I am a Year eight student at my school. My favourite subject at school is Mathematics, my favourite maths teacher is Mr Swanepoel, and I would like to share with you a typical period from our maths class. This is my story.
Once we have taken our seats at his direction, Mr Swanepoel always greets us and wants to know how we are, he then asks the dreaded question of “can you still remember what we covered at in our last lesson?” When asking him one day why he always asks that question, he responded and explained that the reason is two-fold: (1) he uses that to judge our previous learning, and (2) he uses the question to form part of his lesson introduction. Apparently, according to Mr Swanepoel, every good lesson needs a good introduction. I’ll have to take his word for that …
What I like about Mr Swanepoel’s teaching is the fact that he uses a lot of real-life, everyday maths examples that we understand and can associate with. Some of the more complicated maths problems that stretch our brains quite a lot would have been very hard to understand and solve if we were not provided with some real-world examples which make it a lot easier to understand and solve those tricky problems. Mr Swanepoel often projects photos or images of those real examples on the overhead digital screen using Powerpoint or some other software.
Talking about computers and technology – or ICTs as Mr Swanepoel calls them – he is quite old school and struggles with the technology sometimes, but he still tries to use it as much as possible in our classroom and even sometimes asks us for our help when he gets stuck, which is awesome! When we behave well, we also get to play Kahoot! once in a while, which we always enjoy!
Lately, Mr Swanepoel has been talking a lot about some SAMR-model, modification, redefinition, and how ICTs may be used very effectively for our deep and critical understanding, knowledge and learning of complex mathematical processes and their application in real life scenarios. Again, I’ll have to take his word for that …
We are also encouraged to use blogs and wikis for collaboration, knowledge and information sharing, and discussion of challenging, complex mathematical problems that we have to solve collaboratively amongst ourselves. Mr Swanepoel says that – as opposed to the years that he went to school – we can nowadays communicate and share information and knowledge on a global scale without any time constraints to solve mathematical problems that would have been otherwise very difficult and time-consuming to solve on our own without modern-day technologies. Of course that’s old news to us ‘contempo’ students – we have been using blogs and wikis a lot longer than Mr. Swanepoel can probably remember (that is if you go by his name memory skills of course - which well and truly suck!).
To be truly honest though, even we were initially challenged by this idea of global, collaborative problem-solving and knowledge sharing, but we – like Mr Swanepoel – can now start to appreciate the benefits that come with that. Just sharing knowledge around and communicating casually on Facebook and Twitter however is not enough - according to Mr Swanepoel – instead we are encouraged to communicate on a world-wide scale to find the solutions and answers to some of those more complex, difficult maths problems.
Talking about global collaboration and knowledge sharing, and as if we do not have enough on our plates as it is at the moment, Mr. Swanepoel has now tasked us with an assignment to develop a mathematical web calculator where the code for the web calculator will run in any browser. He (Mr. Swanepoel) does not want us to simply use already existing formulas and resources to compute volumes for rectangular and triangular prisms, instead we are required to create our own solutions for this task by engaging with relevant digital technologies and producing and using coded web calculators to develop those volume-based solutions for rectangular and triangular prisms.
I must admit – even for a digital native like myself – this stuff is a bit beyond me. When we quizzed him why we had to engage in such complex stuff, he mentioned something about ‘stretching goals’ and a ‘growth mindset’ – beats me! Oh well, he is the teacher after all, what do we know?
Actually, come to think of it, Mr. Swanepoel often claims that he doesn’t know nearly as much as we think he does or give him credit for. Again, he often talks about ‘collaborative learning’ and how we all learn together in class, instead of him as the teacher knowing everything. I’ll have to take his word for that, I suppose.
Anyway, back to our latest assignment. Phase one consisted of a project brief and preliminary preparation. We were provided with a work brief that defined the main task and expected task outcomes. One whole mathematics lesson was devoted to web calculators and the necessary code required and the process involved in writing a mathematical application as a web calculator. We discussed the set of rules of the open web to allow us to run our programs and to share it on the worldwide web, and Mr Swanepoel conducted a brief revision of shapes, areas and volumes prior to us commencing with the task. Safety, privacy and ethical digital protocols were thoroughly considered and discussed, including considerations such as copyright, cyber safety, ethical considerations and privacy protocols. Mr Swanepoel also pointed our attention to the Creative Commons and Queensland Government Cybersafety web sites for consultation during the on-line component of our assignment.
During phase two we finalised our task planning and preliminary, concept designs. Applying the literacy definitions from the Australian Curriculum, we were required to document and describe our reasoning, thinking, problem definition and the outcomes we anticipated, and we were expected to work collaboratively to formulate the basis for our designs. As part of phase two, we were required to demonstrate our proficiency with and understanding of geometry and other relevant mathematical principles to arrive at a realistic, workable solution through collaboration and resources sharing. Once we finalised our concept designs, we shared our prototype web calculators on our blogs or wikis for preliminary peer evaluation, discussion and modification or re-design.
Phase three involved implementation of our web calculators, final testing and reporting. During this final phase of our assignment, we had to finalise our web calculators design so that the code for the calculator could be run in a variety of browsers. Prior to launching our web calculators, we carried out one final round of extensive testing on our prototype models and the results were discussed amongst us, any remaining errors or bugs fixed, and the design of our web calculators was finalised for implementation. Following the launch of our web calculators, we were required to submit a professional written report outlining our design rationale, testing and implementation strategies and processes, and final findings and recommendations.
Surprisingly, the whole thing has gone quite well with lots of learning new things, sharing information, ideas, obstacles, problems but also successes. We have all learned a lot from this assignment, even Mr. Swanepoel has learned a lot of new things that he never knew before as we all struggled our way through creating our web calculators. As I already mentioned, the process was not without its trials and tribulations. We are so used to simply using the apps available for our smart phones without having to develop anything, that this task really challenged us on so many levels, even technologically!
Having now completed our assignment, it appears that our web calculators work well and given their global availability we have already successfully shared our calculators around school, but also abroad – one of my overseas friends has already had good use out of it when calculating volumes for rectangular and triangular prisms! We can’t wait for our next mathematics assignment …
During a time of significant educational change, as educators we are forced to address the contemporary question: "What is the real role of the teacher?". Teachers acknowledge that they continue to be central to learning and students still need to develop real skills and real knowledge, however 21st century learners also need to be self-reliant, resilient, and fully capable of re-inventing themselves, meaning that students must learn how to self-direct their learning.
Contemporary teachers establish and design lessons to cater for all student abilities, remaining flexible to adjust their schedules to support individual student needs, while providing opportunities and resources for students to access new knowledge, and facilitating individual learning pathways and learning. Modern-day teachers support collaborative learning in teams, while providing opportunities for real-world, connected, contemporary and practical learning rather than isolated academics. Teachers become proficient in how students learn, not only in teaching.
21st Century teachers should strive towards being co-learners - not just teachers. They should allow themselves to fail often, not avoid areas of weakness and not being afraid to invite mistakes into their lives. This notion is particularly true and relevant when it comes to the use of ICTs in the classroom - older teachers are quite likely to 'fail' at times using ICTs and it may be quite likely that the contemporary students may possess a better knowledge about some of those ICTs than the teacher him- or herself.
Modern-day teachers should embrace change - stepping outside of their comfort zone - not wait until being an expert to introduce something new and they should not be scared of the unknown. Considering the rapidly changeable nature of modern-day technology, the aforementioned statement is particularly true and important for both teachers and learners. To maximise the use of technology in the future, educators need to embrace these technologies that can change the world and make things better. Moving forward into 2017, it is not the technology itself that needs to change, but rather people's attitudes, particularly in education where there is still often stubborn resistance.
Furthermore, teachers should feel secure asking colleagues for help and they should dream big, asking "why not?". One effective way to acquire assistance, gather and share information and knowledge is through professional learning networks (PLNs) and digital curation applications like Scoop.it, and to this end teachers are strongly encouraged to establish their own and join the PLNs of others.
Effective 21st century teachers question everything and model resilience and perseverence while believing that they can learn anything. They move into the student's own worlds and allow learners to work collaboratively, learning together and sharing knowledge. It is wise for teachers to continually consider and accomodate the pedagogical significance of the so-called 'Four Cs' (Critical Thinking, Communication, Collaboration and Creativity) as discussed in my blog reflection elsewhere and identified on the NEA website. Of particular pedagogical importance is the consideration of how the four approaches meet the modification and redefinition levels of the SAMR-model and how those ideas could be further developed to enhance digital pedagogies.
The above also aligns well with the notion of encouraging a growth mindset in both students and teachers, and how it relates to students' learning and academic development. According to Stanford University psychologist, Carol Dweck, the idea of a growth mindset is related to our understanding of its impact on our abilities and learning, and it is agreed that the notion of developing a growth mindset is as equally applicable to staff and teacher performance as it is to students, particularly relevant to the implementation and application of ICTs in the 21st century classroom.
According to Vygotsky (1978) and Masters (2013), students' learning is optimised when they are provided with complex tasks stretching and challenging just beyond their comfort zones while reinforcing their understanding of the effort-success relationship. For students to develop healthy attitudes towards risks, challenges, mistakes and failure, they need to be exposed to challenging tasks and expectations. Furthermore, to support the previous statements, Dweck (2006) states that "unchallenging tasks are a waste of time".
According Masters (2013), students need to understand the relationship between effort and success to develop a growth mindset and to avoid demotivating messages and student disengagement. Similarly, advanced or gifted students need to be extended with more challenging, complex material while setting high expectations for all learners (Masters, 2013). To this end, Masters (2013) and Wiggins (2016) agree that students' self-confidence is reinforced by their observation of the progress they make, appreciation of the improved quality of their work and succeeding with challenging tasks.
One way to encourage critical thinking, communication, collaboration, creativity and to promote a growth mindset by providing learners with challenging tasks while employing digital technologies, is for students to develop their own web calculators where the code for the web calculator runs in the browser. Web browsers enable truly world-changing digital technologies that a lot of educators and students have not taken sufficient note of - building a truly universal computation machine. Such a machine consists of a set of code that adheres to the basic standards for what the browsers all can read.
In contrast, the "app" world has developed around all the various hardware where the software often runs natively on Apple computers, iPhones, Android and Microsoft phones, PCs or embedded machines, which are often not cross compatible. Furthermore, in the case of phones one often has to pay to get digital material shared in a useful way and some of the applications may cease to work properly if the phone is not constantly updated to follow the latest changes in the OS.
Masters, G. (2013). Towards a growth mindset in assessment. Retrieved from https://www.acer.org/occasional-essays/towards-a-growth-mindset-in-assessment
Wiggins, K. (2016). Exclusive: Carol Dweck - 'A growth mindset is even more important after Brexit’, August 8. Retrieved from https://www.tes.com/news/tes-magazine/tes-magazine/a-growth-mindset-even-more-important-after-brexit