Made available in DSpace on 2016-06-02T20:30:08Z (GMT). No. of bitstreams: 1 5469.pdf: 5667566 bytes, checksum: 7aa262cf62b8f3ff9e55a68620bc5e71 (MD5) Previous issue date: 2013-08-23 / The purposes of this study were propose: a pre-math skills evaluation tool for map the students repertoire of the early years of elementary school and analyze the complexity of relations of the tool; and an evaluation and teach program of addition and subtraction skills based on equivalence paradigm, describing method, results and behavior analysis on a speech that could foment the intercommunication with professionals other areas, mainly Math Education. Twelve children of the second at fifth years of elementary school participated of the test of the pre-math skills evaluation tool, all of at a public school by Porto Ferreira/SP. The procedure was compound by twelve MTS and CRMTS tasks that tested these relations: discriminations of numerals, number s names and sets; numerals and number s names naming and quantifying of sets; crescent/decrescent ordering of numerals and sets; before/after relations with numerals and sets; major/minor relations with and without sample; more/less relations with and without sample; equality between numerals and sets; relations numeral-set, set-numeral, name-numeral, numeral-name, name-set and set-name; estimate between numerals and sets; sequences completion with sets and numerals. The results demonstrated the tool s viability for identify on the students repertoire gaps that would interfere in later learning, such as addition/subtraction concepts, and allowed us accomplish a behavior analysis of the component skills. Continuing, nine of the same participants were exposed to the MTS procedure that have composed the evaluation and teach program of addition and subtraction skills, grounded on the equivalence paradigm. The program was organized into three units according to difficulty levels, having the unit 1 values from one to ten, the unit 2 values from ten to twenty and the unit 3 values above twenty. The arithmetic operations were composed by stimuli printed numerals, sets and mathematical signs and the relations between them. Eight participants completed the unit 1 and four of these the unit 2 partially and yet two participants concluded the three teach units. The analysis of the results allowed us verify that the subtraction operations were more difficult for some participants, causing greater errors number, and the operations that had the operation s result as sample stimulus showed have been more complex for some them. The evaluation and teach program of addition and subtraction skills made possible the development of a behavioral analysis of these arithmetic operations and the identification of several relevant issues for future studies, such as the role of the signal mathematic in the formation of equivalence classes, the use of strategies on problem solving, the inverse relation between the addition and subtraction operations, the interrelation between the pre-math skills and arithmetic skills, among others. / Os objetivos do presente estudo foram propor: um instrumento de avaliação de habilidades pré-aritméticas que permitisse mapear os repertórios de estudantes dos anos iniciais do ensino fundamental e analisar a complexidade das relações que compunham o instrumento; e um programa de avaliação e ensino de adição e subtração com base no paradigma de equivalência, descrevendo método, resultados e análises comportamentais em uma linguagem que tenta promover a intercomunicação com profissionais de outras áreas, sobretudo da Educação Matemática. Participaram do teste do instrumento de avaliação de habilidades pré-aritméticas doze crianças do segundo ao quinto ano do ensino fundamental, estudantes de uma escola pública de Porto Ferreira/SP. O procedimento foi composto por doze tarefas ambientadas em MTS e CRMTS que testaram as relações de discriminação de numerais, nomes de números e conjuntos; nomeação de numerais, nomes de números e quantificação de conjuntos; ordenação de numerais e de conjuntos em ordem crescente e decrescente; relação antes/depois com numerais e conjuntos; relação maior/menor com e sem modelo; relação mais/menos com e sem modelo; relação de igualdade entre numerais e entre conjuntos; relações numeral-conjunto, conjunto-numeral, nome-numeral, numeral-nome, nome-conjunto e conjunto-nome; estimativas entre numerais e conjuntos; completação de sequências com conjuntos e com numerais. Os resultados mostraram a viabilidade do instrumento para observar lacunas nos repertórios dos participantes que pudessem interferir em aprendizagens posteriores, tais como em conceitos de adição e subtração, e permitiu fazer uma análise comportamental das habilidades componentes. Dando prosseguimento, nove dos mesmos participantes foram expostos aos procedimentos de MTS que compuseram o programa de avaliação e ensino de adição e subtração, embasado teórica e conceitualmente no paradigma de equivalência. O programa foi organizado em três unidades, segundo níveis de dificuldade, sendo que a unidade 1 contemplou valores de um a dez, a unidade 2, valores de 10 a 20 e a unidade 3, valores maiores que 20. As operações aritméticas foram compostas pelos estímulos numerais impressos, conjuntos e operadores matemáticos e as relações entre eles. Oito participantes completaram a unidade 1 e, desses, quatro realizaram parcialmente a unidade 2 e dois completaram as três unidades de ensino. A análise dos resultados permitiu verificar que as operações de subtração se mostraram mais difíceis para alguns participantes, suscitando maior número de erros, e as operações que tinham o resultado como estímulo-modelo também se mostraram mais complexas para parte dos participantes. O programa de avaliação e ensino de adição e subtração possibilitou a realização de uma análise comportamental dessas operações aritméticas e a identificação de várias questões relevantes para estudos futuros, tais como o papel do operador matemático na formação das classes equivalentes, o uso de estratégias de solução de problemas, a relação inversa entre as operações de adição e subtração, a inter-relação entre as habilidades pré-aritméticas e aritméticas, entre outras.

The two purposes of this study are first, to provide an evaluation of an after-school basic mathematics program at the Demonstration School for the Deaf Junior Secondary School (DemoDeaf) in Mampong-Akuapim, Ghana. Second, it provides an ecological discussion exploring why DemoDeaf students do not have access to quality education. I designed and piloted the math program in 2005 and 2007 as an action researcher and volunteer with the Non-Government Organization (NGO), Signs of Hope International. The program was developed after finding six students in one JSS class could not count to one-hundred and all other students struggled with addition and/or subtraction. The program has been shown quantitatively and qualitatively to have statistically significant and positive effects on DemoDeaf students. In 2007, the number of students proficient in counting increased from thirty-four to forty-four. An analysis of the addition achievement test results indicate students advanced a total of twenty-nine levels; four students learned to add single-digit numbers together, eleven students learned how to add double-digit numbers together, and fourteen students learned how to add triple-digit numbers together. An analysis of the subtraction achievement tests indicate students advanced a total of nineteen levels; six students learned to subtract single-digit numbers, eight students learned how to subtract double-digit numbers, and five students learned how to subtract with triple-digit numbers. Sample-t-tests showed that the increase of students proficient in counting, addition, or subtraction (except for triple-digit subtraction) was statistically significant at the p-value of < .01 or < .05. The stigma and negative stereotypes embedded in the normative culture in Ghana and the majority/minority relations and power dynamics between hearing and deaf groups influence the socializing institutions of the family and deaf schools. The normative hearing culture influences the language choice parents/guardians give their deaf child and how they treat them. The perspectives and values of hearing educators and administrators influence deaf school design and create a hidden curriculum for deaf students. These separate forces meet in the classroom and not only prevent students from receiving a quality secular education, they also reinforce the low status ascription of deaf students in Ghana.