I started logarithms with my (second to bottom) S4 class this week, and I think I managed to introduce it in a way that really helped the students to understand what a logarithm is. First I started the lesson with this recap set of questions on indices. As the students were completing it I realised my error in including 4^(1/2) as this can lead to misconceptions that an index of 1/2 is the same as halving. I probed this after the class completed the questions by asking what 9^(1/2) is, and most of them correctly recalled that it was 3.
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CLT with S3 Continuing to share the ideas of Cognitive Load Theory has been an important part of our collaborative project. We have now started to share it more widely, doing 10 minute sessions in tutor time with our S3 students (1415 year olds). This is a very brief introduction to the idea of our working memory being limited, and the need to prevent overload if we want to learn. I talk a little about being able to complete a task but not learn anything from it, the fact that practice helps to reduce the intrinsic load, and also the different extraneous loads they might experience. At the end of the session we decided to set them the challenge of reducing the extraneous load of talking with friends in class. The tutor is doing a follow up session a few days after our session, where they look at some common examples of myths around cognitive load, with a focus on "distractions". We are now half way through the tutor groups, and although students are engaging in the session, and seem to understand what it is we are saying, the only way it will become habit is with continued reminders. This is the next challenge for us as a group, to come up with how we could extend this past our own classes.
In the final week of the Science of Learning course with Future Learn we looked at a couple of new aspects of learning, then reviewed summaries of our learning, before finally looking at how we as teachers can get more involved in research. We started the week looking at the plasticity of the brain, meaning that there is no set limit to our intelligence. Clearly there are links to the work of Dweck on growth mindset. In terms of the neurosciences, the size of the hippocampus can be increased through learning experiences. This leads to the idea that "learning begets learning". This led on to a discussion about resilience, and in particular, that students' beliefs about learning can have an impact on how they respond to challenges. Believing that ability is plastic and can be improved through effort (as opposed to it being fixed) increases resilience, which helps students learn more. It is a virtuous cycle. By believing in a growth mindset, it is believed that students are able to engage their reward system through challenges. For teachers, we need to understand the plasticity of the brain so that we do not place "restrictions" on what certain students are learning. But we also need to talk about it with our students, to help them understand the importance of hard work in developing ability.
Student Survey Recently I sent my classes a survey to get some feedback on some areas of my teaching that I have changed in the last year or so. There were some useful comments, and I will provide an overview here. 1. Daily Review Starters
Do you find these are helping your learning?  100% said Yes. And 67% said we should continue with them every lesson (the rest said maybe, none said no). In the comments box there were a couple of interesting points:
In Week 4 of the Science of Learning Course we learned about the consolidation phase of learning. This is the final stage of the Engage, Build, Consolidate model for learning that we have been looking at. The consolidation process helps to free up space in working memory by moving learning from the frontal cortex to the automatic regions of the brain. This allows space to learn more things, and is achieved through practice The idea of daily recall is introduced through the work of Barak Rosenshine and his Principles of Instruction (http://www.ibe.unesco.org/sites/default/files/resources/edupractices_21_eng.pdf) and that this strengthens previous learnings and helps develop fluency. The importance of opportunities to practice recalling newly learned information are stressed. Practice is such an important part of learning that it should be used daily to consolidate the new learning.
In week 3 of the Science of Learning course with Future Learn we started looking at how we Build memories, the second stage of the Engage, Build, Consolidate model. I was looking forward to this week, as the process of how we create new learning intrigues me The first video brings to light two very important parts of the process of building new knowledge The first is that all learning is built upon prior learning, and that it is the links between topics that really mean learning new content. This is linked to learning being a two way process of communication, from teacher to pupil and also from pupil to teacher, and that feedback is vital in this process. This is especially true for children, as their frontal cortex is still developing, and so they need help to explicitly make the links to other knowledge. This is also linked to the idea of using starter activities which prime the students for the new knowledge, by recalling related information which we want them to make connections to The second aspect of building knowledge that is immediately important is the fact that this requires "effort, attention and a conscious processing of information". This activates the working memory network in the frontal regions of the brain, and this is where new knowledge is built
I have decided to be more proactive in my reflections on my teaching by recording them here on my blog. My aim is to try to do this every two weeks, with reflections on what went well, what I could improve for next time I teach a topic, and any other things that spring to mind. Varied practice for quadratic functions I introduced my S4 (Year 11) class to quadratic functions this week. They need to be able to recognise both the root form and vertex form of a quadratic, and be able to sketch a graph and also find the equation of a given graph. They do not need to be able to complete the square, however they do have to deal with coefficients of x² which are not 1. I used a set of three desmos pages I had created around the principles of variation theory. I revealed one graph at a time, getting students to sketch a prediction of the graph on a miniwhiteboard, before revealing it. Once revealed, they sketched it in their notes. Over each set they saw the links between the different parts, and even went further than I expected, making links to the yintercept from the equation. By the end of each they were able to confidently sketch any given quadratic in either form (and perform again the next day giving slightly stronger evidence of learning). After a quick example problem pair, students were able to calculate the value of the coefficient of x² for root form problems, and next week I will return to look at vertex form problems. Science of Learning Course I am currently doing an online course on the Science of Learning. I am enjoying it, and finding some useful ideas. I am trying to reflect on how these will become a part of my teaching. I am summarising and giving initial reflections (week 1 and week 2). Weekly Quizzes I have reviewed my weekly quizzes this week, and made the structure a little more standard, and tried to make more use of the hypercorrection effect and students reflecting on their own mistakes. I wrote a full post about this here. Updated IB Maths Studies Class Website I updated the unit resources for the IB Maths Studies class, which now contains links to the lessons from all bar the last two units, which we are currently finishing. I have plans to upload resources for my IGCSE classes too in the near(!?) future. CLT Sessions with Sixth Form
This week I ran four sessions on Cognitive Load Theory with our sixth form students. The idea was to introduce them to the concept of a limited cognitive load, and get them thinking about what they can control. We had a nice discussion about the control they have over intrinsic load (my favourite comment was that they can reduce intrinsic load through practice), and that breaking tasks into smaller, more manageable chunks is a good way to do this. But the main focus was on how students can manage their extraneous load, both in class and in private study time. Students had lots of ideas of things that would "distract" them, and we had a discussion about the study on phones lowering cognitive abilities (http://dfw.cbslocal.com/2017/06/28/utstudysmartphonesreducecognitiveabilityevenwhenoff/). This was after our collaborative working group presented at the recent INSET day on CLT. In an attempt to make use of retrieval practice (also known as the testing effect), I have tried several strategies in my classes. In this post I am going to talk about why I have started using weekly review quizzes, how I run them, and reflect on the successes and failures. Why quizzes? The evidence that retrieval practice is an excellent way to learn is vast (http://markhamtl.wixsite.com/teachinglearning/singlepost/2017/11/07/RetrievalPractice). But retrieval is simply the act of brining something to mind, so do we need to use quizzes? Well, the answer is no, we do not need to, but I think, for Maths at least, they are the most effective form of retrieval. Things like brain dumps are an excellent informal way to make use of retrieval, but in making a quiz I can tailor it to the topics that I know students need to review, and also, the individual aspects of the topic. They also allow me to comment on things such as mathematical layout, the importance of working and other key skills which cross all topics. Another aspect of quizzes that I like is that I am hoping they will help students disassociate tests with grades a little. If they are doing low (or even no) stakes quizzes regularly, then it just becomes part of life, rather than something high pressure to worry about. I am not sure this has taken effect yet, but I am still hopeful! How I run the quizzes
I am currently doing this with my S3 and S4 classes every week. They know that they will be having a quiz each week, and at the start of the year I explained my reasons for doing this. Firstly, there is writing the quiz. It is split into three sections: This Unit; Last Unit; Further Back. This is the second week of the Science of Learning course from Future Learn. Last week one of the biggest "hooks" for me was the Engage, Build, Consolidate model for learning. I was excited to learn more about it, and in week 2 we looked at the Engage part Firstly we get an overview of the concepts of approach response and avoidance response. Fear and anxiety in the classroom increase activity in the amygdala, which has an effect on the frontal cortex. This hinders learning in that it stops us engaging with learning. On the other hand, the brains reward system can spark an approach response in the brain. Our frontal cortex focuses attention on the source of excitement, and this engenders engagement in learning. As teachers, we need to work out what causes this approach response in our students (and it will be a bit different for all)
I am currently enrolled on the Science of Learning course run by Future Learn. In the first week we saw some neuromyths, was introduced to the Engage, Build, Consolidate model, and then looked at engaging with research as a teacher The 6 neuromyths shared were:

Dan RodriguezClark
I am a maths teacher looking to share good ideas for use in the classroom, with a current interest in integrating educational research into my practice. Categories
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June 2018
