Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model

Abstract

Psychol Schs. 2020;57:946-958. wileyonlinelibrary.com/journal/pits 946 | Abstract Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning provides the foundation for advanced mathematics and algebraic reasoning. For students who struggle in mathematics, instruction in multiplication algorithms should ensure conceptual understanding so that students have a foundation for success in advanced mathematics. The concrete representational abstract (CRA) sequence addresses conceptual understanding and the strategic instruction model (SIM) supports procedural knowledge.The current pilot study combined these methods to teach elementary students the partial products algorithm. Twelve students in grades four and five participated in the study, receiving instruction from teachers in their school during an intervention period. Within a pre-experimental design, using pre-and postintervention data, students showed a significant change in performance. The article will describe and show how teachers implemented the CRA-SIM interventions and discuss implications for practice. K E Y W O R D S concrete representational abstract, mathematics, partial products

Mathematics Learning from Concrete to Abstract (1968-2021): A Bibliometric Analysis

“…The effects of the concrete-representational-abstract sequence for students at risk for mathematics failure ) 10. Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model (Flores et al, 2020b) 11. Improvement in elementary students' multiplication skills and understanding after learning through the combination of the concrete-representational-abstract sequence and strategic instruction 12.…”

“…The studies conducted by Flores M.M. were mainly related to the effectiveness of teaching elementary mathematics to students with special needs using a concrete-representational-abstract sequence (i.e., Flores, 2010;, Flores & Milton, 2020Flores et al, 2014bFlores et al, , 2014cFlores et al, , 2016Flores et al, , 2020aFlores et al, , 2020bMilton et al, 2019;Stroizer et al, 2015). Thereupon, the studies are highly relevant in the related research domain with 'concrete-representational-abstract sequence' and 'elementary education' as the top keywords.…”

“…A wide range of research rooted from the mathematics learning theory proposed by Bruner (1966) and Piaget (1952) has been conducted in the past spanning from types of manipulative used (e.g., Litster et al, 2019), teaching approaches (e.g., Flores et al, 2020aFlores et al, , 2020b, content domain (e.g., Braithwaite et al, 2016;Ching & Wu, 2019), grade level (e.g., O'Meara et al, 2020) and learning context (e.g., Sekeris et al, 2020). To synthesise findings of interventional studies related to the use of manipulatives and teaching approaches rooted from Bruner's Theory (1966) and Piaget's theory (1952) in enhancing mathematics learning of students with mathematics disabilities, meta-analysis and systematic literature review has been conducted by several researchers (i.e., Lafay et al, 2019;Park et al, 2021b;Peltier et al, 2020).…”

Teaching the partial products multiplication algorithm to students who struggle using CRA‐I

“…Finally, the abstract phase is implemented by solving problems with numbers only and may include use of a mnemonic strategy. CRA intervention research includes single‐digit operations (Harris et al, 1995; Mercer & Miller, 1992, 1993), number concepts (Hinton et al, 2015, 2020; Peterson et al, 1988), addition and subtraction with regrouping (Mancl et al, 2012; Miller & Kaffar, 2011), algebra (Maccini & Hughes, 2000; Witzel et al, 2003), rate of change (Bundock et al, 2021), and multiplication strategies such as the standard algorithm (Flores & Hinton, 2019; Flores et al, 2014) and partial products (Flores & Milton, 2020; Flores et al, 2020).…”