Collaborative Learning in Junior Mathematics

The Challenge:

One of the assignments in my Junior ABQ course asked teachers to develop an inquiry question around an area of the curriculum. Since I am a math and science teacher at the secondary level, I chose mathematics as my subject area to focus on at the junior level. I am always struggling for ways to make math more interesting and engaging for my students. I feel this is a particularly important topic for junior teachers as junior students are very excited and curious about learning about the world around them. As teachers, we want to harness that enthusiasm for learning and engage students to develop critical mathematical thinkers. I figure a good way to engage students is through group learning. Therefore the question I am going to explore in this post is: How does group work and collaborative learning benefit junior students in learning mathematics?    

“We don’t inquire to eliminate alternatives, but to find more functional understandings – to create diversity, broaden our thinking and ask more complex questions.” (Burke & Short, 1991)

Defining Collaborative Learning:

Moore (2004) suggests that collaborative inquiry or problem solving constructs understanding of the “classroom encounter” – whereby instruction, curriculum, and student actions intersect. Collaboration encourages openness and flexibility, as students are encouraged to develop new questions, solutions and achievement.  Furthermore, student learning is the key driver of group work and collaboration. According to the Ontario Ministry of Education (2010), the role of collaborative learning is becoming a critical part of the daily work of teachers. In fact, the Ministry of Education identifies 7 key characteristics of collaborative problem solving.

 

1. Relevant- Student Learning guides Inquiry
2. Collaborative- Shared process
3. Reflective- Actions are Informed by Reflection
4. Iterative- Progressive understanding grows from cycles of inquiry 
5. Reasoned- Analysis drives deep learning
6. Adaptive- Inquiry shapes practice and practice shapes inquiry
7. Reciprocal- Theory and practice connect dynamically

Research on Collaborative Learning in Junior Mathematics:

                              

 According to Sousa (2006), lecturing results in an average knowledge retention of only 5% whereas methods that require students to practice by doing and teaching others, such as group work, result in 75%-90% of material retention! An interesting study by Van Dat, and Ramon (2012) compared lecture style teaching to group work over the course of 6 weeks among Grade 6 students. Students who participated in group work said they enjoyed working together, teaching others and sharing information. Researchers found group work promoted positive relationships among participants and improved students’ confidence. In addition, students who participated in group work demonstrated higher achievement on a knowledge retention test than those in the lecture style group. Overall, this study found students who learned through group work had significantly higher achievement on retention tests than students who learned through lecture and enjoyed learning.

Ross (2000) adds to the findings of the above study by suggesting a deeper understanding of mathematical ideas develop when students contribute to a solution. By discussing solutions with peers, students make their thinking visible to themselves and their peers. According to Ross (2000), “being explicit makes ideas accessible to others, reveals inconsistencies that can be addressed in dialogue and forces students to reorganize thinking to accommodate the views of others.” (p. 30).  In his study on mathematical reform, Ross (2000) states this occurs when students are placed in mixed ability groups of different mathematical ability, gender, social class and culture. He also suggests all group members are more likely to be involved if the teacher requests one product from the group with the requirement that each group member must provide part of it.    

The Ontario Ministry of Education developed a guide to assist primary and junior teachers with performing effective mathematics instruction. According to the Ministry, group work is especially beneficial to junior students because they benefit from hearing a variety of strategies and processes for problem solving. In order for effective group work to take place, teachers must assign an activity and a discussion to each group. For example “I want you to solve this problem, and this is what I want you to talk about.”

The teacher’s role is to interact with each group and encourage students to share their learning, ask questions and make prompts to promote a deeper level of mathematical understanding.

The Ontario Ministry of Education says that group work can be used to...

• Maximize student participation
• Give students opportunities to learn from one another
•  Provide a structure that encourages students to do a great deal of talking and sharing
•  Provide students with immediate feedback from their peers
•  Promote risk taking in students as their comfort level increases
•   Provide students with opportunities to develop independence and confidence a
• Provide English language learners with opportunities to work with other students who speak the same first langauge
• Expose students to varying viewpoints
• Reinforce students’ skills in cooperating with others (e.g., in listening actively to others, providing constructive feedback to others, and building acceptance and tolerance of others’ ideas)
• Assess students’ learning skills (e.g., group participation, cooperation, abilities in conflict resolution)
• Give students the opportunity to consolidate their understanding of a mathematical concept (e.g., by having them play a game as a group)
•  Foster a sense of community in the classroom

My Conclusion

From researching and reading a variety of different sources, it is clear to me that group work in mathematics benefits junior students in numerous ways. However, like anything in life, group needs to be done in moderation. Students still need whole class lecturing at times to help them learn a specific skill or knowledge piece. They also need time to work on their own and come up with individual solutions and strategies for solving problems. I think the place where group work fits quite well is during practice. Once students have a preliminary understanding, they can work with other students to share their thoughts and get feedback on their ideas. In doing so, they will learn to think in different ways and realize there is always more than one way to solve a problem. Students will also work towards building positive relationships with their peers, learning to communicate their ideas in clear and effective ways and having fun learning math!    

What Teacher’s Say About Group Work….

“The data or the ‘student work’ is actually more than just the finished product, [it’s] the process, the behaviours, the conversations and the non-verbal and verbal communication.“

“We have learned that perhaps the highest impact we can have on our students is taking the time to talk with them and connect with them.

"Teachers shouldn't just stand and teach whole class stuff. That's an old-fashioned way of doing things. If children learn in groups consistently, then they really can learn to work together."

Lastly, check out this video, it shows how just how group work and collaborative learning can be used among other instructional strategies for teaching mathematics to junior students.

References:

Moore, A. (2004). The good teacher: Dominant discourses in teaching and teacher education. New York, NY: RoutledgeFalmer.

Ontario Ministry of Education. (2010). Capacity building series: collaborative teacher inquiry. Secretariat, 18: 1-8.

Ontario Ministry of Education. Retrieved on March 8, 2014 from http://www.eworkshop.on.ca/edu/resources/guides/Guide_Math_K_6_Volume_2.pdf.

Ross, J.A. (2000). Mathematics reform: do some students benefit more than others? The Orbit, 31(3):30-32.

Sousa, D. A. (2006). How the brain learns (3rd ed.). Heatherton, Vic: Hawker Brownlow Education.

Van Dat, T. and Ramon, L. (2012). Effects of cooperative learning on students at An Giang University in Vietnam. International Education Studies, 5(1): 86-99.   

Self-Assessment and Reflection of Growth

Create your free online surveys with SurveyMonkey , the world's leading questionnaire tool.

As a final assignment for my course, I was asked to create a self-assessment based on what I learned and how I did in the different components of the course. I decided to design my own personal survey with the help of surveymonkey.com. In my survey, I asked myself questions based on what I believe the big ideas are around the course. Then, I answered the questions based on the activities we did in class, the discussions we had, and the literature we read. Doing this, helped me to see the knowledge and skills I have learned throughout this course.

When assessing and determining how you have grown and changed as a result of new knowledge, I find it beneficial to compare where you started from to where you have ended up. On the first day of the course we were handed a syllabus that contained the KNOW, DO, and BE that we were to develop by the end of the course. Looking at it on day 1, I realized that lot of what was already on the list were things I already knew and did as a teacher. However, I still believe I have learnt a lot from this course and have witnessed a big change in response to each of the 3 categories. In order to assess my growth and development throughout the course, I will compare my KNOW, DO, and BE from the beginning of the course to the end.



By comparing how I have changed in each aspect of the course, I am able to see how I have grown and what new skills I have acquired. Below is my self made report card explaining how I have changed in each area and how I can continue to improve.

Allison's 21st Century Learner Report Card

One of the biggest ways in which I believe I have changed is that I now think everything we teach within the classroom needs to be based within the real world. No longer should we as teachers be forcing students to memorize knowledge that may have no application to them later on in life. We need to be teaching today’s students how the knowledge they are learning fits within their world and how they can apply it. I also see the value in global learning. Not only having students collaborate with others in their own classroom, but from around the world. In today’s world we are more connected than we have ever been before. That being said, we need to harness that connection and teach today’s young people how to use it to better tomorrow. By working together, we can develop innovative solutions for the betterment of our world.

Lastly, as I discuss in my report card, we must be open to taking risks and failing. For too long we have thought of failure as a "bad thing" as something we need to avoid at all costs. Why??? Think about every time you have failed in your life (I bet you can remember most). Now think about what you learned every time you failed, how you were able to move forward and how you grew because of it. I think failure is something that we should strive for, encourage from our students. With the endless possibilities that technology provides, there is no doubt that we will struggle, however there is also no doubt we will create many great and wonderful things. For another look at why failure is necessary for success watch this Nike commercial, one of my favourites of all time.

Next Steps 

Now that I am at the end of my M.Ed program, I feel as though I am in a place of wonder and new beginnings. This is a place that is terrifying and also exhilarating at the same time. As a brand new teacher stepping into the world, I feel as though I am seeing it much differently from the lenses I saw it as a student. As a student, I saw school as a very boring place that I could not wait to leave. As a teacher, I now see it as a place with endless possibilities that I cannot wait to go back to. As part of my self-assessment, I wanted to create something personal for myself that I can continually refer back to. I decided to make a Wordle as a reminder for myself of all the aspects of a 21st century learner. My plan is to hang this Wordle up in my classroom in a place where my students and I can view it everyday. This will serve as the learning goals for both myself and my students as we embark on the journey of learning in the 21st century.  

As a 21st century educator, I will make the commitment to embracing technology in my classroom. However, I will not be able to do this alone. I will rely on my students to help me through this transition. After all, they are the experts when it comes to interacting online. I will model for my students what it's like to take risks, be passionate about something, and how learning never stops. Yes I will make mistakes (probably a lot!), but I will keep going and learning. I will engage my students by bringing real-world problems and social justice issues into our classroom and encourage them to see how they contribute as a global citizen to our world. I will support my students as they try out different roles and different passions and encourage them to never give up on their dreams. As George Bernard Shaw says: 

This is what I believe the 21st century is all about. Creating and designing our own destiny through the digital world.  

Why Schools Have the Responsibility to Bring Online Learning Environments into Classrooms

       In my past blogs, I have discussed 1) the importance of integrating new technological practices with traditional ones and 2) the barriers involved in doing so. As a firm believer of incorporating technology in the classroom, I believe it is now my job to explore why educators need to incorporate technology into everyday lessons and how that can be done. Outside of the classroom, students are using technology to seek out answers to questions, collaborate with others, create media projects, and network with people all over the world. Yet even though technology has clearly become a significant tool within the lives of today’s students, schools have not been successful at capturing the full potential technology offers for pedagogical purposes in the classroom. I believe the use of online learning environments must be implemented in every Ontario classroom (the how). These include social networking sites such as Facebook, Twitter, chat rooms, or online games in which participants interact with other people. In doing so, schools will begin to bridge the gap between students and the education system, promote constructivist learning, and foster just-in-time knowledge (the why).

                                                            Bridging the Gap Between Students and Schools 

           Because today’s students are gathering much of their knowledge and experience from participation in online environments, the majority of their learning comes from the digital world or the Internet. If our schools are going to engage students during the time they spend in the classroom each day, they must begin to recognize and incorporate students’ interests into the curriculum, which includes using online environments. Technology guru Henry Jenkins (2009) suggests that children and youth know more about online environments than parents and teachers; therefore schools do not need to protect students from being online, but engage them in critical discussions that assist students with articulating their understandings of the experiences they have in the digital world.

Wartella, O’Keefe, and Scantlin (as cited in Jenkins 2009) suggest students who have developed comfort with the online world will be the ones who dominate the classroom computers, as the experiences students have in the online world outside of school shape the skills and knowledge they bring with them into the classroom. Incidentally, Castells (as cited in Jenkins 2009) states the “inability to use computers or find information on the web is a matter of stigma, of social exclusion, revealing not only changing social norms, but also the growing centrality of computers to work, education and politics” (p. 19). Thus, integrating online learning environments within the curriculum is crucial for ensuring no student is left behind in terms of the skills and knowledge they need to become successful members of society. By not teaching students to interact in online learning environments, schools are not fulfilling their primary role of preparing students for the future. 

Constructivist Learning

With a focus on collaboration and the sharing of knowledge, online learning environments are often described as being participatory cultures (Jenkins, 2009). Within these environments, participants generate media creations as a collective group instead of individuals, each contributing their own expertise to the final creation. In online learning environments, there are many experts and each member of the group has a voice. The intelligence is distributed among many people instead of one person being viewed as the sole knowledge holder. Through constructivist learning, the members of online learning environments dictate the topic of discussion and the learning that takes place. In this sense, active participation occurs as all members are engaged in the learning process.

Researchers Asselin & Moayeri (2011) highlight that traditional approaches to communicating and presenting knowledge are usually done through student presentations in which the teacher is the main audience and evaluator of student learning. In this case, students are essentially consumers of both knowledge and learning. However, when students are given the role as knowledge producer, as in online environments, they are able to develop new ways of doing things and new ways of being. The possibilities created by online learning environments are endless and students are able to construct their learning in any format they wish.

In the workforce, rarely are employees asked to work on their own, instead collaboration is encouraged. The most successful employees are the ones that can work with others to develop innovative and efficient ways of doing things. In turn, Jenkins (2009) suggests students need “skills for working within social networks, for pooling knowledge within a collective intelligence, for negotiating across cultural differences that shape the governing assumptions in different communities” (p. 33).  The winners will be the ones who know how to work together, to use the expertise of others in order to construct a final project encompassing each individual’s strengths. Hence, students must learn how to  work in collaborative environments.   

Myself and fellow students working with Habitat for Humanity
in Laredo, Tx (May 2012).

Just-in-Time Knowledge

When students learn knowledge that is separate from its context of application the value for learning is strongly diminished. Online learning environments are unique in that they allow knowledge and skills to be learned within the context they are used. In contrast, our current schools teach students to master content and skills in anticipation of a payoff down the line such as acceptance to post-secondary education or a job. The problem with this is that the motivation for learning is unclear. Students do not understand why there are learning what they are learning. This is evident by students constantly asking, “when am I ever going to have to know this.”

           In online learning environments the application for knowledge is clear because information is transferred on demand, when and where it is needed. An example of this is through online gaming, which is popular in online learning environments. During games, participants apply skills they have just learned to move to new levels within the game. Motivation for learning is clear, as individuals are able to see the purpose and meaning behind new knowledge. Games create creative and compelling worlds for students and allow them to feel apart of those worlds because of the active nature of the game. On the other hand, students feel locked out and separated from textbooks because of their depersonalized nature and lack of application (Jenkins, 2009). In online environments, players are encouraged to take risks all the time by making decisions and following through with them. If a wrong choice is made, participants are given the option of starting over and learning from their mistakes immediately.  By restarting, students are able to apply what they have learned to make new choices. Meanwhile, our current schools do not normally offer second chances. Instead, they force students to repeat the entire grade even if they only struggled in one area. In this sense, we are teaching individuals to fear failure. Making a mistake means you must be punished by being held back from your friends. Instead of creating a culture of leaders who take risks we’re creating followers afraid to step out of line. 

Paul Arden taken from wwww. flickr.com

       We can be sure technology is challenging the integrity of schooling. Online learning environments provide endless possibilities and encourage student exploration. Society has embraced the 21^st century in many aspects, yet schools are still built upon a traditional model. In order for today’s students to become successful future citizens, schools need to adapt to the new digital society and provide students with the knowledge and expertise to function in a technological driven world. 

References

Asselin, M. & Moayeri, M. (2011). The participatory classroom: Web 2.0 in the classroom.

Literacy Learning: the Middle Years, 19(2):1-8. 

Castells, M. (2002). The Internet galaxy: Reflections of the Internet, business, and society. In

H. Jenkins (2009) Confronting the challenges of a participatory culture: Media education for the 21^st century. Cambridge, MA: The MIT Press.  

Jenkins, H. (2009). Confronting the challenges of a participatory culture: Media education

for the 21st century. Cambridge, MA: The MIT Press.

Wartella, E., O’Keefe, B., Scantlin, R. (2000). Children and interactive media: A compendium

of current research and directions for the future. In H. Jenkins (2009) Confronting the challenges of a participatory culture: Media education for the 21^st century.