Algebra has long been a gatekeeper to more advanced mathematics and to tertiary education. International assessments, such as PISA, have also shown that this trend extends beyond borders, making the topic of when algebra should be learned quite political. Many reforms have been instituted since the early 1990s to infuse algebraic thinking into…

Many literature studies point out how the process that moves the student from personal reasoning to the arrangement of fruitful argument could help them in the development of mathematical argumentative thinking. Starting from the above assumptions, in this paper we investigate the interaction among teacher/researcher and students in a Digital…

Low-income students and students of color are faced with pervasively lower levels of opportunity to learn compared with their peers, creating unequal opportunities for educational success. Textbooks, which serve as the backbone of the curriculum in most mathematics classrooms, present a potentially powerful tool to help mitigate unequal…

Faded worked examples have been used to promote problem solving performance, such as mathematics performance in many laboratory studies and short-term classroom studies. However, few studies have examined the ways educators may use fading in their own classroom on more accessible platforms that do not require programming experience. Further, few…

We report the results of a study on informal covariate statistical reasoning conducted with 22 students (aged 16 and 18 years). We designed and implemented a task in a digital technology environment to introduce the line of best fit. The task design having elements that foresee misconceptions reported in the literature, and by focusing on four…

In this paper, we discuss the theoretical foundation and implementation of two alternative instructional courses that aimed to support the development of elementary school students' early algebraic thinking. Both courses approached three basic algebra content strands: generalized arithmetic, functional thinking and modelling languages. The courses…

Perseverance is vital for the process of learning mathematics with understanding. To do so, students must wrestle with obstacles and amend their problem-solving plan when necessary. I collected qualitative data to investigate the nature of perseverance for 11 ninth-grade algebra students working on a challenging task for which they affirmed…

Solving systems of linear equations is of central importance in linear algebra and many related applications, yet there is limited literature examining the symbolizing processes students use as they work to solve systems of linear equations. In this paper, we examine this issue by analyzing final exam data from 68 students in an introductory…

An executive report to the President of the United States titled "Engaging to Excel: Producing One Million Additional College Graduates with Degrees in Science," predicted that over the next decade, the United States will lack college graduates in the fields of science, technology, engineering, and mathematics (STEM). One contributing…

The rules of indices, e.g. a[superscript n] b[superscript n] = (ab)[superscript n], are a particularly important part of elementary algebra. This paper reports results from a textbook analysis which examined how the shift from integer to rational exponents in the rules of indices is discussed in school textbooks. The analysis also considered…

All students need to discuss mathematics to develop and deepen understanding. However, for English Learners (ELs), peer dialogue is imperative and indispensable to conceptual understanding as they participate in mathematical practices and engage in increasingly sophisticated uses of language (Heritage, Walqui, and Linquanti 2015). As ELs share…

"Wheel spinning" is the phenomenon in which a student fails to master a Knowledge Component (KC), despite significant practice. Ideally, an intelligent tutoring system would detect this phenomenon early, so that the system or a teacher could try alternative instructional strategies. Prior work has put forward several criteria for wheel…

Financial literacy and financial capacity of schoolchildren should be developed to meet the requirements of the rapidly developing society and increasingly complicated financial system of the Russian Federation. The authors focused on the financial education of schoolchildren who represent a special target group in financial relations. The main…

Using correct definitions of the mathematical concepts is crucial for learning and teaching of any mathematical content. Being able to make mathematically correct definition of the concepts is an indicator of teachers' content knowledge. The purpose of this study is to determine how preservice middle school mathematics teachers define the concept…

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…