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Over the last half century, mathematics education has seen numerous reform initiatives and standards. About every ten years, a new wave of documents offers recommendations on how to best teach mathematics. The Common Core State Standards for Mathematics (CCSSM; National Governors Association Center for Best Practices & Council of Chief State School Officers, 2010) builds on the concept of learning trajectories (LT) (Daro, Mosher, & Corcoran, 2011) and outlines the mathematics content and practices to be addressed at particular grade levels. With the widespread adoption of these standards, mathematics teacher educators have worked to share ideas about trajectories with teachers. Because research on learning largely developed separately from research on teaching, the authors' work used LTs to link these two bodies of research. They theorized the concept of Learning Trajectories Based Instruction (LTBI) as a model of teaching where instructional decisions are grounded in research on student learning in the form of trajectories and they interpreted several highly developed domains of research on mathematics teaching in relation to these trajectories (Sztajn, Confrey, Wilson, & Edgington, 2012). Since that time, the authors have worked to share this model with teachers in professional development settings, and their research has empirically examined and elaborated the affordances of LTBI. In this commentary, they critically analyze the LTBI model using Gutiérrez's (2007) dimensions of equity as a comprehensive framework for equity in mathematics education. Through this theoretical examination, they make explicit the assumptions inherent in the initial model and identify opportunities for LTBI to enhance equitable mathematics instruction. First, they briefly introduce current research on LTs and highlight principles of LTs that they contend are aligned with equitable instruction. Next, they present Gutiérrez's framework and a rationale for its selection as a tool for their theoretical analysis, briefly describing each of its dimensions. They detail their analysis of LTBI and conjecture what equity-oriented uses of the model might look like in instruction. The authors conclude with an invitation to the mathematics teacher education community to discuss the potentials and challenges of using LTs to support equitable mathematics instruction.

1Boy Crusoe

By Allan Eric

Also published as" A Yankee Crusoe" . A 15 year old hard working and studious farm boy finds the lure of adventure on the seas as a merchant seaman more than he can resist. This is his story. " I was born in a little town in the State of Maine, near the close of the Civil War. My boyhood life did not differ materially from that of the average farmer's son in the remote country districts of New England--except, perhaps, that I read more and thought more. Hard work on the rugged soil, two terms each year in the little yellow country schoolhouse, a day's fishing now and then filled the early years of my life full to over-flowing. " What he gets is enough excitement and adventure to overflow his wildest dreams. How he experiences disaster and uses his wits and knowledge to overcome every problem makes for a great read. - Summary by Phil Chenevert