Some might argue that there should be room for a *little* anxiety in school life. We don’t want to wrap students up in cotton wool because the real world is not like that. Perhaps a little anxiety helps lead to better coping strategies; more resilience. Perhaps.

*is*true that anxiety can disrupt learning and so we probably want to reduce unnecessary anxiety if we want to maximise learning.

In my earlier post on Jo Boaler’s remarks about multiplication tables, I noted that improvements in competence in a subject lead to improvements in self-concept; how students feel about their academic abilities. So, if we wish to reduce student’s anxiety about mathematics it would seem reasonable to try to increase their self-concept by teaching them in such a way that they become better at maths. I have used this principle, along with others from cognitive psychology, logic and experience to suggest the following four tips to reduce maths anxiety. Please feel free to add your own in the comments.

**1. Have frequent low-stakes tests**

We know that retrieval practice is effective at supporting learning. However, if we test students infrequently then they are likely to see these tests as more of an event and therefore as something to worry about. Instead, we should build frequent, short-duration, low-stakes testing into our classroom routines. Not only will this make testing more familiar, it will increase competence when students tackle any high-stakes testing that is mandated by states or districts and will thus reduce anxiety on these assessments too.

**2. Value routine competence in assessment**

If you were to spend your time reading maths teaching blogs then you might think that they only kind of maths performance of value is when students can creatively transfer something that they have learnt to solve a novel, non-routine problem. This is not the case. Routine competence is also of great value in mathematics. There is a lot to be said for being able to reliably change the subject of equations.

If we communicate to students that it is only non-routine problem-solving that matters then we are likely to make them feel inadequate. We can send such a message explicitly or we can send it implicitly by setting large numbers of non-routine problems on and making these the focus of assessment.

Non-routine problems are great for avoiding ceiling effects on tests and enabling some of the most talented students to shine. However, assessment should also include a large amount of routine problem solving to show that this is also valued. As a general rule, I would advocate a gradual move from routine to non-routine.

**3. Avoid ‘productive failure’ and problem-based learning**

Similarly, some educators advocate framing lessons by setting students problems that they do not yet know how to solve in the belief that this will make them keen to develop their own solution methods or receptive to learning from the teacher. *Some* children might find this motivating but others – and particularly those with a low maths self-concept – are likely to feel threatened. Motivational posters will not help.

It *is* true that some studies seem to show that this kind of approach leads to improvements in learning. However, these are often poorly designed, with more than one factor being varied at a time (see discussion here). And it is a matter of degree. In the comments on this blog post, Barry Garelick suggested asking students to factorise quadratics with negative coefficients one they have been taught how to factorise ones with positive coefficients. This still requires a little leap but it is far less of a jump than asking students to develop their own measure of spread from scratch such as in the experiments of Manu Kapur.

Given that there is a wealth of evidence in favour of explicit instruction, where concepts and procedures are fully explained to students, it seems that productive failure is risky and could backfire through its interaction with self-concept.

**4. Build robust schema**

It *is true* that you can survive without knowing your multiplication tables. You can survive without knowing most of the things that students learn in school. If you just have a particular gap in your knowledge then you can develop workarounds.

The question is; why would you want to? Knowing common multiplications by heart makes mathematics easier to do because it is one less thing to process. Building and valuing such basic knowledge is both a way of generating little successes for students to experience and a way of aiding the process of more complex problem solving. I think that this is one of the reasons why the ‘basic skills’ models in Project Follow Through were so successful at generating gains in more complex problem-solving.

**A guiding principle**

In reducing maths anxiety, we should focus primarily on teaching approaches that are likely to make students better at maths. Increase maths competence to reduce maths anxiety.

Reblogged this on The Echo Chamber.

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Your description of productive failure and problem-based learning would include “just in time” learning. This approach prescribes giving students an assignment or problem which forces them to learn what they need to know in order to complete the task. The tools that students need to master are dictated by the problem itself. For example, students might first encounter long division in a lesson, late in their education, about repeating decimals, where it is an essential ingredient. Many reformers consider long division too tedious and unproductive to teach until it is absolutely needed. The question of how repeating decimals work supposedly motivates students to overcome this barrier. This is like teaching someone to swim by throwing them in the deep end of a pool and telling them to swim to the other side. The teacher shouts the instruction to the students, who are expected to swallow the method whole along with mouthfuls of pool water, in one go. The students who by some miracle make it to the other side are apt to say, “I don’t know how I got here, but I sure don’t want to do that again!”

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Very old post, but never mind 🙂

If you read this, what is your take on memorizing addition family facts? I am talking about things like

3+8=11

8+3=11

11-8=3

11-3=8

à la “Big Maths”, if you know what it is.

At our Schools (in Scotland) this is the fashion and they do it pretty much through they 7 years of primary. Tame tables begin in P3 (2-5-10) continue in P4 (three more) and you finish them off in P5 (the rest). In P6 and P7 you revise them.

Now, my questions are:

1) is it useful to memorize addition facts, especially considering that it takes such a large part of the maths curriculum?

2) Is it a good idea to postpone for such a long time the times tables?

Personally, we are doing times tables at home because I cannot stand the idea of my children being unable to do a simple multiplication/division, but more importantly, without times tables you cannot calculate areas, prices, volumes, etc. In other words you find it pretty much impossible to solve the easiest of problems and you have to defer the learning of multiplications and divisions till the latter years of primary.

That makes no sense to me.