An abundance of empirical evidence has amassed supporting the effectiveness of having students explain why correctproblem solutions are correct (Aleven & Koedinger, 2002; Hilbert, Renkl, Kessler, & Reiss, 2008) as well as why incor-rect problem solutions are incorrect (Durkin & Rittle-Johnson, 2012; Grosse & Renkl, 2006). However, despite strongtheoretical background for the approaches (e.g., Sweller, 1999; Siegler, 2002) and the growing amount of empirical ev-idence collected in real-world classrooms for students in middle school and above (e.g., Adams et al., 2014; Booth etal, 2015) it is yet unknown whether prompting self-explanation of correct and incorrect examples could be effectivelytranslated for elementary school mathematics classroom. In this project, we worked with elementary school teachers andmathematics coaches to construct developmentally appropriate worked-example assignments for 4th graders; the presentstudy tests the effectiveness of these collaboratively developed assignments for different topics in ethnically diverse 4thgrade classrooms.

Success in Algebra I often predicts whether or not a studentwill pursue higher levels of mathematics and science.However, many students enter algebra holding persistentmisconceptions that are difficult to eliminate, thus, hinderingtheir ability to succeed in algebra. One way to address thesemisconceptions is to implement worked-examples and self-explanation prompts, which have been shown to improvestudents’ conceptual knowledge. However this effect seems tobe greater after a delay. The current study sought to exploresuch time-related effects on algebra conceptual knowledge. Ina year-long random-assignment study, students either studiedworked-examples and answered self-explanation prompts (n =132) or solved typical isomorphic problems (n = 140). Athree-way mixed ANCOVA (pre-algebra knowledge xcondition x time) found a significant condition by time effect.The growth of algebra conceptual knowledge was greater forstudents studying worked-examples than for those solvingtypical problems.

Algebra I is considered a gatekeeper course for highereducation, high-paying jobs, and access to STEM careers, yetmany students find themselves struggling to learn algebra.Prior research links intrinsic motivation for learning mathwith mathematics achievement, particularly duringadolescence. The current study measured middle schoolstudents’ interest in algebra and their procedural skills acrossthe span of an algebra unit to determine whether students whoshow declines in algebraic problem-solving also show adecline in a particular type of intrinsic motivation – interest inalgebra. Pre-test and post-test scores were used to categorizeparticipants into those who showed declines in problem-solving skills and those who did not. Of the overall sample (N= 367), a group of 25 students showed declining skills overthe course of the unit. These students also showed significantdeclines in interest in mathematics from pre- to post-test incomparison to students who did not show procedural declines.Our findings support the relationship between performanceand motivation in the classroom, particularly in algebra class.Educational implications are discussed.

Recent studies have established that students knowledge about fractions is predictive of their readiness, performance, andlearning in Algebra (Booth & Newton, 2012; Booth, Newton, & Twiss-Garrity, 2013). However, it is yet unknown whetherthe relationship between fractions and algebra is causal; that is, would improving students’ knowledge of fractions causeimprovements in their ability to perform in and learn Algebra? The present study examines the impact of improvingfraction computation and fraction magnitude knowledge in real world classrooms on middle school students’ learningof key concepts and problem-solving techniques in Algebra. Individual differences in the impact of improved fractionknowledge will also be investigated and discussed.

Adaptive optics is a relatively new field, yet it is spreading rapidly and allows new questions to be asked about how the visual system is organized. The editors of this feature issue have posed a series of question to scientists involved in using adaptive optics in vision science. The questions are focused on three main areas. In the first we investigate the use of adaptive optics for psychophysical measurements of visual system function and for improving the optics of the eye. In the second, we look at the applications and impact of adaptive optics on retinal imaging and its promise for basic and applied research. In the third, we explore how adaptive optics is being used to improve our understanding of the neurophysiology of the visual system.