When we administered the Test of Understanding of Vectors (TUV) to students who were completing a physics university remedial course (which covers subjects of a traditional high school physics course), we observed that they had considerable difficulties in interpreting the dot product as a projection. As a result of this, we decided to design a…

This is an experimental study, made used of the non-randomized experimental and control groups, pretest-posttest designs. The experimental and control groups were two separate intact classes in Algebra. For a period of twelve sessions, the experimental group was subjected to the scientific heuristic method, but the control group instead was given…

The purpose of this study is to investigate the effect of manipulatives (concrete learning materials) both on the academic achievement of secondary school students in mathematics and on their attitudes towards mathematics. Pretest-posttest control group experimental model, which is one of the quasi-experimental research designs, was used in the…

This study aimed to reveal the effects of teaching with concrete learning objects taken from the history of mathematics on student achievement. Being a quasi-experimental study, it was conducted with two grade 8 classes in a secondary school located in Trabzon. The experimental group consisted of 27 students and the control group consisted of 25.…

The effectiveness of two instructional interventions was investigated in the context of teaching Arithmetic Combinations (ACs) of multiplication and division to students with Learning Disabilities (LD) or Mild Intellectual Disability (MID). The intervention for the control group (LD = 20, MID = 10) was based on principles of effective instruction,…

This study explored secondary students' learning experiences in mathematics through digital game building. In this study, students were asked to become designers and builders in order to coauthor their own mathematics learning. Grounded in enactivism, this study examined the impact of game building on students' achievement. In addition, it…

This article examines the estimation of two-stage clustered designs for education randomized control trials (RCTs) using the nonparametric Neyman causal inference framework that underlies experiments. The key distinction between the considered causal models is whether potential treatment and control group outcomes are considered to be fixed for…

Students in U.S. public schools have consistently recorded substandard scores on measures of school performance in mathematics. This substandard performance could adversely affect the nation's future economic competitiveness, growth, and welfare. Educational and political leaders have sought school reforms that will result in U.S. students scoring…

In this paper, we provide evidence of the impact of early algebra (EA) over time. We document this impact in the following ways: (a) by showing the performance over time of an experimental group of 15 children on an algebra assessment, from 3rd to 5th grade; and (b) by showing how the performance on an algebra assessment of children from an…