\nOther technology<\/td>\n | 1<\/td>\n | 0<\/td>\n | 0<\/td>\n | 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n The reference classified as \u201cunspecified technology\u201d in LDM occurred at the introduction to the statistics chapter, where statistical software is mentioned as one of several technologies that are used in data analysis.<\/p>\n MBP<\/em>.<\/strong> In the preface of MBP, the authors list three underlying themes for the book: problem solving, deductive reasoning, and technology. Referring to this third theme, \u201cVarious forms of technology are an integral part of society and can enrich the mathematical understanding of students when used appropriately\u201d (MBP, p. xii). These references to technology are located in many parts of the book: within both the main text and activities, and at times optional or implied, but most frequently required.<\/p>\nWe identified 451 technology references in MBP, and 393 were coded as mathematical action technologies. Of these, over half (199) referred to calculators (see Table 6). As with LDM, certain activities in MBP were marked with an icon that implied the use of technology. A unique feature of this book was the inclusion of a large number of e-manipulatives; these were available on the book\u2019s companion website and often required when they were mentioned within activities. These e-manipulatives were integrated within various content areas: number and operation, geometry, and statistics and probability.<\/p>\n The reference coded as \u201cunspecified technology\u201d was located in a sidebar and mentioned the role of technology in the workplace to perform lower order tasks such as computation. The \u201cother technology\u201d referred to an adding machine, contained in a historical discussion of computational devices.<\/p>\n SSN<\/em><\/strong>. In the preface, the authors posit that \u201cmathematics is not just about getting answers to questions but rather about developing insight into mathematical relationships and structures\u201d (SSN, p. xiii). From this perspective, the authors sequence activities, discussions, and questions throughout the main portion of the text. The book is divided into four major parts. The greatest number of technology references were found in the final part, which focused on statistics and probability.<\/p>\nWe identified 119 technology references, with 96 of them coded as mathematical action technologies. As shown in Table 7, the most common type of technology was in the form of a website, such as the NCTM Illuminations. Almost all of these website references were located within activities; half of these required the use of a website, and in the other half the use was optional. Calculators were mentioned in the main text, but occurred less frequently in activities.<\/p>\n Table 7 \n<\/strong>Counts of Technology References Within SSN<\/p>\n\n\n\n \nType of Technology <\/strong><\/td>\nMathematical Action \nTotal<\/strong><\/td>\nMathematical Action and Activity-Required<\/strong><\/td>\nMathematical Action and Activity-Optional<\/strong><\/td>\n<\/tr>\n\nWebsite<\/td>\n | 26<\/td>\n | 12<\/td>\n | 12<\/td>\n<\/tr>\n | \nCalculator<\/td>\n | 22<\/td>\n | 2<\/td>\n | 5<\/td>\n<\/tr>\n | \nComputer<\/td>\n | 13<\/td>\n | 1<\/td>\n | 1<\/td>\n<\/tr>\n | \nMotion detector<\/td>\n | 9<\/td>\n | 3<\/td>\n | 0<\/td>\n<\/tr>\n | \nSpreadsheet<\/td>\n | 4<\/td>\n | 0<\/td>\n | 0<\/td>\n<\/tr>\n | \nDynamic statistics software<\/td>\n | 4<\/td>\n | 1<\/td>\n | 3<\/td>\n<\/tr>\n | \nUnspecified technology<\/td>\n | 15<\/td>\n | 6<\/td>\n | 3<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n <\/p>\n This textbook was unique within our sample, in that it used motion detectors; these references occurred exclusively within a single chapter, entitled \u201cUnderstanding Change: Relationships Among Time, Distance, and Rate.\u201d This text also incorporated dynamic statistics software, namely Fathom. Most of the \u201cunspecified technology\u201d references required the reader to select a form of technology, with instructions similar to, \u201cUse appropriate technology to complete this task.\u201d<\/p>\n This book also includes appendices with technology content: links to videos of students doing mathematics, instructions for using technology such Geometer\u2019s Sketchpad, the TI-73 calculator, Fathom, Excel, or the NCTM Illuminations website.<\/p>\n References That Impact TPACK<\/h3>\nIn order to develop TPACK\u00a0within prospective elementary teachers, textbooks may provide multiple opportunities that utilize different types of technology across all areas of mathematics. Some tools, such as calculators, graphing calculators, and spreadsheets, are widely available and can be used for a number of diverse mathematical topics. Other types of technology are more specialized, such as dynamic geometry software or online resources. These, along with customized e-manipulatives like dynamic geoboards, can be used for specific tasks.<\/p>\n When technology is incorporated in a mathematics content course, prospective teachers\u2019 technological content knowledge (TCK) and technological pedagogical knowledge (TPK) may be impacted. Koehler and Mishra (2008) define TCK as, \u201can understanding of the manner in which technology and content influence and constrain one another\u201d (p. 16), while TPK is, \u201can understanding of how teaching and learning changes when particular technologies are used\u201d (p. 16). Prospective teachers may also develop TPACK, which is, \u201can understanding that emerges from the interaction<\/em> of content, pedagogy, and technology knowledge\u201d (p. 17, emphasis in original). We searched the literature on TPACK development, but found no studies or recommendations related to the content of textbooks. On the other hand, there were abundant examples of activities and experiences designed to impact the development of TPACK (e.g., AACTE Committee on Innovation and Technology, 2008; Niess et al., 2009). After reviewing these, we created a list of features of technology references within mathematics textbooks that have the potential to impact a prospective elementary teacher\u2019s TPACK. This list is not exhaustive, but provides a few examples that may be present in technology references. Namely, these references:<\/p>\n\n- Highlight the inclusion and use of technology within mathematics curriculum materials;<\/li>\n
- Describe or discuss the reason(s) for choosing to use, or not use, particular types of technology within the context of teaching mathematics;<\/li>\n
- Require prospective teachers to explain, in a manner that a student could understand, the output of various types of technology;<\/li>\n
- Illustrate students\u2019 use of technology, using video or descriptions of student work;<\/li>\n
- Make explicit statements about, or provide examples of, how technology may be used in the school classroom.<\/li>\n<\/ul>\n
These examples, while not prevalent within the textbooks, were nonetheless present in some of the references to technology. If the goal is to prepare teachers to use technology in their future classrooms, such features should be emphasized on an even greater scale. In the following section are\u00a0some examples from each textbook that contain some of these features and, thus, have the potential to impact the development of TPACK in a prospective elementary teacher.<\/p>\n Highlight Technology in Curriculum Materials. <\/em><\/strong>Most of the textbooks in our sample included pictures of pages from textbooks used in elementary schools. For example, MBP includes a picture of a page from a fourth-grade textbook (MBP, p. 155). On this page, there is a \u201cMath Online\u201d sidebar that lists the publisher\u2019s website and the resources that are available, such as extra examples, activities, and video tutorials. Within BLL, the authors included a \u201cSchool Book Page: Learning with Technology\u201d subsection containing a portion of a sixth-grade textbook (BLL, p. 202). Within this page, sixth-grade students are introduced to the Fibonacci sequence and required to use a spreadsheet to investigate the sequence.<\/p>\nDescribe Reasons for Selecting Technology<\/em>.<\/strong> In a chapter on statistics in SSN, after discussing simulations and sampling methods, the authors stated,<\/p>\nWhen statisticians want to find a random sample, they do not usually draw names from a hat, spin a spinner, or toss a die, although these are legitimate ways to sample randomly. To obtain a large sample, these methods would be very time-consuming. Instead, statisticians might use computer simulation software, a table of random numbers, or a computer or calculator with the capability of providing random numbers. (SSN, p. 667)<\/p>\n Therefore, one reason for choosing to use technology is because of the speed at which technology can perform complex or repetitive tasks. On the other hand, in a chapter on operations, the authors of BasM provide a rationale for choosing to not <\/em>use technology for certain tasks:<\/p>\nOur first work with addition in base ten will be doing some addition problems mentally, for a couple of reasons. First, this will require you to think carefully about how your knowledge of place value applies to adding numbers. Second, much of our use of arithmetic does not involve pencil and paper or calculators, but rather mental computation\u2014when estimating or when it is quicker to do a computation or part of a computation in our head than with a pencil or calculators (BasM, p. 81).<\/p>\n With this statement, the authors indicated that there are good reasons to choose to use \u2013 or not to use \u2013 technology in certain situations. Later, in a section on operations with decimals, they made the following statement in support of using calculators.<\/p>\n With the widespread use of calculators, most people no longer do most decimal computations longhand. However, it is crucial to understand why the basic algorithms work because it is often necessary to interpret what the calculator displays. (p. 231)<\/p>\n Thus, the authors of BasM recommended the use of calculators be coupled with a conceptual understanding of number and operations.<\/p>\n We found some technology references in which prospective teachers were asked to compare the merits of different types of technology. For example, the authors of BLL included this prompt within an exercise set: \u201cA student questions whether a spreadsheet or a graphing calculator is more useful to teach algebra concepts. How do you respond?\u201d (BLL, p. 471).<\/p>\n Require Explanations of the Output of Technology<\/em>.<\/strong> Some tasks placed the prospective teachers in situations that they will likely face when using technology in the classroom. For example, consider the situation presented in Bec:<\/p>\nRon used a calculator to determine that 0.35 \u00d7 2.4 = 0.84. Ron wants to know why the rule about adding up the number of places to the right of the decimal doesn\u2019t work in this case. Why aren\u2019t there 2 + 1 = 3 digits to the right of the decimal point in the answer? Is Ron correct that the rule about adding the number of places to the right of the decimal points is not correct in this case? Explain. (Bec, p. 207)<\/p>\n A similar activity in SSN also referenced calculators:<\/p>\n A student says, \u201cMy calculator shows that [the square root of 2] \u00a0is 1.4142136. And 1.4142136 =\u00a0[14,142,136\/10,000,000], which is a rational number. But you said [the square root of 2] is an irrational number. Which is it, rational or irrational?\u201d How would you respond to the student? (SSN, p. 119)<\/p>\n Specifically, these activities require an understanding of how one must thoughtfully interpret the output of a calculator and explain that output to a student.<\/p>\n Illustrate Students\u2019 Use of Technology<\/em>.<\/strong> Each of the textbooks in our sample provided instructions for using technology in various mathematical tasks, but the examples were primarily instructive to the reader as a user of technology. We did not identify any descriptions of elementary students\u2019 interactions with technology beyond instances similar to the examples given in the previous section. Although some textbooks included references to videos of students doing mathematics, none of the videos incorporated technology.<\/p>\nExplicitly Describe the Use of Technology in Schools.<\/strong> <\/em>The authors of LDM illustrated the benefits of using dynamic geometry software for making a geometric constructions more enjoyable and less tedious:<\/p>\nConstructions made with tangible materials – paper, dowels, rubber bands, and so on \u2013 continue to have an important role to play in teaching and learning the principles of geometry. However, increasingly, classrooms are also taking advantage of the computer. Geometry software…allows figures to be constructed on the screen, colored, manipulated, explored with measurement tools, and printed out for display and further investigation. (LDM, p. 684)<\/p>\n In a section entitled, \u201cMental Math, Estimation, and Calculators,\u201d the authors of MBP described a specific calculator:<\/p>\n The TI-34 II, which is designed especially for elementary and middle schools, performs fraction as well as the usual decimal calculations, can perform long division with remainders directly, and has the functions of a scientific calculator. One nice feature of the TI-34 II is that it has two lines of display, which allows the student to see the input and output at the same time. (MBP, p. 141)<\/p>\n Adjacent to this paragraph on the page, there is a sidebar citing Reys and Reys (1987), who listed benefits of calculator use in the classroom, such as a more positive attitude toward mathematics.<\/p>\n These examples are provided to demonstrate how textbooks may provide opportunities for prospective teachers to develop TPACK. However, the instructor has a great influence on how a textbook is used within a course. In the next section are recommendations for textbook selection, curriculum development, and future research directions based on our research.<\/p>\n Recommendations<\/h2>\nTextbook Selection<\/h3>\nNot all mathematics textbooks for prospective elementary teachers are the same. This study highlights the variation in the extent and nature of the use of technology in teaching and learning mathematics. It is important to note that these findings provide a description, but not an evaluation, of the textbooks in the sample. The goals of the course, the role of technology, and the availability of technological resources must be considered when selecting and implementing a textbook.<\/p>\n Any content analysis of a textbook should also be viewed in light of the fact that textbooks are not self-implementing. In any course, the instructor will naturally choose to implement some portions of a textbook, omit others, and possibly use other resources that are not in the textbook. In this paper, we have provided an overview of how an instructor can make informed decisions about the amount and type of technology to be used in a course. The instructor should find our categorization of technology by its location, type, and role a useful starting point when considering how to implement the content of the textbook. Beyond knowing the types of technology that can be found in a textbook, information related to the location and role of the technology can affect the instructor\u2019s choice of how to impact students\u2019 learning and, in some cases (such as the example from p. 471 of BLL earlier in this paper) impact students\u2019 understanding of the role of technology in the learning of mathematics.<\/p>\n The textbook is a potentially influential component of a mathematics content course for prospective teachers, but the presence or absence of technology references within a textbook does not necessarily indicate the presence or absence of technology within the course. With respect to a mathematics teacher education program, it is beneficial to have technology represented within content courses. Content courses that include, highlight, and discuss technology fit with the characteristics of mathematics teacher preparation programs that strive to develop a strong TPACK foundation within their teacher candidates. \u201cA successful program would probably not overly separate technology, content, and pedagogy across the coursework of teachers. In other words, the required courses within the mathematics department would include strong technology use and effective pedagogy of presentation,\u201d (Grandgenett, 2008, p. 161). As Niess and colleagues (2009) noted, individuals progress through a series of levels as they develop TPACK. By selecting a textbook that incorporates technology within a content course, instructors may help prospective teachers progress through the initial stages of Recognizing and Accepting, particularly in the themes of Curriculum and Assessment, Learning, and Access.<\/p>\n One limitation of our work lies in the challenge to identify all of the references to technology within each textbook of our sample. While we were diligent in examining every page, each textbook in our sample contained hundreds of pages of content. Therefore, it is possible that we missed some references. Another limitation arises because the use of technology within an activity was not necessarily clear cut. For example, while an author and instructor may intend for a student to use a calculator to compute 76<\/sup> with a calculator, we did not include such an activity in our analysis unless a calculator was specifically mentioned or a special icon was present. Therefore, in some sense, our counts provide a floor for the level of technology integration for each of these books.<\/p>\nAs we mentioned earlier, another limitation of our study is that two textbooks in our sample (BLL and MBP) are not the most current editions available. In fact, according to the publisher\u2019s website for MBP (John Wiley & Sons, Inc., 2016), the latest edition includes QR codes and new videos of children solving mathematics problems. This new content would have been included in our analysis, had we examined this edition. Therefore, instructors of mathematics courses for prospective elementary teachers should regularly review new editions of textbooks, as a review of new features will provide useful information for the textbook selection process.<\/p>\n Curriculum Development<\/h3>\nTextbook authors must naturally wrestle with the question, \u201cWhat technologies may we assume<\/em> students and instructors may access and use?\u201d In academic institutions in the U.S., it may be the case that all students have access to computer labs and the internet. Furthermore, the low cost of calculators, or their availability inside the classroom, (or their automatic inclusion among the apps of a smartphone) may allow textbook authors to design tasks that utilize such resources without worries that not all students may have access. Even as technology advances, this question must be addressed.<\/p>\nWithin a teacher preparation program, prospective elementary teachers need opportunities to (1) learn how to use specific types of technology for learning mathematics (ISTE, 2008), (2) observe how technology is used to teach mathematics (AMTE, 2006), (3) practice teaching mathematics with technology (NCTM, 2011), and (4) develop an inclination towards teaching and learning mathematics with technology, including technologies that have not yet been developed (AMTE, 2006; ISTE, 2008; NCTM, 2011). This is quite a tall order for teacher preparation programs, and cooperation must exist alongside content courses, methods courses, and practical field-based experiences.<\/p>\n There are textbooks that emphasize the use of technology for teaching mathematics at the middle and secondary levels, such as those that emerged from the Preparing to Teach Mathematics with Technology <\/em>Project (Hollebrands & Lee, 2012; Lee, Hollebrands, & Wilson, 2010). Future curriculum development efforts may need to focus on teaching and learning mathematics content from the elementary level. Furthermore, recent developments in online curriculum materials and e-textbooks may lead the way for the seamless integration of technology tools and mathematics tasks.<\/p>\nOverall, we recommend that new textbooks, and new editions of existing textbooks, attend to the features of tasks that potentially impact a prospective teacher\u2019s TPACK. In particular, we encourage authors to utilize videos that illustrate students\u2019 use of technology in the elementary classroom. The authors of MBP have shown that adding videos to a new edition of the textbook is feasible (John Wiley & Sons, Inc., 2016); we recommend that some of these videos include students interacting with electronic technology to solve mathematics problems.<\/p>\n Future Research Directions<\/h3>\nSeveral avenues exist for future research along these lines. First of all, while this study examined many of the popular textbooks for this type of course, other textbooks exist. It would be interesting to see if other textbooks are similar to those in our sample, or if even more variation exists. One interesting branch of research in this vein involves comparing U.S. textbooks to textbooks used in courses for prospective elementary teachers in other countries.<\/p>\n Second, many current textbooks have been through multiple revisions. It may be interesting to look at previous editions of these textbooks and see how they have evolved along with technology. For example, what types of technology were mentioned in the first editions of such textbooks, and how do those correspond with the advent of various types of technology? A quick glance at an earlier edition of LDM revealed a section titled, \u201cGetting the Most Out of Your Calculator,\u201d that has since been eliminated. Perhaps the reasons for such changes would be best gathered by interviewing the authors.<\/p>\n A third direction for future study focuses on the implementation of such textbooks within content courses. That is, if you know an instructor is using a certain textbook, how does the technology mentioned in the textbook actually get used in the class? This would be particularly fascinating in relation to e-textbooks.<\/p>\n Conclusion<\/h2>\nThis study has revealed that textbooks for mathematics content courses for prospective elementary teachers do contain references to technology, but the presentation of technology varies with the textbook. While it may be the case that teacher preparation programs in the past did not utilize technology, current textbooks do provide some opportunities to learn and teach mathematics with technology, particularly with calculators and online resources. At the same time, mathematics teacher educators must be diligent in effort to prepare teachers to effectively use technology in the mathematics classroom. Taking the perceived problem up a level, mathematics teacher educators may not have learned to teach mathematics with technology during their preparation, either. Further research on the development and implementation of curriculum and its relationship to technology will help steer us toward the goal of teaching mathematics effectively in the digital age.<\/p>\n References<\/h2>\nAACTE Committee on Innovation and Technology (Ed.). (2008). Handbook of technological pedagogical content knowledge (TPCK) for educators<\/em>. New York, NY: Routledge.<\/p>\nAssociation of Mathematics Teacher Educators. (2006). Preparing teachers to use technology to enhance the learning of mathematics: A position of the Association of Mathematics Teacher Educators. <\/em>Retrieved from http:\/\/amte.net\/sites\/default\/files\/amtetechnologypositionstatement.pdf<\/a><\/p>\nBassarear, T., & Moss, M. (2014). Mathematics for elementary school teachers <\/em>(6th<\/sup> ed.). Boston, MA: Cengage Learning.<\/p>\nBeckmann, S. (2014). Mathematics for elementary teachers with activities <\/em>(4th<\/sup> ed.). Boston, MA: Pearson.<\/p>\nBull, G., & Bell, L. (2009). TPACK:\u00a0A framework for the CITE Journal.\u00a0Contemporary Issues in Technology and Teacher Education<\/em>,\u00a09<\/em>(1). Retrieved from https:\/\/citejournal.org\/vol9\/iss1\/editorial\/article1.cfm<\/a><\/p>\nBillstein, R., Libeskind, S., & Lott, J. W. (2010). A problem solving approach to mathematics for elementary school teachers <\/em>(10th<\/sup> ed.). Boston, MA: Addison Wesley.<\/p>\nDick, T. P., & Hollebrands, K. F. (2011). Focus in high school mathematics: Technology to support reasoning and sense making. <\/em>Reston, VA: National Council of Teachers of Mathematics.<\/p>\nConference Board of the Mathematical Sciences. (2012). The mathematical education of teachers II. <\/em>Washington, DC: American Mathematical Society and Mathematical Association of America.<\/p>\nFinzer, W. (2002). Fathom dynamic data software (Version 2.1) [computer software]. Emeryville, CA: Key Curriculum Press.<\/p>\n Grandgenett, N. F. (2008). Perhaps a matter of imagination: TPCK in mathematics education. In AACTE Committee on Innovation and Technology (Ed.), Handbook of technological pedagogical content knowledge (TPCK) for educators<\/em> (pp. 145-165). New York, NY: Routledge.<\/p>\nHollebrands, K. F., & Lee, H. S. (2012). Preparing to teach mathematics with technology: An integrated approach to geometry<\/em>. Dubuque, IA: Kendall Hunt Publishing Company.<\/p>\nInternational Society for Technology in Education. (2007). ISTE standards for students<\/em>. Eugene, OR: Author.<\/p>\nInternational Society for Technology in Education. (2008). ISTE standards for teachers<\/em>. Eugene, OR: Author.<\/p>\nJones, D. L. (2014). The role of technology for learning stochastics in U.S. textbooks for prospective teachers. <\/em>Paper presented at the International Conference on Mathematics Textbook Research and Development, Southampton, United Kingdom.<\/p>\nKoehler, M. J., & Mishra, P. (2008). Introducing TPCK. In AACTE Committee on Innovation and Technology (Ed.), Handbook of technological pedagogical content knowledge (TPCK) for educators<\/em> (pp. 3-29). New York, NY: Routledge.<\/p>\nLee, H. S., Hollebrands, K. F., & Wilson, P. H. (2010). | | | | | |