Hyperdocs

I love technology, I love technology in teaching, I love trying new things. Even with this passion and love I find it a challenge to seamlessly integrate opportunities to develop learners digital skills in my maths lessons, sorry! I was once observed teaching plotting linear functions. I was exceeding teaching standards in all areas apart from developing digital IT skills. I asked the observer for how they would have done it in the lesson and they said to get the learners to plot the functions using Geogebra. Now I took an issue with this. Mainly because I felt it would have been impractical to fire up the aging PCs and get the learners logged on just to complete this activity and the time it would take to do all of this when we could be learning or developing skills. The observer said but this would be developing their digital skills. I challenged this and said, no it isn’t it is ticking a box for my observation. You can feel the eerie silence even now! My point was that as GCSE is a paper based linear subject the learners are not assessed on being able to plot linear functions online. They are assessed on being able to do it on the exam paper at the end of the course. Also what development of digital skills am I doing by asking learners to insert numbers and the application draws the linear function? I argue very little. Most learners are capable of plugging in values to an application to generate an output. I also argue that their time would be better served accurately plotting coordinates and linear functions than doing this online. You can imagine the observer was relieved when I signed my feedback sheet and the feedback session was over! I am not a fan of doing something for the sake of doing things. We have a lot of boxes to tick as teachers and educators and it is too easy to take a linear approach to this when planning lessons and include activities for the sake of them. I am a fan of integrating things into lessons that have meaningful impact and develop value in the learning that it taking place. I am so passionate about this as once I was in a Head’s debrief of a day one of an OFSTED when she said that anyone who hasn’t been seen needs  to include some ICT (it was a while ago!) as the inspectors haven’t seen any yet. I immediately re-did my beautifully planned lesson to an ICT maths lesson and instantly regretted it when the inspector turned up as I was uncomfortable with the activity and it showed! 

Knowing my inadequacies in integrating meaningful Digital IT skills into my lessons I am an avid reader of all things technology and all blogs, American or from anywhere around the world. Like a YouTube spiral, reading blogs can lead me to another blog to another blog and so on. One day I landed on a blog talking about teaching maths with Hyperdocs. 

Here is a great Padlet made by Kristine Vester @kavester  https://padlet.com/kvester/mathhyperdocs

There are also templates and examples on https://hyperdocs.co/index.php/templates

A hyperdoc is a Google Doc that asks learners to explore, digitally, concepts and evaluate approaches, thinking critically and developing their skills. It isn’t an interactive worksheet. Most Hyperdocs ask learners to  engage, explore, explain, apply, share, reflect, extend the learning. One example that I found on the Padlet was this one for solving equations.

I like Hyperdocs for a few reasons. They allow learners to participate in a meaningful learning experience without my input. Not that I am doing myself out of a job but, taking from Alice Keeler, this allows me more quality time focussing on the learning that that individual needs. Likewise this learning experience can happen outside of the classroom. I use them as prior learning, so that we can tackle the harder stuff in class. I am a firm believer that a lesson will be more productive if a learner arrives prepared and engaged, I’m not a fan of keeping lesson topics as a surprise, I like them to take an interest and try to get ahead! I am under no illusion that not every learner will arrive prepared and there comes a challenge of how to catch those up who haven’t prepared and develop those that have, but the Hyperdoc allows those that haven’t prepared the opportunity to do it independently in the lesson whilst the rest move on. Hyper docs help me with my long term absentees. Those who realise that the next stage in life is locked away to them (around Easter time) because they haven’t attended and are unlikely to achieve their GCSE maths. That panic of how to catch them up and reintegrate them in lesson is overcome with Hyperdocs. Teaching performing arts students around Christmas time when it is panto rehearsal can be a challenge but giving them access to the Hyperdoc and creating a bespoke 1to1 session in the lesson had a deeper meaning and was more powerful for my learners than me chasing them for attendance. No I am not an expert on Hyperdocs and nor have I had the time to create my own without a template, but if there’s such good resources out there, I don’t see the need. Hyperdocs have enhanced my learners experience and reduced my chalk and talk time, they’re a winner for me! 

Plotting functions

We call it plotting linear functions,  we may call it plotting line graphs, we may also call it drawing graphs. You may also call it y = mx + c. There are many different ways that we can call plotting linear functions. However not many of these ways mean anything to our learners. Yes we could loosely and tentatively link in English and explore the language of plotting linear and define the term functions. After we define the words, use a thesaurus, come up with synonyms and then devise our own definition and then create our own lesson objectives we have probably used a full hour?!

This might be a nice activity but actually it's not going to help with the knowledge that we need in the first instance because when we start teaching this topic what were actually teaching them to do is complete tables of values. I appreciate you may not teach it this way but this seems to be the way I have seen it or across many different schools. And when were completing a table of values again we're calling it something that means nothing to our learner's. This whole idea came from the excellent Will Emery http://www.greatmathsteachingideas.com/ . It was Will who said why do we call it table of values when actually it's a table of coordinates? And it was that simple changing language that cracked it for me with the bottom set year 8 in a school I was in that all of a sudden could plot linear functions. Which is why I'm a great advocate of finding a different way to say something to remove are complicated mathematical language where appropriate. Yes I still call it prime factor decomposition and yes I will still refer to this as plotting linear functions and completing the table of values but my lesson objectives will refer to completing tables of coordinates. Because as in the blog post that I read from Will Emery that is essentially what they're creating a table of coordinates. Just such a simple language change makes all the difference. 

Once we have called it a table of coordinates we may not be good to go, as I learned! Think of the typical question, something like “plot the table of values for the function y=2x+3 for the values of x -5 to 5.”  Channelling Will Emery’s post it it struck me that actually if you start with the positive end of the table of coordinates (values) you can spot the linear pattern and then complete the negative values. In the function y = 2x + 3 for the values of x -5 to 5 , 

I would substitute in 5 first 5 x 2 is 10 + 3 13.  

Then I would substitute in for 4 x 2 is 8 + 3 is 11 

Then I was substituting 3 so 3 x 2 is 6 plus 3 is 9.

I can now see a pattern in that is going down by two. I can now complete the rest of the table of values without having to actually multiply negative numbers by continuing the pattern. Yes multiplying with negative numbers is important. I would always encourage students to check that they are correct my substituting in negative numbers. But if you think about what we are trying to achieve in this lesson, it is to plot functions, not multiply negative numbers. I am aware that these skills should be secure and should time allow I would love to recover and remain on negative numbers until the were secured. However, I prefer to look at and explore why a linear function generates a linear sequence rather than focus on the practical application of multiplying negative numbers which may not be secure knowledge for learners. Once they have discovered the pattern, we can then ask why is there a pattern and explore algebra through the interest that plotting linear functions has generated.