Conocimiento matemático para la enseñanza

The first issue brought up in the interviews about timed mathematics tests related to the ability to manage the time limit and any associated anxiety. The issue of anxiety was evident to some

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extent for seven of the adults interviewed and was most often discussed in the context of a timed test as shown in the extracts included below. For example, some adults found having a time limit difficult because it made them feel under pressure to recall methods and facts fast and calculate quickly. Omulade and Lisa express this clearly;

…let me do this quickly, quickly and before you know it the time is not on your side…far gone. Omulade

you have to look at the clock all the time…you know how to do it but don't have time to do it. Lisa

Ryan said that the time limit sometimes causes him to make mistakes in the examination and he related these errors to anxiety affecting his thought processes;

Because whenever I am under timing pressure I speed up and that's when I make all my mistakes. These are simple mistakes that if I was outside the constraints of a timed boundary I wouldn't make. My natural impulse is that whenever I feel the clock is ticking I will not read the information what is in front of me correctly so these are just linguistal kind of things that I should really be able to understand but my processes are getting full of anxiety because I am worried that I am gonna not do it in time and I'm gonna miss out you know I'm trying to answer all the questions but I'll…you know I'll have made loads of mistakes which could have been avoided.

Adele also mentioned that she feels that she would perform better if there was not a time limit. She recalled that she always felt that she needed longer to process material than other people so that running out of time was a recurring situation for her throughout her mathematics education;

…in a kind of test scenario, if I had extra time I'd probably get more marks but it's just to do with the timing of tests for me, that's like frustrating cos I can't seem to work at this kind of fast pace for example. We had a maths test last week and it was one minute per question we had and, for me, that's like daunting cos it's not necessarily me not knowing the answers it's the fact that 'a minute for a question' whereas if I had longer I feel I could achieve a much higher grade.

For Dorcas the issue was that she speaks English as a second language and it therefore took her more time to read and understand the questions. Dorcas alludes here, perhaps, to the difficulty of understanding the cultural context of some questions;

I have last week maths, three question really it's difficult because functional skills maths it is not only maths it's English also it is including English 'we have like eight boxes something, we fill something something' this is like you have to understand…only people from England like must understand English. That is not maths that is like knowledge thing. Something like that tricky thing it is really helping us to give us more time.

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For some adults the time limit plays a significant part in their feeling anxious both before and during a test;

I panic when I look at the paper…I am jumping, jumping. Lisa

This is the worst thing, the worst [time limit]. If you give me now an exercise and said 'just solve it' without saying 'you have ten minutes or two minutes' I will solve it. If you say 'you have five minutes, two minutes, I will just thinking with the time and, you know, I am like that. Shafiqa

In general those who were concerned about a time limit also tended to express anxiety about tests (see Table 8 below) and this link between time limit and anxiety is supported by the fact that those who felt confident about having a time limit did not express anxiety about taking tests. It is valuable to also look at those adults for whom a time limit did not seem to be an issue and explore the reasons behind this. Rachel, for example, said that she did not feel under time pressure in examinations and feels that a time limit reflects what happens outside the classroom;

…it is just knowing what to do and doing that because it's got to be limited with time because the same way you do things under exam conditions you take that skill in life to say 'well I am going to do this at home now, ten minutes, fifteen minutes'

Rachel and Ana both stated that time pressure was not an issue for them in tests because they knew they understood the material deeply;

…it's not like history you are going to forget the name of something or the date of something; no, it's a rule and if you really understand you just do it. Ana

Amelia mentioned that she was fine with a time limit because she is fast at calculating;

…a few of the other pupils on this class have commented and they've said I'm quite fast and I think it's just a natural… I'm ok with exams, for maths anyway.

Several people felt confident because they had successful prior experiences with timed tests and had good study skills to support them through revision and practice.

It is clear from the preceding analysis that some of the adults interviewed would probably feel less anxious and pressured with summative assessment models that do not involve a time limit. It is likely that this would reduce anxiety for some adults and allow them a better chance to show what they can do. The data also suggests that deep understanding of the material may reduce the need for memorisation which may, in turn, reduce anxiety in test situations for some adults. Since teaching to the test can often result in surface learning (Hutchings 2015), it could be argued that this practice may actually lead to more anxiety that could inhibit performance in the test. An exclusive focus on the test is also likely to affect school children in their GCSE year and adults and young people in FE Colleges where they may be resitting their exam.

Another assessment literacy mentioned by some of the adults interviewed was the need to perform well on the day of the test as Ryan explains;

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You might have been ill that day, you might have been full of anxiety, you might have been really kind of…had a good night's sleep that day and feeling really great, you know…all these different kind of influences, you know, that can affect your ability and your output.

Hannah reflects how an issue unrelated to the subject affected her result when taking her ‘O- level’ mathematics examination;

Well, I remember it distinctly because I was upset, something upset me so I went into the exam and most of the things that I learned, the formulas and everything…couldn't remember it and …that was a personal issue away from that and so…I didn't do well and that's the reason I ended up with an E.

Some adults mentioned the need to memorise methods and formulae and the need to show your working as essential to success in timed mathematics tests;

…it's a test of memory really isn't it and once again it's like one size fits all and I do feel with some people, if they had a bit longer, they'd achieve a higher grade and it seems a measure of memory rather than…just what you remember. Adele

I find the layout and the working…the method the hardest to remember because they want it doing in a specific way…you need to show everything on the piece of paper and because I'm so used to doing a lot of stuff in my head I'll miss out…bits and I'll just put…the answer down…Amelia

Hannah and Amelia said that they like to be thorough and check their answers. Amelia said that having a time limit in an examination makes it difficult for her to work in her usual way and that a timed test is therefore not a good measure of her mathematics skills;

I can just go off the exam I have just done: you can tell my working out is at a good standard…I am checking like I am using two different methods for making sure the answer is correct, I am double checking the question and double checking my answers…I am very thorough and I think this is another reason why it takes me a lot longer; I like to do things thoroughly…