Backward transfer is when learning about a new topic influences an individual's prior ways of reasoning about a topic they previously learned about. This study looked at how quadratic functions instruction differentially influenced students' prior ways of reasoning about linear functions. Specifically, we compared students at three levels of…

As proof and proving are the key elements of mathematics, several frameworks evaluating this process have been presented. Proof image, being one of them, was introduced by Kidron and Dreyfus (2014) through analyses of two mathematicians' activities. Authors clarified it in the context of components, and emphasized its relation with formal proof.…

Having the ability to make informed decisions about health, financial investments, and even the weather are all important to our everyday lives. However, most people receive no formal education on how to read and understand data presented in formats such as data tables and graphs. Research within the field of statistical reasoning demonstrates a…

We apply an advanced data visualization technique, "Sankey diagram," to explore how middle-school students (N = 343) solved problems in a game-based algebraic notation tool. The results indicate that there is a large variation in the types of students' strategies to solve the problems, with some approaches being more efficient than…

Students with a learning disability (LD) are experts in their lived experiences within the classroom. Yet, little is known about the ways in which students with LD perceive their instruction in mathematics and whether this instruction meets their learning needs. Similarly, the mathematical thinking and content knowledge of students with LD is…

Analogical reasoning has played a significant role in the development of modern mathematical concepts. Although some perspectives in mathematics education have argued against the use of analogies and analogical reasoning in instructional contexts, some attempts have been made to leverage the pedagogical power of analogies. I assert that with a…

Background. Placement in developmental education in college is associated with negative effects on credits earned, course achievement, and degree attainment (Valentine, Konstantopoulos, & Goldrick-Rab, 2017) and requires substantial investments with costs to students and institutions estimated at $1.3 and $7 billion (Ganga, Mazzariello &…

The Tesla coil is one of the most famous and popularly recognizable high voltage devices. Utilizing the fame of recognizability of the Tesla coil in a "Build Your Own" laboratory exercise is a great way to create a successful and highly interesting learning activity. Classical Tesla coils utilize a spark gap as the primary switch,…

Algebra, which is one of the learning domains of mathematics, is one of the most difficult ones for students as operative and semantic. For this reason, it is necessary to emphasize required importance on teaching algebra from early periods. Teachers have major roles in this process. The courses, taken by pre-service teachers in undergraduate,…

An essential skill for success in upper-division physics curricula is the ability to work with and apply mathematical and physical concepts through Cartesian and non-Cartesian coordinate systems. These skills are most notably necessary in electricity and magnetism, wherein students must build and solve integrals and perform vector derivatives in…

Mathematical connections are widely considered an important aspect of learning linear algebra, particularly at the introductory level. One effective strategy for teaching mathematical connections in introductory linear algebra is through inquiry-based learning (IBL). The demands of IBL instruction can make it difficult to implement such strategies…

In first- and second-year algebra classrooms, the all-too-familiar whine of "when are we ever going to use this in real life?" challenges mathematics teachers to find new, engaging ways to present mathematical concepts. The introduction of quadratic equations is typically modeled by describing the motion of a moving object with respect…

Teachers play a critical role in supporting students' mathematical engagement. There is evidence that meaningful student engagement occurs more often in student-centered classrooms, in which the teacher and the students mutually share mathematical authority. However, teacher-centered instruction continues to dominate classroom discourse, and…

A small percent of high school students are performing above satisfactory on end-of-course assessments, especially in Algebra 1 and Geometry. This is indicative that mathematics instruction may need to improve. One innovation in mathematics instruction is the incorporation of storying as an instructional strategy, as there is considerable research…

Although research and policy documents provide recommendations to inform secondary mathematics teacher preparation, no single study has addressed the "big ideas" of courses in multiple programs and how those big ideas may be interpreted through the lens of recent research and policy documents. To answer this need, we focused on big ideas…