In prior work, we fit the mixture Rasch model to item responses from a fractions survey administered to a nationwide sample of middle grades mathematics teachers in the United States. The mixture Rasch model located teachers on a continuous, unidimensional scale and fit best with 3 latent classes. We used item response data to generate initial…

Rational numbers are represented by multiple notations: fractions, decimals, and percentages. Whereas previous studies have investigated affordances of these notations for representing different types of information (DeWolf et al., 2015; Tian et al., 2020), the present study investigated their affordances for solving different types of arithmetic…

In this study, it is aimed to comparatively examine practice questions and sample solved questions about the multiplication of fractions in mathematics textbooks in Turkey and Singapore. In this direction, document analysis was used as a research method. Descriptive analysis was used in the analysis and the questions in the books were examined in…

Students entering sixth grade operate with three different multiplicative concepts that influence their reasoning in many domains important for middle school. For example, students who are operating with the second multiplicative concept (MC2 students) can begin to construct fractions as lengths but do not construct improper fractions as numbers.…

This paper builds on our previous research and investigates how students' fractional competence and reasoning can provide clear evidence of non-symbolic algebraic thinking and its progressive transition towards fully generalised algebraic thinking. In a large-scale study, 470 primary students completed a written paper and pencil test. This…

In the present study, we illuminate students' multiplicative reasoning in the context of their units-coordinating activity. Of particular interest is to investigate students' use of three levels of units as given material for problem-solving activity, which we regard as supporting a more advanced level of multiplicative reasoning. Among 13 middle…

Mathematical coherence is a goal within the Common Core State Standards for Mathematics. One aspect of this coherence is how student mathematical thinking is developed across concepts. Unfortunately, mathematics is often taught as isolated ideas across grades. The multiplicative field is an area of study that needs to be examined as a space to…

The present study examined preservice elementary teachers' performance on the problems of multiplication and division of fractions and compared their performances and analyzed the misconceptions. An instrument including 11 fraction multiplication and division tasks was given and the task involved three contexts: making own story problem,…

In the body of knowledge in mathematics education research, fractions are one of the researchers' concerns. The reason is because fractions are very difficult for students to understand. This study explores elementary school students' knowledge and obstacles in dealing with the multiplication of fractions. This study employs descriptive…

This article introduces unit transformation graphs (UTGs) as a tool for diagramming the ways students use sequences of mental actions to solve mathematical tasks. We report findings from a study in which we identified patterns in the ways preservice elementary school teachers relied on working memory to coordinate mental actions when operating in…

This study was guided by the question, how do we understand the multiplicative reasoning of upper high school students and use that to give insight to their performance on a standardized test? After administering a partial ACT assessment to a class of high school students, we identified students to make comparisons between low and high scoring…

A one-on-one dialogue-based mathematics intelligent tutoring system (ITS) for learning multiplication and division of fractions was developed and evaluated in this study. This system could identify students' error types and misconceptions in real-time by using a block-based matching method. The adaptive dialogue-based instruction was supported by…

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises…

In this paper, we have tried to clearly explain the meaning of fractions and operations with fractions. Also, we have tried to illustrate with some examples how to apply the rules of operations with fractional numbers, giving different practical techniques through different figures, visualization methods, and concretizing problems. The paper…

The purposes of this study are to report current Preservice Teachers' (PTs) decimal abilities regarding the types of error patterns that they commit and to analyze characteristics of the errors in the problems posed for multiplication and division in decimals. We have determined common concept- and procedure-based errors made by the PTs. 37 PTs in…