Reflections on Teaching with a Standards-Based Curriculum: A Conversation Among Mathematics Educators

Many teachers and researchers have written about the challenges inherent in adopting new teaching practices in mathematics classrooms (e.g., Chazan, 2000; Clarke, 1997; Heaton, 2000). The authors of this article, all with secondary mathematics teaching experience, are convinced by research suggesting that Standards-based mathematics curricula are beneficial for student learning.1 However, the first three authors had not used such curriculum materials in their own classrooms, and we desired experience using a Standards-based mathematics curriculum with secondary students. To this end, we taught a week-long summer course with a focus on linear functions to high school students who had previously struggled with algebra and volunteered to participate

Intended Mathematics Curriculum as Represented in State-Level Curriculum Standards: Consensus or Confusion?

Full Report published by: Information Age Publishers. http://www.infoagepub.comThis report represents the first detailed analysis of the grade placement of particular learning goals across all state-level curriculum documents published and current as of May 2005. The report documents the current situation regarding grade-level mathematics curriculum specification in the U.S. and highlights a general lack of consensus across states. As states continue to work to improve learning opportunities for all students, we hope this report will serve as a useful summary to inform future curriculum decisions.This report is based on the work of the Center for the Study of Mathematics Curriculum, supported by the National Science Foundation under Grant No. ESI-0333879. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation

National Trauma and Romantic Illusions in Percy Shelley’s <i>The Cenci</i>

Percy Shelley responded to the 1819 Peterloo Massacre by declaring the government&#8217;s response &#8220;a bloody murderous oppression.&#8222; As Shelley&#8217;s language suggests, this was a seminal event in the socially conscious life of the poet. Thereafter, Shelley devoted much of his writing to delineating the sociopolitical milieu of 1819 in political and confrontational works, including The Cenci, a verse drama that I argue portrays the coercive violence implicit in nationalism, or, as I term it, national trauma. In displaying the historical Roman Cenci family in starkly vituperous manner, that is, Shelley reveals his drive to speak to the historical moment, as he creates parallels between the tyranny that the Roman pater familias exhibits toward his family and the repression occurring during the time of emergent nationhood in Hanoverian England, which numerous scholars have addressed. While scholars have noted discrete acts of trauma in The Cenci and other Romantic works, there has been little sustained criticism from the theoretical point of view of trauma theory, which inhabits the intersections of history, cultural memory, and trauma, and which I explore as national trauma. Through The Cenci, Shelley implies that national trauma inheres within British nationhood in the multiple traumas of tyrannical rule, shored up by the nation&#8217;s cultural memory and history, instantiated in oppressive ancestral order and patrilineage. Viewing The Cenci from the perspective of national trauma, however, I conclude that Shelley&#8217;s revulsion at coercive governance and nationalism loses itself in the contemplation of the beautiful pathos of the effects of national trauma witnessed in Beatrice, as he instead turns to a more traditional national narrative

ANALYZING PSTS INSTRUCTIONAL MOVES THROUGH CULTURAL-HISTORICAL ACTIVITY THEORY

In this hour long session I will provide an overview of the session in order to focus the participants of the hour-long experience. Then I will provide the rationale for the study, discussing how and why CHAT can impact our work as mathematics teacher educators. Then,: I will share results from my analysis detailing the specific tensions PSTs faced and the subsequent instructional decisions they made. Specific examples will be shared. These findings will be used to discuss implications for mathematics teacher education during the discussion phase of the presentation. Participants will form small groups to share their thoughts and ideas regarding how PST education as well as in-service professional development benefit from approaching teaching from a CHAT perspective. Participants will also be encouraged to brainstorm ideas where this perspective can be used. After a brief time (10-15 minutes) of small group discussion, each group will then be asked to share the best ideas and thoughts stemming from the small group interaction. A summary of the ideas gleaned from participant and presenter discussion, as an avenue for next steps will be provide

Classroom Research: Prediction Questions in the Elementary Classroom

The mathematical knowledge needed for teaching in elementary schools is a multi-faceted paradigm that requires a solid understanding of the mathematical content and a firm grasp of pedagogical methodologies. Teachers also must possess the ability to understand students\u27 thinking, and pose productive questions, while making important instructional decisions in the moment. There is a burgeoning concern among researchers, educators, and policymakers to develop teacher capacities through professional development, empowering teachers to use effective and instructional practices that will improve student learning and achievement. Incorporating prediction questions into mathematics lessons has been shown to have effectual results in the teaching and learning of mathematics. In this paper we share the preliminary results of a pilot study in which we investigated how the use of prediction questions might transfer from a mathematics-teaching professional development experience into the elementary mathematics classroom and serve as a catalyst for promoting reform-teaching practices

Comparative Analysis of CCSSM and State Standards

First Presentation: Over the past three decades, the role of curriculum standards has become prominent in the United States. Once used as a method to articulate components of ideal practice and as a framework to guide measurement for student performance (Tate, 2004), the influence of standards in educational policy has evolved due to increased accountability measures tied to standards, their associated assessments and teacher performance. Today standards have considerable importance in outlining the mathematical content taught at particular grade levels, and provides guidance regarding the content that should be taught in mathematics teacher preparation courses. Furthermore, due to the high stakes attached to the mandated assessments associated with standards, these learning expectations carry considerable weight in determining what students have an opportunity to learn (Weiss, Pasley, Smith, Banilower, & Heck, 2003) and how teachers will be evaluated. This presentation will highlight the findings centered around the implementation of different states across the country. Second Presentation: Using Prediction Questions as a Vehicle for Professional Development (w/Esther Billings) Background Knowledge and Educational Significance In this session we recount our professional-development work where we investigated the ways that K-8 teachers uses of prediction questions transfers from a professional development setting to classroom practice and exhibits reform-teaching practice and share implications for professional development experiences. We then broaden this idea of levels of transfer by exploring how, we as professional developers, can extend this levels of framework to work with practicing and prospective teachers

Using Prediction Questions as a Vehicle for Professional Development

There are many different ways to provide practice-based professional development opportunities for practicing teachers. The use of prediction questions provides one such opportunity. We define prediction as reasoning about the mathematical ideas of a lesson using previous knowledge, patterns, or connections prior to formal instruction (Kasmer, 2009) .Prediction does not imply a simple premature guess. Rather, prediction is a sophisticated reasoning process connecting relevant ideas. In order to make a plausible prediction, students must activate their prior knowledge and connect concepts from previous learning. In this session we recount our professional-development work where we investigated the ways that K-8 teachers uses of prediction questions transfers from a professional development setting to classroom practice and exhibits reform-teaching practice, sharing implications for professional development experiences. We then broaden this idea of levels of transfer by exploring how, we as professional developers, can extend this levels of framework to work with practicing and prospective teachers

12th International Congress on Mathematical Education [ICME 12]

Learning mathematics for many students can be a complex endeavor and learning mathematics in an unfamiliar language often compounds this complexity. In this case study we provide a snapshot of our experience teaching mathematics to students in Tanzania. Through this work we came to understand the difficulties students face in trying to learn, as a result of not understanding what we attempted to convey. Students learning mathematics in a language other than their native tongue often struggle to comprehend the material. The lack of the background knowledge, vocabulary and expressions needed to comprehend mathematics along with the often-abstract content are obstacles that second language learners need to overcome in order to learn. Mathematical terms do not always translate well and often students do not understand key mathematical vocabulary. These two issues contribute to the difficulties students face when learning new mathematical content in a second language. Studies have demonstrated that the lack of proficiency in the language of instruction results in poor performance in the subjects taught when the language is not the students primary language (Cummins, 1981) These ideas are particularly critical for mathematics teacher educators. It is important to provide pre-service mathematics teachers the necessary tools and instructional strategies in order to create equitable learning opportunities for all students of mathematics. Without these important tools teachers cannot help their students make significant progress toward learning and understanding the mathematical content that is taught in a language other than their native tongue