title: Practice Makes the Difference: The Effect of Rate-Building and Rate-Controlled Practice on Retention

authors: McGregor, Susan Jennifer

subjects: Pecision Teaching

abstract: Six home-schooled students and one adult participant each initially practiced to accuracy two decks of five previously unknown multiplication facts. The decks were yoked for practice and reinforcement. Once accurate performance was achieved, overpractice was undertaken using custom computer software that allowed either fast (free-operant) or rate controlled responding. Rate-building practice, to an established fluency performance standard, was used with one deck while practice with the other deck was rate-controlled.  The number of times a fact was practiced was the same for both methods. Response rate and accuracy was assessed after training to accuracy, at the end of overpractice and after 4  and 8-weeks of no practice. The assessment at the end of rate-building confirmed that rate building resulted in fast and accurate responding. It also confirmed that, for the rate controlled facts, response rates did not meet the fluency performance standard. However, the 4- and 8-week retention assessments showed no consistent differences in accuracy or response rate between the rate-controlled and rate built decks. After 8 weeks without practice, performance on the rate-built deck was not significantly different to that prior to rate building. These results suggest that practice to fluency does not lead to superior retention when compared to the same amount of rate-controlled practice. The results also indicate that when a skill is practiced to fluency, a period without practice leads to deterioration, to pre-rate-building levels, of accuracy and response rate. This study highlights the need for research examining the role of maintenance in the effectiveness of fluency based learning like Precision Teaching.

text: Practice Makes the Difference: The Effect of Rate-Building and Rate-Controlled Practice on Retention Six home-schooled students and one adult participant each initially practiced to accuracy two decks of five previously unknown multiplication facts. The decks were yoked for practice and reinforcement. Once accurate performance was achieved, overpractice was undertaken using custom computer software that allowed either fast (free-operant) or rate controlled responding. Rate-building practice, to an established fluency performance standard, was used with one deck while practice with the other deck was rate-controlled.  The number of times a fact was practiced was the same for both methods. Response rate and accuracy was assessed after training to accuracy, at the end of overpractice and after 4  and 8-weeks of no practice. The assessment at the end of rate-building confirmed that rate building resulted in fast and accurate responding. It also confirmed that, for the rate controlled facts, response rates did not meet the fluency performance standard. However, the 4- and 8-week retention assessments showed no consistent differences in accuracy or response rate between the rate-controlled and rate built decks. After 8 weeks without practice, performance on the rate-built deck was not significantly different to that prior to rate building. These results suggest that practice to fluency does not lead to superior retention when compared to the same amount of rate-controlled practice. The results also indicate that when a skill is practiced to fluency, a period without practice leads to deterioration, to pre-rate-building levels, of accuracy and response rate. This study highlights the need for research examining the role of maintenance in the effectiveness of fluency based learning like Precision Teaching.

year: 2006

title: Domain and range operations in semigroups and rings

authors: Stokes, Tim E.

subjects: Science & Technology

abstract: A D-semigroup S is a semigroup equipped with an operation D satisfying laws asserting that for a ∈ S, D(a) is the smallest e in some set of idempotents U ⊆ S for which ea = a. D-semigroups correspond to left-reduced U-semiabundant semigroups. The basic properties and many examples of D-semigroups are given. Also considered are D-rings, whose multiplicative semigroup is a D-semigroup. Rickart *-rings provide important examples, and the most general D-rings for which the elements of the form D(a) constitute a lattice under the same meet and join operations as for Rickart *-rings are described.

text: Domain and range operations in semigroups and rings A D-semigroup S is a semigroup equipped with an operation D satisfying laws asserting that for a ∈ S, D(a) is the smallest e in some set of idempotents U ⊆ S for which ea = a. D-semigroups correspond to left-reduced U-semiabundant semigroups. The basic properties and many examples of D-semigroups are given. Also considered are D-rings, whose multiplicative semigroup is a D-semigroup. Rickart *-rings provide important examples, and the most general D-rings for which the elements of the form D(a) constitute a lattice under the same meet and join operations as for Rickart *-rings are described.

year: 2015

title: Te mātauranga whakatere waka

authors: Tuaupiki, Jackie Whetumarama

abstract: Hei tēnei tuhinga e whai ake nei, ka tirohia te hangarau waka a ngā tūpuna o Te Moana nui a Kiwa i whakawhiti ai rātou ki ō rātou moutere tae atu ki te mātauranga whakatere waka me te arotahi o te titiro ki te whakatinanatanga o aua mātauranga. Ka tāmutu i konā, ka pūhia te titiro i runga i ngā huarere o Poronīhia e kite ai tātou i ngā āhuatanga o Tāwhirimātea i ōna moutere me ngā wero ki te whakatere waka i ērā huarere.

text: Te mātauranga whakatere waka Hei tēnei tuhinga e whai ake nei, ka tirohia te hangarau waka a ngā tūpuna o Te Moana nui a Kiwa i whakawhiti ai rātou ki ō rātou moutere tae atu ki te mātauranga whakatere waka me te arotahi o te titiro ki te whakatinanatanga o aua mātauranga. Ka tāmutu i konā, ka pūhia te titiro i runga i ngā huarere o Poronīhia e kite ai tātou i ngā āhuatanga o Tāwhirimātea i ōna moutere me ngā wero ki te whakatere waka i ērā huarere.

year: 2017