This article presents an overview of the ways technology is presented in textbooks written for mathematics content courses for prospective elementary teachers. Six popular textbooks comprising a total of more than 5,000 pages were examined, and 1,055 distinct references to technology were identified. These references are coded according to location within the textbook, role of technology, and type of technology. The treatment of technology varied across the textbooks in the sample. The number of references to technology ranged from 71 to 451. Two textbooks mentioned technology on less than 10% of the pages, while one mentioned technology on over one fourth of the pages. For each textbook, the majority of references were to mathematical action technologies. Across the sample, calculators, websites, and e-manipulatives were most frequently mentioned. Examples of textbook activities that may influence the development of technological pedagogical content knowledge in prospective elementary teachers are provided. Recommendations are made for future directions in curriculum development and research to address the challenge of preparing teachers to effectively teach mathematics in the digital age.
Prospective elementary teachers at three universities engaged in online modules called the Virtual Field Experience, created by the Math Forum. The prospective teachers learned about problem solving and mentoring elementary students in composing solutions and explanations to nonroutine challenge problems. Finally, through an asynchronous online environment, the prospective teachers mentored elementary students. The researchers assessed the prospective teachers’ solutions and explanations to problems at the beginning of the semester, at the middle of the semester after completing the training in mentoring, and again at the end of the semester after the mentoring was completed. The researchers observed improvements in the prospective teachers’ abilities to write explanations to problems. Specifically, growth was seen in prospective teachers’ communication of their explanations and their ability to construct viable arguments and critique the reasoning of others (Common Core State Standards Initiative, 2010, Standard for Mathematical Practice 3), and attend to precision (Standard for Mathematical Practice 6).
In a course emphasizing interactive technology, 19 students, including 18 mathematics education majors, mostly in their first year, reinvented the definition of limit of a sequence while working in small cooperative groups. The class spent four sessions of 75 minutes each on a cyclical process of guided reinvention of the definition of limit of a sequence for a particular value, L = 5. Tentative definitions were tested systematically against a well-chosen set of examples of sequences that converged, or not, to 5. Students shared their definitions and the problems they were having with their definitions with their peers through whole class presentations and public postings on a course electronic forum. Student presenters received feedback from their peers both in person and through the forum. The approximation, error, error bound framework was used to help structure students’ thinking. The use of interactive examples with epsilon bands and movable N values, in which students could zoom in to adjust the value of epsilon or zoom out to find a value of N, proved especially helpful in the process. The changes in their tentative definitions show the difficulties students had as well as the learning that occurred.
Teaching mathematics for understanding requires listening to each student’s mathematical thinking, best elicited in a one-on-one interview. Interviews are difficult to enact in a teacher’s busy schedule, however. In this study, the authors utilize smartphone technology to help mathematics teachers interview a student in a virtual one-on-one setting. Free from physical constraints and preconceived biases, teachers can concentrate on building questioning, listening, and responding skills when noticing student mathematical thinking. Teachers engaged in four communication types when working with students through this technology: clarification, verification, and either extension or redirection.