Purpose: A growing trend in instructional improvement efforts is the use of formative assessment informed by research-based developmental trajectories of how students gain deeper understanding of subject matter content over time. This article reports the findings of a large-scale experimental study of an innovative mathematics professional…

Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. The authors discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment.

In this article, I analyze episodes from two third-grade classrooms drawn from a larger classroom teaching experiment to explore how these students began to incorporate nonnumerical symbols in their mathematical expressions when asked to represent indeterminate quantities. The article addresses two research questions: What understandings did these…

This article describes a learning trajectory on expressions and equations based on the sixth-grade Common Core State Standards for Mathematics (NGA/CCSSO, 2010). A classroom teaching experiment using design research (Lamberg & Middleton, 2009) was conducted. The data was analysed using Corbin and Strauss' (2014) Constant Comparative method and…

A repeated crossover experiment comparing learning among students handing in pen-and-paper homework (PPH) with students handing in web-based homework (WBH) has been conducted. The system used in the experiments, the tutor-web, has been used to deliver homework problems to thousands of students in mathematics and statistics over several years.…

This research is an action research which aims to implement contextual teaching and learning (CTL) approach to learn mathematics, focus on the integration subjects. The approach utilizes the use of mathematics manipulative so that students can understand a mathematical concept to construct their own. The method which used in this research are…

To investigate student difficulties in solving word problems in algebra, we carried out a teaching experiment involving 51 Indonesian students (12/13 year-old) who used a digital mathematics environment. The findings were backed up by an interview study, in which eighteen students (13/14 year-old) were involved. The perspective of mathematization,…

Thus far, it is unclear how students can learn most effectively from their own errors. In this study, reflections on the rationale behind self-made errors are assumed to enhance knowledge acquisition. In a field experiment with pre/post/follow-up design, the authors practiced fractions with 174 seventh- and eighth-grade students who were randomly…

This research aimed to examine the effect of the application of contextual teaching and learning (CTL) approach to the enhance of mathematical critical thinking ability (MCTA) of Primary School Teacher Students (PSTS). This research is an experimental study with the population of all students PSTS who took algebra subject matter of one university…

This teaching experiment provided students with continuous engagement in a problem-solving based instructional approach during one mathematics unit. Three sections of sixth-grade mathematics were sampled from a school in Florida, U.S.A. and one section was randomly assigned to experience teaching through problem solving. Students' problem-solving…

Understanding an arithmetic operation implies, at minimum, knowing the direction of effects that the operation produces. However, many children and adults, even those who execute arithmetic procedures correctly, may lack this knowledge on some operations and types of numbers. To test this hypothesis, we presented preservice teachers (Study 1),…

The intention of the present study was to see the improvement of students' intuitive skills. This improvement was seen by comparing the Realistic Mathematics Education (RME)-based instruction with the conventional mathematics instruction. The subject of this study was 164 fifth graders of elementary school in Palembang. The design of this study…

Visual representation has been recognized as a powerful learning tool in many learning domains. Based on the assumption that visual representations can support deeper understanding, we examined the effects of visual representations on learning performance and cognitive load in the domain of mathematics. An experimental condition with visual…

When young children attempt to locate the positions of numerals on a number line, the positions are often logarithmically rather than linearly distributed. This finding has been taken as evidence that the children represent numbers on a mental number line that is logarithmically calibrated. This article reports a statistical simulation showing…

As evidence-based reform becomes increasingly important in educational policy, it is becoming essential to understand how research design might contribute to reported effect sizes in experiments evaluating educational programs. The purpose of this study was to examine how methodological features such as types of publication, sample sizes, and…