Some CPD ideas I have picked up from Twitter.

This is my second blog, and it made sense to write it on the CPD that has mainly come from using twitter (as well as any other resources). These ideas are CPD that I have introduced into my lessons myself, there are obviously other ideas that have come from school CPD sessions.

Not Enquiry Based Learning:

The first module on my MA course was Learning Through Enquiry Using ICT at the University of Hertfordshire. I have taken the following definition for Enquiry based learning (EBL):

“EBL describes an environment in which learning is driven by a process of enquiry owned by the student.” (1)

I immediately did not like the idea that a student learns best through the enquiry, and I still do not. My biggest misgiving was that just because a student finally works something out for themselves does not mean they have learnt anything, they might quickly forget how they reached the end point, especially if they took many routes to get there.

Second, I do not believe that students are more engaged in their learning using EBL. There are too many opportunities to give up, or to feel that they cannot do maths as they struggle to further their learning.

Thirdly, I believe that once a student (incorrectly) learns something then it is harder for them to relearn the correct way. I know there are a number of articles that would disagree with me, but I like the quote

“..In fact, without working memory energy set aside for self-regulation and input from a teacher, learning is not likely to occur” (2)

Direct Instruction:

I am also rather old school and still remember the teacher either doing one question and then telling us to do the next 20 questions or rambling on for so long that interest was soon lost by the students. I have struggled since starting with how to actual make my input to the lesson effective. I think now that using Direct Instruction I am doing the best for my students.

Geoff Petty summarises Direct Instruction and details two models of it, #1 Active Teaching Model and #2 The Present, Apply, Review model. (3)

My teaching was closest to the (second) PAR model, so it seems sensible to start with this and apply ideas and strategies that I have found useful.

The start of my lesson has always included a retrieval task (see later for more detail), whether it be Diagnostic Questions (4), or low stakes quiz. Depending on the class and the topic the task might not be related to what we will be doing in the lesson. My only constraint is that this task is fairly quick, I want to ensure that the students understand the topic, and if they don’t then I need to find time in a later lesson to go over retrieval; I do not want the lesson to be hijacked by a topic that has previously been done. It is also imperative that feedback is given and that the students know how much they have recalled and why they went wrong.

I present the latest topic to the class. Questions I try to introduce are, is this topic related to anything we have previously done? what might follow on from this topic and (the inevitable) how does this fit into the real world? I use to often show a video, but I now follow Craig Barton's advice and I prefer to work through an example on the board with the students. One exception to this is anything to do with drawing shapes, I have no artistic talent and me drawing on the board is going to confuse the students, so bring on Corbett Maths (5) or a YouTube video.

Retrieval Practise

I have only ready about this recently and now I am kicking myself for the years of wasted opportunities

There is more to retrieval practise than just setting different questions. At her website (6) Jennifer Gonzalez describes the crux of it as

“Retrieval practice is the act of trying to recall information without having it in front of you.”

As teachers we should, after teaching a number of topics, be trying to encourage students to retrieve ideas and concepts instead of just trying to reteach or revise a lesson. Some ways of doing this is to use low-stake quizzes, where the student marks are not recorded and do not directly affect the end grade for the students; indirectly, research shows that the student grades are improved. Another method is to give an open-ended question, or a thinking map and ask the students to write down everything they remember, without using their books.

The following episode demonstrates a recent exchange between a student and myself that I think would be classed as retrieval. Instead of me going through a past topic with the class I told them that my input into the lesson would be minimal, so the work had to come from them. Some students took on the challenge and smashed through it. Others were blank for a while and needed some teacher input, but each time I fought the urge to reteach:

e.g. Write 0.5333 as a fraction.

Me: What do we start with?
S: Wait, is this the one where we call it x? (Nod from me).
S: Then I say 10x = 5.333?
Me: OK but would that work?
Student realised that 5.333 – 0.533 would not give a whole number.
S2: Multiply x by 100 as well?
Me: Why?
S2: Because 53.3333 – 5.3333 gives a whole number.

Interleaving.

Another method of implementation is interleaving, (7). It seems to be obvious (now that it has been pointed out), that students are not taking an exam on just one topic, so why do we set work on just one topic? If we block questions by topic the students might immediately ‘get it’, carrying on with these same questions would therefore by of little benefit. However, by giving students questions from other areas of the course we are forcing them to retrieve information, which should allow for greater long-term learning. In this excellent article there is the caveat that students need some block practise.

To me this caveat makes sense. Recently a student teacher was teaching a proportion lesson, but some of the questions included fractions. The students had to therefore tackle a new topic and overload themselves with how to divide fractions. To me it would have been sensible to use whole numbers to really get them comfortable with proportion. Then at a later lesson some interleaving could have been done, and these could have included fractions. I feel the students would then have been better prepared to tie the two topics together.

I am really enjoying writing this blog, but I am not as proficient as some of the others who have written maths blogs, so I will write a new one, with some more of my thoughts (for what they are worth) soon.

References:

(1) (http://www.ceebl.manchester.ac.uk/ebl/).

(2) taken from https://eic.rsc.org/opinion/the-caseagainst-inquiry-based-learning/2010103.article.(3) www.geoffpetty.com/downloads/WORD/DirectInstruction.doc