Using PBL and student-centered activities in Math classes
Image: Shutterstock/Tyler Olson
Let’s start from the beginning. How many times have we heard from our students the question: “Why do we have to study this?” As opposite to the (unfortunately, so common!) perception of Maths as being an abstract, mechanic, repetitive and boring subject, the kind of un-escapable every-day ordeal, by means of creative and imaginative projects, it can become interesting, helpful, surprising, flexible, intriguing, fun. Students can become aware of Mathematics’ role in our physical and cultural environment, as well as in our cultural heritage. It can become much more than just a class in their daily timetable, a vehicle for mutual understanding and knowledge.
What are the benefits of PBL in our effort to get out of the Maths class routine and how can it help?
During the development of a successful project, the teachers’ role is not the same for the entire duration of the project. Once the main preconditions are entailed (a good plan, based on clear aims and targeted competences, as well as on common syllabus content, and a safe and efficient environment), the focus is on the participating students. From this moment on, the teachers’ task is mainly to facilitate and stimulate the students’ involvement, while encouraging their independence and their responsibility for their own learning process.
Students will be the main progress source of the project, because they are going to be achieving the transformation of effort into learning. New skills, experiences, knowledge will be developed as a result of their involvement throughout the project, starting from its earliest stages. Furthermore, it is important that this involvement continues even after the project is concluded.
Generally, Maths is more valued for developing our students’ analytical and critical thinking, rather than their creative thinking, and this is also the focus of the Maths curriculum, in most cases. But one of the most wonderful capacities of the early age is creativity and curiosity that children are born with. How can we nurture those in our Math classes?
Curiosity and creativity can be stimulated in project-based learning, from the very beginning of a project, and throughout all its duration, as well as in any other Maths class. Let’s go back to project work. Setting as a starting point the connection between Maths and a seemingly opposite domain, such as literature, Arts, cooking, can exalt fantasy and free students’ imagination. Fostering and challenging curiosity and creativity from the very starting point of the project can be a good incentive and empower students’ motivation. New types of activities can also motivate the students by letting them use the skills they had not previously had the opportunity to put to work and display. Their particular skills can thus be put to work, according to the multiple intelligences’ theory, making learning much more effective and motivating.
Videos and dramatizing or even writing poems can be used as learning tools and thus make learning more effective and active. Instead of asking pupils to just study, take notes or solve, they can be asked to experience, experiment and create.
Pupils can be asked to look for more peculiar and odd mathematical objects: magic squares, the Moebius’ strip, paradoxes, special numbers. Their curiosity and investigation spirit can thus be stimulated, so they will hopefully get used to research and analyze, to look for unusual solutions, rather than wait for ready-made knowledge. Dramatizing and performing can bring a more personal approach, by asking students to “put themselves into the scientists’ shoes” and “re-living” the important moments in their lives.
Connecting Maths to every-day life and to our real environment gives Maths topics a purpose and a meaning. Remember that question that students ask: “Why do we have to study this?”? In order to avoid it, we can try to show them how Maths can be applied to other sciences, such as Biology studies, but also how one can use it in every-day tasks such as cooking, cost-effective packaging, gardening, in order to make difficult situations simpler and above all getting to know more about each other. Task such as treasure hunts can combine Google Maps, Geometry and information about partners’ environments. Once more, studying episodes from the History of Maths can emphasize its appearance as an answer to practical, every-day life questions.
Here is an article about the way to use Google Maps in Maths classes and great inspiration can be also found on Real World Math, a site that offers ideas and resources for using Google Earth in the Math curriculum. Yummy Maths is another site that aims “to provide teachers with an easy way to bring real-life into their math classrooms” according to the idea that “when math is explored in contexts that are familiar and of interest to students, they will be more engaged to do math, reason, think critically, question and communicate.” Maths can also be connected with sports, a very attractive topic, as proven in the activities here, news, fashion, music or even space travel. NASA also offers a wide array of Maths-related activities on its site http://www.nasa.gov. And here are some NASA videos about real world use of Maths. You can take a look at the Algebra in the Real World Movies, for more ideas!
Communication means both dialogue and understanding. The study of Maths in a second language is not very common, therefore the tasks should not require too demanding levels of communication. Students enjoy all types of communication, but one of their favourite are the videoconferences, because they have the opportunity to be in direct contact with their partners. Skype in the Classroom, for example, is a way to empower students’ communication. It’s important for students to feel that they have embarked in a journey with real partners, despite the virtual work environment. Project activities have to involve all or at least part of the consortium, rather than take place in parallel. A wide array of common activities can be approached, such as editing a magazine/blog together, writing a collaborative book or celebrating Maths events (such as Pi Day) together. Working cooperatively, even in transnational teams, not in parallel, will create a collaborative learning environment and will empower communication under different forms.
“Without play, education becomes a force of compliance, not intelligence” (De Castel, 2003). Games are a very powerful tool. Game-based learning promotes active learning and students’ responsibility for their own learning. They stimulate the acquisition of new skills and a hands-on, problem-solving attitude, as well as curiosity and research activities. Games motivate players by offering rich emotional experiences, as well as opportunities for collaboration, competition and recognition, and therefore foster affective learning. Games can improve visual and spatial perception and skills, reasoning skills, multi-tasking abilities, memory. All these features make GBL a very effective and flexible teaching tool, whether the approach is based on playing already made games or designing new ones.
In a study conducted by Robertson and Miller in 2008, about the role of GBL in improving mathematical skills, the results showed significant progress in terms of time taken to complete the tasks, the students’ academic work, the attitude towards learning and school. Of course, game-based learning is not a substitute for traditional teaching, but an aid and, as any tool, is only effective when used according to students’ learning needs and characteristics.
In Maths projects, partners can propose games or riddles to each other, then solve them according to their personal cultural background and compare the strategies. It’s a very good method to learn divergent thinking. Teams can play a lot of games while working in projects, from funny ones to more serious ones, from quizzes to treasure hunts, compete on running a lemonade stand or play animated games.
Playing roles is also very appealing to students, they enjoy being journalists, script-writers, actors, directors, cooks, researchers and so on. Stories can be great for younger students and they can turn a common Maths task from a boring one into an adventure. Instead of just having to find all the nets of a cube, we had to dress Mr. Cube, an imaginary alien who had just arrived on Earth coming from a distant Cubic Planet where no clothes were necessary. Instead of just studying the connection between the area and the perimeter of a rectangle, an animated character called Mr. Macaroni asked us to calculate the largest surface area that can be surrounded with a pack of spaghetti.
Using ICT is not a purpose in itself. “A teacher who could be replaced by a machine should be.” (Arthur C. Clarke) Using ICT tools allows digital differentiation, that is “designing and facilitating student driven learning experiences that are fueled by standard based essential questions and powered by digital tools to provide students with flexible learning paths for success” (Susan Oxnevad).
Although digital devices and video games are often considered as a nuisance rather than a potential educational medium (Prensky, 2004; Jenkins, 2004), by using the tools they are familiar with, students’ involvement can be enhanced. Mobile technologies allow them to study anywhere, anytime, at their own pace, using the tools they like/are familiar with: mobile technologies, podcasts, iPads, augmented reality and so on. Videos are one of the most effective teaching tools. But in order to use them effectively in the class and avoid a passive students’ attitude, the teacher has to plan very carefully all the sequences of the learning activity, from the objectives that are envisaged to the evaluation. For example, you can turn a video into an interactive activity by adding a quiz to it. For doing that, you can use blubbr or ESL Video.
There are lots of video hosting sites where you can find useful videos, such as Khan Academy, MathATube, Math Videos, Maths Pickle, Tutor_USA, Mr. Rob’s Math just one example of channel on Youtube, WatchKnowLearn or TenMarks. Here is an interesting website dedicated to sharing movies about many different math topics, all created by students http://www.mathmovienetwork.com/.
You can decide to have your students create their own videos (for example, in a collaborative way, using an online tool such as WeVideo) and thus empower the use of new skills and multiple intelligences. Choose a safer and more accessible site to host your students’ creations. Just keep in mind our initial idea: due to the specific features of Maths projects and to the “arid” nature of the subject, the Maths projects should have an incentive aspect, that can be achieved through the types of activities that are planned, the degree of collaboration and the tools that are used. Mathematics can thus become a “vehicle” for learning about the partners and for the mutual understanding of our cultural environment.
No matter the tools and the strategy, the starting point should be your students’ needs and capacities. Any more ideas?
Article written by Irina Vasilescu, Scientix Ambassador
Tags: digital, mathematics, maths, PBL, Students