I have produced a poster/stick in with 8 tips for students on how to learn Maths. My plan is to refer back to these regularly. They are Maths specific ideas from some of the research in cognitive science. Feel free to use, and feedback. |

Over our winter break I had most of my display boards replaced with extra whiteboards. I now have 6 big whiteboards around the room. This week I have made the most of them on several occasions.

My IB Maths Studies class did the Buildings Around the World task (https://www.tes.com/teaching-resource/surface-area-and-volume-of-buildings-6428047) where I printed two building per page and stuck them to the middle of each board. In pairs students had to find the volume and surface area of the two buildings, and check with me. Once they got the correct answers, I swapped the sheet for the next one.

Following this, we looked at compound volumes, and I projected some shapes on the projector, and again students worked in pairs to find the volume and surface area on the whiteboards. This time I controlled the pace a bit more as all pairs worked on the same one. When one pair was struggling, they could easily get a "hint" from another pair by looking around the room.

With my S3 class I projected this fantastic Show That activity (from Catriona Shearer available in the last two slides here), and got them to again work in pairs to do each one.

In both classes I found that the students maintained focus on the task for a significantly longer period of time than if they did the same thing in their books, even if they were working in pairs.

My favourite thing about the whole process, though, was that I could easily see there work (as could their classmates). This made it really easy for me to pick up on mistakes and misconceptions, but also to help students improve their layout, something I have long wanted to improve.

I am definitely going to be making use of this new workspace as much as I can, both for student work and also my own instruction (see below).

Quadratic Equations with S3

We have just finished our 3 week winter break, and upon coming back I needed to spend a little more time looking at Quadratic Equations with my S3 (year 10) class. We had already looked at solving them, but still had to look at solving problems involving quadratic equations.

We have just finished our 3 week winter break, and upon coming back I needed to spend a little more time looking at Quadratic Equations with my S3 (year 10) class. We had already looked at solving them, but still had to look at solving problems involving quadratic equations.

In the retrieval starter, I asked students to name the three methods for solving a quadratic equation (for the IGCSE this is factorising, formula and graphing using the GDC), and then to solve an equation using them.

We then recapped the need to rearrange equations into the form ax²+bx+c=0 (unless using the GDC in which case they can just graph the left hand side and the right hand side and find the intersection).

Finally we moved on to looking at solving problems.

I made full use of my new whiteboards, as I left each stage on the boards, as shown in the images above. This meant that students could refer back to them, but also made it very clear that they were only adding one extra stage each time. I could constantly refer back to the previous work as it was still visible. I think this is what people mean when they talk about the Japanese method of boardwork.

This worked really well as a way to recap what they had already done before the holiday, and build it up into the problem solving that was the aim of the lesson. I have been trying to focus more attention on the incremental build up to complex processes, and felt this approach worked well in the moment. We will see how well they remember it next lesson!

]]>I have been reading a lot about the science of learning lately, in particular around cognitive science. This explains empirically what works in terms of memory, which obviously impacts learning. I have boiled it down to 6 key points that I think all teachers should be aware of.

- Learning is not the same as performance (Soderstrom and Bjork, 2015)
- Learning is a change in long-term memory (Kirschner et al, 2006)
- Learning is built upon prior knowledge (Willingham, 2006)
- Learning is effortful and requires spaced retrieval (Bjork, 2018)
- Memory is the residue of thought (Willingham, 2010)
- Working memory is limited (Sweller et al, 2011)

I will be writing a more in depth blog post about this in the upcoming weeks.

My plan is to incorporate these into the staff training programme for the next year, but I have not decided how best to go about this just yet.

My plan is to incorporate these into the staff training programme for the next year, but I have not decided how best to go about this just yet.

References

Bjork Learning and Forgetting Lab (2018) Research [ONLINE] Available at: https://bjorklab.psych.ucla.edu/research/. [Accessed 4 July 2018].

Kirschner, P. A., Sweller, J., and Clark, R. E. (2006) Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching, Educationsal Psychologist, 41(2), 75-86.

Soderstrom, N. C., and Bjork, R. A. (2015) Learning Versus Performance: An Integrative Review, Perspectives on Psychological Science, 10(2), 176-199.

Sweller, J., Ayres, P., and Kalyuga, S. (2011) Cognitive Load Theory, Springer.

Willingham, D. T. (2006) How Knowledge Helps, American Educator, Spring.

Willingham, D. T. (2010) Why Don't Students Like School? A Cognitive Scientist Answers Questions About How the Mind Works and What it Means for Schools, Jossey Bass.

Bjork Learning and Forgetting Lab (2018) Research [ONLINE] Available at: https://bjorklab.psych.ucla.edu/research/. [Accessed 4 July 2018].

Kirschner, P. A., Sweller, J., and Clark, R. E. (2006) Why minimal guidance during instruction does not work: an analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching, Educationsal Psychologist, 41(2), 75-86.

Soderstrom, N. C., and Bjork, R. A. (2015) Learning Versus Performance: An Integrative Review, Perspectives on Psychological Science, 10(2), 176-199.

Sweller, J., Ayres, P., and Kalyuga, S. (2011) Cognitive Load Theory, Springer.

Willingham, D. T. (2006) How Knowledge Helps, American Educator, Spring.

Willingham, D. T. (2010) Why Don't Students Like School? A Cognitive Scientist Answers Questions About How the Mind Works and What it Means for Schools, Jossey Bass.

T&L Newsletter 5

I published the latest issue of our T&L Newsletter last week, which can be found here (https://drive.google.com/file/d/1RGSA7beQAJ0zDGl_78h2x2Akm3y1liwZ/view?usp=sharing). I have enjoyed putting this together, and staff seem to be looking at it. I print copies to leave in the staffroom for people to have a look at, as well as emailing it round to all staff.

I published the latest issue of our T&L Newsletter last week, which can be found here (https://drive.google.com/file/d/1RGSA7beQAJ0zDGl_78h2x2Akm3y1liwZ/view?usp=sharing). I have enjoyed putting this together, and staff seem to be looking at it. I print copies to leave in the staffroom for people to have a look at, as well as emailing it round to all staff.

Introducing Logarithms with S4

I blogged about a series of lessons I did on Logarithms with my S4 class here.

I blogged about a series of lessons I did on Logarithms with my S4 class here.

Class Website

I finally got round to updating my class website to include all the resources for the IGCSE course (http://classes.interactive-maths.com/igcse.html), so that students can use it in preparation for their mocks. For each unit I copy the objectives from our scheme of work, and link to a video for as many as I can. Then I include the work booklet that I print and give to all students, and the PowerPoint lessons, which include solutions to exercises, and the notes that students have to fill in on the work booklet.

I finally got round to updating my class website to include all the resources for the IGCSE course (http://classes.interactive-maths.com/igcse.html), so that students can use it in preparation for their mocks. For each unit I copy the objectives from our scheme of work, and link to a video for as many as I can. Then I include the work booklet that I print and give to all students, and the PowerPoint lessons, which include solutions to exercises, and the notes that students have to fill in on the work booklet.

Make It Stick

I recently finished the book Make It Stick, and wrote a summary of the main ideas for our school T&L Blog (http://markhamtl.wixsite.com/teaching-learning/single-post/2018/07/11/Make-It-Stick).

]]>I recently finished the book Make It Stick, and wrote a summary of the main ideas for our school T&L Blog (http://markhamtl.wixsite.com/teaching-learning/single-post/2018/07/11/Make-It-Stick).

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.

Next I used the idea from James Tanton's Take on Logs where I wrote some on the board like this

power2(8) = 3

power5(25) = 2

Your turn!

power3(27) = ___

power10(100) = ___

power2(8) = 3

power5(25) = 2

Your turn!

power3(27) = ___

power10(100) = ___

I didn't use the examples from his essay, but rather used ones that linked to the questions from the starter (the answers were still projected), and wrote them from scratch on the whiteboard. Students could easily see the link between the two. As they grew confident I started to use some that were not from the starter. Towards the end I threw in a couple of impossible situations such as power1(73) = ? and power5(-1) = ?. As James suggests, I then made a big deal out of changing power to log, and explaining that we just use a different name for the function. As we went through these examples I stuck to a particular routine. So, for example, for the question power3(27) = the back and forth went like this:

Me: "Maria, what is the actual question being asked?"

Maria: "3 to the power of what is 27"

Me: "And the answer is?"

Maria: "3"

Me: "Maria, what is the actual question being asked?"

Maria: "3 to the power of what is 27"

Me: "And the answer is?"

Maria: "3"

I used cold call from Teach Like a Champion 2.0 throughout this process, writing a question up and asking a student. The class came to the phrase "3 to the power of what is 27" as a group rather than me telling them.

At this point a student asked "Why do we need logs". Fortunately I had this slide from Dr Frost Maths ready, and launched in to talking about how logarithms are the inverse of exponentials and that we need them to solve equations where the unknown is in an index.

We then did an example problem pair, just to reiterate the process, and again I asked what the question was saying.

Then I set them this exercise that I put together in the style of the ones from the amazing variationtheory.com by Craig Barton. I designed it to try to get students thinking about the connections between each question, though I admit that I still need to work on this aspect of running an exercise like this. However, the questions did bring out some interesting ideas, and many of them were able to spot the impossible ones.

In going through the answers we once again used Cold Call, and rattled through them pretty quickly, again following the same dialogue as above. That was the end of the first lesson.

In the second lesson I started with a few simple questions as retrieval from the previous day, and then students filled in this stickable from Sarah Hagan, with the slide with information given below.

We then did these excellent place the log on the number line activities from the Mathematics Vision Project.

And finished with students writing their own set of Two Truths and a Lie cards (again from Sarah Hagan) based on logarithms. I collected these in, and in the next lesson we started using these, which I projected through the visualiser. Students then used this ordering activity from Susan Wall.

After this I will be going on to teach the laws of logarithms and solving simple exponential equations using logs.

You can find my folder of resources on this topic here. It includes a work booklet for students, the powerpoints I used, along with some other activities.

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 (14-15 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.

Boosting Achievement with Messages that Motivate

I read this article and wrote a blog post on it for my school's T&L blog.

I read this article and wrote a blog post on it for my school's T&L blog.

Science of Learning Week 5

I completed the Science of Learning course last week, and my reflections for the final week can be found here. In a couple of weeks I plan to reflect on the whole course in a little more depth and what implications it has for my future teaching.

I completed the Science of Learning course last week, and my reflections for the final week can be found here. In a couple of weeks I plan to reflect on the whole course in a little more depth and what implications it has for my future teaching.

Slow Education

Carl Honoré came to speak to us this week about the SLOW movement, and, in particular, slow education. The idea of the slow movement is one that has interested me for a while, and much like Carl himself, the birth of my son last year has been a catalyst in changing my priorities (more time at home, less screen time, etc). To find out a little more about this side of things, I strongly recommend watching Carl's TED Talk. I want to reflect on a few of the points he made specifically about education here.

Carl Honoré came to speak to us this week about the SLOW movement, and, in particular, slow education. The idea of the slow movement is one that has interested me for a while, and much like Carl himself, the birth of my son last year has been a catalyst in changing my priorities (more time at home, less screen time, etc). To find out a little more about this side of things, I strongly recommend watching Carl's TED Talk. I want to reflect on a few of the points he made specifically about education here.

Firstly, he talked about the pressure on students to be involved in a myriad of activities, and the "need" for these to improve university applications. This is something I have felt for a while, and that we sometimes push students to do too much. It is better to focus on one thing and do it well, and improve in that. No top athlete/musician/actor/businessman/anything else you like to think off got to where they are by spreading themselves thinly. They focused on improving in one thing, and becoming excellent at that. As Carl said, "We've forgotten how to do one thing at a time" and we should be aiming for "…not as fast as possible, but as well as possible". Should we be limiting students to one activity?

Carl also talked about the impact of technology on our lives, and specifically on education and learning. He cited an OECD study which found that there was a negative correlation between student computer use and learning outcomes. From a quick glance over the report it looks like a small amount of computer access is beneficial, but lots has a negative impact on outcomes. This is something I have been thinking about a lot recently, and finding this study is certainly of interest. I am looking forward to diving into it in a bit more depth.

Carl also talked about the digital native myth and the fact that we have not evolved in 20 years to learn differently than we did before. Though he did not labour this point as much as I might have liked, it was certainly refreshing to hear this from him. He also discussed briefly the myth of multitasking, and that this is actually just switching between things quickly.

Whilst Carl was talking there were lots of times when my mind drifted to the ideas of Cognitive Load Theory (and interestingly one of my colleagues made the same links). For example, the extraneous load of technology in the classroom, or the load caused by having too many external pressures from activities. He also talked about other ideas that are staples of good teaching, such as wait time (he called it the 5-minute warning).

Coming out of the session, it was clear that all teachers were thinking about the slow movement, and accepting that it is important to slow down at times. Although he did not quote Willingham, his idea of time to think links to "Memory is the residue of thought" very well. And if we are getting teachers to think about the thinking students are doing then that is great.

But, what about the slow movement for teachers? If we know it is more productive for our students to slow down, then surely the same is true for teachers? As a school we need to be careful that we don't take this to the extreme and push teachers so hard to incorporate it that they are always in a rush!

Logic in 6B

I am teaching Logic for the first time to my IB Mathematical Studies class at the moment (and I never studied it at University either). This is the second time in this course that I have had to teach myself some Maths that I have never studied myself (the first was Chi Squared tests for independence), and before that I had never been in that situation. There have been times when I have had to relearn something (when teaching Higher Level IB, Mechanics and Statistics at A-Level for example), but nothing that I have never seen before! It has been an interesting experience, and once I have finished teaching it, I will have to reflect on how to improve for next year.

I am teaching Logic for the first time to my IB Mathematical Studies class at the moment (and I never studied it at University either). This is the second time in this course that I have had to teach myself some Maths that I have never studied myself (the first was Chi Squared tests for independence), and before that I had never been in that situation. There have been times when I have had to relearn something (when teaching Higher Level IB, Mechanics and Statistics at A-Level for example), but nothing that I have never seen before! It has been an interesting experience, and once I have finished teaching it, I will have to reflect on how to improve for next year.

Graphs with S4

After the disaster I described last week, I managed to pull it back when looking at finding the constants of different types of graphs. I have been thinking a lot about try to use consistent methods for solving problems lately, to help students create links between related ideas. So I decided to teach finding the equations of lines, quadratics, reciprocals and cubics separately (in light of cognitive load theory), but using the same method (as shown in the summary image below). After doing a little practice on each, I presented the mixed examples, and then an interleaved exercise. I have found that using the colour coded way of linking the same steps is really helpful for students to see the connections (and I got them to do the examples in their books in a similar way).

]]>After the disaster I described last week, I managed to pull it back when looking at finding the constants of different types of graphs. I have been thinking a lot about try to use consistent methods for solving problems lately, to help students create links between related ideas. So I decided to teach finding the equations of lines, quadratics, reciprocals and cubics separately (in light of cognitive load theory), but using the same method (as shown in the summary image below). After doing a little practice on each, I presented the mixed examples, and then an interleaved exercise. I have found that using the colour coded way of linking the same steps is really helpful for students to see the connections (and I got them to do the examples in their books in a similar way).

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.

Next we reviewed the EBC model, and were once again reminded that it is not a model for a three stage lesson plan, but rather all should be happening at various stages. We are encouraged to think about how engagement, building of knowledge and consolidation of knowledge fit in our teaching, and to think actively about these when planning lessons.

We were then given a very handy summary of all the key points, and asked to reflect on our own teaching by using the concepts to justify our teaching approach, and justify new things we will try in the classroom.

The last part of the course was aimed at further engaging in research. We were given links to Best Evidence In Brief (__https://the-iee.org.uk/what-we-do/best-evidence-in-brief/__), the Learning Scientists (__http://www.learningscientists.org/__), Tom Sherrington's blog (__https://teacherhead.com/2018/03/19/evidence-informed-ideas-every-teacher-should-know-about/__), ResearchED (__https://researched.org.uk/du__), Impact (__https://impact.chartered.college/__) and the EEF (__https://educationendowmentfoundation.org.uk/school-themes/__).

We were asked to think about the last time we changed our practice in light of evidence/research, and why we did it. We were then guided towards the EEF projects (__https://educationendowmentfoundation.org.uk/projects-and-evaluation/__) to think about which ones we might like to get involved in, either individually, as a school, or actually through the EEF.

Then we were given some guidance on doing an action research project, with the following steps:

- Choose a question or focus
- What research is already out there?
- Plan how you will carry it out
- Implement change
- Collect the data
- Analyse the data
- Reflect on your findings
- Decide who else will benefit from knowing about your results and share

Finally we reflected on our learning, thinking to how our definition of "What is learning" had changed over the course, and taking the post course audit to compare with the pre course audit.

The idea of plasticity of the brain is clearly important, and helping students develop a growth mindset is something we should be doing in the classroom, and the wider school community. However this does not mean just put up posters about Growth Mindset, but rather work with students to see that if they put in the effort then they will improve, and also to be very careful about the language we use when talking about ability/achievement/attainment.

Reflecting on the EBC model is a useful strategy, and I have identified the need to engage my classes a little more. By this I do not mean make the activities fun, but make sure their brains are engaged for learning. Yes, this includes creating some interest from them, but also teaching them about how they learn, and creating the right environment for that to happen. I am going to try to reflect on the EBC model as I plan lessons over the next few weeks, and we shall see how it goes.

In terms of action research, I am not sure now is the right time to jump into this right now, both for personal reasons (young baby at home doesn’t leave much time) and professional (there are changes happening at school that I need to work on). But the idea of measuring the impact is a part of our collaborative project system at school, and I am pushing staff to think about how they can do this. As I am in a project looking at CLT, we are also discussing ways we can measure how much impact the changes we are making are having. Not a full action research, but a step in the right direction.

I have really enjoyed this course, and feel that there was a healthy balance of ideas I knew about and those I didn't to make it of interest to me. I will be looking back over these notes over the next year or so to refresh my memory of what we looked at, and see how I can incorporate some of the bits into my teaching.

]]>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.

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:

- A few students wanted more variety in the form of the starters, one even suggesting Kahoot;
- I need to give them a little more time to complete them;
- Several students suggested I should ask them which topics to include for the following week.

Do you find the booklets useful? - 100% said Yes.

The best thing about the booklets was split mainly in three: the example problem pairs; the questions all being together; and it is a useful resource for revision.

A few of the things suggested to be improved:

- Including a contents page;
- Cosmetic issues (more space, hole punched, bound instead of staples);
- Include more/less exercises;
- Making a completed booklet available to catch up missed lessons.

Do you find the example problem pairs useful to your learning? - 100% said Yes.

No groundbreaking suggestions here, but all students like this way of doing examples. One student asked for more pairs to help them better understand.

Do you feel that the quizzes meet the purpose? 92% said Yes, the rest said sometimes.

The comments about the quizzes were all positive, although some said they were too long (it is sometimes hard to judge when using topics from a long time ago).

I am really happy with the results of this survey. Although I would never make decisions based purely on what students say (we are the professionals in the room after all), it is good to see that they believe the things I do in the classroom are good for their learning (even if they complain about it sometimes). In particular I am happy to take on board the feedback to ask them for input on topics they would like to see in the daily review starters, and also to include a contents page in future booklets. I was also happy to see that they really do see the benefit in the weekly quizzes, even though some of them think they are too difficult because of the spacing since last studying certain topics.

Science of Learning Weeks 3 & 4

I completed weeks 3 and 4 of the Science of Learning course from Future Learn. Full blog posts on my reflections of these here:

I completed weeks 3 and 4 of the Science of Learning course from Future Learn. Full blog posts on my reflections of these here:

Vectors with S3

I always start the unit of vectors with this clip from Despicable Me (__https://www.youtube.com/watch?v=A05n32Bl0aY__) and this time was no different. We discussed the meaning of direction and magnitude and then went on to look at the definitions and basics of vectors. When talking about the resultant of adding two vectors I made a big deal about walking around the classroom, starting at my desk and walking to a column in the middle of the room. I have to walk via two separate vectors to get there because of desks in the way.

I called one vector a and the other vector b and we looked at a+b and how it was the same as b+a. We then looked at going backwards to the desk, and that this was the vector -a-b (or -b-a). The we talked about where I would end up if I did a-b, b-a, 2a, etc.

The movement really helped the students get what we meant by vectors, and moving on to questions was relatively easy. This linked to something that came up on the Science of Learning course about multisensory learning. In future I think I will make a bigger deal of this, perhaps go out to the field and set up some cones.

I always start the unit of vectors with this clip from Despicable Me (

I called one vector a and the other vector b and we looked at a+b and how it was the same as b+a. We then looked at going backwards to the desk, and that this was the vector -a-b (or -b-a). The we talked about where I would end up if I did a-b, b-a, 2a, etc.

The movement really helped the students get what we meant by vectors, and moving on to questions was relatively easy. This linked to something that came up on the Science of Learning course about multisensory learning. In future I think I will make a bigger deal of this, perhaps go out to the field and set up some cones.

Graphs with S4

After a successful lesson a couple of weeks ago on quadratics, I had a bit of a trainwreck lesson this week on general graphs. Students have to recognise linear, quadratic, cubic, reciprocal and exponential graphs for the IGCSE, and be able to determine the equations using points on the graph. My plan was to show a few examples of each, then get students on desmos to explore with the sliders what the different constants affected. I really misjudged the amount of structure and scaffolding they would need for this task. We got there in the end, but I had to improvise a lot of questioning to guide them to what they needed to find.

The following lesson I did make use of the "graph dances" by asking students to show me the shapes of graphs with their arms under different conditions, and at least some were able to do bits of that, so I guess it wasn't a total flop. Over the next few lessons I am going to have to patch the holes, probably with more dancing, and lots of mini whiteboards!

]]>After a successful lesson a couple of weeks ago on quadratics, I had a bit of a trainwreck lesson this week on general graphs. Students have to recognise linear, quadratic, cubic, reciprocal and exponential graphs for the IGCSE, and be able to determine the equations using points on the graph. My plan was to show a few examples of each, then get students on desmos to explore with the sliders what the different constants affected. I really misjudged the amount of structure and scaffolding they would need for this task. We got there in the end, but I had to improvise a lot of questioning to guide them to what they needed to find.

The following lesson I did make use of the "graph dances" by asking students to show me the shapes of graphs with their arms under different conditions, and at least some were able to do bits of that, so I guess it wasn't a total flop. Over the next few lessons I am going to have to patch the holes, probably with more dancing, and lots of mini whiteboards!

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/edu-practices_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.

The benefits of practice appear to be creating deeper knowledge of our learning, and the use of questioning can help create these deep connections of material. If we have a deeper knowledge we have more ways to recall the information, which means we "know" it better.

Variability in the recall of knowledge helps to deepen learning even further. Discussing it in new forms creates new associations in the brain, making that knowledge more accessible to retrieval. Every time you recall a piece of information, it is stored in a new way in the brain and becomes easier to recall in the future.

Three strategies are shared for regular retrieval opportunities:

- Mini whiteboards for effective drills
- Think Pair Share gets students to explain their thinking
- Wait time and Random Name Generators to get all students thinking

Task to review a unit of work thinking about when we get students to: recall the learning; make connections to previous learning; apply the learning in new situations; discuss the learning with others; express the learning in new forms. These are all great ways to practice and deepen understanding.

Next we learn about the impact of sleep on learning, and that when sleeping, new learning is transferred from the hippocampus to the cortex for storage in long term memory. Brain imaging shows that whilst sleeping the brain reproduces activity from the hours before sleep. It happens in deep sleep, and extracts the "gist" of the memory, a form without the unnecessary details.

Not sleeping enough has two main effects:

- You are not ready for the new learning
- You lose some of the learning from the day before.

Playing computer games can affect sleep patterns, disrupting deep sleep, and thus stopping the brain from being able to do the consolidation of new learning.

My reflections on Week 4

"Practice makes permanent" is a phrase that springs to mind from the first half of this week. The importance of practise in consolidating new learning should not be underestimated. However, practise does not have to be doing endless problems of the same type. In fact it is better if practise causes students to think, as this will enable them to make more connections within the brain, and hence make retrieval easier. This links nicely to the ideas of variation theory, or intelligent practice as Mr Barton likes to call it, where each question links to the next in some and thinking about these connections helps students create a larger, deeper understanding of the new knowledge.

"Practice makes permanent" is a phrase that springs to mind from the first half of this week. The importance of practise in consolidating new learning should not be underestimated. However, practise does not have to be doing endless problems of the same type. In fact it is better if practise causes students to think, as this will enable them to make more connections within the brain, and hence make retrieval easier. This links nicely to the ideas of variation theory, or intelligent practice as Mr Barton likes to call it, where each question links to the next in some and thinking about these connections helps students create a larger, deeper understanding of the new knowledge.

Practice can also take the form of questioning sessions where students are asked to elaborate on what they remember and apply it in new situations. I spend a lot of time focusing on the recall of learning, but need to make a big effort to ensure I also give students opportunities to express their learning in new forms and make connections to other learning.

All teachers know that a student who didn't sleep well will not learn well the next day. But what was new to me was the idea that sleep is an essential part of the consolidation process, and that by not getting enough sleep, students are actually losing the opportunity for the brain to consolidate new learning. I want to do some more research on this, and talk about this side of lack of sleep with colleagues and students.

]]>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

The ideas of building on prior knowledge are further explored in the next article, where some different activities (class discussion, concept cartoons, KWL grids, Plickers) are suggested as good tools for formative assessment. The whole purpose is for the teacher to identify what the students already know in order to create meaningful connections between these thing and the new learning

We then learn more about the immature prefrontal regions of the brains in children, even up to the late teenage years. This means that we as teachers need to "encourage and help students make connections with their prior knowledge" as they may not be able to do this themselves without guidance

We then move on to the limitations of working memory, and the idea that we can only hold seven chunks (plus or minus 2) in our working memory at any one time. The idea of chunks (or schema) is discussed and the example is given of when learning to read, kids need to hold each individual letter in working memory, but as they gain experience they can hold whole words and phrases, making reading easier

Try to remember this sequence of letters

MCB IRB RDN AFO UFV NAA

How many can you remember without looking?

Now try to remember this sequence of letter

BBC RAF MRI UFO DNA VA

How many can you remember this time?

This is given as an example of chunking information

We see brain images that show that after extensive practice the frontal areas of the brain have reduced activity when solving problems, and there is more activity in the unconscious central areas. This suggests that after practice we do not use our working memory as much, freeing it up to focus on other things

Now we start to talk about Cognitive Load Theory, and in particular, we start with the idea of visual and auditory distractions overloading our working memory. One example given is the idea of reading and listening to text at the same time, and that these both use the auditory channel, hence causing overload

However, this is then contrasted with the ideas of multisensory learning, and the fact that making use of different senses in the learning process is important for making connections and hence stronger memories. My understanding of this is that we should make use of different sensory activities for learning, but not at the same time, as this could lead to cognitive overload

This is extended to the idea of "active" learning, and how we can use physical movement to link learning. BUT, this is not learning styles. The difference is exemplified in that multisensory learning means all students should see all the different sensory approaches (not just their preferred style), and that this experience should be separated by time and linked together, rather than all done at the same time

Reflections on Week 3

Lots of the theory from this week was stuff I had already encountered, but the links to the actual activity in the brain, and the applications were very interesting. There was so much of importance in the steps this week that all teachers should be aware of

Lots of the theory from this week was stuff I had already encountered, but the links to the actual activity in the brain, and the applications were very interesting. There was so much of importance in the steps this week that all teachers should be aware of

First the implications of new knowledge being built on prior knowledge. Is this the reason why knowledge is so important, as Daniel Willingham (__https://www.aft.org/periodical/american-educator/spring-2006/how-knowledge-helps__) argues. But most importantly, the direct implications of this are that we as teachers need to know what prior knowledge our students have. This is the purpose of formative assessment, and a very strong reason to make it such an integral part of our everyday teaching. But it was the idea that children actually have not fully developed frontal cortexes, and the implication that they are actually often unable to make the necessary links between new knowledge and prior learning, that really interested me. This is not something I had heard before, and it is one of the best arguments I have heard for working on students reflecting on their learning, and actively giving them insights into the connections between topics

The importance of practice is known to all teachers, but it was interesting to see the movement of activity in the brain after sustained effortful practice. And the links made with Cognitive Load Theory at this stage (as this is really just reducing the intrinsic load of a task by automating the basic concepts). I will not discuss CLT here, as I have done that elsewhere

The final point of interest was the difference between multisensory learning and learning styles, where the main differences were that all students should experience a range of sensory learning opportunities for a given concept (and be encouraged to link these), and also that these should be separated by time (so as not to cause cognitive overload). This is something I need to work on. With changing my approach with my reading around CLT, the multisensory components of my lessons have definitely taken a hit. I need to really think about how I can incorporate this into my teaching, and most importantly, how I can make the links between the different aspects

]]>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 mini-whiteboard, 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 y-intercept 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.

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 mini-whiteboard, 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 y-intercept 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).

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.

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.

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/ut-study-smartphones-reduce-cognitive-ability-even-when-off/). This was after our collaborative working group presented at the recent INSET day on CLT.

]]>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/ut-study-smartphones-reduce-cognitive-ability-even-when-off/). This was after our collaborative working group presented at the recent INSET day on CLT.