The Effects of Cumulative Practice on Mathematics Problem Solving

Abstract

This study compared three different methods of teaching five basic algebra rules to college students. All methods used the same procedures to teach the rules and included four 50-question review sessions interspersed among the training of the individual rules. The differences among methods involved the kinds of practice provided during the four review sessions. Participants who received cumulative practice answered 50 questions covering a mix of the rules learned prior to each review session. Participants who received a simple review answered 50 questions on one previously trained rule. Participants who received extra practice answered 50 extra questions on the rule they had just learned. Tests administered after each review included new questions for applying each rule (application items) and problems that required novel combinations of the rules (problem-solving items). On the final test, the cumulative group outscored the other groups on application and problem-solving items. In addition, the cumulative group solved the problem-solving items significantly faster than the other groups. These results suggest that cumulative practice of component skills is an effective method of training problem solving.

The effects of interleaving versus blocking on foreign language pronunciation learning

“…Other studies have reported benefits of interleaving on the learning of geometric concepts (e.g., Taylor & Rohrer, 2010) and algebraic rules (e.g., Mayfield & Chase, 2002). A small but growing number of studies has also reported benefits of interleaving for other types of cognitive and motor tasks as well (for reviews, see Dunlosky, Rawson, Marsh, Nathan, & Willingham, 2013;Rohrer, 2012).…”

“…Students worked through practice problems in an order that was either blocked by type of figure (i.e., all problems pertaining to one type of figure were finished before the student moved on to the next type of figure) or interleaved such that the same problems appeared in an order that was shuffled and unpredictable. On a later test requiring students to calculate the volumes for similar types of figures, students scored higher if they had learned the information through interleaving, as compared with blocking.Other studies have reported benefits of interleaving on the learning of geometric concepts (e.g., Taylor & Rohrer, 2010) and algebraic rules (e.g., Mayfield & Chase, 2002). A small but growing number of studies has also reported benefits of interleaving for other types of cognitive and motor tasks as well (for reviews, see Dunlosky, Rawson, Marsh, Nathan, & Willingham, 2013;Rohrer, 2012).…”

Deficiência intelectual e aquisição matemática: currículo como rede de relações condicionais

“…Fonte: Elaboração dos autores relações, sem que houvesse necessidade de ensiná-las diretamente. Neste procedimento, um novo membro foi adicionado ao conjunto de estímulos para ser discriminado dos outros previamente dominados, o que é denominado de programação cumulativa (Mayfield & Chase, 2002). Mayfield e Chase (2002) argumentam que a justaposição de diferentes tipos de problemas, em uma programação cumulativa de ensino, possibilita a aprendizagem de múltiplas discriminações.…”

Produção analítico-comportamental brasileira sobre comportamento matemático e de ensinar matemática: dados de 1970 a 2015

“…1455 de número, a resolução de problemas de adição e subtração e o ensino de frações, para diferentes populações, inclusive, pessoas com desenvolvimento atípico (e.g., Escobal, Rossit, & Goyos, 2010;Lynch & Cuvo, 1995;Prado & de Rose, 1999;Santos, Cameschi, & Hanna, 2012;Santos, Simonassi, Rodrigues, & Magri, 2014). Diversas pesquisas visaram identifi car formas de tornar o aprendizado de Matemática mais fácil e efi caz pela avaliação de diferentes métodos de ensino ou do estabelecimento de comportamento pré-requisito (e.g., Levingston, Neef, & Cihon, & 2009;Mayfi eld & Chase, 2002) ou, ainda, por meio do desenvolvimento de estratégias especí-fi cas, como o emprego de uma balança virtual para resolver problemas de adição e de subtração (e.g., Iégas & Haydu, 2015). Também têm sido desenvolvidas propostas para o ensino de habilidades complexas como é o caso da Estatís-tica inferencial (e.g., Critchfi eld & Fienup, 2010;Fienup & Critchfi eld, 2011).…”