Effect of Modifying Intervention Set Size With Acquisition Rate Data While Practicing Single-Digit Multiplication Facts

Abstract

Incremental rehearsal (IR) has consistently led to effective retention of newly learned material, including math facts. The number of new items taught during one intervention session, called the intervention set, could be used to individualize the intervention. The appropriate amount of information that a student can rehearse and later recall during one intervention session is called the acquisition rate (AR). The current study taught single-digit multiplication facts with factors of 6, 7, and 8 to 55 third- and fourth-grade students. Each student was randomly assigned to be taught two multiplication math facts, eight multiplication math facts, or a set size determined by each student’s AR. The average AR was 4.05 ( SD = 0.71). Set size led to a significant and large effect on retention, percentage of multiplication math facts retained, and efficiency as computed by math facts retained per minute of intervention time. IR appeared to be an effective intervention when AR data were used to determine the intervention set size, and it was more efficient to do so.

Assessing the Effects of Instructional Set Size on Learning

“…The ISS values were selected based on prior research. ISS-5 corresponds generally with the mean AR found in previous research and corresponds with the lower bound identified as short-term memory capacity (Burns et al, 2015). We conceptualized this as a probable lower bound for an ISS for most individuals.…”

“…Results showed that, on average, learning was more efficient in the condition in which the number of unknowns was based on the AR assessment, but that generalization data were inconsistent. A subsequent study extended the analysis of the interaction of AR and IR to single-digit multiplication facts for a single session in a between-groups design (Burns et al, 2015). In this study, participants practiced two unknown, eight unknown, or a number of unknown equations that was determined by the AR.…”

“…Perhaps the first line of research to begin to address this problem was conducted by Burns and colleagues, whose studies have examined the impact of acquisition rate (AR) on learning and retention (Burns, 2001; Burns & Helman, 2009; Burns, Zaslofsky, Maki, & Kwong, 2015; Haegele & Burns, 2015). AR is the amount of new material that can be learned before interference occurs and has been assessed using an IR procedure (see Burns, 2001).…”

“…The work of Burns and colleagues on bringing assessment to bear to increase instructional efficiency is both seminal and a bit paradoxical (Burns, 2001; Burns et al, 2015). This research is seminal in that it is the first systematic work to examine the possibility of tuning instruction to maximum efficiency through assessment data.…”

“…We anticipated that ISS-5 could be more effective for some learners based on prior research suggesting this as a plausible set size (Haegele & Burns, 2015), based on the increase in the number of learning trials per relationship, based on prior studies demonstrating advantages of smaller learning sets (Shaughnessy, 1973), and the lower cognitive load created by the smaller set (Cheng, Lu, & Yang, 2015). We anticipated that ISS-20 could be more effective for some learners based on prior research suggesting that under some conditions, higher cognitive load is more effective (Crossley et al, 2018; Phan et al, 2017), that devoting time to rehearsing known relations is less efficient (Cates et al, 2003), that CTD can be efficient in teaching a large set of responses (Mattingly & Bott, 1990), that when learning sets are too small they can result in participants learning a lower percentage of the targets (Burns et al, 2015), and based on concerns that repetitive rehearsal of a small learning set may undermine student attention and motivation. Thus, our central research questions were, would ISS be associated with differentiation in responding, and would differentiation vary across participants?…”