Student Connections between Algebraic and Graphical Polynomial Representations in the Context of a Polynomial Relation

When establishing connections among representations of associated mathematical concepts, students encounter different difficulties and successes along the way. The purpose of this study was to uncover information about and gain greater insight into how student processes connections. Pre-calculus students were observed and interviewed while performing a task that required connections among graphical and algebraic representations of a polynomial relation. Their reasoning and processes on the task were examined. This revealed more detailed information about the nature of their connections and misconceptions. The study reveals different types of student connections among graphical and algebraic representations.     

Expertise reversal effect in using explanatory notes for readers of Shakespearean text

The reported study compared the instructional effectiveness of Modern English explanatory interpretations of Shakespearean play extracts integrated line by line into original Elizabethan English text, with a conventional unguided original text condition. Experiment 1 demonstrated that the explanatory notes group reported a lower cognitive load and performed better in a comprehension test than the control group when students had no prior knowledge of the text. In Experiment 2, a reverse effect occurred when the same material was presented to a group of Shakespearean experts. Experiment 3 replicated the results of Experiment 1 using a different Shakespearean play. The study demonstrated that the relative effectiveness of instructional conditions depended on learner levels of expertise. In accordance with the expertise reversal effect, the benefits of guided instruction reversed and became detrimental for learners with high prior knowledge levels. Retrospective verbal protocols indicated that the explanations were redundant for expert readers.     

Rescuing Magical Thinking from the Jaws of Social Determinism

Although there is otherwise much to recommend it, by riveting attention too narrowly on the contents of magical thought, and by recasting what is left of process in exclusively substantiative terms, this target article works to create the unwarranted impression that the magical thoughts of children and adults are all of a common piece. This commentary reads these oversights and omissions as symptoms of an unspoken new-situationalism working behind the back of Woolley's review.