Spartan Daily, February 5, 1975

Volume 64, Issue 4https://scholarworks.sjsu.edu/spartandaily/5937/thumbnail.jp

The Pacifican, December 7, 1973

https://scholarlycommons.pacific.edu/pacifican/2131/thumbnail.jp

The Limits of Rational Belief Revision: A Dilemma for the Darwinian Debunker

We are fallible creatures, prone to making all sorts of mistakes. So, we should be open to evidence of error. But what constitutes such evidence? And what is it to rationally accommodate it? I approach these questions by considering an evolutionary debunking argument according to which (a) we have good, scientific, reason to think our moral beliefs are mistaken, and (b) rationally accommodating this requires revising our confidence in, or altogether abandoning the suspect beliefs. I present a dilemma for such debunkers, which shows that either we have no reason to worry about our moral beliefs, or we do but we can self-correct. Either way, moral skepticism doesn’t follow. That the evolutionary debunking argument fails is important; also important, however, is what its failure reveals about rational belief revision. Specifically, it suggests that getting evidence of error is a non-trivial endeavor and that we cannot learn that we are likely to be mistaken about some matter from a neutral stance on that matter

Examining the Specialized Math Content Knowledge of Elementary Teachers in the Age of the Common Core

Mathematical standards for students have increased with the development of the Common Core State Standards for Mathematics and its accompanying high stakes testing. Teachers need strong conceptual knowledge of the mathematics they teach in order to give students the opportunity to learn that math deeply. An earlier study (Ma, 1999) found that US elementary teachers lack the deep knowledge to teach math conceptually. Given the mathematics standards movements of the last two decades, it is plausible that the knowledge base of teachers has changed. Using the framework of Specialized Content Knowledge (SCK), which is the knowledge required to teach math that extends beyond the knowledge to do math, this study examines the current level of SCK held by practicing elementary teachers. It also examines themes in the explanations they give for the four topics: subtraction with regrouping; multi-digit multiplication; division with fractions; and area, perimeter, and proof. This study used a multiple-case study design and an interview protocol with current elementary teachers (N=18). Analysis of teacher interviews indicates that elementary teacher SCK can vary with the topic being addressed, with all but two of the participants falling into different SCK levels across the mathematical content areas. This points to the need for assessments that offer topic-level data so we can determine the support individual teachers need. Most of the current teachers studied have strong Specialized Content Knowledge in areas of whole number calculation, such as subtraction with regrouping and multi-digit multiplication. In those topics they are able to create representations and justify the standard algorithms. In the areas of division with fractions and area, perimeter, and proof, however, Specialized Content Knowledge was frequently much lower, and many of the teachers struggled to create representations or explain the mathematics contained in the algorithms. This indicates a need for teacher education and professional development that extends beyond whole number operations and focuses on conceptual understanding of these challenging topics