In a world where new technology and new problems arise every day, the ability for students to identify what knowledge they need to solve a problem is going to be an essential skill. In relation to math, that means they will need to be able to apply their mathematical procedural skills, and conceptual understandings to help solve authentic problems.Therefore, my goal for my final project is to provide opportunities for my students to practice this skill through PBL (Problem Based Learning) . For me as a teacher, it means I will be modifying the way I teach (refer to below chart), and I want to see if my students prefer the ‘current style’ of learning math, or PBL. I will continue to use technology in multiple ways. Google slides will be used to house resources and present problems to my students, ensuring that I think of the ‘Zen’ slide and use creative commons for any images I may need. Google documents will be the main format for sharing resources with students, some of which will be on-line manipulatives that aren’t otherwise available to them. Examples of videos from a range of sites that will either teach / reinforce concepts for my students will also be made available via this document.
The goal of Problem Based Learning (PBL) as defined by Eductech Wiki is for students to learn about a subject through the experience of solving an open-ended problem. It also enables skills such as knowledge acquisition, enhanced group collaboration and communication to be developed. With this in mind, what I have chosen to do is switch the way I teach my students. Rather than giving them an authentic problem to solve after they have mastered the necessary skills needed to solve it, I am going to give them the problem first, and let them guide their learning by deciding what skills they need to use and / or learn to solve it. At the end I will ask which style of learning they preferred and why.
Interestingly enough, I was reading an article by Kaplinsky, ‘What does it mean to understand mathematics,’ which highlighted the inability of some students to transfer procedural skills to solve real life problems. This reinforced for me the exact reason why I wanted to try PBL in my program, so my students could actually make this transfer. Therefore, after reading his article, I took a period to implement something similar with my grade 7 students, whom I will be working with on my final project. The results were the same as Kaplinsky’s findings. Only one student out of 7 could solve both procedural and authentic problems, even though they were asking the student to carry out the same mathematical concept. By using PBL as a method to teach part of my units, I am interested to see if it will strengthen my students transfer of procedural / conceptual skills to authentic situations.
Currently for each math skill being taught, there is at least one authentic problem to solve. Students either have direct teaching of a particular concept, and /or they watch a video on the concept, then teach me / peers what they have learnt. Similar to a flipped classroom, except the time taken to learn the content is part of our class time as I don’t believe my students need additional homework. Students then refer to a resource google document, and can choose the way in which they will practice and reinforce that particular math procedural / conceptual skill. The tools can come from online manipulatives such as PhEt simulations, or illuminations or National Library of Visual Manipulatives. Resources include paper / on-line skill procedures, or written problems, or on-line games, or hands on games with partners. After they have ‘mastered’ that skill, they work with a partner, or in a group of three to apply that concept / skill to an authentic problem. I use the google Problem Based Lesson Search Engine, produced by Robert Kaplinsky, for authentic problems. Students always have a choice to use manipulatives, whiteboards, devices, BenQ, any available resource that will help them. I incorporate games where appropriate, or working with a partner, as I believe this increases the engagement factor for the students. As we know, when students work together and have to explain their thinking or reasoning, it helps them consolidate their own learning. Therefore, saying all of that, my major difference as stated above, when implementing PBL is that this process will be flipped. Students will be given the authentic problem first, and then use the resource document to identify any area they need to learn about to solve that particular problem.
As my students are engaged in PBL, I hope to see their communication skills improve as they take an active role in solving the problem. Being aware of what they do know and what they need to know and ways they can solve it, will also develop their metacognitive awareness. From this, I hope they can express how they learn best, and why. I also believe it is important that the students understand where math is used in every day situations. Throughout this the internet will be used as a resource, plus at the end of the unit, students will have the opportunity to work either individually or with a partner / small group to identify and create an authentic problem for their peers to solve. They will present this problem in a digital format of their choosing, so that it can become part of a resource bank for future students to refer to, to learn / practice particular skills.
I have asked my students if I can video them and take photos of their work, and of course they are very excited to be part of ‘my study’, so we will see what results we obtain over time.