Wait for it . . . Delaying Instruction Improves Mathematics Problem Solving: A Classroom Study

Abstract

Engaging learners in exploratory problem-solving activities prior to receiving instruction (i.e., explore-instruct approach) has been endorsed as an effective learning approach. However, it remains unclear whether this approach is feasible for elementary-school children in a classroom context. In two experiments, second-graders solved mathematical equivalence problems either before or after receiving brief conceptual instruction. In Experiment 1 (n = 41), the explore-instruct approach was less effective at supporting learning than an instruct-solve approach. However, it did not include a common, but often overlooked feature of an explore-instruct approach, which is provision of a knowledge-application activity after instruction. In Experiment 2 (n = 47), we included a knowledge-application activity by having all children check their answers on previously solved problems. The explore-instruct approach in this experiment led to superior learning than an instruct-solve approach. Findings suggest promise for an explore-instruct approach, provided learners have the opportunity to apply knowledge from instruction.

Improving conceptual and procedural knowledge: The impact of instructional content within a mathematics lesson

“…Finally, the solve-instruct approach could be more effective for students with particular characteristics, such as mastery goal orientation (DeCaro, DeCaro, & Rittle-Johnson, 2015). Other prior research has investigated the solveinstruct approach with elementary-school children in one-on-one tutoring contexts and has yielded mixed results (DeCaro & Rittle-Johnson, 2012;Fyfe, DeCaro, & Rittle-Johnson, 2014;Loehr, Fyfe, & Rittle-Johnson, 2014). Thus, future research is needed to evaluate the potential of a solve-instruct approach for supporting knowledge in elementary-school classrooms, including identifying critical features of such an approach.…”

Effects of Cover Stories on Problem Solving in a Statistics Course

“…Before instruction, students are given a problem set or problem solving worksheet and are asked to invent a method that solves the problems. This approach has been found to improve conceptual understanding of statistical and mathematical concepts (Loehr, Fyfe, & Rittle-Johnson, 2014;Schwartz & Martin, 2004;Wiedmann, Leach, Rummel, & Wiley, 2012;Wiley, Goldenberg, Jarosz, Wiedmann, & Rummel, 2013). In this paradigm, having knowledge and interest for the cover story could play a bigger role.…”

Activation of Operational Thinking During Arithmetic Practice Hinders Learning And Transfer

“…We, therefore, agree with calls from mathematics educators to determine what changes can be implemented in US elementary mathematics curricula to foster the development of relational thinking in elementary school (Baroody & Ginsburg, 1983;Carpenter, Levi, Franke, & Zeringue, 2005;Jacobs et al, 2007;McNeil, 2008;Schliemann, Carraher, & Brizuela, 2007;Stephens, Blanton, Knuth, Isler, & Gardiner, in press). Fortunately, there is mounting evidence that even minor differences in curricula, such as teaching the equal sign in concert with inequality symbols , altering the timing of practice and conceptual instruction (Loehr et al, 2014), presenting problems in concrete form (Sherman & Bisanz, 2009), writing addition facts in non-traditional, c = a + b formats (McNeil et al, 2011), and practicing addition facts organized by equivalent sums can increase this relational thinking.…”

“…Instead of viewing it relationally as a symbol indicating that two quantities share a common value and are, thus, interchangeable within a mathematical context, they tend to view it operationally as a signal to add up all the numbers and put the total in 'the blank' (Alibali, 1999;Baroody & Ginsburg, 1983;Behr, Erlwanger, & Nichols, 1980;Falkner, Levi, & Carpenter, 1999;Jacobs, Franke, Carpenter, Levi, & Battey, 2007;Li, Ding, Capraro, & Capraro, 2008;Kieran, 1981;Loehr, Fyfe, & Rittle-Johnson, 2014;McNeil, 2005McNeil, , 2008Perry, 1991;Powell & Fuchs, 2010;Renwick, 1932;Weaver, 1973). This is worrisome because this operational way of thinking does not generalize beyond simple arithmetic, and a relational understanding of the equal sign is critical for success in algebra (Falkner et al, 1999;Jacobs et al, 2007;Kieran, 1992;National Research Council, 2001;Steinberg, Sleeman, & Ktorza, 1990).…”