MET:High School Mathematics Knowledge Building Communities

Page Authored by Kenton Hemsing 2011

Page edited by David MacKinnon 2013

This page is devoted to exploring how aspects of Knowledge-Building Communities and social learning may be helpful in furthering the mathematical understanding of secondary students. In the following sections, aspects of social learning, Knowledge-Building Communities and social media will be explored in relation to development of learning opportunities for secondary mathematics students.

Knowledge-Building Communities are often created as a means of providing individuals with a common interest a chance to work together to create and share knowledge. The community may consist of experts and learners who participate in an interdisciplinary approach to share information and understanding in an open and transparent environment. Scardamalia and Bereiter (1994) support the inclusion and development of Knowledge Building Communities through the restructuring of schools for all levels of learners. Scardamalia and Bereiter (1994) show through their research that students are better able to acquire knowledge through inquiry (p.270).

Mohamed Chatti, Matthias Jarke and Dirk Frosch-Wilke (2007) show that the rapid development of Web 2.0 tools for learning and the increase in social media has had a major effect on learning and knowledge management for students. In their paper, Chatti, Jarke and Frosch-Wilke (2007) show that the use of social networks and online communities have the ability to be content-centric which leads the user to a more enriched learning environment (p. 412). It is this content centered approach that is helpful for discussing the use of Knowledge-Building Communities in secondary mathematics to develop a greater understanding of concepts.

It is this idea of learning through inquiry and content centered approach that has led many institutes of higher learning to include Knowledge-Building Communities as part of the student experience. It is with the success of Knowledge-Building Communities at higher learning environments that may fuel their introduction to secondary school levels. An example of a Knowledge-Building Community for a higher level learning can be found at Evergreen State College, which is commonly referred to as a pioneer in ensuring students involvement in Knowledge-Building Communities. (Tinto, 2004)

History and Characteristics of Knowledge Building Communities

Knowledge-Building Communities can be found throughout history as a means for educating those in society. In its earliest form, a learning community consisted of members from a particular area of interest that came together to discuss topics of importance. Using this as a guide these communities have existed throughout history from ancient Greek scholars to the English Royal Society of Sciences to modern online groups of individuals. The members of these groups shared knowledge and ideas with each other to improve human understanding. Knowledge-Building Communities are most successful when participants are not only sharing knowledge, but constructing new knowledge from interactions with others in the community. It is the construction of the new knowledge of participants that makes the use of Knowledge-Building Communities successful and practical for secondary students. Knowledge-Building Communities are most successful when participants are not only sharing knowledge, but constructing new knowledge from interactions with others in the community.

The term "Knowledge Building Communities" was not given to the practice unit the late twentieth century by Scardamalia and Bereiter (1994). In their definition of Knowledge-Building Communities, Scardamalia and Bereiter (1994) included several important aspects of Knowledge-Building Communities that make their contribution to student learning successful. In summary, a Knowledge-Building Community must:

• Focus on problems and depth of understanding: Those individuals involved must be working together on a common problem and use their previous knowledge with one another to deepen their understanding of the concepts and issues at hand.

• Decentralized with a focus on collective knowledge: Students, teachers and experts who are members of a Knowledge Building Community must not create a hierarchy of individuals, rather, all members work together on equal ground and all knowledge that has been shared is taken at equal weight regardless of the individuals’ background or academic success.

• Have a broader knowledge community: • Have a broader knowledge community: Participants within the Knowledge-Building Community must bring with them their own individual experiences, expertise and understandings and be willing to share these with the other participants. This sharing leads to further understanding of concepts that are contained within the Knowledge-Building Community as well as furthers understanding to topics that may or may not be tangential to the original purpose of the Knowledge-Building Community. (p.274-275)

The Knowledge Forum

The Knowledge Forum was established to further incorporate the traits of successful development of Knowledge-Building Communities as developed by Scardamalia and Bereiter (1994) as a productive knowledge-building community. The Knowledge Forum is a simple online learning management system that allows users to post questions and answers on discussion forums, uploading documents for others as well as completing online assignments. The design of the Knowledge Forum is aimed at encouraging students to build and construct new knowledge by working together.

Fle3

Fle3 (future learning environment) is a web-based learning environment designed to promote collaboration amongst users. This program is open source, and is free so it should fit easily into your budget. For an insight into the possibilities of using a program like this, check out the picture below.

Group collaboration on a climate change problem

Social Learning

Social constructivism is well recognized to have roots tracing back to Vygotsky, who produced theories focusing on the role of society in learning. Jaramillo argues that student learning occurs through interactions with the instructor and their peers inside the classroom. (Jaramillo, 1996) In von Glaserfeld's publication on radical constructivism, Konold stresses the importance of incorporating the three following domains in a learning activity: (1991)

1. How do my beliefs compare with the beliefs of others?
2. Are my beliefs consistent within my own framework, or are there inadequacies or conflicts within my own reasoning?
3. Are my beliefs consistent with empirical data?

The first two domains align perfectly for incorporating social learning. Through social interactions, students can strengthen their conceptions, modify their conceptions or even learn to recognize their own misconceptions.

Currently the use of online social networking sites such as Facebook and Twitter has started to influence social learning within the classroom. These online social networks allow learners to share information and find new resources with relative ease. These sites encourage learners to communicate and share knowledge regardless of physical distance and personal background. Educators have been attempting to integrate these social networking sites into student learning outcomes in recent history.

McLoughlin and Lee (2010) also support the use of online social networking applications to support learning for students. . McLoughlin and Lee (2010) found that when learners were engaged in social media they had a high tendency to participate and share with the greater community. This supports social learning in that it may help engage students in thinking about their learning as participants. This interaction with the community serves as a reproduction of their knowledge and this action will either be reinforced by the community or not.

Facebook For Learning

Facebook is a social networking service that was developed in the early twenty-first century. Users are able to connect and communicate with each other with relative ease. Many educators attempt to use Facebook as a method of establishing Knowledge-Building Communities where the students are part of a large group that includes experts and outsiders from the class; however, there is little continuation of student participation upon completion of the class for which interaction was required. Del Siegle (2011) maintains that there are many ways in which Facebook can be useful for teachers. Teachers are able to use the tools within Facebook to communicate with students and allow students to communicate with one another. The tools for email, chats, and discussion boards all exist within Facebook and students who are on Facebook are relatively comfortable with the use of these tools . This shows the great potential that Facebook holds for creating a Knowledge-Building Community for students. Below you can see a math help forum located on facebook.

Math Help Forum on facebook

The creator of Facebook, Mark Zuckerberg, originally designed the precursor to Facebook in preparation of an art history final where he and his classmates were able to share notes and comment on images from the class that were to be studied (see http://en.wikipedia.org/wiki/Facebook). This shows that there is potential in the use of social networking websites to influence learning and knowledge building if students are able to participate and share knowledge.

Twitter For Learning

Twitter is a micro-blogging tool that allows users to share information and updates in a limited number of characters. Many educators are currently using [www.twitter.com Twitter] as a personal educational tool. Using Twitter to develop their own Professional Learning Network allows teachers and educators to gather resources, thoughts and feedback on new ideas and world events.

Allowing students to access this type of community to help develop their own personal understanding will allows themselves students to communicate with other members of a specific community. Using Twitter's hashtags, students can follow discussions about specific topics and areas of interest.

Some secondary teachers have reported using classroom twitter accounts to post questions to authors, editors, media personalities and scientists. This has allowed students to be engaged in a community of likeminded individuals outside the school walls. This can be expanded to include mathematics learning by communicating their thoughts and ideas to members of community who are like minded. The reward of using Twitter for mathematics lies in the instant feedback that a student can get from posting a questions and thoughts to the members of the community. These short and simple messages will help mathematics students grasp concepts and further their understanding.

Kate Messner (2009), makes a good case for the use of Twitter in the classroom as a way of engaging the students in their learning . In her paper, Messner (2009) shows that the use of Twitter in the classroom has the power to engage students, enhance questioning opportunities and motivate students to enhance their learning. These are aspects that fit within the guidelines of Social Learning Theory as well as Knowledge-Building Communities.

Discussion Forums for Learning

The use of discussion forums for learning has been documented at both secondary and post-secondary levels. Qing Li (2003) claims that for teachers to feel comfortable using these types of online Knowledge-Building Communities effectively, they must first feel comfortable using the tools themselves . The use of discussion forums allows participants time to reflect on and refine their solutions and understanding by observing other participants express their thoughts and ideas before deciding how to respond appropriately.

Qing Li (2004) supports that for teachers to entertain the idea of Scardamalia and Bereirer style Knowledge-Building Community, students cannot act as islands, but instead are involved with each other. This will enhance the learning that students are achieving inside and outside the classroom. Qing Li (2004) suggests that the use of a threaded discussion helps learners revisit what has been discussed and reinforce their learning and knowledge. This is in line with the ideas put forward by Scardamalia and Berierer (1994) as necessary to help students achieve true knowledge acquisition. Using an online discussion forum allows students to follow a conversation that may be spread over several days, review what has been discussed to help retain pertinent information, apply the knowledge gained from the discussion to a problem and finally have their efforts reinforced by others in the community as correct or not.

There are many free versions of discussion forums available for educators to use within their classrooms, and discussion forums are also common applications made available through learning management systems such as Blackboard and Moodle. Free forum hosting services may be found through sites such as http://www.forums.com, http://www.lefora.com and http://tal.ki as well as many others. Having students participate in online discussions is a viable way to include them in a Knowledge-Building Community. These discussion forums allow students the opportunity to interact in ways that are different than face-to-face; this allows students time to process discussions and refine responses to solidify their understanding.

Mathematics Learning Using Knowledge-Building Communities and Social

The development of a successful Knowledge-Building community in a secondary setting that is guided by constructivist philosophy must include social interactions for the learners of today. These interactions will most likely happen online and a productive way to mediate these interactions is to have students involved in a discussion forum or online social network about their topic of interest. The creation of these Knowledge-Building Communities for Mathematics students must hold all the proper traits of successful social learning as well as successful Knowledge-Building Communities.

I will use the Math Help Forum as an example of such an online Knowledge-Building Community that naturally integrates aspects of social learning.

This help forum is set up in different categories, making it easy for users to search and find appropriate content. The site is organized around problems, the idea being that you post a problem and others will help you to come to some sort of resolution. For example, if you had a specific factoring problem you would post your question under the algebra problem area. Clear organization of content also allows users to search prior to posting a problem (maybe someone has already posted a problem similar to their own).

The forum is set up such that anyone can help form a solution to the problem. After a person posts a problem on the forum, there can be a variation of different responses. It is possible to see some responses including different approaches to solving the problems, similar problems they have encountered, verification of original ideas, etc. As there is no resident expert who will ultimately solve each problem, you often find people helping to guide others to solutions. This decentralized focus allows for students to feel confident in expressing their views and fosters collaboration amongst users. See snapshot of the Math Help Forum below:

Math Help Forum

As users see the variation in responses to their original problem, their initial conceptions are challenged and potentially changed. Discussing these problems with users in similar situations allows to students to discover where there conceptions hold strong and where they might be proven inadequate. Another feature of the website is a rating system that allows other users to see how helpful the user has been in the past. This feature offers an incentive for an individual to help others and is a natural motivator to promote social learning.

Several other examples of mathematics based knowledge building communities can be found on the internet currently. These communities encourage novice users to get involved in helping others understand complex mathematical problems. These communities also consist of experts in the field either as main contributors or as casual respondents to user’s queries. These Knowledge-Building Communities are available for students from all over the world to come together and build on each other’s knowledge. Some additional examples of mathematics communities can be found below, although it should be mentioned that they do not fit the exact profile of a knowledge building community.

• http://www.math.com/
• http://mathforum.org/dr/math/
• http://www.themathleague.com/index.php?option=com_content&view=article&id=64&Itemid=67

Conclusion

Social learning and Knowledge-Building Communities have an almost limitless potential for helping secondary students gain further understanding of mathematical concepts. The social learning media that has been discussed on this page serves to show a very small number of popular options that available to students to help further their understanding. Through creation of Knowledge-Building Communities, students will be better able to find solutions to their problems, offer help to fellow classmates and share their passion for mathematics.

Teachers of secondary mathematics should make use of these tools inside and outside their classrooms to further the mathematics learning of students. The use of Twitter, Facebook, discussion forums as well as other available online learning management systems will help ensure learners become members of Knowledge-Building Communities. This inclusion in a community that is devoted to their understanding and furthering their learning will ensure students succeed in their academic pursuits.