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Edward A. Silver
How much do you know about presidents of NCTM? For each of the 50 past or present leaders of NCTM, try to match the timeframe of their leadership and the state from which they hailed.
Milan F. Sherman, Charity Cayton, Candace Walkington and Alexandra Funsch
Research has demonstrated that textbooks exert a considerable influence on students’ learning opportunities and that technology has the potential to transform mathematics instruction. This brief report provides a systematic analysis of how technology tasks are integrated into secondary mathematics curricula by analyzing a sample of 20 textbooks. The results indicate that across the entire sample, nearly 15% of tasks incorporated technology, and of those, 21% used it as a reorganizer of students’ mathematical thinking; calculators were the predominant technology utilized. Investigative textbooks were not more likely to incorporate technology than conventional texts, but algebra 2 texts were more likely to include technology than geometry texts. Implications for instruction and teacher preparation are discussed.
Sean P. Yee, George J. Roy and LuAnn Graul
As mathematical patterns become more complex, students' conditional reasoning skills need to be nurtured so that students continue to critique, construct, and persevere in making sense of these complexities. This article describes a mathematical task designed around the online version of the game Mastermind to safely foster conditional reasoning.
Douglas H. Clements, Julie Sarama, Carolyn Layzer, Fatih Unlu and Lily Fesler
Early education is replete with debates about “academic” versus “play” approaches. We evaluated 2 interventions, the Building Blocks (BB) mathematics curriculum and the BB synthesized with scaffolding of play to promote executive function (BBSEF), compared to a business-as-usual (BAU) control using a 3-armed cluster randomized trial with more than 1,000 children in 84 preschool classrooms across three districts (multiracial or multiethnic, low income, 27% English Language Learner). Impact estimates for BBSEF were mixed in sign, small in magnitude, and insignificant. Most impact estimates for BB were positive, but only a few were statistically significant, with more in the kindergarten year (delayed effects), including both mathematics achievement and executive function (EF) competencies. Gains in both mathematics and EF can be mutually supportive and thus resist the fade-out effect.
Jessica Hunt and Juanita Silva
We investigated the extent to which one elementary school child with working-memory differences made sense of number as a composite unit and advanced her reasoning. Through ongoing and retrospective analysis of eight teaching-experiment sessions, we uncovered four shifts in the child’s real-time negotiation of number over time: (a) initial “2s” and symmetry to consider counting on, (b) participatory awareness of 10 and use of algorithmic knowledge, (c) break apart and growing anticipation of tacit counting, and (d) advanced participatory tacit double counting. The results suggest a possible link between the child’s participatory knowledge and the extent to which her enacted activity met her goals for solving the problem more than her current “knowing.” The implications regarding a possible proof of concept toward implicit, intensive instruction are shared.
Micah S. Stohlmann
An escape room can be a great way for students to apply and practice mathematics they have learned. This article describes the development and implementation of a mathematical escape room with important principles to incorporate in escape rooms to help students persevere in problem solving.
Matt Enlow and S. Asli Özgün-Koca
Equality is one of the main concepts in K–12 mathematics. Students should develop the understanding that equality is a relationship between two mathematical expressions. In this month's GPS, we share tasks asking students one main question: how do they know whether or not two mathematical expressions are equivalent?