Using the iPad to Develop Preservice Teachers’ Understanding of the Common Core State Standards for Mathematical Practice

The Standards for Mathematical Practice as delineated in the Common Core State Standards for Mathematics describe the processes, proficiencies, and habits of mind that students are expected to develop through their engagement with mathematics (Dacey & Polly, 2012). The purpose of this chapter is to discuss, anecdotally, how the iPad, a tablet computer designed by Apple ™, can be used to develop preservice teachers’ understanding and implementation of the Standards for Mathematical Practice, most specifically Mathematical Practice Standard 3: Construct viable arguments and critique the reasoning of others. Under examination are the authors’ experiences using the iPad as an observational tool during student teaching and as a teaching tool in their mathematics methods courses. The chapter concludes with suggestions for additional uses of the iPad to support preservice teachers as they work to develop their understanding of the Standards for Mathematical Practice.

TPACK Pathways that Facilitate CCSS Implementation for Secondary Mathematics Teacher Candidates

Implementation of the Common Core State Standards in Mathematics has provided teacher educators a great opportunity to reexamine whether teacher preparation programs adequately provide the experiences to develop the base of knowledge and 21st century skills necessary to be effective teachers. The Mathematics TPACK Framework provides a roadmap for a series of pathways to integrate three knowledge components that are essential in teacher development: content knowledge, pedagogical knowledge, and technological knowledge. In this chapter, the authors examine how a teacher preparation program has evolved to integrate meaningful uses of digital technologies in content and pedagogy that are relevant to the teaching and learning of mathematics through the lens of implementing the Common Core State Standards.

The Impact of Investigations and the Interactive Whiteboard on Students’ Mathematical Practice in Investigations Classrooms

This chapter relates the classroom experiences of 44 teachers across the United States, implementing Investigations in Number, Data, and Space, an elementary school mathematics curriculum. These teachers participated in a “tryout” of Investigations for the Interactive Whiteboard with their students. Investigations for the Interactive Whiteboard was developed in collaboration by Pearson, TERC, and SMART Board. The teachers’ reactions showcase how the use of this technology enhanced the teaching and learning of mathematics. These vignettes illuminate the essence of Common Core Standards for Mathematical Practice (CCSSI, 2010), which describe how students should engage with the mathematical skills and concepts of the Common Core Content. The use of the interactive whiteboard engaged all students, motivated them to participate beyond their norm, allowed modeling of the mathematics which opened access to all students, and encouraged students to explain, argue, and defend their ideas while listening to and critiquing others, the essences of the Standards for Mathematical Practice.

Common Core Standards for Mathematical Practice and TPACK

This chapter seeks to answer the guiding question: How does the TPACK (Technological Pedagogical Content Knowledge) framework influence how technology can support the implementation of the Common Core Standards for Mathematical Practice? The authors provide an overview of the Standards for Mathematical Practice and an application of the TPACK framework to the Common Core State Standards for Mathematics. Classroom scenarios describe how teachers can use the TPACK framework to integrate technology into the Standards for Mathematical Practice from kindergarten to eighth grade. The authors conclude with implications for professional developers, teacher educators, and administrators as they work to develop teachers’ TPACK and prepare teachers for implementing the Common Core State Standards for Mathematics.

Supporting Pattern Exploration and Algebraic Reasoning through the Use of Spreadsheets

As teachers prepare to teach the Common Core State Standards for Mathematics (CCSSM), students’ exploration of patterns and relationships between numbers has gained more importance. Specifically, students’ conceptual understanding of numerical patterns is critical in middle school, as it lays a groundwork for fostering mathematical thinking at all levels. Educational technologies can enhance student’s explorations of patterns by providing opportunities to represent patterns, test conjectures, and make generalizations. In this chapter, the authors illustrate how spreadsheets can support students’ explorations of both arithmetic and geometric patterns in the middle grades.

PhET Interactive Simulations

This chapter focuses on the design and use of interactive simulations as a powerful tool for learning mathematics. Since 2002, the PhET Interactive Simulations project at the University of Colorado Boulder (http://phet.colorado.edu) has been developing and studying the use of interactive simulations in teaching and learning STEM. While the project’s initial work focused on science learning, the project now includes a significant effort in mathematics learning. In this chapter, the authors describe the PhET project, including theoretical perspective, design goals, and research-based simulation design principles. They demonstrate how these design principles are applied to simulations, describe how they support achievement of the Common Core State Standards for Mathematics (CCSSM), and provide supporting evidence from individual student interviews. Finally, the authors discuss various approaches to using these simulations in class and provide guidance on leveraging their capabilities to support knowledge construction in mathematics in a uniquely engaging and effective way.

Digitizing Students’ Voices

This chapter focuses on how assessment for learning can be used to promote the development of student understanding of mathematics and mathematical practices as described in the Common Core State Standards for Mathematics while emphasizing the affordances of digital technologies. The mathematical focus centered on the families of functions connected to the mathematical practice of constructing viable arguments when using the digital technology tool, VoiceThread. The chapter describes an iterative model for implementing assessment for learning practices where VoiceThread gave voice to preservice teachers’ mathematical justifications. Findings are taken from a study set in an algebra course designed for preservice elementary teachers working towards a minor in mathematics. Preservice teachers noted the positive impacts of using VoiceThread in improving their justification skills and the benefits of assessment for learning practices on their learning process.

LessonSketch

This chapter describes how the authors have utilized digital graphics and Web 2.0 technologies to design an information technology environment, LessonSketch. In LessonSketch teachers can learn about mathematical practice in instruction through the transaction of representations of practice. The authors describe the main features of LessonSketch, its collection of lessons, and its authoring tools, and illustrate what teacher educators have done with them.

Implementing Common Core State Standards using Digital Curriculum

Teachers and educators transitioning to the Common Core State Standards face a significant challenge of creating new lessons and resources, as well as formative assessments that match the increased rigor required. Teachers must ensure that each student achieves and demonstrates higher levels of understanding. Many aspects of this transition can be mitigated, supported, and enhanced through blended learning. Blended learning leverages digital curriculum to assist teachers in creating a student-centered learning experience while providing a curriculum that meets the new standards. Students receive individualized instruction at their own pace, achieve mastery, and experience success in high school. They are equipped with a deeper level of understanding and the critical thinking and problem solving skills needed to succeed in college and work.

Sketchpad®, TinkerPlots®, and Fathom®

The Common Core State Standards for Mathematics (CCSSM) include overarching Standards for Mathematical Practice that cite dynamic geometry® software as one of the tools mathematically proficient students should know how to use strategically. Dynamic geometry software or more generally, dynamic mathematics software, provides visible and tangible representations of mathematical concepts that can be dragged and manipulated to discover underlying properties, investigate patterns and relationships, and develop deeper understandings of the concepts. The Geometer’s Sketchpad®, TinkerPlots®, and Fathom® are examples of dynamic mathematics software. This chapter outlines how dynamic mathematics software supports the CCSSM. Specific mathematic content examples are described using these three resources to model the use of dynamic mathematics software for learning mathematics. Challenges for successfully integrating dynamic mathematics software are described with suggestions for training and support.