The Effects of Copy, Cover and Compare with and without Additional Error Drill on Multiplication Fact Fluency and Accuracy (original) (raw)
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A Preliminary Investigation of the Relationship Between Fluency and Application for Multiplication
Journal of Behavioral Education, 2005
Research suggests component skill performance has a strong positive relationship with composite skill performance. This study examined the association between accuracy and fluency for the component-composite relationship within multiplication. One hundred and fifty-seven fifth-graders did one-minute assessments for single-digit, and multi-digit multiplication problems. The results demonstrated the students achieved high levels of accuracy but low levels of fluency. Strong correlations between the component-composite skill fluency suggest that fluent component skills may have a significant role in composite skill performance. Moderate/low correlations between component and composite skill accuracy indicate that more than one skill component may contribute to composite skill acquisition.
DEVELOPING MULTIPLICATION FACT FLUENCY
Advances in Social Sciences Research Journal, 2015
Using specific components of three broad learning theories-cognitive, socialinteractional, and behavioral-students in 3 rd , 4 th and 5 th grade classrooms were given multiplication fact fluency instruction over a period of five weeks for 10-15 minutes each day.
Heterogeneity of math difficulties and its implications for interventions in multiplication skills
Math learning disability (MLD) is a heterogeneous condition characterized by severe and persistent difficulties in learning math, including difficulties in learning multiplication facts. Objective: In this article, we compared the responses of two MLD children to multiplication facts training. Methods: One of the children was a 9 year-old girl (HV) who presented mild math difficulties associated with lower accuracy of the Approximate Number System (ANS). The other was an 11 year-old boy (GA) who presented severe math difficulties related to impaired phonological processing due to developmental dyslexia. Both children underwent an intervention for multiplication, comprising conceptual instructions and retrieval practice of the times table. Results: HV's accuracy and response speed improved consistently on both training tasks, while GA's accuracy improved on the Simple Calculation Task only. Error analyses indicated that, after training, HV produced fewer errors of the type "close miss", and GA produced less omission but more operand errors. Conclusion: We argue that these differences between their responses to the training tasks were caused by differences in the mechanisms underlying their math difficulties. These results support the notion that individual specificities regarding math disabilities should be taken into account during preparation of training interventions. HeterogeneidAde dAs dificuldAdes nA AprendizAgem dA mAtemáticA e suAs implicAções pArA intervenções específicAs nAs HAbilidAdes de multiplicAção resumo. O transtorno de aprendizagem da matemática (MLD) é uma condição heterogênea caracterizada por dificuldades acentuadas e persistentes na aprendizagem da matemática, incluindo déficits na aprendizagem dos fatos de multiplicação. Objetivo: No presente artigo, nos comparamos a resposta de duas crianças com MLD em uma intervenção da multiplicação. Métodos: Uma das crianças, HV, sexo feminino, 9 anos de idade, apresentava dificuldades menos acentuadas na matemática, associadas a um déficit no Sistema Numérico Aproximado (ANS). A outra criança, GA, sexo masculino, 11 anos de idade, apresentava dificuldades na matemática mais acentuadas associadas a um comprometimento no processamento fonológico devido a um quadro de Dislexia do Desenvolvimento. Ambas as crianças passaram por um programa de intervenção para a multiplicação, o qual se consistia em instruções conceituais e práticas de memorização da tabuada. Resultados: HV apresentou uma melhora consistente na acurácia e tempo de resposta nas duas medidas de desfecho, enquanto, GA apresentou uma melhora apenas na Tarefa de Cálculos Simples. Análises nos tipos de erros evidenciam que, após a intervenção, HV cometeu menos "erros de aproximação", ao passo que, GA cometeu menos erros por omissão, mas mais erros de operando. Conclusão: Nossa hipótese é de que as diferenças na resposta a intervenção dos participantes estão relacionadas a mecanismos subjacentes distintos à aprendizagem da matemática. Esses resultados reforçam a necessidade de que as especificidades nas dificuldades na matemática de cada paciente sejam levadas em consideração durante o planejamento das intervenções. Palavras-chave: multiplicação, intervenção, transtornos de aprendizagem, discalculia.
A cognitive-pragmatic approach to error analysis
Questions and Answers in Linguistics, 2015
The purpose of the present paper is to analyze L2 and L3 production and comprehension from a cognitive-pragmatic point of view, taking into account Relevance Theory (Sperber and Wilson, 1986; Wilson and Sperber, 2006), Mental Models Theory (Johnson-Laird, 1983) and the Graded Salience Hypothesis (Giora, 1997). Special attention is paid to error analysis and to the detection of error sources, especially in the case of errors not attributable to transfer, interference or overgeneralization. The paper is based on three studies involving, first, L2 and L3 production (Study 1), both production and comprehension (Study 2) and L3 comprehension (Study 3). In general, the phenomena observed can be explained by a combination of Relevance Theory, Mental Models Theory and the Graded Salience Hypothesis. In fact, even when transfer is used as a strategy, its use is relevant to the learner, who assumes that it will be relevant to the recipient as well. The results also shed some light on the multilingual mental lexicon and multiple language processing.
2019
DOI: 10.14812/cufej.463588 The aim of this study is to determine the effect of Cover-Copy-Compare (CCC) interventions to increase the level of fluency in basic multiplication facts of a student having low performance in math, whether the student can maintain the level of fluency that she attained after a period of time and the social significance of the obtained data. A multiple-probes-across tasks (sets) design was employed in this study. The participant is a 9-year-old female student who is attending the second grade in general education (in the last two months of the second semester). Besides, she receives four hours of individual special education per week in a research center providing special education services for students with developmental disabilities at a state university. The findings of the study indicate that the education done with the CCC technique is effective in increasing the level of fluency of the student in basic multiplication operations in all sets, and she m...
The Development and Tryout of a Program Designed to Increase Students' Multiplication Fact Fluency
2015
Fluency skills are fundamental to the ability to complete relatively more complex problems using less mental energy. Most math curriculums do not stress the importance of automaticity of math facts. Variations in teaching styles and teaching modality seem to negate the true purpose for cementing and rapidly retrieving math facts. This study put to the test a program that was designed to increase students’ ability to retrieve multiplication facts fluently. The program exercised cognitive structures and enabled students to retrieve multiplication facts quickly. The results of a matched-pairs t-test indicated that after the students completed the course of the program, there was a statistically significant different in the students’ ability to retrieve multiplication facts accurately and speedily.
Jackson Natalie Deanne Simple Arithmetic Processing Fact Retrieval Mechanisms and the Influence of Individual Difference Surface Form Problem Type and Split on Processing Phd Thesis Murdoch University, 2007
Current theorising in the area of cognitive arithmetic suggests that simple arithmetic knowledge is stored in memory and accessed in the same way as word knowledge i.e., it is stored in a network of associations, with simple facts retrieved automatically from memory. However, to date, the main methodologies that have been employed to investigate automaticity in simple arithmetic processing (e.g., production and verification) have produced a wide variety of difficulties in interpretation. In an attempt to address this, the present series of investigations utilised a numerical variant of the well established single word semantic priming paradigm that involved the presentation of problems as primes (e.g., 2 + 3) and solutions as targets (e.g., 5), as they would occur in a natural setting. Adult university students were exposed to both addition and multiplication problems in each of three main prime target relationship conditions, including congruent (e.g., 2 + 3 and 5), incongruent (e.g., 2 + 3 and 13), and neutral conditions (X + Y and 5). When combined with a naming task and the use of short stimulus onset asynchronies (SOAs), this procedure enabled a more valid and reliable investigation into automaticity and the cognitive mechanisms underlying simple arithmetic processing.
Verification of Multiplication Facts: An Investigation Using Retrospective Protocols
The American Journal of Psychology, 2006
Retrospective verbal protocols collected throughout participants' performance of a multiplication verification task (e.g., "7 3 = 28, true or false?") documented a number of different strategies and changes in strategy use across different problem categories used for this common experimental task. Correct answer retrieval and comparison to the candidate answer was the modal but not the only strategy reported. Experiment 1 results supported the use of a calculation algorithm on some trials and the use of the difference between the candidate and correct answers (i.e., split) on others. Experiment 2 clearly demonstrated that participants sometimes bypassed retrieval by relying on the split information. Implications for mental arithmetic theories and the general efficacy of retrospective protocols are discussed.