraction, 3 multiplication, and 3 division problems that were solved using algorithms with paper and pencil and then they were solved using manipulatives. In analyzing the cognitive assessment tasks and responses, some general misunderstandings and misconceptions were revealed by many of the students. The students struggled with understanding numeration, especially regrouping, distinguishing between different types of problem solving operations and modeling them with manipulatives, and many students had memorized facts and algorithms without any meaning in the symbolic mode. Overall the students showed tremendous individual progress and have been able to attach meaning to many mathematical concepts. They have been able to demonstrate their learning and understanding through discussions, explanations, and written work. As a result of teaching students what they are both developmentally and cognitively ready to learn, they displayed more confidence in their written work and explanations.
Subject	Mathematics -- Study and teaching (Elementary) -- Connecticut
Department	Department of Mathematical Sciences
Advisor	Halloran, Philip P
Type	Text
Digital Format	application/pdf
Language	eng
OCLC number	713734939
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