This week – no.8

This week was a pretty poor teaching week for me. I felt that most of my lessons were pretty lacklustre. I think the problem was that all my time was taken up with other school related tasks that my own planning got put to the end of my list. I don’t like when this happens but it’s the reality that occurs sometimes. After a tough week I was feeling like I didn’t want to attend the Moray Maths Conference on Saturday. However, I am really glad I went. The conference reenergised me and I came away with lots of ideas to implement. My only concern is that I won’t have time to do this – but I must try to make time as it is important to focus on teaching and learning.

So this post I am going to write about my takeaways from the conference instead of my lessons from the past week. Hopefully there is something useful for other teachers to takeaway too.

The conference started with a key note address from Professor Adam McBride. I have heard him speak a few times now and always enjoy his talks. Professor McBride has such a passion for maths that it is infectious and it is so inspiring. He shared why he thinks maths is the BEST and that it doesn’t always have to be useful and have real world applications – sometimes it can simply be enjoyed for its beauty. Here is a task that Professor McBride shared with us.

Choose a number:

• if it is even, divide the number by 2
• if it is odd, multiply the number by 3, add 1 then divide by 2

The example given was for 12: 12 – 6 – 3 – 5 – 8 – 4 – 2 – 1. This has 7 steps to it.

It is similar to the caterpillar activity I have used before but will definitely use it with my S1/S2 classes next week to see who can find the largest number of steps.

He also talked about prime numbers and encryption, magic squares and the Knight’s tour. If you ever have the opportunity to hear Professor McBride speak then you should. A lovely way to start the day.

The next address was given by Andy Brown (@AndyBrown314). Andy works for Education Scotland as part of the Maths and Numeracy Northern Team. Andy spoke about some questions that we should consider in order to improve the teaching and learning of mathematics. Here are a few of them:

• does the task set maximise learning?
• have you considered pre-requisite knowledge?
• are questions carefully chosen and sequenced?
• how do we go beyond the textbook?
• what learner dialogue do you promote?
• what questions do you ask? Why?
• what questions do you want learners to ask?
• have you considered likely misconceptions?
• can you collaborate with a colleague when planning?

I will definitely be thinking about these over the coming weeks and hope do discuss with my department at future departmental meetings.

Then it was off to the first of three workshops. My first workshop was with Iona Coutts (@onycoutts). Iona was sharing how we can improve performance in Higher mathematics through attention to mathematical detail. As a marker for the SQA, Iona shared three key areas that require improvement:

1. notation and communication
2. arithmetic skills
3. algebra skills

None of these came as a surprise to me as they are often the things that I pick up on when marking pupil work. How do we address this?

One way is to show pupils examples of answers given by previous candidates and allow pupils to find the errors and comment on the solution.

Examples of candidate work can be found on the SQA Understanding Standards website. I have used these previously with teaching staff but never with pupils. These will provide useful for revision tasks over the coming weeks.

Iona also shared that many pupils do not carefully read questions and will automatically work through a whole process even if not required. For example, pupils are so used to being asked to find stationary points and their nature that when the question only requires the x-coordinate many go further than they need to. She stressed the importance of showing pupils a wide variety of questions for every topic so that pupils understand the importance of fully reading a question.

Iona then gave examples of websites where we could find different types of activities that are beneficial for pupils to do. The first was www.ssddproblems.com (from Craig Barton). Whilst I have know about this website for a while now, I have never really used it. Something that is going to change. Here is the example Iona shared with us:

It’s no wonder my pupils get muddled with questions when so many topics look “the same”. This will make a perfect review set for my class and I will be exploring the website to see what else is there.

Goal free problems were also mentioned. This is where information is provided but no question and pupils have to work out everything and anything they can from the information. Here’s an example:

Another fantastic way for pupils to retrieve all they know from a variety of topics and not be constrained by a specific question. To create these questions, I could use old exam questions but there is also a website from @MrMattock www.goalfreeproblems.blogspot.com which has a large bank of questions ready for use.

My second workshop was from Andy Thompson (@thompo71). Andy is the Northern Alliance Numeracy and Maths lead. Andy was delivering a workshop about fractions and the challenges they present to learners at all levels. It was clear from his talk that we need to improve pupils conceptual understanding of fractions and go beyond procedural calculations. The importance of not only considering a fraction as a part-whole relationship was also stressed. There are many interpretations of a fraction (as a quotient, a ratio, parts of a whole, …).

Andy showed this picture:

My realisation is that I rarely discuss fractions on a number line. I don’t know why but I don’t. Maybe it stems from thinking this would be part of Primary maths and not necessary for me or probably more likely is that it is not something I properly considered. I will be looking at how I can add this into our BGE course in the very near future.

For my last workshop I was back with Iona. This time Iona was talking about how to build confidence in teaching and learning of mathematics. Confidence comes from building on prior learning, not jumping in too fast, and having little and often approach with lots of re-visiting.

Iona shared more resource ideas which included another shout out to Craig Barton with his www.mathsvens.com – yet another website that I was aware of but never really explored or used. I will now though.

We worked through this task and I was amazed how much thinking it required. Each table worked away quietly then gradually built up into discussion as we shared answers and realised mistakes we had made. Instantly I was planning to get blank Venn diagrams printed to use in class.

We looked at how a simple counting stick can be used with all ages/stages. This one is from www.mathsbot.com Initially I was a bit sceptical about how I could use this but Iona showed us how it could be used. Here are some examples:

Iona then discussed some ideas for retrieval practice including using questions in the format last day, last week, last month, last year and the use of flashcards. I already use last day, last week, last month, last year as my starter for N5 classes but will look to use with BGE classes too.

After the workshop it was time for the closing key note talk. This was given by Chris McGrane (@ChrisMcGrane84). I have been to many presentations by Chris and always learn something new and take away many ideas to process. This was no different.

Chris split his talk into four statements. These are all statements that Chris disagrees with and in the talk he shared why.

1. Treating instantaneous performance as learning
2. Telling kids to have a growth mindset makes a difference
3. “There is so much to learn that we have to keep moving on”
4. Being able to get answers is what matters

Chris discussed the differences between spaced and massed practice as well as blocked and interleaved practice. This is an area which I have given lots of attention too but still not convinced I have got quite right. The main thing that struck me is that I am still giving my pupils too many questions that are repetitive and that do not have enough variation. These slides really hit home:

Giving pupils more problems did not improve attainment. In order to improve attainment the practice needs to be spaced out. So rather than give 10 questions one lesson, give 3 questions over 3 lessons. This gives the same amount of practice but should improve retention.

Growth mindset had been talked about for quite awhile now and I have a lovely set of posters up in the maths corridor which noone ever looks at. This quote from Thomas Guskey sums it up nicely:

“Don’t try to convince learners that they should have a growth mindset – change their experience so they develop it themselves”.

It is often thought that motivation leads to achievement but it is more likely the other way around, If pupils experience mathematical achievement then they will become more motivated to learn. So how can you get an unmotivated learner to achieve? That is the question for me to consider.

Statement 3: “There is so much to learn that we have to keep moving on” was very thought-provoking for me. I have often worried about covering the content of N5/Higher and complain about the amount of content. However, Chris demonstrated that they are many topics we teach differently in maths that could all be solved in the same way – using proportion. Here are some examples:

There was also a slide for speed, distance and time. The point I took away is that there are many topics in maths that are connected and we should teach them in a way so that pupils see the connection and not think of maths as a series of unrelated topics.

The point of maths is not always about getting an answer. Often it is more important to explore connections and relationships, find starting points and attempt different strategies than just to get a correct answer. Chris shared some tasks which explores relationships not just answers.

I have used some tasks like this with pupils but need to do more of it.

Chris showed this from www.mapmathshell.org This is the Teaching for Robust Understanding Framework which looks at what happens and what should happen in the classroom.

Whilst I have used this site many times for the lessons and tasks I have never delved into the other resources there. Another item to add to my to do list!

Now this is merely a snapshot of the day and there was so much more I took away. It was a great day with a chance to catch up with colleagues, hear new and familiar ideas and refresh my motivation for teaching. Plus, as a bonus, we are getting a copy of the new book from Craig Barton “Reflect, Expect, Check, Explain”. I can’t wait until it arrives.