Using critical incident reflections: a self-study as a mathematics teacher educator

In this paper, I report the results of a 4-year study into how my students learn to become mathematics teachers during the combined 15-week methods and field placement course I teach. At the start of most weekly methods class meetings, groups of three or four students reported their critical incidents to each other, and then chose one incident to report to the whole class. Each student then submitted a written report of 10 critical incidents for grading. At the end of each semester, I administered a questionnaire about the usefulness of each of the elements of the course. Using these two main data sources, along with my own personal reflections on the course, this paper answers the question “What are the critical incidents preservice teachers encounter during their field experience, and what do they learn about teaching for understanding through reflecting on those critical incidents?” My analysis of the students’ incident reports found that the issues raised focused on four main areas: teaching and classroom management; student factors such as pre-requisite knowledge, understanding, resistance and motivation; issues concerning relationships with colleagues, students and parents; and school organizational issues such as policies and access to resources. Their learning about teaching for understanding focused on three broad areas: the conditions necessary to teach for understanding; facilitators of teaching for understanding; and barriers to teaching for understanding. The paper concludes with a discussion of the lessons learned about fostering reflection in novice teachers, and suggestions for further research.     

Construction and Validation of an Eight-Iron Approach Test

Abstract

The purpose of this study was to construct a golf test which would be usable for assessing the ability to perform an eight-iron approach shot at a distance of 12 yards from the pin. A good approach shot was defined as one which is high enough to avoid potential hazards between the point of contact and the pin and which comes to rest at or near the pin. Pilot studies were conducted to determine target size, number of trials and days of testing, hitting distance, objectivity, and reliability. The revised test was administered to 424 beginning golfers. Reliability estimates determined by analysis of variance procedures and by correlation techniques indicated that the test was reliable for the subjects involved. Logical validity was claimed and was further supported by comparing mean scores of a beginning and an experienced group. The test confidently differentiated the performance of the two groups.     

Phantoms and fabrications:young children's detection of implausible lies

The present study investigated whether young children are gullible and readily deceived by another's lies. Specifically, this study examined whether young children believe a lie teller's statement when the statement violates their developing knowledge of a distinction between reality and fantasy. In the first three experiments 3- to 6-year-olds (N = 293) were presented with either a story or a live staged event in which an individual made an implausible statement about a misdeed (claiming that a ghost jumped out of a book and broke a glass). A significant age effect was obtained: 5- and 6-year-olds tended to report that the individual who made the implausible statement had actually committed the misdeed, whereas 3- and 4-year-olds tended to accept the claim of the protagonist. Experiment 4 revealed that 5- and 6-year-olds (N = 43) not only disbelieved an individual's implausible statement but also inferred that the individual was lying and had a deceptive intent. In contrast, Experiment 5 revealed that 3- and 4-year-olds (N = 41) had difficulty disbelieving an individual's implausible claim about an inanimate object (i.e., the claim that a chair came alive and broke the glass). The findings suggest that 5- and 6-year-olds are not so gullible as previously thought, and that they use their well-developed real-world knowledge to detect scapegoating lies. In contrast, many younger children tend to believe another's implausible lies, perhaps due to the fact that the knowledge needed to detect such lies has not yet been consolidated.