COVID has placed me in a box!

“When patterns are broken, new worlds emerge.” —Tuli Kupferberg

Like so many things that have been postponed, cancelled or spoiled by COVID, teaching has had its challenges with this pandemic. For many of us teachers, we are now forced to teach literally from the front of the room or our desk -whether you sit or stand or walk 5 steps to and from the white/blackboard is a matter of perspective…. or just the need for a bit of exercise.

The following is an account of a conversation I have almost every week since we returned to school at the beginning of September:

Student: ‘miss, can you come please?’ or ‘miss, I need help, come please.’

me: ‘Ah, no. Remember we are trying to limit the spread of the virus so I have to stay in my bubble… and you in yours’ or I simply raise my eyebrows and hold out my red lanyard to show them that I am afraid of the virus… even if they are not. (Whenever I do this gesture they almost always laugh, at me I suppose)

This virus has placed me in a box, with the marker tape on the floor to remind me not to stray… robbing me of that individual support I love to give to struggling students or that need to check on what my troublesome students have not been doing or to congratulate and reassure those working ever so hard and making progress.

“Adaptability is about the powerful difference between adapting to cope and adapting to win.” —Max McKeown

Ultimately, since we do not have much of an option, for our safety and that of our students and our families, we have to deal with this and learn to think outside of the box.

Consequently, I must admit (hope you will not be jealous) but my school (and HOD) are amazing and had a good vision to invest in essential technology before the pandemic. I am very grateful that we have Wacom Graphics Tablets and visualisers to demonstrate to the pupils while we sit at our desk. These are tools that help to make the lessons interactive, especially in our current climate, and are very useful tools for online teaching also. So get your school to invest in them if they haven’t already.

Another way that we have been coping in my maths department where marking and feedback is concerned, is that we have been making use of Do Now / Lesson Starter Booklets far more often than usual. We use these to assess prior knowledge and close gaps that would have widen due to the lockdown. We then collect these in a container weekly or bi-weekly and leave them to ‘cool off’ over three days before we then check what the students have been doing, or not doing, and to monitor the progress that they have been making, or sadly the lack of progress. Nevertheless, these booklets help to give additional insight into the learning that has been taking place and we are using them to help us plan strategic interventions where necessary. (Read my article on Effective Lesson Starters to get a better idea of what this booklet look like:https://easymathslpt.com/2020/02/16/effective-lesson-starters/(opens in a new tab) )

Thinking outside the box is a common phrase that most of us are familiar with and perhaps have even been doing willingly. In this pandemic, our limitations, our constraints and our inability to teach in our familiar settings coupled with our need to help our students learn and grow are the perfect ingredients for the perfect challenge that I am confident we will rise above and surpass our imaginations to better our best.

As always, I look forward to reading your emails and your comments. How are you coping?

Cheers,

Lotoya 

Teaching Low-Ability Students

“Maths is fun when you are learning!” Fatima (one of my bottom-set students)

If you are anything like me, you would never raise your hand excitedly to teach a group of bottom set students / low-ability students! In fact, if it was a matter of choice in a department meeting, this would be your cue to go to the toilet or grab a cuppa coffee or better yet, slide as far down in your chair as possible just to hide! (At this moment in writing this, I am hoping that my principal is totally unaware that I have a blog or that she never sees this post! shhh)

Seriously, does any of this sounds vaguely familar….? or am I in the naughty corner all by myself?

Ok. I hear you agree with me quietly. That’s ok.
The description above WAS me, until recently. You see, I had the privilege of sitting in a colleague’s lesson once per week for a term and not only was I captivated by her calm demeanour and her assertiveness but I was totally amazed at just how well her set 7 students were working (we had 8 sets)! The atmosphere in the room was so positive, vibrant too, but very purposeful! There was a level of yearning and aspiration that transcend the room and vibrated through me! It was beautiful and I loved it so much that I would frequently tell other teachers about it.

  “Good artists copy and great artists steal.” Picasso


I kept wondering how this teacher, newly qualified at the time, did it. I commended her but, as you probably know already I followed Picasso’s advice and stole her strategies. I now have a set 7 class and I absolutely love love teaching them! It’s unbelievable I tell you! They work very hard in lessons, at least 90% always complete homework to a very high standard and they seem to prefer to stay in lessons to do more MATHS rather than go for lunch! I am still in a state of disbelief! Furthermore, even the students seem to also be in shock as they often make some weird but interesting comments each week in lessons, for example, last week while learning Trig one student said out loud ‘miss this is FUN!’ and in agreement her classmates said ‘ain’t it!’ and ‘yea!’ (just to point out that we were simply working some problems, some which were quick wins as well as some challenging ones, but obviously they were enjoying the thinking process)

Anyway, in a casual conversation with Nazanin about teaching low ability students I said to her ‘you must share your strategies because I have benefitted so much from watching you’. Surprisingly or not, on the spur of the moment I said ‘how about I put some questions together and you see how best you can put your magic into words and I will share it with readers on my blog!’ with my mouth wide open (ta- dah, light bulb moment) and fingers and legs crossed hoping she will say yes. And yes it was, without hesitation.

so, grab a cup of tea or your favourite drink and read on…..

Without further ado, here are some details of how Nazanin manages to be a Super teacher at raising the aspirations, expectations and attainment of so-called low-ability students! 

How do you normally approach or get ready for each lesson with a low ability class?

From the first lesson that I had with them I shared with them a plan that I had drawn out for their revision during our weeks to come. They were given a list of revision topics that was taken from mathsgenie (https://www.mathsgenie.co.uk/gcse.html) for getting grades 3, 4 and 5 and had to stick that to their books so they also were aware that there was a structure and there was a goal to attain. After covering each topic students were then given topic-specific papers for a mock test in the  class. This would not only ensure that they familiarised themselves with each topic but was interesting to see how it affected their self confidence and interest when they could answer real GCSE questions and score high grades. Further more I tend to pick topics from across the grades rather than finishing one grade and moving to next. For instance topics are taken from grade 4 followed by grade 5 and then grade 3. I believe that by concentrating on just grade 3 you are already programming them to expect low whereas by showing them that topics under grade 5 is what I expect you to learn and later what you scored 70% in the topic paper raises their self- confidence and reassures them that the grade 5 topics are not unachievable.

The mentality is to enforce that I as your teacher can see in you that you can do it and expect you to do well. Then prove it to them by letting them excel in a particular topic by scoring high in their topic- test.

Every lesson has already been planned to make sure a specific topic is well covered from basics to the level of sitting a topic test with confidence. The relationship between topics across the grade boundaries is also emphasised (e.g. Substitution in algebra, in linear graphs and quadratic graphs).  

Do you normally have to go to these lessons with a ‘bank’ of plans for various methods of scaffolding? How different is your instructional plan for a low ability group compared to a mixed or a more abled group? 

I believe that the use of various methods in low ability students is often confusing and they are better at taking in just one (or may be two) simplified,  easily understandable solid method that can be retained by the mind is what I have seen to have a better outcome. So I enjoy it when I hear remarks like: Is that it?, Oh but that’s so easy now! 

How do you know when students learn what was intended? 

During the lesson questions of various strengths are given and they are encouraged to answer them and even compete for time and correctness by giving them recognition. When the topic is finished they are then given a topic-specific paper from maths genie to do and by scoring high they are encouraged and their self confidence is boosted.

If another teacher was to observe you with this group, what would they be seeing in a normal lesson with your bottom set students? 

Engagement of students and their interest in learning as well as self confidence and the sense of being valued.

How do you get the students productively engaged? How do you know when this is being achieved at the desired level? 

Cold calling, rewards and competition as well as group work. 

What is your advice to teachers who are struggling to see progress with their bottom set students or to teachers who are demotivated by or with these classes. 

Start with teaching topics that would be easily understood and follow it by giving real GCSE questions so that the students build self-confidence and a personal reputation in your eyes as their teacher. Show them that you expect no less from them than those in other groups and hence the choice of topics the choice of doing real exam questions Once they truly believe that you believe in them and therefore expect them to achieve, they would not only gain the confidence but also try best to keep up with your  standards. That is when you know that they are themselves eager to learn and score high and subsequently aim high in their lives.

I really hope you did get to the end of this post and as always, as I aim to better my best in this area, I look forward to learning from you on how you raise the attainment of students who are considered as low-ability.

Cheers,

Lotoya


Preparing For the New School Year Post COVID-19

“Every day the clock resets. Your wins don’t matter. Your failures don’t matter. Don’t stress on what was, fight for what could be.“ -Sean Higgins

What will learning look like in the new school year? How will social distancing be practiced effectively? Can you teach effectively from the front of the classroom? Will I be able to teach effectively without going to help individual students? How will I manage to resist walking around my class to check work? OMG! Can you believe that much of what many of us called normal, will suddenly be … a thing of the past (at least for a while)?

WOW! Ok. Now breathe. As my 3-year-old daughter would say (when it is convenient for her) ‘mommy count 1, 2, 3, 4. Breathe and don’t be angry’.

I am also saying this to you, as much as I am trying to reassure myself: we will be alright. We are teachers! This profession makes us resilient and very adaptable to changing times and seasons and this will be one change that I am confident we will sail through and land safely on shore (perhaps extremely exhausted).

So, now we got over talking about the main hurdle, let’s think about how we will be planning for our students.

As you are very much aware, depending on your own country and school statistics, the rate of student engagement has been significantly lower online as opposed to face to face.

As such, two of the strategies I believe may be helpful for the ‘catch-up curriculum’ is to consider

  1. Implementing a delayed scheme of work.

This is where the plan for a typical year as it relates to the topics taught, is put on hold for the first half term. This would then allow teachers to focus on some of the most fundamental and connected topics that were covered remotely during the lockdown. There are a number of ways to go about selecting these topics, for example students can be assessed in the first week back at school to gather information on where the biggest gaps exist and use these as the topics to zoom in on. Or if data was collected during the lockdown, this could be used to inform this intervention.

2. Targeted or strategic weekly topic interventions.

This is perhaps more pleasing to the ears, as the thought of pressing the pause button on the curriculum may be too drastic for many to consider. So, my next suggestion is to use the information from an early September assessment (baseline assessment of where students should be at the start of the new academic year or using the end of year exam that would have been done had schools not closed) to plan weekly intervention lessons. The topics to be focused on should be those that are most essential to bridging gaps.

NOTE: While there are talks of U.K schools allocating extra curricula time to core subjects (https://www.gov.uk/government/publications/actions-for-schools-during-the-coronavirus-outbreak/guidance-for-full-opening-schools#section-3-curriculum-behaviour-and-pastoral-support), it is very important that this ‘extra’ time be given serious thought on how effectively this time is used. A large number of students will still have gaps to be filled. Also, for those students whose knowledge is secure, considerations should be given on how they can be stretched and challenged.

Whatever method is used, the planning needs to be carefully considered, implemented and monitored.

I am very keen to hear how you or department is planning for next year, so do email me or comment below.

Now, did I hear the word FREE? I did. Below are links to some websites, many of which I am a regular user (especially since COVID-19 lockdown).

FREE Resources

Website to explore interactive teaching of mathematics

https://www.geogebra.org/?lang=en-GB

My top four websites to get GCSE or A-Level, CXC/CSEC past papers and help with lesson planning (including topic tests):

https://www.mathsgenie.co.uk/

https://www.csecmathtutor.com/

https://www.mathsisfun.com/

https://diagnosticquestions.com/

Finally, I could not end without ensuring that we are bettering our best by catering to our own development as teachers: here are a list of websites that I recommend for your personal professional development to ensure that as teachers we are ever sharp and kept abreast in our field.

FREE Professional Development courses to explore

Well-being / mental health

http://allianceforlearning.co.uk/covid-19/mental-health-and-wellbeing-resources-for-adults/

Teaching and Learning as well as some general education courses

https://elearning.creativeeducation.co.uk/

https://www.open.edu/openlearn/education/free-courses/?filter=date/grid/569/all/all/all/

https://app.senecalearning.com/courses

Special educational needs and disabilities (SEND)

https://alison.com/course/working-with-students-with-special-educational-needs-revised

THE FINE PRINT:  A number of these professional development sites were recommended to me by colleagues and I have used some of them. This is not a promotion for any of these sites but rather helping to add to your list of websites to explore.

I am now officially on HOLIDAY (from blogging at least). Thank you for reading, commenting, sharing and joining me on this learning journey. ‘See’ you back the first Sunday in September (or October) 2020.

All the best for the planning of your new school year and ENJOY THE SUMMER as much and as safely as you can.

Cheers,

Lotoya

Promoting Better Understanding of Ratio and Proportion

‘By three methods we may learn wisdom: First, by reflection, which is noblest; Second, by imitation, which is easiest; and third by experience, which is the bitterest.’ –Confucius

Since the 1970s, which is as far back as my research took me, maths educators have all been asking the same questions about the same issues on why so many students find ratio and proportion so challenging. Why are the students of each generation making the same mistakes on this challenging topic and how can we fix it?

Well, approximately 50 years into the future and we are (or at least I am) still asking these questions. While the challenge of teaching and learning Ratio and Proportion is not unique to the United Kingdom The National Centre for Excellence in the Teaching of Mathematics (NCETM) has been taking a proactive approach to solving this problem in hopes that the next generation will no longer struggle with these issues. It is by being involved in NCETM Challenging Topics at GCSE Maths Hubs that I have gained confidence in teaching this topic. (See Maths Hubs link to get involved or view their projects: https://www.mathshubs.org.uk/)

Three years ago I would get a bit nervous when it was time to teach ratio & proportion especially to a year 10 or year 11 class. Why? Well, my only key tip was always ‘the key students, is to find the value of 1 unit, then you will be able to find any amount even 1 million’. But even with that tip, some of my best students were not sure how to start the more sophisticated problems. They needed a structure to help them see the problem and
a) I didn’t think of that
b) none of my research then, which was obviously limited, gave me any helpful answers – it was all abstract.

Who got it right?
Singapore mathematics education, the envy of the world, has gotten it right. They have reflected and embed a culture of using Concrete Pictorial Abstract approach to teaching mathematics. Many of us are familar with this CPA approach but don’t use it all the way, especially in secondary schools, we often ditch the C & P and go straight to the A.

However, much to their advantage, the Singaporeans used this approach thoroughly to develop a nation of problem solvers. So how does this relate to ratio and proportion? Two words: Bar Models. The bar models (rectangular boxes) is a pictorial approach that can be used to help students see the structure of a problem and then figure out what missing information is needed. The NCETM have been promoting this model over the years and it is a model that I can now safely and confidently say has helped me to understand ratio and proportion much better and thus, my students have been and will be the recipients of this knowledge.

Do the maths:

Here are three basic, but essential problems that a number of students struggle with, especially number 2 and 3:

1.  Will and Olly share £80 in the ratio 3 : 2. Work out how much each of them get.

2.  Rajesh and Gudi share some money in the ratio 2 : 5. Rajesh receives £240. Work out the amount of money that Gudi receives.

3.  Pritam, Sarah and Emily share some money in the ratios 3 : 6 : 4. Sarah gets $15 more than Emily. Work out the amount of money that Pritam gets.

As you look at these problems, I would like you to think about how you would have solved each problem prior to seeing the bar modelling. Also think about the misconceptions or the mistakes that your students (weak and middle ability) would have likely made at their attempt at each problem and how you would have helped them to understand the problem(s).

Attached is my demonstration of the bar modelling of the problems above:

Finally, the NCETM (https://www.ncetm.org.uk/) is free to subscribe and has more on this and many other useful resources on best practices in maths education.

As always, I am keen to hear from you as I aim to better my best and hopefully inspire reflection and action among other practitioners. 

Cheers,
Lotoya

Should Children Learn The Basic Times Table By Memorisation?

“To attain knowledge, add things everyday. To attain wisdom, remove things every day.” ― Lao Tse.

I know, if you just completed your teacher qualification or if you are fairly new to the profession (less than 2 years) your answer would likely be a very strong “NO! Students should be taught the concept of multiplication and not just recalling facts!” Am I right?

Well, this was me in my first three years or so of teaching. But when I started teaching 14-year olds who did not know their 3-times table much less the entire 12-times table, I took a sharp U-Turn and here is my reasoning:

There are many good literature on educators suggesting that students should or should not memorise their multiplication table. Those who are against it seem to suggest that this limits students understanding of the concept of multiplication and that learning by rote may do more harm than good (I agree to some extent example when learning about area and perimeter). Whereas, those in favour of students memorising their multiplication table explains that this ability is fundamental to future success in mathematics. This I agree with 100%. I think some things, you can learn the facts first, then understand the whys and hows later. So, perhaps now, during this period of school closure, students can learn or recall their times table?

In the book I am currently reading, How To Teach For Mastery by Dr Helen Drury, Dr Drury compares the teaching strategies of countries in the East vs those in the West, countries such as China vs United Kingdom and what the data from PISA tells about high performing students. On page 119 her extensive research summarizes why memorising facts can be particularly helpful:

“Quick recall of number bonds, tables and key formulas is vital for problem solving. Students need to spot links, patterns and have an idea of what could be done to tackle a problem. We need students to have rapid recall of certain key number facts, and to be able to use these to calculate efficiently. Speed and memorisation are therefore essential for high-level mathematics but they are not the only very important skill.”

My Experience
In my 7+ experience of teaching, the students who know their times-table usually progress so much faster that those who had to stop to draw circles or who had to write 3 × 9 as 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 or on the good days as 9 + 9 + 9. Now, while these were mainly acts of low ability sets, they were significant enough to spot the huge gaps in attainment. Gaps that will continue to widen among disadvantage children if they leave primary education without such a vital skill as knowing their multiplication table.

Consequently, both breadth and depth of teaching would often have to be put on the back seat while you addressed the basic prerequisites. So what do you do in these scenarios? How do you teach a lesson on factorising to a year 9 or a year 10 class when there is an issue with students not knowing or recalling their times table?

1. Secretly (if it is a mixed ability class) give that student a multiplication table to ’study’ at home? (Just to let you know, the student may still be embarrassed even when this is done discreetly)
2. Give all the students a multiplication table to  ‘study’ at home? (In the case where it is a low ability class and majority of them struggle with this skill).
3. Ensure that you have the multiplication table mounted in your classroom….and hope they will ‘cheat’ or actually look up at the chart and tell you the correct answer?
4. Teach them the concept of repeated addition and hope that they will apply it to other situations?

I am not telling you what to do?  After all, I am but one teacher who simply read and experiment in my classroom. But, teachers of years 6 and secondary school, I am genuinely interested in what you actually do when faced with this problem.

Needless to say, my husband has been teaching our 3 year old daughter her multiplication table and even I could not have convinced him otherwise (not that I want to).

As always, I look forward to hearing and learning from you as I aim to #bettermybest.

Cheers,

Lotoya

Interleaving in mathematics for better results

If You Always Do What Youve Always DoneYoull Always Get What Youve Always Got.” ~ Henry Ford.

My fellow educators, I first want to ask, how are you? Really?

It is nice to be writing this month’s blog, but I must admit that, I had to change the order of my topics (shift the next few topics down) and frankly, I wasn’t sure what to write about this month for obvious reasons.
Firstly, most of my readers are on holiday, no not COVID 19 holiday, it is Easter Break in the U.K starting this week, though it may not feel that way,
and secondly, unless you live in a cave or under a rock, the world’s schools have been under lock down for fear of spreading the deadly COVID-19 virus, and rightly so.

So, with all this unprecedented events, we have been forced to turn up the volume on our creativity in how we educate our students from a distance for an uncertain length of time – most of us are perhaps now experts at using Google Classroom, Google Meet, Zoom, Schoology or even Whatsapp and Youtube. This spark in creativity has touched not just education but many other sectors – hospitals being built in record time, 3D printing being utilized to a higher level to help meet the needs within the health sectors, manufacturers making a 360 degrees turn to make products that they have never even thought of, among so many other things.

A Jamaican phrase that came to my mind and fits this well is ‘when trouble tek yuh, pickney shut fit yuh’, which translate to ‘when you are in trouble, a child’s shirt will fit you’. This can be interpreted as, when faced with difficulties, you will certainly find a way to make it through. And we will. We will come out stronger on the other side.

Interleaving in maths
Well, I decided to share a snippet of what I have been up to prior to schools closing and also what I have done in recent days since we have been working from home as teachers.

In order to make my training sessions useful and for teachers to want to return to future sessions, I usually embark on extensive research to plan my sessions.

One of the things that resonated with me having read a number of examiners’ reports of the two main U.K exam boards, Edexcel and AQA for (2017, 2018 and 2019), it was quite alarming to see the findings from these exam boards – which says that too many students fail to make connections between and across topics/concepts in mathematics. This, as you can imagine, would significantly affect a student’s chance of doing a good job in their examination. Take for example, the link between Expanding brackets and Factorizing, so many foundation students especially struggle at factorizing even the simplest expressions. Why is this? Are teachers teaching these two concepts as two completely separate concepts with no connections? Would it be more beneficial if expanding of single brackets was taught immediately before teaching factorizing using H.C.F, and then encourage students to see the links in checking their answers by expanding the bracket? Would it be useful to teach expanding double brackets immediately before teaching factorizing quadratics, then encouraging students to check their answers by expanding?

OR is the popular method of teaching everything on expanding brackets (expanding single brackets and double brackets), then two weeks’ later, or at some other time, teach everything on factorizing more effective? Well, if this popular method is more effective, where are we going wrong? Why are so many students still failing to understand and make the connection between these two concepts?

Another aspect of the GCSE syllabus where exam boards have said students find challenging is solving inequalities. Why is this? Well, there could be a number of reasons but, here is one suggestion: how about getting students to make the explicit connection between solving an equation with solving an inequality? What if when we are teaching inequality, we give students a similar equation, ask them to solve the equation, then present them with the same numbers and variables except this time it is an inequality that they need to solve? I bet you they would know the steps to take right away and your main job then would be to teach them what to do with the inequality symbol.

You see, very few things in maths will be totally new to students once they get to year 9, everything they will learn in year 9 and beyond will very, very, likely be connected to or be a follow-on of something they have already been introduced to. So, while you plan your lessons or set your tasks on whatever platforms you may be using now, how about checking to see if there are any really obvious connections you can make or help students to make to improve retention and comprehension.

https://easymathslpt.files.wordpress.com/2020/04/interleaving-in-mathematics-for-better-results-making-links-worksheet.docx
Attached is a document I created and shared at a training session with maths educators from other schools, the feedback from using this worksheet in class have been very positive, most importantly, students found it helpful. Perhaps you could assign it to a relevant set of students on Google Classroom or when we return to the normal mode of teaching. Please let us know how it worked. I was inspired by Craig Barton’s https://variationtheory.com/ and I hope you will be inspired to create your own, and perhaps share with us.

Finally, I have flipped my classroom and have been recording my lessons, which many of my students are happy for the familiar voice. The link below shows how I make the connection between solving inequalities and solving equations. Feedback encouraged and very much welcomed. https://www.youtube.com/watch?v=QR2LLwnqF0c&t=41s

Remember, I am also learning and would love to hear from you. How have you helped your students to perform well in maths and in their exams? This is a safe place to share so that we can all better our best, and I am always eager to learn new and effective strategies to keep helping my students do better.

Keep safe
#StayHomeSaveLives #Clapforouressentialworkers

Cheers,
Lotoya

How To Foster Critical Thinking Skills In Children

“Five percent of the people think;
ten percent of the people think they think;
and the other eighty-five percent would rather die than think.”
― Thomas A. Edison

In a recent training I delivered, I emphasized my researched and experienced belief that critical thinking is a skill like driving (which can be very difficult to learn for some of us); essentially, if we need our pupils to give us high-quality answers, then we need to teach them the skill to think critically.

I have seen my classes matured from a sea of ‘I don’t know’ and minimum participation to eager hands being thrust in the air by even the shyest student, and when I am using ‘no hands up’ a vast majority of students are obviously itching to raise their hands or clearly hoping I would select them.

You may be wondering what magic potion I cooked up or if I promised them something nice or maybe more realistically – did I have the principal or visitors in my classroom. Well, if you are wondering any of that, the answer is yes to some of the questions, I normally start the New Year or term by promising my kids that they can only win when they participate in my lessons. Now, I am by no means saying that the ‘I don’t know’ have disappeared, they are just no longer the norm. Furthermore, when I do get students saying they have no idea, I would get another student to help by answering a part of the question (or I may provide some help if this is not working ) and then I go back to the student who said that he didn’t know what to do. This is explored in Teach Like a Champion by Doug Lemov and is referred to as ‘no opt-out’, which has helped them to see that they will still have to give an answer and a plausible one.

So what else has changed? How did I get the vast majority of my pupils to be more engaged, focused, and eager to try, and give sensible answers?

Well, over the years I have been consistently using at least three features of critical thinking skills to foster this very important ability of my students to think critically; BE WARNED it takes TIME for this to become the normal routine for the students, but it is worth it.

1. Giving students time to think.
Doug Lemov describes this in his book Teach Like a Champion as Wait Time. According to Lemov, a typical teacher allows about one to one and a half seconds of wait time before taking an answer. He points out that allowing 3 to 5 seconds of wait time after a question can increase the quality of the responses given by students.

2. Asking more effective questions:
Asking how

How did you work that out?
How did you get that?
How do you know you need the area and not the length?
How did you get your answer? How do you know or how can you check that it is correct?

Asking why
Why did you do that?
Why did you do it that way?
Why is it squared cm and not simply cm?
Why do you multiply instead of add?
Why is the negative answer not suitable for length?

Asking what if
What if I changed the area of the room, what effect would this have on the amount of money needed to tile the floor?

Another question I truly love is asking if something is always, sometimes or never true. And, asking students to explain to another student how to solve a problem.

Now, while these are really simple questions, you will be amazed at how rich the responses become. Secondly, as well as allowing students to take responsibility for their own thinking, you are creating the environment for students to not just learn content, but to learn how to think and how to make real connections between concepts. Moreover, oftentimes these and similar questions either highlight or clarify common misconceptions. After a while, students start to ask similar questions of each other and they may surprise you by asking you wonderful thought-provoking questions that you did not even think of.

I have uploaded a set of critical thinking sentence starters that can be used for any subject. It is produced by nrich.com and the link below has a cheat sheet of critical thinking starters.

Click to access critical-thinking-sentence-starters-nrich.pdf

https://wabisabilearning.com/blogs/critical-thinking/critical-thinking-skills-cheatsheet-infographic

Finally, since we are teachers of more than just content, why not take a look and see how you can teach your kids, by modelling through questioning, how to think critically.

Perhaps you are already very good at fostering critical thinking skills in your pupils, we would welcome your knowledge in this and other teaching and learning tips, so why not use this space to share your ideas so that we too can better our best.

Effective Lesson Starters

‘If the hook is weak, there may be trouble ahead.’ LOtoya Patrick-Taylor​

Planning a lesson is very similar to planning a speech or a presentation; there are three main parts – the introduction, the body and the conclusion. Similarly, in our lessons, we have the starter task, the main explanation or activation of the main concept for the lesson and finally the plenary.

Some key features of an effective lesson starter are the ability of the starter:

  • To get students settled – an effective starter gets the vast majority of students engaged in the task. This can be an excellent behaviour management tool.
  • To get students thinking – an effective starter uses a variety of questions to allow access but also to stretch and challenge pupils. This is especially useful when teaching mixed ability groups.
  • To diagnose – an effective starter seeks to assess what students already know about the topic of the day in order to inform the teaching of that topic.

One of the things to remember about lesson starters is to use the concept of ‘less is more’ – to give less questions for students to complete in the starters. This will allow pupils to complete the starter within a 5 minutes time frame.

As an example:

Below, I have attached a starter booklet I created for my middle set year 9 mathematics students using GCSE past paper questions as well as questions from https://www.piximaths.co.uk.

Click to access year-9-do-now-spring-ht-1-2.pdf

– Each page represents the starter (Do Now task) for a separate day.

– Each page has three questions. A fourth question, my diagnostic question, is written or projected on the board. Students are required to copy the fourth question in their booklet. I always use a question from https://diagnosticquestions.com/)

Do Now Format

Below is the format that I generally use and have also promoted due to the significant impact it has shown to have on students’ performance over a period of time:

Do Now / Starters (maximum time = 10mins including feedback): 

–       Aim for 3 to 4 questions per starter task:

a. Students should not need more than 5 minutes to complete the questions

b. Teacher should not take more than 5 minutes to feedback to the class on how to answer the questions.

–       Questions should be of the format:

  • One or two questions that test Previous knowledge to help with recall and long term retention of concepts (does not have to be the immediate knowledge learnt in the last lesson – could be something learnt in the previous term or two weeks prior to current lesson) – preferably one of these questions should connect the previous knowledge to the new concept you will be teaching.
  • Diagnostic question to assess what students already know about the concept you will be teaching. This could be done by using questions which highlights common misconceptions in the specific topic. See https://diagnosticquestions.com/ for some really good multiple choice questions that highlights common misconceptions.
  • An extension question that allows for much deeper thinking – this does not have to be labelled ‘extension’ and does not have to be the last question. It should be obvious from the amount of thinking requires / difficulty of the question.

Additionally, it is important that the first or at least the second question is accessible to all students (hopefully all J ). This is crucial since this early success usually motivates students to at least attempt the other problems.

Finally, as much as possible, it is important to circulate (walk around) to ensure that all students are on task.

What about you?

Is there a format you use consistently in your lessons which have produced great results? If yes, this is the perfect place to share those ideas so that we can better our best and get better results from our students.

A Bit About Me & My Intentions

Passionate, driven and called to be a teacher. My name is Lotoya Patrick-Taylor, a sister, a wife, a mom, a friend and a teacher.

I was trained to be a teacher in Jamaica, where I received my Teaching Diploma in Mathematics at Church Teachers’ College and my BA in Mathematics from Southern New Hampshire University (Hons), U.S.A. I am also a U.K accredited SSAT Lead Practitioner.

I have been teaching high school mathematics for just over eight years. Taught for four years in Jamaica, worked as a mathematics coach and delivered workshops to various maths departments. I am currently in my fourth year in the United Kingdom, where I am the Lead teacher of maths at my school.

In addition to being a classroom teacher in the U.K, I am a maths coach and I also deliver training sessions at my school and to a network of schools. Roles I thoroughly enjoy – I love people and I love collaborating, sharing and learning (hence, the reason I decided to start this blog).

One of the things that I am well known for in all my circles, is that I am always sharing ideas which I think are worth sharing – I share them with my friends, with my family, and I share ideas with my fellow co-workers and teacher friends in different parts of the world. However, as we all know, ideas are great, reading about them is wonderful (applause for all those who love to read and research), however, they are almost worthless if you let all these jolly good ideas remain on the pages. You must take Action!

So this is why I am always experimenting with researched strategies on best practices to teach and learn mathematics. And, this is the core behind this blog:

a. to share some of my experience using various teaching strategies in mathematics;

b. to collaborate with you, educators, on what strategies you have tried that have worked ‘magically’ (to this end let’s just say, it worked so good you couldn’t believe it yourself…at least in that moment)

c. to use this space to learn, to share, to tap each other on the shoulders, and perhaps most importantly, to better our best at teaching mathematics.

The Impact of Peer Observation on my teaching and student progress

Peer Observation…is it helpful?

Be yourself; Everyone else is already taken.

— Oscar Wilde.

It is often said that experience teaches wisdom and mistakes make you stronger. However, the art of teaching is one which, in my opinion, is a life long journey of learning; you can always better your best. Indeed, even though I believe in these sayings, I was still hoping to find a shortcut – become a master teacher of mathematics in three to five years (pretty ambitious). After all, how hard could it be? It is the same content. So isn’t it like reading the same script five days a week for three years?

Now, fast-forward to 7 + years later and I am still learning so much about the same content.

While I have certainly honed my craft through reading much research about how to teach various concepts in maths, watching loads of Youtube videos and of course lots of practicing the problems before I go in front of my students; I believe one of the things that impacted my teaching the most was Peer Observation.

Peer observation deserves so much more credit and should be widely practiced. It builds reflective practitioners, it encourages discussion around teaching and learning and when used effectively, our number one clients – students – reap significant benefits.

Inviting other teachers to come into your lesson can itself be quite daunting, the fear of criticisms, thinking of all the things that could go wrong – class control, not being able to adequately answer a question posed by students and so many other things. However, these are exactly the reason why peer observation should be considered. Moreover, it is informal and so the pressure is minimal.

Having other teachers observe me, was having another set of eyes, except with 20/20 or perhaps a 360° vision – the observer sees much more than I did and so was able to give me tips on little things that had big impact.

On the other hand, I enjoy observing other teachers teach – this is the short cut to experience that I was hoping for! There is always something to learn, so many good practices and, as Picasso said ‘Good artists copy; great artists steal.’ I took his advice and I would steal literally every good practice I observed. I would be so excited to try something I learnt from my peer observation in my lessons to see if the ‘magic’ would work for me too. Surprisingly, 9 out of 10 times it did!

I saw more progressed being made by pupils during lessons and on assessments and of course, my classroom management improved significantly.

In my department, we observe each other frequently, and I value the discussions in our feedback sessions because I find them very useful.

This is the first post on my new blog. I’m just getting this new blog going, so stay tuned for more. Subscribe below to get notified when I post new updates.