Assessing and building on students prior knowledge (#blogsync)

Last month saw the very first #blogsync. If you missed it - check out my first entry on 'The Universal Panacea - Time' here.

This month's #blogsync is centred around classroom practice and all the blog posts are aimed at 'a teaching and learning strategy intended to elicit the highest levels of student motivation in my subject'. For this month's #blogsync I have chosen to discuss assessing and building on students prior knowledge. The reasons for me doing this is that I feel it is one of the most important things we do as teachers, as if we don't properly assess students prior knowledge we'll just end up going over old ground - over and over again; students learning nothing new.
Also, a secondary reason for me doing this topic is that as part of being an NQT one of the standards I have to collate evidence against is standard 2 'promote good progress and outcomes of pupils' of which one of the bullet points is 'be aware of pupils' capabilities and their prior knowledge, and plan teaching to build on these'. So, it has been my aim, this past half term, to focus my teaching on this bullet point, and in turn, write this post and reflect on my ability to do this in my lessons and how it has impacted on those lessons and my students' progress.

This will be just one of the posts in the series of blog posts on the topic above (in bold), to see the rest go to http://share.edutronic.net/.

So, when I was choosing my topic for this month's #blogsync I was trying to think of how I get students motivated in my subject (Mathematics) and there were a number of ways I achieve this. However, I can have the most practical of activities, put the lesson in a context my students will relate to, use as much ICT and music as I desire but none of that would matter if what I was teaching the students was something they'd done before. And so it seemed to me that the best way of me eliciting the highest levels of student motivation was to pitch the lesson right in the first place - the only way of doing this...checking what they already know and then building upon it!

I see Mathematics as a set of building blocks; blocks that can be built upon, but without the basics, can often fall apart leading to students easily forgetting concepts, or even whole topics. I like the layered approach you can often work with in Mathematics in terms of you know how to do 'x' and so we can now use 'x' to do 'y'. Sure, some topics can be taught as 'one off' lessons, but the majority involve using something you'd learnt previously to access a new problem.
There are however, those topics in Mathematics that students fail to grasp throughout their schooling that inevitably have to be taught year after year, or at least revised with classes. This, I believe, should happen in the 'assessing students prior knowledge' part of teaching any topic. Ideally students will be presented with something they should have learnt before, tested on it, and then moved on to a new problem using their prior knowledge. It's at this point I, as a teacher, would see where the class were at and then teach my lesson accordingly. If this meant going over gaps in knowledge or covering misconceptions the students may have then great, if it means that all students are ready to move on, even better.

So, in order to show how I have assessed my students prior knowledge, what I did with it and what affect it had on the lesson and my students' learning I will talk about 3 different lessons (and 3 different ways of assessing students prior knowledge). I have chosen these 3 lessons as these lessons were the ones in which I was teaching the class a new topic for the first time. As I have been in my current school since September I don't have the luxury of having taught the students before (last year, the year before etc - I have been teaching them since September!) and so don't know what they may/may not have covered last year. Sure, I have held conversations with colleagues who did teach my classes last year as to what they did with them, but will my students have actually retained this information and still have a working knowledge of it? This, is what I will be essentially checking in each of the lessons I have highlighted. I must point out at this stage that I am very much still learning how best to assess my students prior knowledge and, indeed, how to plan a lesson following this initial assessment and being flexible enough to go in whichever route the class need to venture down! So, that being said, if anyone has any pearls of wisdom they can share I'd be more than grateful to hear from you.

Lesson A1 - Year 9 - Linear Equations
(Socrative) see http://mrcollinsmaths.blogspot.co.uk/2013/01/socrative.html for my 1st post on using Socrative.

Before teaching this lesson I received an e-mail from my HoD with a Socrative quiz he had used in his class and having used one of his quizzes before (see blog post above) I thought this would be a great way of assessing what my top set year 9 class may already know from last year. The quiz only consisted of 10 questions, all ranging throughout the topic that I was just about to teach the class - Linear Equations. The only objectives for that topic that the quiz didn't cover explicitly were plotting inequalities and shaded regions, which the class would eventually go on to once I was confident they knew how to plot a linear equation, recognise the gradient and y-intercept from its' equation and be able to recognise parallel lines and lines that were parallel with one of the axes.

So, I introduced the quiz to the class and the minute I said they'd need to get their mobile phones out there was an immediate joy about the room! The students, all, in turn, completed the online 'live' quiz and I had the results coming up on the board so I could see how the students were doing and how many of the 10 questions they were getting correct; the competition between them was fantastic. The only problems with the Socrative quiz and assessing my students prior knowledge at this point was that on the 'live' screen you just see a mark out of 10 for each student and so as much as I could see generally how many questions they were getting right, I couldn't tell which ones exactly they had got correct/wrong. However, at the end of the quiz, once all students had submitted their answers you are able to send yourself a report of the students answers to peruse and use in your lessons. So, as not to embarrass any students I didn't delve into these too much in the lesson, and perhaps I should have done as I needed the time to go over the individual questions and assess where I needed to go next. However, this I could do later! I was almost helped by the fact that the time left of the lesson wasn't exactly that plentiful. Due to students having to share mobile devices/my computer/my iPhone the Socrative quiz ended up taking a good half hour to complete fully. So, for the remainder of the lesson I did two things...

The first was to go over each question in turn, covering any misconceptions the students may have had and also giving them instant feedback on the questions they had just answered. The benefit this had for them is that they could see which ones they had got wrong and why. I heard a lot of 'oh yeah...' noises coming from the class as I was explaining each question; I went through the quiz on the IWB just like they would have done on their mobile devices and then added notes to the board where needed for them to jot down.
The second thing I did, for the remainder of the lesson (about 10-15 minutes) is I got the students up at the board and in pairs, using my IWB buzzer resource I found online [see http://www.tes.co.uk/teaching-resource/IWB-Buzzer-6258257/], I asked them various questions on the quiz and new topic we were starting - I tried to cover here the misconceptions they had previously with some of the questions.

So, the lesson itself turned into a whole period of assessing prior knowledge and covering the misconceptions and gaps they may have had. This was more than I had wanted to spend, but in hindsight it actually allowed me to consider more what they had learnt before and it helped refresh their memories. Plus, I was then able to build on this in out next lesson.

For our next lesson I had analysed the results from the Socrative quiz and found some common areas of weakness - nearly all students were unaware of parallel lines and that the gradient of parallel lines being the same and therefore the equation only different by the y-intercept. Also, the students seemed to lack knowledge of equations of lines parallel to the axes, namely lines like x = 1 and y = -3 etc. The common misconception here was that they believed that horizontal lines had an equation x = c and vertical lines had an equation y = c. So, for our next lesson I chose to do some group work with the students moving around desks in a carousel format. There were 5 different tasks (5 tables of 6/7 students) all linked to the learning objectives in the students topic trackers and based on the questions that were commonly poor from the quiz. Task 2 was with me at the IWB going through equations of lines parallel to the axes as this was the main misconception from the previous lesson.

What I found was that I was much clearer on what I needed the students to do having spent a focused amount of time assessing their prior knowledge and having analysed the results properly. It then allowed me to cover the specific topics that needed work and has now set us up for our lesson on shaded regions and inequalities after half term. Students were fully motivated in both lessons and I feel this was a) down to them being able to use their mobiles to do the Socrative quiz and b) due to the group work lesson (I feel I'm pretty good at managing and facilitating group work lessons) but also down to the fact that students were at that point in their learning where they were (unaided) trying to remember their previous learning and then using my input to then put this into practice in the group tasks I had designed for them in the following lesson.

The one improvement I would possibly make when using Socrative quizzes again is to get the students, in a flipped classroom style, to complete the quiz at home prior to the lesson. This way the class have got some h/w to do to set them up for the next lesson/topic, I could analyse the results and then go from there. The only disadvantage of this is that students are obviously able to look up answers online and so the results may not reflect a completely honest version of my students knowledge?


Lesson A2 - Year 10 - Stem & Leaf Diagrams
(ABCD Fans - quiz) see http://mrcollinsmaths.blogspot.co.uk/2012/11/abcd-fans-revisited.html for my post about my ABCD Fans (and the hassle I've gone through with them [well worth it though])

This lesson with Year 10 was a lesson in which I was asked to teach a class that I do not regularly teach and so the only information I was given is that they needed to be taught stem and leaf diagrams and that they may have done it in the past, but I'd need to make my own mind up as to how much they already knew and how much to start from scratch.
So, with this in mind I thought about how I could check what they already knew and then move on from here. I decided to use my ABCD Fans and a brief 10 question quiz. I also ended up planning a lesson or series of lessons for the aftermath of the quiz depending on where the students would be at. This included me planning a lesson essentially teaching stem and leaf diagrams for the 1st time, a lesson where the students had some prior knowledge but needed to go over a few things (working out the median, mode, range etc) and then a lesson where they were absolutely fine and needed moving on to back-to-back stem and leafs and comparing data sets. I found this useful in terms of my planning and for future use but also very time consuming. I think, naturally, with more experience, I'd be able to do a certain amount of this off the top of my head based on teaching the topic a few times but as I'm a NQT I needed to spend a bit more time planning resources and routes based on what the class would need.

Now, I mentioned the quiz had 10 questions. The first 4-5 questions were just on averages and working out the median, mode and range of sets of data. These questions were completed with relatively little difficulty and I only needed to just check a few things, provide 1 further example with one question and then write some key information on the board for the students to use at a later data. Question 5 or 6 was simply a picture of a stem and leaf diagram, multiple choice answers and the question...'what is this diagram?' They all knew what it was. Next question - how do I work out the median from this diagram - same picture of the stem and leaf diagram with a purposefully tricky set of multiple choice answers whereby 2 of them were just the leaf part of the most common numbers, one was the correct answer with the actual number and one was the amount of the number that appeared the most. All students were slow with answering this one and barely any of the ABCD Fans moved, let alone were held in the air above their heads indicating to me an answer of some sort. So, rather than go through the remaining questions I stopped them there and then got up my ppt on stem and leaf diagrams.
I reminded the students how the data gets put into the stem and leaf and then how you could work out the various averages. I then, as you can see in my previous post [http://mrcollinsmaths.blogspot.co.uk/2013/02/whole-class-stem-leaf-diagrams.html] got them to create a stem and leaf diagram themselves.

The advantage my quick quiz had was that I was able to see quickly where the students knowledge stopped and then was able to build on it and work with what they did know. You could argue that I could have continued with the quiz as they may have known the last few questions but these were checked and covered in what followed in the lesson.

The lesson went fantastically well, and rather than before with the year 9 class where I went over the answers in greater length I was able to stop the activity as soon as I had a judgement on where I needed the lesson to go and then went there. I feel with the Socrative quiz there needed to be a greater analysis of results where as with this approach I could easily see when the students where getting the answers right and when they were 'stumped'.


Lesson A3 - Year 10 - Ratio & Proportion
(DfE Standards Unit - exam questions and sample answers [with mistakes])

The last example of having assessed my students prior knowledge and looking to build on it was with my regular year 10 class when covering ratio and proportion.

Now, this is a topic, that having taught KS3 classes a lot more than KS4 over the past few years, I have a good idea of what is covered prior to students entering year 10. However, I wouldn't want to assume that this knowledge had been assimilated and so used the DfE Standards Unit lesson on proportion with the intention of taking from it the bits that my students needed and then moving them on to looking at direct/inverse proportion and the constant of proportionality.
I chose the standards unit task as the lesson is based on students being initially given 4 exam style questions involving proportion, answering these with their partner and then being given some sample answers (with mistakes and correct answers included) and then marking this work just as if they were a teacher.
The advantage this had is that as the pairs were working on the 4 questions I was able to make my way around the room and ask the students questions as to how they were going about answering the questions. This, in itself, highlighted some prior knowledge and equally a good amount of missing knowledge. However, from when the students got the sample answers to correct, the missing knowledge was partially sorted as the students were able to see methods of working and were able to correct them or just tick them. I think for a lot of them it was a case of knowing how to get started with the questions and understanding what it was they were being asked to do. Once they saw the initial workings they were able to correct the mistakes the sample material had made (adding denominators of fractions for example).

After this initial paired work I asked the class questions as to how they went about completing the questions and then covered all of the mistakes in the answers before moving on. I used the flow diagrams part of the lesson to link proportion to multiplication and checking the students new the unitary method. We didn't quite have enough time to get on to looking at direct/inverse proportion in the lesson for the amount of time I felt we needed on this. So, without moving on too fast I got students, again in their pairs, to finish off the last part of the lesson which was to come up with their own proportional problems for their partner to solve using the flow charts we had discussed.


What I have learnt from focusing more heavily on students prior knowledge is that my students are challenged more so than what they may have been had I assumed some sort of prior knowledge and decided personally on where I thought the class would be. I have also learnt from this that I need to continue to do this at the start of each topic and come up with new ways of checking what my students already know. I think that in subsequent years I will naturally have a better idea of what my students will already know, especially if I am to keep certain classes over the next few years etc. However, the experience I have now gained from doing this #blogsync and reflecting on what it has meant for the motivation of my students and the impact on their learning, even if I don't teach the same classes I will have a much better idea of how to effectively assess their prior knowledge and adapt to it.

Thank you to those of you that have taken the time to read this - I know it's been a bit of a long one and thanks to those of you that may suggest other ways in which I can go about assessing students prior knowledge.

Remember...go and check out the other posts on http://share.edutronic.net/.