Background/Context: Despite the surge in efficacy studies, a recent meta-analysis indicates that the relative effectiveness of any two math interventions is largely unknown (Nelson & McMaster, 2019). Additionally, policy makers rarely choose educational programs based on an assessment of costs and cost-effectiveness (Hollands et al., 2016;…

We examined relations between symbolic and non-symbolic numerical magnitude representations, between whole number and fraction representations, and between these representations and overall mathematics achievement in fifth graders. Fraction and whole number symbolic and non-symbolic numerical magnitude understandings were measured using both…

Even though there numerous books, articles, research studies, and other publications written since National Council of Teacher of Mathematics (NCTM) published "Curriculum and Evaluation Standards of School Mathematics" in 1989 have advocated the use of manipulatives in the teaching of mathematics, there is no conclusive evidence showing that the…

In this paper, we analyze an investigative situation proposed to a class of 5th graders in a primary school. The situation is based on the following task: In a sale with group rates on a sliding scale, the students must find the lowest possible purchase price for a given number of tickets. A study of students' arguments made it possible to…