{"id":7149,"date":"2017-02-07T01:33:50","date_gmt":"2017-02-07T01:33:50","guid":{"rendered":"https:\/\/citejournal.org\/\/\/"},"modified":"2017-05-18T20:18:14","modified_gmt":"2017-05-18T20:18:14","slug":"the-presentation-of-technology-for-teaching-and-learning-mathematics-in-textbooks-content-courses-for-elementary-teachers","status":"publish","type":"post","link":"https:\/\/citejournal.org\/volume-17\/issue-1-17\/mathematics\/the-presentation-of-technology-for-teaching-and-learning-mathematics-in-textbooks-content-courses-for-elementary-teachers","title":{"rendered":"The Presentation of Technology for Teaching and Learning Mathematics in Textbooks:\u00a0Content Courses for Elementary Teachers"},"content":{"rendered":"

With rapid and recent advances in electronic technology, it is not surprising and, perhaps, is even expected that veteran teachers of mathematics received little to no instruction on how to use such technologies for teaching and learning mathematics. Some forms of technology have only recently been developed, while others that have been in existence for some time may not have been a part of a teacher\u2019s precollege or teacher preparation experience. As technology evolves, so do the materials used for preparing teachers in the current era.<\/p>\n

This article presents an overview of how electronic technology is presented in textbooks written for mathematics content courses for prospective elementary teachers (i.e., those teaching students in kindergarten through Grade 8). The commonalities present across a sample of popular textbooks, as well as the features unique to individual textbooks, are discussed. Specific attention is given to the examples in which a textbook may influence the development of technological pedagogical content knowledge (TPCK; Mishra & Koehler, 2006; Niess, 2005) in prospective teachers. For the purposes of this paper, electronic technologies are defined to be calculators (either four-function, scientific, or graphing), tablets, and computers, which include the use of Web and social media resources, along with computer software such as spreadsheets and dynamic geometry software.<\/p>\n

Background<\/h2>\n

Professional organizations such as the International Society for Technology in Education (ISTE, 2007, 2008), the National Council of Teachers of Mathematics (NCTM, 2000, 2011), and the Conference Board of the Mathematical Sciences (2012) have advocated for the use of electronic technologies in the teaching and learning of mathematics. An ever-growing number of technological resources are available to both students and teachers. Some of these resources are content-generic (e.g., computers, tablets, SMARTBoards), while others are mathematics-specific, and can be designed for use in specific content strands of mathematics.<\/p>\n

In statistics, for example, handheld calculators may be utilized or preprogrammed to compute measures of center, spreadsheets have capabilities to quickly produce graphical displays, and some specially designed software programs allow the user to design and run simulations. Other tools (and functions of these same tools) allow for learning and teaching within other content strands, such as arithmetic, geometry, and algebra.<\/p>\n

Prospective teachers need experiences with these various types of technologies in order be prepared to teach mathematics in the digital age (Association of Mathematics Teacher Educators, 2006; ISTE, 2008; NCTM, 2011). In the United States, such experiences may occur within a mathematics content course. While a multitude of factors influence what actually occurs in the classroom, the textbook is a common feature in such courses.<\/p>\n

In this article, we use this common feature \u2013 the textbook \u2013 as a lens to see how prospective teachers may use technology in learning and preparing to teach mathematics. To that end, we will address the following research questions:<\/p>\n

    \n
  1. How is technology presented within textbooks for mathematics content courses for prospective elementary teachers in the United States?<\/li>\n
  2. In what ways may such textbooks influence the development of technological pedagogical content knowledge?<\/li>\n<\/ol>\n

    Role of Technology<\/h2>\n

    In the mathematics classroom, different types of technology may be used for various purposes. Dick and Hollebrands (2011) provided a helpful distinction between two different roles that technology may play: conveyance <\/em>and mathematical action<\/em>. \u201cConveyance technologies<\/em> are those used to convey, that is, to transmit and\/or receive information\u201d (p. xi, emphasis in original), and include technology used for presentation, communication, sharing\/collaboration, and assessment\/monitoring\/distribution. Furthermore, conveyance technologies may be used for both mathematical tasks and nonmathematical tasks; one may use presentation software or the Internet in the same way for mathematics, science, literature, or history. \u201cConveyance technologies are not mathematics specific,\u201d the authors said (p. xii). Examples of conveyance technologies include presentation software, the Internet, and clickers.<\/p>\n

    By way of contrast, \u201cMathematical action technologies<\/em> are those that can perform mathematical tasks and\/or respond to the user\u2019s actions in mathematically defined ways\u201d (Dick & Hollebrands, 2011, p. xii). Mathematical action technologies include computational and representational tools such as calculators and spreadsheets, dynamic geometry environments, microworlds such as those found in virtual manipulatives for mathematics, and computer simulations. Additionally, while the Internet, writ large, is a conveyance technology, it does provide access to many different mathematical action technologies.<\/p>\n

    In this study, we identified the technology referenced in textbooks. When possible, we classified each reference as one pointing to a conveyance technology or a mathematical action technology. The following section connects our present study with the existing literature of mathematics textbook research.<\/p>\n

    Previous Textbook Analyses<\/h2>\n

    Little research has been published on textbooks used in mathematics content courses for prospective elementary teachers in the U.S. Three notable examples are found in McCrory (2006), the National Council on Teacher Quality (NCTQ, 2008), and McCrory and Stylianides (2014). In each of these studies, the authors examined between 16 and 20 textbooks intended for use in mathematics content courses for elementary teachers \u2013 nearly the entire population of such textbooks. While these studies did not specifically address technology, they did provide grounding for the selection and examination of textbooks.<\/p>\n

    McCrory (2006) presented an analysis of 20 textbooks for prospective elementary teachers. She stated, \u201cMost of the books are encyclopedic, including every topic that might be covered in K-8 classrooms, and treating each topic as a separate entity\u201d (p. 21), while others were more focused on a few big ideas and presented with a narrative approach. She found that the four textbooks in her sample written by research mathematicians were more narrative in style. These four textbooks also had a higher quality of mathematical coherence and rigor than the subset of 16 textbooks not written by research mathematicians.<\/p>\n

    In a study of U.S. teacher preparation programs, the NCTQ (2008) examined the syllabi of 118 mathematics courses at 77 institutions. A total of 19 different textbooks were identified across these syllabi, and an expert panel was asked to rate the books according the adequacy of coverage of the content areas of numbers and operations, algebra, geometry and measurement, and data analysis and probability. According to the panel\u2019s ratings, about two thirds of the courses they examined used textbooks that did not adequately cover all four of these areas. The criteria for rating was based on the presentation of 36 mathematical topics; the report gives no indication as to how references to technology may influence the quality of the presentation.<\/p>\n

    In a study of reasoning-and-proving in textbooks, McCrory and Stylianides (2014) analyzed 16 mathematics textbooks for prospective elementary teachers. Because reasoning-and-proving may be related to various topics in mathematics, they first examined the table of contents and index for references to reasoning-and-proving, such as generalizing or conjecturing. Next, they examined the pages containing the references to characterize the nature of reasoning-and-proving. Their methodology provided insight about how an instructor or student may use the textbook to gain insight on this particular mathematical activity.<\/p>\n

    As with reasoning-and-proving, technology may be applied to various topics in mathematics. However, we chose to examine each page of every chapter for technology references, instead of limiting our search to those pages referenced in the table of contents or index. Additionally, we viewed these textbooks as instruments that may impact a prospective teacher\u2019s knowledge. In the next section, we summarize the research literature regarding various types of knowledge.<\/p>\n

    Types of Knowledge<\/h2>\n

    Pedagogical content knowledge (PCK) is the unique blending of content expertise and skill in pedagogy to create a knowledge base that allows teachers to make robust instructional decisions. Shulman (1986) defined PCK as \u201ca second kind of content knowledge\u2026which goes beyond knowledge of subject matter per se to the dimension of subject matter knowledge for teaching<\/em>\u201d (p. 9). Since the time of Shulman\u2019s initial work, electronic technologies have been developed at an ever-increasing rate, and it is difficult to overestimate the impact of technology on teaching and learning, particularly in the area of mathematics.<\/p>\n

    To investigate teachers\u2019 knowledge for teaching with technology, Niess (2005) expanded on the concept of PCK and described the construct of technological pedagogical content knowledge (TPCK; later referred to in the literature as technology, pedagogy, and content knowledge, or TPACK) as \u201cthe integration of development of knowledge of subject matter with the development of technology and of knowledge of teaching and learning\u201d (p. 510). This characterization has been so useful that, in their editorial, Bull and Bell (2009) specifically suggested using TPACK as a framework for the research of technology in mathematics teacher education.<\/p>\n

    Mishra and Koehler (2006) distinguished TPCK from the related areas technological pedagogical knowledge (TPK) and technological content knowledge (TCK). Briefly, TPK is the knowledge of using technology for teaching, using tools that may be content-neutral, such as using social media or online surveys for real-time feedback and formative assessment. On the other hand, TCK is the knowledge of how technology may be used to teach particular content, such as using dynamic statistics software to conduct a large number of trials of a simulation and, thus, provide students with an understanding of the central limit theorem. According to McBroom (2012), \u201cStudents who use technology in learning are likely to possess TCK, but they are not likely to possess TPACK. Teachers, who teach with technology, should have TCK, but they also should have TPACK in order to teach effectively\u201d (p. 18).<\/p>\n

    In this study, we sought to identify activities within textbooks that had the potential to influence the development of a prospective teacher\u2019s TPACK. In the next section, we provide details of our research methodology.<\/p>\n

    Research Design<\/h2>\n

    Sample Selection<\/h3>\n

    We analyze textbooks used in mathematics content courses for prospective elementary teachers in the United States, using existing studies of mathematics textbooks for elementary teachers (McCrory, 2006; McCrory & Stylianides, 2014; NCTQ, 2008) to assist in the identification of the most commonly used titles. Six textbooks comprised the sample for this study and are listed in Appendix A<\/a>\u00a0along with abbreviated names used in this paper.<\/p>\n

    All six of these textbooks (or other editions) were analyzed by McCrory and Stylianides (2014) and NCTQ (2008). The first five textbooks listed were identified as the most commonly used textbooks in the NCTQ study, and were also analyzed by McCrory (2006). The sixth textbook, SSN, was also analyzed by the NCTQ, although it was relatively new at the time. It was selected for this study, in part, because of its use at the authors\u2019 institution.<\/p>\n

    A limitation of our sample lies in the nature of textbook publication. It is common practice for publishers to print a new edition every 3 or 4 years. In fact, two of the textbooks in our sample (BLL and MBP) have now published newer editions than those in the sample. This limitation has particular implications addressed in the Recommendations section of this paper.<\/p>\n

    Only the student editions of the textbooks were examined for this study. Furthermore, only chapter pages \u2013 those pages that were a part of the marked chapters of the textbook were examined. Other portions of the text, such as the table of contents, preface, and index, were not examined. Similarly, activity manuals and ancillary resources were not examined. In particular, the activity manual for Bec is bound with the rest of the textbook, but the manual was not examined. We did not analyze any appendices, except to note the titles of any appendices that referenced technology.<\/p>\n

    Methodology<\/h3>\n

    In a prior study, Jones (2014) examined the technology references within chapters of mathematics textbooks for prospective elementary teachers that addressed topics in statistics and probability. The study described in this article extended that prior study and included every chapter of each textbook. Each chapter page was examined for references to technology. References were identified when (a) the word \u201ctechnology\u201d appeared, (b) a specific type of technology was mentioned, or (c) a portion of text was marked with a technology-related icon (e.g., a calculator or computer mouse). Internet addresses (URLs) were included as technology references. On the other hand, instances of the phrases similar to, \u201cwithout using a calculator,\u201d were not coded as technology references.<\/p>\n

    Once a reference was identified, it was coded according to the type of technology (e.g., calculator, website, or computer) and the role of technology. We used the categories of conveyance technology<\/em> and mathematical action technology<\/em> (Dick & Hollebrands, 2011), as well as the neutral code term<\/em> for those cases where it was not possible to identify whether the reference referred to technology in a conveyance or mathematical action role. To clarify, consider these three references from MBP:<\/p>\n