Instructions and recipes in mathematical proofs

Educational Studies in Mathematics - In mathematics education research, proofs are often conceptualized as sequences of mathematical assertions. We argue that this ignores proofs that contain...     

Why and how mathematicians read proofs: an exploratory study

In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, Journal for Research in Mathematics Education 39:431–459, 2008) and the philosophical literature on mathematical proof, we identify three general strategies that mathematicians employ when reading proofs: appealing to the authority of other mathematicians who read the proof, line-by-line reading, and modular reading. We argue that non-deductive reasoning plays an important role in each of these three strategies.     

A “Library School:” Building a Collaborative Preschool-Library Partnership to Support Whole Family Engagement

Early Childhood Education Journal - Preschools and public libraries are natural partners in that they share similarities in their support for early learning and family engagement for the young...     

Addressing the Needs of First‐Generation College Students: Lessons Learned From Adults From Low‐Education Families

The fact that 1st‐generation college students have lower retention rates than their peers and confront barriers hindering college success is well known. However, less information exists about the effect that 1st‐generation college status has after college completion. In this qualitative study, the career development experiences of adults from families without college education were examined. Three themes were identified: the role of the father, expectations about career, and expectations about college. Implications for college counselors are provided.     

Exploring the validity of assessment in anatomy: Do images influence cognitive processes used in answering extended matching questions?

Assessment is an important aspect of medical education because it tests students' competence and motivates them to study. Various assessment methods, with and without images, are used in the study of anatomy. In this study, we investigated the use of extended matching questions (EMQs). To gain insight into the influence of images on the validity of test items, we focused on students' cognitive processes while they answered questions with and without images. Seventeen first‐year medical students answered EMQs about gross anatomy, combined with either labeled images or answer lists, while thinking aloud. The participants' verbal reports were transcribed verbatim and then coded. Initial codes were based on a task analysis and were adapted into final codes during the coding process. Results showed that students used more cues from EMQs with images and visualized more often in EMQs with answer lists. Ready knowledge and verbal reasoning were used equally often in both conditions. In conclusion, EMQs with and without images elicit different results in this think aloud experiment, indicating different cognitive processes. They seem to measure different skills, making them valid for different testing purposes. The take‐home message for anatomy teachers is that questions without images seem to test the quality of students' mental images while questions with images test their ability to interpret visual information. It makes sense to use both response formats in tests. Using images from clinical practice instead of anatomical drawings will help to improve test validity. Anat Sci Educ 7: 107–116. © 2013 American Association of Anatomists.     

Teacher behavior, student interest and affective learning: putting theory to practice

Students of Project Adapt (PA), an instructional program for at-risk middle school students in Brooklyn NY, have displayed startling improvement on cognitive outcome measures. Teacher given grades and standardized tests illuminate the progress students have made since entering the program. The current investigation attempts to analyze PA on students' affective responses in a pre/post-test experimental design. Upon entering PA, students completed measures of interest, affect, and their previous teachers' behavior (pre). These ratings were then compared to end of year ratings on the same instruments (post). Results indicate students' perceive PA teachers utilizing different behaviors than their previous teachers. Additionally, student affect and interest increased significantly. Results of this study have implications for both instructional researchers and educational practitioners.