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

Published by lotoyalpt

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) in the U.S.A. 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 department. 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).

6 thoughts on “Interleaving in mathematics for better results

  1. I enjoyed reading that and I have encountered the same problem with pupils. I remember my teacher telling me that solving inequalities is like solving equations, the only difference is the sign. I say the same and show the same to my pupils (like in your video!) but they sometimes easily forget the connection.

    Liked by 1 person

    1. Thanks for sharing. My students are very similar to yours. Perhaps it will help them in the long term if we try to let them see the connections between and among as many concepts as possible as often as we can and hopefully these relationship are also being made in primary education.

      Like

  2. Dee(Jamaica seconday teacher)
    I have enjoyed reading that article and have experience a level of disconnection between topics in maths from my students, for whatever they reasons, the students failed to see the connections between the topics.Perhaps, in my opinion it is the way that the maths syllabus is structured. Will definitely be trying some of your strategies.

    Like

    1. Thanks for sharing Dee. You are right, maybe some of these problems can be fixed by rearranging topics in the maths curriculum or scheme of work on a department level. I look forward to hearing more from you.

      Like

  3. So, in my school we’re in the process of rewriting our curriculum for the umpteenth time. And the same old questions reappear. Depth or breadth. Which puts interleaving at the forefront.

    Thank you Lotoya for sharing. I’ll definitely be passing on to my colleagues.

    Like

    1. Thank you Krista. I agree with you that thinking of how to make the best connections among topics will help to get a richer curriculum, which should also solve the problem of how deep to go into topics and how many topics need be covered in a year.

      Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

%d bloggers like this: