The science of mathematics has developed through collaboration. Every theorem, statement, and axiom builds upon the work that other mathematicians have done. With this in mind, new theorems that we develop today relate to the work mathematicians have done across time, back to the earliest mathematician, Euclid, who documented his calculations. If humans had not collaborated, we would not be as advanced as we are today. Imagine that if every time we wanted to drive to the store we had to reinvent the wheel, then reinvent the cart, then the steam engine, and then the car: our lives would be exhausting! Instead, we work together, using the knowledge of others and our own knowledge to combine ideas and create something greater than the sum of its parts.
Humans naturally want to collaborate, but this skill needs to be learned and honed. As infants, we learn to speak so that we can communicate with others to get the things we need. As children, we work with others to develop our ability to collaborate; we learn to ask questions, we learn to investigate and research, and we build on the ideas of others.
In today’s blended, flipped, or fully online classrooms, and through all of the technology that goes with them, collaboration has taken a great leap forward. Students not only have the opportunity to collaborate with their classroom peers, but these learners also interact with peers from anywhere in the world. But with all of these advancements, true collaboration would not be possible without first developing the necessary skills. Students learn to interact cooperatively through activities in school.
In Hekademia’s Algebra 1 course, a variety of examples utilize collaboration as an integral part of the learning process. Throughout every topic, students have to connect what they are learning to their classmates and the world around them. In the Algebra 1 course we call these “Unplug” activities, and they serve several purposes. With technology being such an integral part of the learning process, it is important for students to be reminded to step away from their devices to see how the concepts they are working with relate to larger issues. Typically, the Unplugs take a mathematical concept and ask students to make a ‘real life’ connection. Then, students share their discoveries with classmates face-to-face, through a live chat, or by posting their findings on a discussion board. Educators in Hekademia’s Algebra 1 course provide opportunities to collaborate in the learning process because such experiences are fundamental to our pedagogical practices, and are necessary in every learning environment.
In addition to the Unplug activities in Algebra 1, we’ve designed collaborative assignments that are suitable for use in any type of classroom. For example, in the Data Management Unit, students play a dice simulation of a basketball game to demonstrate an understanding of experimental and theoretical probability. They begin the game by drafting their team based on their theoretical free-throw average, play an opponent, and then reflect on their results as a pair or group. An example of a question following the game is: “how did your players’ theoretical free-throw averages compare to their performances during the game? Discuss your results with your partner.” These conversations fuel students’ interests in mathematics and consolidate their learning.
We have provided teacher resources in the Modeling Unit and, have included several discussion questions that instructors can choose to use in ways that best suit their students. Depending on the learning environment, the teacher may choose to pose the questions and have face-to-face discussions with the class, host the topics in a video conference, or perhaps post them on a discussion board. The opportunities are endless and are adaptable to the teachers’ and the student’s needs.
At Hekademia, collaboration is a key component of our everyday work. Our main office contains no closed rooms or cubicles. We operate in departmental pods. As content developers, we have experienced occasional barriers, collaborated with a co-worker, and then saw our initial idea blossom into an exciting new project. In fact, this blog post has been a collaborative effort between two team members; we worked together to brainstorm collaboration, each writing a portion of the blog post, and then editing each other’s work at the same time, and in the same document from our individual computers. Collaboration is paramount to our continuing success in developing mathematics courses at Hekademia, and we are passionate about creating opportunities that will allow students to work together, share ideas, and learn from one another.