Seedbed: Sowing the Seeds – Numeracy

What do we mean by Basic Maths? Is numeracy the same as maths? I was expecting that one. It always comes up. Does it matter? I always feel a sense of deflation about the use of the terms. Maths is around higher level stuff while numeracy is the basics, the simple stuff that everyone leaving school is supposed to know and do, isn’t it? Yet, as I’ve found out over the years, sometimes when taking out a mortgage, other times sorting out a divorce settlement, basic maths can be anything but basic. I prefer to see the connections, the overlapping areas between numeracy and maths. In between, joining them together as the glue or jam are common sense, experience and imagination.

One of the tutors had brought along a new initial assessment she had made for her course, jewellery-making. She gave it for us to practise on and get feedback. After finishing it, one person had drawn very curvaceous, flowing lines for a matching pairs exercise. I was struck by how artistic it looked. What’s in a name, she asked us?

‘Get into Shapes!’

It raised lots of questions. What information will it give you about individual strengths and levels to start off with? How important is it to present the tasks in a relaxed and postive manner? Why not announce it as the ‘Test’? Surely, better to introduce it as part of the course naturally, the front end, and explain how helpful you and they will find it; that, without this background knowledge, you will be wildly guessing. And how can you make it fun!

When do you carry out initial assessment? What does it look like? Among our group, we suggested it is a process over the initial period of the course. For some groups, it is right at the start, the first session, or even better, before the course has started, especially if they are aiming for something specific. For others, it’s ok to spread this out over one or two sessions, if that works best. If it’s linked to the subject matter the learners are studying, so much better! I particularly like this approach, although it is the most demanding. It requires a great deal of careful thought, of trial and error but I thing the effort and practice will reward you in spades. It can look like a series of questions and/or practical tasks, observations recorded by the tutor. It’s nearly always reinforced by the first pieces of coursework handed in. Don’t be suprised if you find some learners have improved greatly in a short time. Scores are often affected by levels of confidence and anxiety.

The problem my tutor with the shapes identified was how do you know what level your learners are at if your IA only gives results at a particular level? She had realised she needed to know how to map tasks to the core curriculum for numeracy to tell her what she needed to know about each individual learner.

My own feelings about maths were just below the surface. Please don’t ask me any difficult questions. I thought in horror. Why am I delivering this module? I should have got a maths specialist to do it. The one thing I’m not going to do, I told myself, was try to work out a maths question, unprepared, on the flipchart (the SMART board being temporarily unavalable). My own experience of learning maths is chequered. I’d failed O-level maths twice at school and, consequently, had a bit of a block about it. On a Saturday morning, though, delivering loaves of bread for Scott’s Bakery as a teenager, I’d no problem doing long multiplication in my head, as I worked out the cost of 4 white, two brown and a tray of buns. Give me simultaneous equations or Venn diagrams though and my heart sank. I can still feel it.

My confidence in understanding aspects of maths grew when I started to teach it to adults. This was in the days before the core curriculum came in and specific teaching qualifications were introduced. It slowly came to me what percentages were all about. The sense of achievement was enormous! Was I in any way letting the learners down by not being a ‘proper’ maths tutor? I fretted about this often. Yet, I was learning a lot and drawing on my language skills, particularly listening skills to help me. A lot of my learners felt like me about maths. What they needed most was their confidence building and the numbers game demystifying. Most of what I was doing involved effective communication, working together and trust building. The maths part became increasingly straightforward by comparison. When learners were ready, they would move on, I hope, with greater confidence.

Meanwhile, back to the session. The first activity we did was to draw segments on a circle representing 7 areas of numeracy. Most estimated the size of the segments. Some used rulers, others drew freehand.  One person calculated each angle before transposing them onto the chart using a protractor. It showed there was more than one way to do it.

We discussed how we each of us, even within our own communities, use language to express numerical terms every day. How many different ways, for example, can you decribe the symbol +? We found there were many. I argued that, based on my own experience, the single most significant discovery I had made while teaching maths was to ask the student to ‘talk me through it’. This helped me understand where the learner was going wrong and why. It also reminded me of the futility of showing how I did it and expecting a light to go on inside their head. The fact that I could do it one way was no guarantee of my student picking this up too.

We spoke of keeping it relevant. We shared stories of buying rice in cups or using rules of thumb often related to body measurements with which learners are familiar. Get them to say what they do. It can enliven a lesson as well as being informative.

The language we use is important. It can include or divide us. There had been a headline on the radio that week telling us that for the first time in Britain, there were more people living alone than with others, 52%. Yet each person is part of a larger grouping in their area, We call it a community or common, implying more than one. How important is it for people to be able to understand and express maths terms? How comfortable are we with financial language – apr, interest rates, loans and payback times, for example? How does this affect the choices we canmake?

By chance, I came across this quote a few days later:

The root meaning of the word “integrity” calls for wholeness. The word comes from the Latin integritas, which refers to a state or quality of being complete, that is a condition of wholeness. The word “integrity” and the mathematical term “interger” have a comon meaning. When we look at this common meaning of “integritas”, or “integrity”, it points to a unity, that, when applied to persons, we call community. Integrity creates a sense of togetherness and belonging when applied to persons in community. Integrity forms the basis for a covenant relationship in which persons exercise a sense of responsibility and accountability toward one another.

We need to begin to live the way we want the world to become, rather than the way the world is now…(Wilmer A. Cooper, 1991, quoted in Whitmire C, Plain Living, 2001, Sorin Books)

I cannot help but relate this to the debates about sustainable living and economic justice now taking place as I read this.

Time rushes on. We had performed a subtraction sum and were sharing how we had worked it out. We’d all used the ‘borrow and pay back’ method. I enthusiastically started telling them about other methods.One, decomposition I found so simple to use when my children were learning it that I dashed to the board to show them. Oh, no, I’d made the classic mistake of trying to work it out in front of the group. It certainly generated a lot of interest, though.

Well, there you have it, what do you think? Do you need to be a specialist maths tutor to teach maths? You tell me!


Seedbed – Writing

The group came together again on another Wednesday evening to work through the next Seedbed module on Writing (skills). We covered the stages of writing, various formats and purpose/audience we write for; sparked discussion about spelling and misunderstood the phrase ‘running dictation’, thereby, leaving us all breathless.

During all the practical stuff of writing learning materials, members of the group brought forward a number of revealing observations.

The quickest learner, the loudest one, the one who finishes first isn’t always the best learner in the group. How surprising it is still to find even among experienced tutors a certain level of anxiety, not grasping a point while thinking others are racing ahead.  I explained how, when placed in a small group with people I didn’t know well or yet trust, I need to reassure myself I’m not stupid. Some of us, after all, are thinkers (theorists or reflectivists) as well as doers (activists). We like to take time over an  issue.

Speaking up for reflective learners, I extolled proudly how I often came up with a crucial piece of the problem to solve it (actually, not that often, If I’m honest) but it does happen from time to time. Once, I went on a singing weekend. We had a problem in that how could we position ourselves without blocking the pianist? Several suggestions were made but none were satisfactory till I saw the simplest thing. Why not move the piano away from the wall and we could all stand around it. Simple and effective!

So, thinking I  should call the task I’d set the group to an end now. They were coming up with creative ideas for writing using a selection of random objects, including a green dragon, a red fire engine and, oh, the Eiffel tower. But I remembered I’d given them a finish time and so decided to allow the exercise to run. While the two groups which finished ahead of time were waiting, they started ‘chatting’. It seemed to me they were actually getting to know one another better. The atmosphere felt a more relaxed, still studious. I felt more relaxed inside too. A nice feeling,  ‘Ahh, this is going well, isn’t it?’ Do other tutors talk to themselves while teaching, I wonder? At some point, we mentioned that tutors are always running a backing track which acts as part editor, part judge of the lesson in progress.

It’s not always possible to know if someone has a disability or a barrier holding them back. My eldest son, for example,  has an acquired head injury, is studying at university and needs extra time to break information and knowledge down into more manageable chunks for him to make sense of it.

Someone else has a stammer. This was certainly not obvious to the rest of us but she said it could hold her back.Thinking about it afterwards, how great then that she was the one who volunteered to read the ‘running dictation’ out at pace!

Or what if English is not your first language? Anyone who has tried to speak a foreign language abroad will know how draining it is over an extended period of time. Exciting, stimulating, even inspriring but also very, very tiring. What if someone is translating from English into their first language, then back again into English before replying?

This led us on to talking about the power of language. If decisions are being made in one language and some of the participants do not feel included, can this increase their sense of frustration and isolation? I’m not only thinking about language but also register and accent here. People using the same language can still be divided because of their educaton or class background.

One learner recounted a meeting where local people met with their community representatives. The process was going in a relatively stilted manner. Sometime later, they decided to use interpreters and what a difference it made. People were speaking, thinking and listening more fluently. They felt more involved in arriving at decisions which affected their lives. The results were much more satisfying and longer lasting.

One word jumps out at me, confidence. How important is this? Yet, it doesn’t just happen. The tutor needs to build trust between individuals, get them working together, allow time for their insights and skills to emerge. This may lead to sharing ‘deeper’ thoughts, making us all more aware.

I’d also given the group the choice of who they worked with. I sat back and it was interesting to watch, amusing too. They swopped around for the next activity. Giving them the decision was making them think.

At a completely different meeting, a skills for life curriculum meeting, one member spoke of the goal of ESOL classes being to raise levels in reading, writing and speaking and listening. While this is necessary, I hope this is not all our tutors do. By breaking down barriers, building trust and cooperation through various games and activities, by allowing learners to make more and more of their own decisions, the tutor builds confidence, raises awareness, increases expectations. Students start to hold people to account, including the tutor. Isn’t this what we as tutors and staff ought to be aiming for?