We share results from a one-year early algebra classroom intervention. One kindergarten, one first-grade, and one second-grade classroom participated in the intervention and three classrooms of the same grade levels served as control sites. The intervention addressed the structure of even and odd numbers, mathematical equivalence and equations,…

Classification is a complex process that involves scientific concepts and higher-order mental processes such as abstraction, generalization, and pattern recognition. Even though it is an important competence for understanding the world, dealing with data and information, and solving complex problems, the education system embeds just its simplest…

Processing rational numbers is difficult for many children. The natural number bias is one possible explanation for why children struggle with rational numbers. It refers to the tendency to overgeneralize the properties of natural numbers. In this study, it is argued that in order to be successful in rational number tasks, individuals need to…

The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…

This study explored how a scenario-based (SB), one-semester professional development program influenced the instructional practices of preservice early childhood mathematics teachers. The participants completed a 15-week program in which they engaged with modeled in-class teaching experience and subsequently answered a number of questions that…

Recently, abstracted quantitative structures (AQS), a construct from quantitative reasoning, has been offered as a means to conceptualize and study mathematization during mathematical modeling. Extending this theoretical work, we provide empirical evidence that an intervention targeting participants' AQS can assist in aligning modelers' models…

The study discussed here aims to describe students' understandings of the definition of a mathematical function, which was achieved through a pilot case study of clinical interviews with four participants -- two ninth graders and two twelfth graders. The participants were recruited from the same urban public high school in the northeast of the…

In this study, we examined one experienced mathematician's class practices, with particular attention to cognitive model described in genetic decomposition. Our findings indicate that students only had limited opportunities to be familiar with the first three steps in genetic decomposition, which may potentially lead students to answer limit tasks…

The ability to interpret mathematical symbols and understand how they capture contextual relationships is a critical element of algebraic thinking. More often than not, students see algebra as merely a list of rules for manipulating abstract symbols, with limited to no meaning. Instead, for students to see algebra as a powerful tool and rich way…

Creative thinking in mathematics is an essential 21st Century skill that can be developed and encouraged through an exploration of mathematical concepts. In the context of the new "Australian Curriculum: Mathematics," this article explores the possibilities that are unlocked when students engage with tasks creatively in mathematics. By…

The understanding of analytical chemistry and its application in different areas of life science is something that should be encouraged for students studying chemistry, and also something that appeals to many students. Life science includes a vast variety of areas, out of which some are more easily approached in student projects. The chemical…

This study investigated in-service teachers' conceptualization of the pure imaginary number, within the Cartesian form, "a" + "ib" where "a" and "b" are real numbers and "i" is the imaginary unit. As part of a larger design-based research study, in which a professional development (PD) program was…

This paper aims to clarify how the use of the GeoGebra dynamic geometry program helps students understand the relationships between different representations of a linear function and develop the ability to plot a linear function. The study was based on a quasi-experimental design. In control classes, the topic of functions was presented without…

Textbooks play an important role in teachers' instructional decisions (Jones & Tarr, 2007), which consequently affects students' learning. This paper reports on a comparison of the elementary mathematics textbooks used in Iran and the United States, the Go-Math textbook. I analyzed topic sequences, frequency of the tasks, and cognitive demands…

This paper reports the results of research in which the objective was to explore the preconceptions of slope in seventh-grade students. Preconceptions are understood as students' knowledge prior to the formal teaching of a certain concept. For data collection, task-based interviews composed of ten tasks applied to 21 Mexican students were used.…