Why do we count in 4s?

 Why do we count in 4s in England?

As a former maths teacher who chose to work in #FEmaths I think we may need to look at assessment at age 16.

I give the analogy of a pilot in my book.

A pilot proves knowledge has been acquired and retained on key aspects of flying in an exam. But to fly a plane commercially they accrue hours of competency. They evidence, over time, how they apply this acquired knowledge. They progress in their roles held in a hierarchical structure with flying hours a key part.

When I think about assessment in England, we assess at 16 a whole course approach and those who don't achieve the desired grade 4 are immediately affected for the rest of their lives. 

Imagine a student who achieved a grade 3 in maths but 7s in all other subjects. They gain 4 A levels (not in maths). Go to university and achieve a BA. They do an MA and then decide to get a job.

The first qualification that is often required is a grade 4 in English and maths. The rest of this students brilliant study doesn't get taken into account unless that grade 4 is there.

The 4 is what counts.

Sure the student can re-sit alongside other study but the point is, we place all our emphasis on this assessment designed for students aged 16.

What were you like at 16?

We don't take into account experience, skills, evidence of learning over time. 

We count in 4s.

I say this having taught an adult who worked as a healthcare assistant in a hospital, during covid, who wanted to be a nurse. They re-sat maths 6 times. They earnt a healthcare assistant wage for the 6 years of re-sits they took. They gained vast care and medical experience in that time. The year of covid they passed maths and immediately began a nursing qualification. Upon completion all the years experience were recognised and they entered nursing at a higher band salary than would be usual.

The experience counted but only after we counted in 4s.

So I come back to the pilot example, yes a skills test of the basics. Then a process of evidencing learning over time, applying the subject to real life, showing what you know in a variety of non exam ways. Sounds like a good maths course for 16-19 years olds, no?

These are not our decisions to make but we can raise our voices and show how we think change would deliver better for our students.

We need to stop counting in 4s.

This analogy and other arguments for disruption are in my book which is raising funds for charity. It is also available as an audio listen along version as well. Info at www.whatthetrig.co.uk 

Angles in parallel lines

I have to admit that this is not a topic I am personally brilliant at. Every time as a department we did a mock paper there would always be a heightened anxiety I had if there was an angles in parallel lines question on the paper. I am not great at spotting F and Z angles. I struggled with it at school. I was taught it as F and Z angles and they’re no longer allowed as descriptions! It’s just not my kind of topic, I have a brain that means I have to work harder with shape space and measure topics! I have some great lessons to demonstrate alternate and corresponding angles and I heavily rely on these to be clear in my demonstrations. I have to admit in my early years of teaching I had my fingers crossed that all the students would get on board with it and there wouldn’t be many questions! As the years have gone on I am more confident to field the questions that learners have on the topic but I can’t help but empathise with those learners that just don’t get it!

Have you ever sat in a training session thinking, nope no idea where this is going, what time is lunch? You can see that look on learners' faces sometimes and I see it more often than not in angles on parallel lines. One year I had a learner who was in a bridging provision, not quite an alternative provision but not a mainstream school placement, she just couldn’t grasp angles in parallel lines. I went back to teaching angles on a straight line and recapped that. She turned and looked at me and said “yeah what’s that got to do with this stuff though?” and I thought, oh yeah she’s right! It made me think. What is the best way to sequence angles on parallel lines? I wasn’t sure I had it right? I went back to the exam boards scheme of work. I then checked another exam boards scheme of work and both indicated angles in polygons and angle facts on lines were the building blocks to angles in parallel lines. So yes, what did it have to do with this new topic of angles in parallel lines?

I questioned myself. I know it is 2 sets of lines and angles facts but why do I teach it as an abstract standalone topic? Was it because of my previous lack of knowledge in the topic? Was I projecting my fears onto my learners? So being brave and taking the risk with my next group of learners I taught angle facts on straight lines and around a point then in the lesson on angles in parallel lines I left it as a challenge for them to calculate missing angle values in parallel lines. Unsurprisingly with their existing knowledge they were able to answer the problems. Obviously their reasons weren’t alternate and corresponding angles but their numerical value answers were correct. I then taught my usual lessons edited a bit so that we covered the reasons for parallel lines in the following lesson.

Now I teach GCSE resit to 16+ learners. I teach 16-18 and 19+ learners and as you can imagine both groups require different approaches. I find that 19+ often crave the knowledge for perfect answers and will tackle angles in parallel lines with greater ease than 16-18 learners. 16-18 learners have sat the exam already, if not more than once. They have seen angles in parallel lines in many forms already, they’ve learnt F and Z to help them remember but then had that crutch taken away and ‘should’ know how to calculate missing angles in parallel lines with reasons. However they haven’t achieved a grade 4 and have to sit the exam again and what if they still ‘can’t’ calculate angles in parallel lines? So I now teach it as 2 sets of angles on a straight line problem and that the angles repeat. For example:

When you look at the mark scheme, the majority of the marks are for the numerical values, 

This is taken from Edexcel Foundation Paper 2 2018. ¾ marks are for numerical calculations. This example had an isosceles triangle included as well as parallel lines. I have now, almost, enjoyed teaching angles in parallel lines this way. I find that if their angle fact knowledge is secure I can introduce the labels on top for alternate and corresponding angles easier. 

You may not have the difficulties I had with angles on parallel lines, you may not even teach maths! My point is had I not been challenged with “but what does that have to do with this stuff though?” I would never have looked at my sequencing on the topic. Perhaps you have a topic that often falls flat in class? It may be worth re-evaluating your sequencing up to that point, does it make sense, almost ask yourself, yeah so what? Why am I teaching it this way? I don’t need to remind you if you are in education of the need for impact impact, IMPACT! If you taught it this way what would be the intended impact and if you taught it that way what would be the intended impact? What is the actual impact? Can you trial both ways? 

We must, as educators evaluate where we have been on the learning journey in order to guide our learners to their intended destination. We don’t often have the time or prioritise the time to undertake such evaluations but hopefully this post inspired you to take a moment and think? 

Blended Learning Quick Wins

I have just published my blog on what I plan for September and I wanted to follow it up with how I will do it. 

Cast your mind back to a lesson that required cutting paper. Perhaps they were making their own loop cards, or cutting triangles to prove Pythagoras. Remember the times you needed to stick work into books. Your lesson was planned, it ran well, but you probably had a frantic 5 minutes at one point because of the extra equipment, I know I did. In my experience finding the scissors posed a challenge, including the left handed ones. Finding the glue sticks too. Handing them out in the class, realising some students had 3 pairs and others had none. Losing glue sticks lids, the time lost to equipment diverted from valuable learning. All of this happened on more than 1 occasion to me and can still heighten anxiety, including now when I reflect. What caused me the problems was the extra equipment, to make things flow I like to give my learners everything that they will need all in 1 place. In my physical classroom I have a helpdesk where they can come up and grab maybe a device to check an idea, watch a video. It might have the scaffolding sheet for the topic, a broken down task. It might have the help sheet or template to help write a cheat sheet or multiplication grids pre drawn. It may have foreign language dictionaries. Everything that they need to access the lesson themselves, helping them be independent no matter how much assistance they need to get there.

Blended learning is going to be no different. I am going to want to put everything in one place for them. Hyperdocs then come into their own as do Hyperbooks. A hyperbook is a notebook digitally held, maybe for a unit of work. A hyperdoc is a lesson plan of everything they need for the lesson. There are different types of hyperdocs. Ones that guide through each stage of a topic, discover, explain, explore and others that are choice board in style.  I can see benefits of all of these. Mainly they help the learners be independent and progress through their learning at their own pace. The true meaning of asynchronous learning. Slidesmania is my go to place for these things. Well worth checking out. Imagine a hyperbook of tabs all within shape space and measure. Once for area, one for perimeter, one for circles, sectors, compound shapes, problem solving tiling questions, sounds good! Sounds like a lot of work from the teacher, but when was teaching not a lot of work? We are planning for a new way of learning and perhaps we could save some time in this and insert a video on the first page of each section that already exists? Is there a youtube video we could insert? Yes of course there is! Can I take a moment to recomment the brilliant Mars Maths videos, worth checking out! All we need to do in Google Slides is click Insert>Video and search for the best video for our needs.

 The beauty of Google Slides we can start the video at certain points, so only the first 2 minutes are relevant to your group? No problem! Use the start and end times! 

I accept building a hyperbook on a series of lessons within a unit is a lot of work, but ready made videos can be a real help. Like Alice Keeler says 'stop pretending Google doesn't exist' Let's use the videos that are available. Personally I will be mixing it up. I like the way I explain certain topics, you can see in my blog about, SASSYLASS for Pythagoras, ADAM for ratio, TERRY for transformations and DIN0 for nth term. I will be using a mixture of Loom, Screencastify, Hippo Video and Screencastomatic to record my explanations. I will be recording my desktop whilst I talk over my slides that I would normally use in class.

I have begun doing this for lessons and recording over my slides. In what would have been a 3 hour lesson previously I have found the actual teacher talk element is only 20 minutes when recorded. I have used the exact same slides I would talk over in class. No editing. What I found that when I would normally set them to work on the topic I have explained I have asked them to pause the video. This means that I can edit the videos into shorter videos later or leave it as 1 long video. I found that the problem with doing this is I am assuming they will get to the end point I am anticipating. I think there needs to be a mix of my own videos and ready made ones. I can select and curate existing videos to show progression, of topics I think they will get to and signpost it as such. This one is only if you got 100% on the quiz on that one. This one is if you struggled in that quiz. You get my meaning. This will all be trial and error but I was surprised that in a 3 hour lesson I only talk for 20 minutes! It feels a lot longer!

OK what about questions? Could we insert hyperlinks to a quiz in our hyperbook? I think so! 

Quizzes are quite easy, if not easier to replicate online. I think many have been using Kahoot for a while in the physical classroom. Now you can assign Kahoots for home learning. You could insert the link on a page in a hyperbook, the beauty of Google Slides is you just need to click INSERT>LINK or use CTRL+K. There are lots of existing quizzes already on Kahoot.

Another favourite for quizzing is Quizizz. You can post the quiz to your class and they can do it at home. Again there is a wide library of quizzes to choose from, so if the one you are looking for doesn't exist on Kahoot, Quizziz is a good place to look. If both of these are familiar to you and you want to change things up a bit, there are lots of others but Assistments is a good tool too. The old Transum quizzes, although can't be assigned and tracked are still great. 

Transum was around when I began teaching, starter of the day was everyone's form time activity! I like to insert the link to Transum in the hyperbook in Google Slides and ask the learner to insert a screenshot of their results underneath when finished.

Many of them are levelled and differentiated allowing learners to push on if they are finding it easy. I like that there is no sign in, they show progression, sure I accept I don't hold all the results in a nice Google Sheet, but I could type them up myself if I really wanted to! Transum has self marking on all sorts of activities and topics so for me it's on my list of places to link to.

Don't forget that in our Hyperbook, because it is in Google slides we can insert our own Google sliddes from our lesson presentation to help learners follow the topic too! Copy and paste in our summary slides or our nice examples into the hyperbook, sure! In our hyperbook then we have video, explanations, questions. All in one place! I think that if we could create a hyperbook on a unit sectioned by topic it would be a great experience for our learners. I'm now thinking it doesn't seem that much work? Maybe a little more but I think I see a way of suing some stuff that already exists?

Now what about robust questions? Teaching GCSE resit in FE means there have to be some GCSE exam questions in there. I am a big fan of both the old 1MA0 topic questions which you can find from Mr Barton here and the Corbett maths ones here. In my physical classroom I love handing these out as my consolidation exercise. Putting what we have learned in the lesson into exam context practise. But we have a problem. They are paper based pdfs, much like the real GCSE! (Which will obviously have to move on...but we will save that for another day!) This is where I hit a snag, how can I move these online? Then I hit upon ilovepdf and my life was complete! 

I convert the pdf to powerpoint. I then save the powerpoint at Google Slides. 

Once in Google Slides I insert textboxes for learners to insert their answer. This bit is fiddly but they could insert their own, I'm just being super organised! I plan to share these with the answers so it can be self marked. Whoa you say, self marking, they will all get 100% surely! Ah but the beauty of Google Slides is we can use FILE>VERSION HISTORY and see when the changes were made and what it originally looked like! 

Obviously not all my ideas are acceiboe for all, I am HUGE fan of Texthelp and for those with additional needs I would leave the pdf as is and encourage them to use the pdf reader from Texthelp. We can then screenshot or save their edited version. I haven't gone into it too much on here as I wanted to present an affordable acheivable work flow. We could use this method for all but not everyone subscribes to Texthelp products. 

There are a thousand more ideas that I could talk about for blended or distance learning but I have tried to keep it as simple as possible and as free as possible. Through my work I have seen that not all schools have access or subscriptions. I think and feel it is doable to create a unit workbook using a Slidesmania template. Inserting videos, inserting self marking quizzes and linking to exam workbooks in Google Slides format. What would be really great if we got learners to find the videos that spoke to them, if they created the content in their workbook. They research the topic, curate the resources, and design their own template. That is my aim but I know that as new as blended learning will be for me in September it will be multiplied and magnified for my learners and we can build to the top of any learning mountain. But to start with we are at the base camp and I need to help them pack their rucksack with all the right tools for the job and I think a hyperbook is the way to go!

Here is my rough first draft, welcome to copy and adapt, please click FILE>MAKE A COPY. Many thanks to Slidesmania for the template.

Example