This study aimed to produce learning trajectory with rowing context that can help students understand addition and subtraction of fractions. Subject of the research were students IV MIN 2 Palembang. The method used was research design with three stages, those are preparing for the experiment, the design experiments, and the retrospective analysis.…

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…

Empirical arguments rely on examples without necessarily addressing all cases. Students should be skeptical of empirical evidence and should seek more secure arguments for generalizations, such as those that explain why a generalization is true for all cases. Generalizing on the basis of patterns in data is an important mathematical practice;…

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…

Previous research has illustrated the importance of acquiring knowledge from authentic contexts; however, without full engagement, students' learning performance might not be as good as expected. In this study, a Team Competition-based Ubiquitous Gaming approach was proposed for improving students' learning effectiveness in authentic learning…

The equipartitioning learning trajectory (Confrey, Maloney, Nguyen, Mojica & Myers, 2009) has been hypothesized and the proficiency levels have been validated through much prior work. This study solidifies understanding of the upper level of co-splitting, which has been redefined through further clinical interview work (Corley, Confrey &…

Learning algebra is difficult for many students in part because of an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt…

Several previous researches showed that students had difficulty in understanding the basic concept of multiplication. Students are more likely to be introduced by using formula without involving the concept itself. This underlies the researcher to design a learning trajectory of learning multiplication using Permainan Tradisional Tepuk Bergambar…

Learning the concept of perimeter and area is not easy for students in grade 3 of primary school. A common mistake is that students think that if the area is the same, the perimeter also has to be the same. It is difficult for them to understand that for a given area, there are many possibilities of perimeter and vice versa. When student are not…

The meaning of fractions with integer multiplication is something that is difficult to understand by students. They tend to think that the product it produces a larger number, while the multiplication of fractions with integers, the result can be any number larger or smaller. This study is a research design that aims to develop a local…

An increasing number of K-12 school teachers have been using handheld, or palmtop, computers in the classroom as an integral means of facilitating education due to the flexibility, mobility, interactive learning capability, and comparatively inexpensive cost. This study involved two experiments in handheld computers: (a) a comparison of the…

Analogous thinking has been commonly discussed as being an inherent and distinguishing characteristic of human cognition (e.g., Gentner, 2010; Goldstone, Day, & Son, 2010; Holyoak, in press; Rittle-Johnson & Star, in press). Gentner (2003) has argued that as part of the human cognitive toolbox, comparison accompanied by the relational language to…

We present an inference algorithm for perturbation models based on Poisson regression. The algorithm is designed to handle unclassified input with multiple errors described by independent mal-rules. This knowledge representation provides an intelligent tutoring system with local and global information about a student, such as error classification…

Conventional testing systems usually give students a score as their test result, but do not show them how to improve their learning performance. Researchers have indicated that students would benefit more if individual learning guidance could be provided. However, most of the existing learning diagnosis models ignore the fact that one concept…