All courses have a duty to prepare students for the digital world that they are to navigate. How can we build more digital teaching into our GCSE maths lessons? Furthermore, GCSE mathematics is still a paper-based linear exam... With this restriction in our minds, how do we bend this rigidity to suit the digital learning needs of our students?
Jon Swain and Malcolm Swan developed some key principles for effective teaching of mathematics in their Thinking Through Mathematics Report. Although focussed on adult numeracy, the principles work for all ages studying GCSE maths.
build on the knowledge your learners bring to sessions
expose and discuss common misconceptions
develop effective questioning
use cooperative small group work
emphasise methods rather than answers
use rich collaborative tasks
create connections between mathematical topics
use technology in appropriate ways
Technology in the GCSE maths classroom should enhance what is being taught. It might not be appropriate for every lesson to use digital tools, yet there are many other appropriate ways to use technology across other areas of GCSE maths.
Thinking about principle 7, creating connections between mathematical topics, teachers can begin to link topics with the use of digital notes. Graphic organisers in Google Drawings allow students to note down connections important to them as they progress through their maths GCSE. Digital notes allow students to refresh and revisit ideas over time. A Google Slides notebook for revision throughout the course can be adapted and modified to meet the individual student's needs, a feature that paper-based notes don’t easily have. When students develop their knowledge of averages to mean from a table, they may now have secure knowledge of calculating the mean for simple data sets and no longer need to hold that revision note. If graphic organisers are digitally held, students can evidence their development of knowledge as topics connect and their knowledge grows. Progress over time can be celebrated with students via version history in Google Slides.
One topic that relies on connecting previous learning is plotting linear functions. All the principles of algebra that have gone before, up to rearranging formulae, combined with plotting coordinates (which may have last been seen when studying a statistics scheme of work) come together in this topic. It is no surprise then that misconceptions can easily arise. Principle 5 is key here to address the misconceptions, we often focus on the method of plotting linear functions rather than the answers. Paper-based sketching of functions can take significant periods of time. This reduces the time students can spend exploring variables and visually seeing relationships between lines. If we move from paper-based activities to the digital platform of Math Whiteboard, we can visually see plotting functions with a swoosh of the mouse.
Math Whiteboard allows students to plot multiple functions on axes easily and investigate the relationship between the variables. The lines are interactive and the axes can be adjusted to show how lines go on forever beyond the plotted segment. From simply writing the equation it only takes one swoosh to plot the function and one click to open up a completed table of values. Math Whiteboard is also collaborative, supporting principle 6: allowing rich collaborative tasks to be created. By sharing the web-based link, students can collaborate on the same Math Whiteboard. As it is web-based with no sign-in required, Math whiteboard is mobile-friendly and suitable for the bring-your-own-device (BYOD) classroom.
Math Whiteboard also creatively supports principle 5 of emphasising methods rather than answers in its highlight equivalence feature. Terms that are of equal value are highlighted in the same colour. This can be particularly useful for fraction simplification and algebra tasks.
In this example, as we have progressed to solving for k we have made an error and the coloured pink highlight has changed to alert us to where our error lies. Principle 2 comes alive here with the coloured highlight of Math Whiteboard exposing misconceptions. Ahead of lessons, these misconceptions could be created by the teacher and in the lesson students can make use of the text feature in Math Whiteboard to explain what errors have arose and how to correct them.
By effectively exposing and discussing misconceptions, teachers can embed principle 3 of effective questioning. Teachers can ask students to explain why the incorrect work has errors and what misconception has been applied. Students can show their level of understanding by being able to diagnose the errors made. In Google Jamboard, teachers can upload incorrect work as a background. By choosing Google Jamboard, students can annotate over the incorrect answers highlighting the errors. Here the student has highlighted the errors and explained what steps should have been taken in the sticky note.
Google Jamboard is also useful for creating collaborative tasks for students. Teachers can upload key questions as the backgrounds of frames and assign students into small groups to research, explore and begin to devise solutions together.
Paper-based GCSE’s are here for the foreseeable future, but that doesn’t mean we can’t add in digital elements. Thinking back to Granny’s Garden on the BBC computer in maths that we saw once or twice a year. There was no room for collaboration - in fact, we fought to take turns! Technology has advanced rapidly since then, as have our digital skills.; thus, we should look to build in more digital elements into our GCSE lessons. As teachers, we are educating the whole student, not just the GCSE maths student sat in front of us. A little bit of digital in a GCSE maths lesson never did anyone any harm.
Trevor Johnson, Granny's Garden loaded via Econet from an Archimedes
Attribution-ShareAlike 2.0 Generic (CC BY-SA 2.0)
Sammy White is a freelance education consultant, who also continues to teach GCSE maths in a college group. Sammy works with colleges and schools across the UK developing teaching and learning and educational technology strategies as well as delivering training to staff too. Sammy is a certified Google Educator, Trainer, Innovator and Coach. Sammy has taught in alternative provisions, secondary and further education settings as a GCSE maths teacher, including at Leeds City College. Whilst at Leeds, Sammy was an Advanced Practitioner for Technology Enhanced Learning, supporting over 1000 staff and 20000 students.