With the exponential growth in technology, the integration of digital tools in the mathematics classroom has gained in popularity over the last two decades (Alacaci & McDonald, 2012) and currently there are a variety of sophisticated digital tools specifically designed for mathematics learning. Tools that are designed to do and learn mathematics include dynamic software programs such as Geogebra: https://www.geogebra.org/, Autograph: http://www.autograph-maths.com/ and Desmos: https://www.desmos.com/ , computer algebra systems such as Maplesoft: https://www.maplesoft.com/, graphical display calculators, spreadsheets, electronic manipulatives and applets to name a few. Digital tools that facilitate mathematics teaching include Googles Apps for Education: https://edu.google.com/?modal_active=none, GAFE, and applications that allow for formative and summative assessment.
Research has suggested that educators are often resistant to utilizing technology for instructional practice and more professional development needs address this issue. Garrison, Anderson, and Archer (1999) contend that research efforts need to focus on how to include valuable learning experiences for teachers in online professional development environments. Courses on teaching specific technological tools have proved to be unsuccessful in preparing teachers for technology use in classroom instruction. A more embedded, implicit approach where the technology is used with content and pedagogical knowledge has proved to be more successful as prepares teachers better for classroom instruction (Mcknight et al., 2016).
TPACK by Mishra & Koehler (2006) is a model that useful when considering designing curriculum and takes into consideration different knowledge areas for successful technology integration. TPACK (Technological, Pedagogical, Content Knowledge) for technology integration takes into account the pedagogical, content and technological knowledge of the teacher. The three knowledge areas combine and interact to promote successful integration of technology strategies for the classroom. This is also known as the TPACK framework and can be illustrated by a Venn diagram in figure 1, where the intersections of two knowledge and all three knowledge areas need to be considered for successful technology integration. The TPACK model can be used to guide curriculum design and Mishra & Koehler call this approach “learning technology by design”.
Figure 1 The TPACK model framework
Reproduced by permission of the publisher, © 2012 by tpack.org
Niess, van Zee, and Gillow-Wiles (2010) conducted a study which looked at the effectiveness of using the TPACK framework to deliver online professional development to teachers about the use of dynamic spreadsheets in the mathematics and science classrooms. The study consisted of module in a master’s online course and addressed teachers’ development of TPACK. There were four units to the course and they consisted of:
1) exploring the capabilities of dynamic spreadsheets for specific math and science units
2) developing teaching units to integrate the use of dynamic spreadsheets
3) assessment consideration when solving problems in math and science using dynamic spreadsheets
4) curriculum planning and scaffolding student learning with spreadsheets and each teacher was required to design a final electronic portfolio project. The final portfolio project consisted of three elements: collection of minimum 10 spreadsheets problems with accompanying worksheets and scoring rubrics, a plan of how to incorporate these problems in their classroom and finally an in depth reflect in integrating spreadsheets in their classroom. Each participant was evaluated on a TPACK level (recognizing to accepting, adapting, and exploring) at the beginning and at the end of the course and additionally a paired t test was used to compare teachers’ TPACK self-efficacy before and after the course.
Results from this study showed that, by integrating the use of the technology into the course design of the online course, most participants experienced shifts in their TPACK level and improved. There were also significant positive increases in TPACK self-efficacy beliefs. Another interesting finding was that the teachers who experienced the most growth in their TPACK and reached the exploring level adopted more student centered instructional approaches such as using collaboration and team work in their classrooms prior to the commencement of the course. Teachers at the exploring level also valued the use of dynamic spreadsheet to develop deep conceptual understanding. These teachers valued developing conceptual understanding (Skemp, 1987) over procedural approaches when solving problems. Teachers who were at the accepting level of the TPACK model adopted more teacher centered, traditional instructional approaches and view spreadsheets as motivational tools rather than as tools to develop conceptual understanding.
The findings of the study by Niess, van Zee, and Gillow-Wiles (2010) suggest the development of TPACK can be supported by integrating spreadsheets as learning tools into the design of an online course. The design of the professional development course encouraged teachers to engage in activities to think about how to integrate spreadsheets into their own instruction rather than focus on teaching the mechanics of any specific digital tool (Harris & Hofer, 2009). Niess, van Zee, and Gillow-Wiles (2010) conclude by saying that online professional development opportunities for teachers need to be focused on TPACK rather than on any specific digital tool.
Another model developed by Beuadin and Bowers (1997) is the PURIA model which is a framework that describes the different stages teachers go through when they learn about computer algebra systems. PURIA has now been adopted as a model for teacher’s professional development for introducing innovation (Hoyos, 2012). The five stages of PURIA are: Play, Use, Recommend, Incorporate, and Assess. Learning to use and integrate technology into the mathematics classroom requires teachers to play with the tool first and then use as an instrument for doing mathematics. The “Incorporate” and “Assess” stages encourages teachers to use the technology as a pedagogical tool while the “Recommends” stage marks the transition from mathematical to pedagogical aspects of the digital tool (Zbiek & Holebrands, 2008). Table 2 shows the PURIA model to support teacher’s development in terms of technology proficiency (Beaudin and Bowers, 1997 and extended by Zbiek and Hollebrands, 2008).
Table 2 The PURIA Model: Play, Uses, Recommends, Incorporates and Assesses
In the PURIA model, teachers progress onto the next level once they feel confident about the current level. Levels do overlap and teachers are encouraged to be self-paced while following this model. Generally, Zbiek and Hollebrands (2008) have observed that teachers spend the most time at the Play stage to the Recommend level and problems could arise with guiding students about any the digital tool if any stages are skipped by teachers. The authors also recommended that during the Use, Recommend, Incorporate and Assess stages, teaches are provided with more guidance in the form of technical assistants, workshops, manuals and workshops as this results in teachers more willing to persevere and progress further.
Another framework that supports teachers transformative use of technology in the classroom is Puentedura’s (2011) SAMR (Substitution, Augmentation, Modification, Redefinition) model. The four levels of SAMR represent a hierarchy of technology use, with new teachers often starting at the lowest level: the substitution level. This level may result in gains in efficiency however there are no gains in student learning. Examples include typing an essay instead of handwriting an essay or using a PowerPoint presentation instead of writing notes on the board in a lesson. The next level is augmentation which results in small learning and digital tools that are used in this manner add functional value and improvement. An example of technology used at the augmentation level would be if students collect survey results using online survey tools. The ultimate goal is to encourage teachers to work at the upper two levels: modification and redefinition of the learning task. An example would be to ask students to create a video subject to peer feedback and editing. The way technology is used in this task provides increased multimodality, collaboration and co-construction of knowledge and understanding. Puentedura has reported that a full-time teacher may need around three years of exposure to digital tools to move from substitution level to redefinition level. Figure 3 show the SAMR levels and descriptions for each level.
Figure 2 The SAMR model for Technology Use
The SAMR model. Source: Puentedura (2011), under CC BY-NC-SA 3.0 licence.
The three models outlined: TPACK, PURIA, and SAMR are useful when helping teachers to develop the use of technology in a meaningful way and which, ultimately enhances learning in mathematics. Regardless of the actual digital tool, how the actual digital tool is integrated to instruction and how the tool is utilized as a pedagogical strategy should be the focus of any successful professional development on technology integration in the mathematics classroom.
Alacaci, C., & Mcdonald, G. (2012). The Impact of Technology on High School Mathematics Curriculum. Turkish Journal of Computer and Mathematics Education, 3(1), 21-34. Retrieved November 27, 2017, from http://dergipark.gov.tr/download/article-file/201353
Beaudin, M., & Bowers, D. (1997). Logistic for facilitating CAS instruction. In J. Berry (Ed.), The state of computer algebra in mathematics education. UK: Chartwell-Bratt.
Garrison, D. R., Anderson, T., & Archer, W. (1999). Critical inquiry in a text-based environment:
Computer conferencing in higher education. The Internet and Higher Education, 2(2–3), 87–105.
Harris, J. B., & Hofer, M. J. (2009, March). Technological pedagogical content knowledge (TPACK) in action: A descriptive study of secondary teachers’ curriculum-based, technology-related instructional planning. Paper presented at the annual meeting of the American Educational Research Association (AERA), San Diego, CA.
Hoyos, V. (2012). Online education for in-service secondary teachers and the incorporation of mathematics technology in the classroom. ZDM, 44(6), 775-786.
Mcknight, O'Malley, Ruzic, Horsley, Franey, & Bassett. (2016). Teaching in a Digital Age: How Educators Use Technology to Improve Student Learning. Journal of Research on Technology in Education, 48(3), 194-211.
Mishra, P., & Koehler, M.J. (2006). Technological pedagogical content knowledge: A framework for integrating technology in teacher knowledge. Teachers College Record, 108(6), 1017-1054.
Niess, M. L., van Zee, E. H., & Gillow-Wiles, H. (2010). Knowledge growth in teaching mathematics/science with spreadsheets: moving PCK to TPACK through online professional development. Journal of Digital Learning in Teacher Education, 27(2), 42+. Retrieved from http://cmich.idm.oclc.org/login?url=http://go.galegroup.com.cmich.idm.oclc.org/ps/i.do?p=AONE&sw=w&u=lom_cmichu&v=2.1&it=r&id=GALE%7CA243635653&asid=64db4846c4677712a2a02df3fdffb452
Puentedura, R. R. (2011, December 8). A brief introduction to TPCK and SAMR. Freeport workshop slides. Ruben R. Puentedura’s weblog. http://www.hippasus.com/rrpweblog/archives/2011/12/08/BriefIntroTPCKSAMR.pdf
Skemp, R. R. (1987). Psychology of learning mathematics. Hillsdale, NJ: Lawrence Erlbaum
Zbiek, R.M. & Hollebrands, K. (2008). A research informed view of the process of incorporating mathematics technology into classroom practice by in-service and prospective teachers. In M.K. Heid and G.W. Blume (Ed.s). Research on Technology and the Teaching and Learning of Mathematics: Volume I Research Synthesis, (pg. 287-344). National Council of Teachers of Mathematics and Information Age Publishing, Reston, VA