This research aims to describe students' level of algebraic reasoning based on the adversity quotient types of climber, camper, and quitter in solving PISA model mathematics problems. This research is descriptive research with a qualitative approach. The research began by administering a questionnaire to determine the student's adversity quotient…

This study aims to describe how subjects construct explicit warrant derived from implicit warrant when completing mathematical proof. This research was conducted on seventeen students of mathematics education study programs by providing tests on vector material in elementary linear algebra courses. The test results show that there are four…

The aim of the study was to determine the arithmetic and algebraic problem-solving approaches of prospective mathematics teachers in the Department of Elementary Mathematics Education, and mathematics teachers in secondary schools. The study adopted mixed methods research design using exploratory sequential pattern. The participants of the study…

Students in secondary school often struggle with symbol sense, that is, the general ability to deal with symbols and to recognize the structure of algebraic formulas. Fostering symbol sense is an educational challenge. In graphing formulas by hand, defined as graphing using recognition and reasoning without technology, many aspects of symbol sense…

We studied the impact of metacognitive reflections on recently-completed work as a way to improve the retention of newly learned problem-solving techniques. Students video recorded themselves talking through problems immediately after finishing them, completed ongoing problem-solving strategy maps or problem-sorting exercises, and filled out…

Many students with Learning Disabilities (LD) experience low motivation and confidence in algebra as a result of the content challenges and the lack of mathematics success they have experienced previously (Kortering, de Bettencourt, & Braziel, 2005). The combination of multiple content deficits, an ongoing lack of success, and low motivation…

The Common Core Standards require students to learn content and mathematical practices, and so teachers must have content knowledge and be able to engage in practices themselves. This raises the question of how novice teachers learn to engage in mathematical practices. I investigate pre-service secondary teacher learning of mathematical practices…

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. 382 students from a calculus-based and an algebra-based introductory physics course were administered a quiz in the recitation…

Within the current test-centered educational reform movement, considerable emphasis is placed on using assessment results to make instructional decisions for individual students. Test scores are used to estimate a student's current level of skill, monitor his or her progress during instruction, and identify whether the student has gained the…

In this study, we examine introductory physics students' ability to perform analogical reasoning between two isomorphic problems which employ the same underlying physics principles but have different surface features. Three hundred sixty-two students from a calculus-based and an algebra-based introductory physics course were given a quiz in the…

The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these…

The purpose of this study is to apply the attribute hierarchy method (AHM) to a sample of SAT algebra items administered in March 2005. The AHM is a psychometric method for classifying examinees' test item responses into a set of structured attribute patterns associated with different components from a cognitive model of task performance. An…

The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

This descriptive study was aimed at looking into how Primary 5 pupils solve pre-algebra problems concerning patterns and unknown quantities. Specifically, objectives of this study were to describe Primary 5 pupils' solution strategies, modes of representations and justifications in: (a) discovering, describing and using numerical and geometrical…

Differences among students can yield rich benefits as well as pose difficult problems during collaborative learning. Students can draw on diverse individual experiences to exchange information, to understand different expressions of shared commonalities, and to construct new possibilities jointly. However, they also face the potential pitfalls of…