Blogs in Mathematics Classrooms:
One Possible Lane on the Blended-Learning Highway to Constructivism
The issue that I am presenting in this paper is how to use a blended learning environment to make a shift in methodology towards constructivism, specifically through the use of a class blog. When I first started the MET program, my goal was to learn how to discern which technologies were the most effective in the classroom and how to implement them. My journey through the program and my first hand experience with constructivism through the MET courses that I have taken, have gradually shifted my focus from merely discovering technologies to how to use them to change my teaching strategies altogether. I see technology as a powerful tool and medium for creating rich, constructivist learning environments and am now focussing on how technology can help me achieve this change in methodology. In the setting in which I currently teach, the availability of technology for the students to use in the class is limited, so I am specifically looking for ways to integrate technology use outside of the physical classroom situation.
In research for previous courses, I became aware that blended learning environments can help students achieve higher levels of learning and classroom engagement, as well as encourage metacognition (Kramarski & Mizrachi, 2006; Wingard, 2004). In reviewing the videos connected with learning environments 1 and 2 (LE1 and LE2) in our video case assignment, I was struck by how both videos portrayed teachers using technology in blended environments to change how they taught. The teacher in LE2 specifically stated that the technology allowed him to move from a “transmissive to a transactive” style. In the discussion forum that focussed on our own interview cases, the idea of using a blended learning environment to alter one’s teaching style was reiterated. In a post titled, “Support and dialogue in a Blended Learning Environment”, DS made the following observation:
“… through the use of technology the teacher has been able to implement a system that encourages dialogue and reflection. In particular, the older physics 12 students seemed to appreciate the blended learning. … The teacher repeated a few times that it takes the students a while to be comfortable with sharing their dialogue, but that it allows him to take a more constructivist approach in the classroom.” (Post by DS, private discussion forum, January 24, 2012).
This post reminded me of the research from previous courses and of the use of online, asynchronous discussion forums in mathematics. There is a movement in mathematics education away from rote learning and repetitive drills towards higher order thinking and metacognition (Ontario Ministry of Education, 2004; Western and Northern Canadian Protocol, 2008). Constructivism encompasses this change in methodology and involves collaboration, problem solving and deeper, more meaningful learning. I feel that the use of a blended learning environment, specifically involving the use of asynchronous, online communication in the form of a blog has the potential to create a meaningful, collaborative learning space for high school mathematics students. The research reviewed in the following annotated bibliography provides information from current literature to support this theory.
Annotated Bibliography
Three of the articles below were found through ERIC (EBSCO interface) using the key words: mathematics, blogs, constructivism and technology in various combinations. I began with a search of “constructivism and technology and mathematics” and found a meta-analysis study of the effects of computer technology in learning mathematics. I included this study because it was an overview of current research and documented the combined effects of constructivism and technology. The keywords “blogs and mathematics” only revealed seventeen entries. I narrowed the search by choosing research based articles and then reviewed the abstracts and read a number of the articles in entirety. Although the research on blogs at post-secondary levels provided insight, I chose the two articles that researched the effects of a blog in a K-12 setting as they were most similar to my situation. The fourth article was chosen in accordance with the guidelines for this assignment through CiteULike. To choose it, I went through every title in the ETEC 533 Group library in CiteULike and read the abstract (where available) of any that seemed pertinent. I narrowed the list down to three or four articles and then chose the one I have included based on the overall information it provided on constructivism and how it relates to technology use.
Cadiero –Kaplan, K., (1999). Integrating technology: Issues for traditional and constructivist pedagogies. Journal of Computing in Teacher Education, 15(2), 14-18.
This article is an academic opinion paper discussing the role of technology in both traditional and constructivist environments. Cadiero-Kaplan (1999) sees technology in the traditional classroom as a tool to support what the teacher does or an avenue for students to practice what has been taught during the lesson. In contrast to this, Cadiero-Kaplan (1999) sees technology used in constructivist classrooms as an integral part of the learning. Technology becomes the medium in which students collect, evaluate, analyze and express their learning. The key difference is that in a constructivist classroom, students engage in building their own knowledge rather than having it disseminated to them via the teacher, and the different uses of the technology reflect the difference in teaching methodology.
Although the article is older, the author provides a clear and concise summary of the differences between traditional methods and constructivism and how the different approaches incorporate technology differently. Cadiero-Kaplan (1999) makes the point that in order to use the affordances of technology to foster a constructivist environment technology needs to be readily available to students in classrooms. This is an issue in my setting. I found it very interesting that many of the questions the author raises about technology use and availability are still being asked 13 years later. For example, “…how do teachers move towards a constructivist pedagogy … while integrating the wealth of technology into their teaching practices?” (Cadiero-Kaplan, 1999, p. 15-16) and “In order to be successful in providing a learner-centered environment with technology integration, teachers must be willing to continually develop technological skills, reflect on their own teaching processes and strategies…” (p. 17). Cadiero-Kaplan (1999) also discusses the changing needs of the students as we move towards 21st Century learning. The issues the author raised in 1999 are my issues in 2012.
Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22(3), 215-243.
This study is a meta-analysis designed to determine if there is a difference in mathematics learning when computer technology (CT) is incorporated into the classroom compared to when it is not and to determine what types of settings or conditions resulted in the largest effect sizes when CT was used. 46 primary studies involving a total of almost 37,000 students were reviewed and statistically analyzed. The studies included were chosen based on their use of CT, date of publication (1990 – 2006), sufficient data for statistical analysis, type of experimental design and that they studied K-12 settings. Li and Ma (2010) reported an overall positive effect in mathematics learning when CT is used and identified several conditions that had a strong impact on the effect of CT in mathematics. As with any meta-analysis, this research can show trends but cannot provide cause and effect, nor does it have any control over the integrity of the original research. The authors attempted to mitigate that factor by creating strict inclusion guidelines and only keeping research that met specific criteria for methodology.
Li and Ma (2010) reported that one of the strongest effects was found when CT was used in conjunction with constructivist methodology. They also reported that the effect of CT was stronger for elementary aged students than high school students. It would be interesting to determine if constructivism plays a role in that result. Perhaps a constructivist approach is more common in elementary classrooms or perhaps the technology is integrated differently, resulting in different effects. Cadiero-Kaplan (1999) suggested that the way technology is used in a classroom reflects the style of teaching, supporting the theory that if constructivism is more common in elementary schools, a stronger effect size could result. More research is needed to determine why the effect size is higher for elementary students and how to improve learning with CT at the high school level.
Pyon, S. M. (2008). Why math blogs? Teaching Children Mathematics, 14(6), 331-335.
This article presents an action-research study implemented by a grade 3 classroom teacher, Shirley Pyon. Pyon (2008) was looking specifically at whether or not a blog would encourage mathematical discussion and metacognition. Her analysis was qualitative and used examples from the blog. She reported that the blog resulted in higher level thinking and increased metacognition in mathematics for her students. There were no quantitative results or descriptions of how this was measured. Some of the results appeared subjective, for example, comparing online, asynchronous discussion with face to face discussions with no data or observations to provide evidence for the conclusions.
This article indicates promising results from the use of a blog at this level, but more quantitative or more structured qualitative data is required to substantiate the results. In many cases, action-research projects are designed to inform and influence teaching practices at a personal level and I do not think that the author intended this research to be empirical or academically rigorous. However, the students’ responses that were quoted in the article and the teacher’s subjective discussion of the experience provides some evidence that blogs were a successful use of technology in this class’ experience. Pyon’s (2008) discussion and quotes from the blog regarding the level of metacognition that the grade 3 students exhibited make it worth taking a deeper look at the suggestions presented in this article and applying them to a high school setting to see if the same results could be achieved.
Luehmann, A., & MacBride, R. (2008). Capitalizing on emerging technologies: A case study of classroom blogging. School Science and Mathematics, 108(5), 173-183.
This research is a case-study of the use of a blog by a high school mathematics teacher. The authors set out to explore how the blog was intended to be used, how it was actually used, its perceived value and how this related to the current literature available regarding the educational use of blogging. The researchers read through one year of postings from a blog for a pre-calculus 11 class and interviewed the teacher. Luehmann and MacBride (2008) analyzed the text qualitatively into themes and assigned codes to the entries, which they re-read numerous times to ensure accuracy and consistency in coding. They concluded that a blog has the potential to dramatically improve student learning and metacognition.
The results of this study and the examples of blog posts provided within the article indicate that the implementation of a blended learning environment through the use of a structured, student-centered, blog can provide opportunities for students to engage in constructing their own knowledge and participate in a community of learners. The results of this study are limited, however, as they stem from one specific classroom and one teacher. Are the results of this study due to the blog or to some unique characteristic of this particular class? The authors acknowledge that the structure of the blog and the teacher implementing it are critical to the success of the blog. Further research is needed to determine if the same results can be replicated in other settings.
Analysis and Conclusion
The development of my original issue, using technology to alter my teaching style to encompass a more constructivist approach is reflected in the first two articles covered. These articles provide a rationale for changing to constructivism, but do not provide information on how to effect that change, or how to incorporate technology when it is not readily available to place in the hands of students during class time. Now that I am confident that the change in styles is a valid choice, my question becomes how do I use technology to make this change in a way that appeals to high school students and works within the parameters of my situation.
One avenue for implementing that change would be to introduce a blended environment where students can access technology outside of the classroom. Both Pyon (2008) and Luehmann and MacBride (2008) present compelling research on how blogs can foster metacognition and collaboration and can provide the opportunity for a teacher to transition to a more constructivist teaching style. These two studies provide examples of how blogs can work at different age levels and yet the small sample size in both and the anecdotal nature of Pyon’s (2008) action research project necessitate further research in this area. My own search for articles pertaining directly to the use of blogs in school mathematics demonstrated the lack of available research done on this topic. I believe, based on personal experience, reflection and current research, that the asynchronous communication afforded by blogs can have a deep and meaningful impact on the learning in a mathematics classroom. Many practical questions arise and are not yet answered by the research. How do you make blogs work for students that do not have access to technology? How can you introduce a blended environment without adding to the workload of the students? What kind of questions or assignments are the most effective in promoting that deep learning and collaboration that is imperative to effective constructivism? Will blogs work for all levels of learners? Luehmann and MacBride (2008) noted that the teacher had a great deal of impact on the success of the blog in their case study. What was it about the teacher that made it work, and, perhaps most importantly, can I be that kind of teacher?
References:
Cadiero –Kaplan, K., (1999). Integrating technology: Issues for traditional and constructivist pedagogies. Journal of Computing in Teacher Education, 15(2), 14-18.
Kramarski, B. & Mizrachi, N. (2006). Online discussion and self-regulated learning: Effects of instructional methods on mathematical literacy. The Journal of Educational Research, 99(4), 218 – 230.
Li, Q., & Ma, X. (2010). A meta-analysis of the effects of computer technology on school students’ mathematics learning. Educational Psychology Review, 22(3), 215-243.
Luehmann, A., & MacBride, R. (2008). Capitalizing on emerging technologies: A case study of classroom blogging. School Science and Mathematics, 108(5), 173-183.
Ontario Ministry of Education (2005). The Ontario Curriculum, Grades 9 and 10: Mathematics (ISBN 0-7794-7940-8). Toronto, Ontario: Queen’s Printer for Ontario.
Pyon, S. M. (2008). Why math blogs? Teaching Children Mathematics, 14(6), 331-335.
Western and Northern Canadian Protocol. (2008) The common curriculum framework for grades 10 to 12 mathematics: Western and northern Canadian protocol. January 2008. Retrieved from: http://www.wncp.ca/media/38771/math10to12.pdf
Wingard, R. (2004). Classroom teaching changes in web-enhanced courses: A multi-institutional study. EDUCAUSE Quarterly, 27(1), 26 – 35.