Logarithms, pivotal in advanced mathematics and real-world applications, often present challenges to students who resort to rote memorization without grasping their essence. While the emotional dimensions of learning mathematics are increasingly recognized, research in this area remains limited. This dissertation addresses this gap by examining a…

One important concept in the development of number knowledge is the cardinality principle, or knowing that the last word counted refers to the total number of items within the set. One prominent theory suggests that children learn this concept by observing sets being both counted and labeled with the correct set size (e.g., 1-2-3! 3!), thus…

Analogy is a powerful learning mechanism for children to learn novel, abstract concepts from only limited input, yet also requires cognitive supports. My dissertation sought to propose and examine number lines as a mathematical schema of the number system to facilitate both the development of rational number understanding and analogical reasoning.…

This study evaluated the effectiveness of a teaching procedure derived from an analysis of joint control to teach math skills to students with autism spectrum disorder. Given the limited amount of evidence on teaching procedures derived from the analysis of joint control to teach students with autism, additional investigations on this topic were…

Research evidence suggests that early mathematics education received before kindergarten can positively influence later mathematics learning. Given these findings, there is a need for the development of interventions and strategies that can successfully target young children's mathematical deficiencies in number sense, and more specifically,…

Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…

The use of logarithms, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. The primary aim of this research, therefore, was to investigate college students' understanding of logarithmic concepts through the use of a series of instructional tasks…

The maturation of multiplicative thinking is key to student progress in middle school as rational number, ratio, and proportion concepts are encountered. But many students arrive from the intermediate grades and falter in developing this essential disposition. Elementary students have historically learned multiplication and division as operation…