Does generating examples aid proof production?

Many mathematics education researchers have suggested that asking learners to generate examples of mathematical concepts is an effective way of learning about novel concepts. To date, however, this suggestion has limited empirical support. We asked undergraduate students to study a novel concept by either tackling example generation tasks or reading worked solutions to these tasks. Contrary to suggestions in the literature, we found no advantage for the example generation group on subsequent proof production tasks. From a second study, we found that undergraduate students overwhelmingly adopt a trial and error approach to example generation and suggest that different example generation strategies may result in different learning gains. We conclude by arguing that the teaching strategy of example generation is not yet understood well enough to be a viable pedagogical recommendation.     

Transition to Science Teacher Educator: Tensions Experienced while Learning to Teach Lesson Sequencing

This self-study investigated the tensions that I (Heidi) encountered when teaching elementary preservice teachers how to develop a coherent sequence of five science lessons. Four lesson planning components guided me in developing a series of lessons to support the preservice teachers with this exercise. Employing self-study methodology, data sources included preservice teachers' artifacts, an audio-recording of the preservice teachers discussing the planning of their lesson sequence, and two reflection journals, one kept personally and one kept collaboratively with my co-author and critical friend (Meredith). Findings indicate that a tension of telling and growth developed gradually during the three weeks of teaching. The collaborative journal revealed that this tension was promoted by two other tensions: confidence and uncertainty, and planning and being responsive. Implications regarding the need for explicit teacher educator coursework and reflective practice opportunities are discussed as potential avenues for Ph.D. programs to consider to lessen the tensions that doctoral students may experience during their transition into the role of teacher educator.     

Learning opportunities from group discussions: warrants become the objects of debate

In the mathematics education literature, there is currently a debate about the mechanisms by which group discussion can contribute to mathematical learning and under what conditions this learning is likely to occur. In this paper, we contribute to this debate by illustrating three learning opportunities that group discussions can create. In analyzing a videotaped episode of eight middle school students discussing a statistical problem, we observed that these students frequently challenged the arguments that their colleagues presented. These challenges invited students to be explicit about what mathematical principles, or warrants, they were implicitly using as a basis for their mathematical claims, in some cases recognize the modes of reasoning they were using were invalid and reject these modes of reasoning, and in other cases, attempt to provide deductive support to justify why their modes of reasoning were appropriate. We then describe what social and environmental conditions allowed the discussion analyzed in this paper to occur.

College Students’ Psychological Needs and Intrinsic Motivation to Learn: An Examination of Self-Determination Theory

Over the last several decades, instructional communication scholars have studied and measured student motivation as an important learning outcome. Unfortunately, this research has lacked theoretical guidance and has treated student motivation as a construct that varies only in quantity, ignoring existing theory that suggests student motivation is best understood as a construct that differs in quality (i.e., intrinsic motivation). To create two new measures that incorporate theoretical explanations of student motivation, three studies (N = 1,067) were undertaken using self-determination theory (SDT) to operationalize students’ intrinsic motivation as a product of basic psychological need satisfaction. In the first two studies, the Student Psychological Needs Scale and the Intrinsic Motivation to Learn Scale were developed and validated. In the third study, parallel mediation analyses supported SDT’s prediction that the fulfillment of students’ psychological needs (i.e., autonomy, competence, relatedness) would mediate the relationship between personalized education practices and intrinsic motivation to learn.     

Take home tests: An experimental study

The take home test was compared with the conventional closed and open book tests at the college level. It was found that scores on knowledge items were significantly higher with the take home test, and that additional time spent looking up answers was important. An additional factor was the level of anxiety, perceived by students to be less with the take home test. Rampant cheating does not appear to be a problem with take home tests.     

State Policy and the Affordability of Public Higher Education: The Influence of State Grants on Persistence in Indiana

The coordination of state finance strategies has been widely advocated as a means of maintaining affordability in public colleges and universities. This article examines the influence of state grants on equalizing opportunity for persistence among full-time resident students in Indiana's public system of higher education. The findings indicate that the state has maintained a commitment to a balanced approach to higher education finance, with increases in state grants that corresponded with tuition increases in the middle 1990s. This investment has been sufficient to equalize opportunity to persist.     

Transformation of a Modern Newsroom Workforce

Digital transformation continues to impact the news industry and news organizations are adapting accordingly through shifts in required skills and prescribed job positions of journalists. In order to examine the changing nature of the modern journalist, a case study was conducted examining the employment histories of New York City journalists (n?=?3587). Social network analysis was used to better understand the career trajectories of journalists within the dataset, with a specific focus on understanding the development of new jobs for journalists in data, analytic, social, and mobile-oriented job positions. Findings demonstrate important differences between traditional employment patterns and those of employees in jobs requiring new skills and knowledge of new technology.     

THE TEACHER INTERNSHIP EXPERIENCES OF PROSPECTIVE HIGH SCHOOL MATHEMATICS TEACHERS

Nine prospective secondary mathematics teachers were interviewed about their teaching internship experience. The results of these interviews revealed that 7 of the 9 participants professed to value reform-oriented teaching and conceptual understanding in mathematics, yet all were paired with cooperating teachers who seemed to value traditional instruction and procedural understanding in mathematics. We explored the reasons that some of these student interns had positive experiences with their cooperating teachers and university supervisors while others had negative experiences. We found that the participants valued (a) critical feedback that was constructive and contained concrete recommendations for improvement, (b) freedom to use their own teaching methods, and (c) a friendly and supportive relationship with their mentors. The differing teaching philosophies of student teachers and their cooperating teachers contributed to negative experiences only when student teachers were not allowed freedom in their teaching methods.