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#### Maths Anxiety

*Until I began taking a keen interest in educational research, I must confess that I did not quite realise just how significant a problem maths anxiety is. Ashcraft defines maths anxiety as a feeling of tension, apprehension, or fear that interferes with maths performance. And that is one of the really sad things about maths anxiety - it stops students reaching their potential. In this section I will discuss a number of papers that have had a profound effect on me, and look at their practical implications for the classroom and beyond.*

**Research Paper Title:** Math
Anxiety: Personal, Educational, and Cognitive Consequences

**Author(s): **Mark H. Ashcraft

**My Takeaway:**

This article is a summary of Ashcraft's 30 years of work into the
study of maths anxiety. There are a number of key points raised in
the paper, but here are a selection that caught my eye:

1) Highly maths-anxious individuals avoid maths. They take fewer
elective maths courses, both in high school and in college, than
people with low maths anxiety. And when they take maths, they
receive lower grades. Highly math-anxious people also espouse
negative attitudes toward maths, and hold negative
self-perceptions about their math abilities. The correlations
between math anxiety and variables such as motivation and
self-confidence in math are strongly negative. Now, of course our
secondary school students cannot formally opt-out of studding
maths until A Level, but they can informally do so. They can study
less at home, take part less in class, and talk themselves out of
even so much as attempting a problem. And with practice in maths
being so vital to success, we end up in a vicious cycle with
avoidance leading to poorer performance, which inevitably adds to
the existing anxiety.

2) Maths anxiety is only weakly related to overall intelligence.
Moreover, the small correlation of 0.17 between maths anxiety and
intelligence is probably inflated because IQ tests include
quantitative items, on which individuals with maths anxiety
perform more poorly than those without maths anxiety. This was a
surprise to me. I had assumed a strong relationship between
intelligence and maths anxiety. But when I think about it, I can
recall many students I have taught over the years who were highly
able mathematically, and yet had (what seemed to that stupid,
uninformed me) an irrational fear of the subject. The next paper
addresses this crucial point further.

3) Timed tests seem to cause anxiety. The researchers found no
anxiety effects on whole-number arithmetic problems when
participants were tested using a pencil and- paper format. But
when participants were tested on-line (i.e., when they were timed
as they solved the problems mentally under time pressure in the
lab), there were substantial anxiety effects on the same problems.
This may seem obvious,. but it in fact poses us with two major
problems. Firstly, every major exam that students encounter has a
timed element to it. Secondly, as we will see in the Fluency
section, without the time pressure students are unlikely to
develop the kind of automatic knowledge of key number facts that
they need to free up capacity in working memory to solve more
complex problems. Perhaps the key is to introduce the timed
element slowly and carefully, in a supportive atmosphere, together
with a policy of never collecting in or announcing students'
scores.

4) Maths anxiety lowers performance because it takes up vital
space in working memory. Anxious individuals devote attention to
their intrusive thoughts and worries, rather than the task at
hand. In the case of maths anxiety, such thoughts probably involve
preoccupation with one’s dislike or fear of math, one’s low
self-confidence, and the like. Maths anxiety lowers math
performance because paying attention to these intrusive thoughts
acts like a secondary task, distracting attention from the math
task. It follows that cognitive performance is disrupted to the
degree that the maths task depends on working memory.

5) Related to this is the finding that maths anxiety to does lower
performance in all areas of maths - just the more cognitively
demanding ones. Routine arithmetic processes like retrieval of
simple facts require little in the way of working memory
processing, and therefore show only minimal effects of math
anxiety. But problems involving carrying, borrowing, and keeping
track in a sequence of operations (e.g., long division) do rely on
working memory, and so should show considerable maths anxiety
effects. Higher-level math (e.g., algebra) probably relies even
more heavily on working memory, so may show a far greater impact
of math anxiety. There are two things we can do to help students
with this. The first is to try to reduce maths anxiety, and the
final paper in this section looks at strategies for this. The
second is to ensure students have the relevant knowledge and
procedures stored in long-term memory to free up capacity in their
working memories. This, of course, is easier said than done, going
back to Point 3).

6) Finally, the authors make what I feel is a key point: note how
difficult it will be, when investigating high-level math topics,
to distinguish clearly between the effects of high math anxiety
and low math competence.

**My favourite quote:**

*Math anxiety is a bona fide anxiety reaction, a phobia, with
both immediate cognitive and long-term educational
implications.*

**Research Paper Title:** Math
Anxiety, Working Memory, and Math Achievement in Early
Elementary School

**Author(s): **Gerardo Ramirez, Elizabeth A. Gunderson, Susan
C. Levine, and Sian L. Beilock

**My Takeaway:**

The key finding from this paper is both fascinating and worrying:
Students with the highest level of working memory capacity show
the most pronounced negative relation between maths anxiety and
math achievement. How can this be? We have seen that maths anxiety
depresses maths performance because it eats up working memory
space. So, wouldn't these students have spare working memory
capacity, so anxiety would have less of an impact? The authors
explain that there is no definite explanation for this, but that
one possibility is that students with the most working memory (WM)
capacity tend to rely on more advanced problem-solving strategies.
High-WM children, for example, are more likely to use direct
retrieval as opposed to finger counting when solving math
problems, and retrieval efficiency is particularly disrupted by
interference. In contrast, low-WM children’s maths achievement may
remain relatively unaffected by maths anxiety precisely because
they use less sophisticated (and less WM-demanding)
problem-solving strategies. Hence, the association between math
anxiety and math achievement may be present among high-WM (but not
low-WM) children because math anxiety disrupts the resources that
high-WM children rely on to retrieve basic facts from long-term
memory and to inhibit competing answers. Even more concerning is
the suggestion that maths anxiety-induced disruption of WM leads
high-WM children to switch to less successful problem-solving
strategies as a means of circumventing the burden of maths anxiety
on WM. Ironically, something that usually helps students in maths
— large working memory capacity— becomes vulnerable to disruption
when they are anxious.

**My favourite quote:**

*In conclusion, our results highlight the potential of math
anxiety to negatively impact children’s math achievement as
early as first and second grade. The finding that children who
are higher in WM may be most susceptible to the deleterious
effects of math anxiety is particularly worrisome because
these students arguably have the greatest potential for high
achievement in math. Investigating the development of math
anxiety from the earliest grades will not only increase our
understanding of the relation between math anxiety and math
performance across the school years but is also a critical
first step in developing interventions designed to ameliorate
these anxieties and increase math achievement.*

**Research Paper Title:** Math
Anxiety: can teachers help students reduce it?

**Author(s): **Sian L. Beilock and Daniel T. Willingham

**My Takeaway:**

This is a wonderful overview of the research into maths anxiety,
including some shocking statistics as to how widespread it is (see
quote below). What I found most useful was the authors offering up
four practical strategies teachers can employ to help reduce maths
anxiety in their students:

1) Ensure fundamental skills. Once again we see the importance of
knowledge, not just for thinking but for reducing anxiety. The
authors state that enhancing both numerical and spatial processing
may help guard against the development of maths anxiety in younger
students.

2) Focus on teacher training. The is based on the finding that a
teacher's anxiety about maths can be transferred to their
students. Ensuring teachers are confident both in their knowledge
of the subject and effective ways to communicate content may help
with this. I would argue that well-planned lessons following a
model of explicit instruction, with worked examples and structured
purposeful practice, are easier to deliver and "control" than more
inquiry based lessons.

3) Change the assessment. We have seen the maths anxiety is more
strongly linked to poor performance when students take a timed
test due to the burden it places on working memory. So removing
the time element is likely to be beneficial by reducing worries
and giving students time and space to consider their answers

4) Use a writing exercises. I must admit,l I had not considered
this one. Giving students around 10 minutes to write freely about
their emotions concerning an upcoming event (such as an exam) can
alleviate the burden negative emotions place on working memory and
hence boost test performance.

5) Think carefully what to say when students struggle. Often
consolation in the form of "it's okay, not everyone can be good at
these kind of problems", validates students' view that they are
not good at maths. Better to focus on how you are convinced that
hard work will help them get better, crucially following this up
with concrete, effective study strategies like those outlined in
the Revision section.

**My favourite quote:**

*Math anxiety is not limited to a minority of individuals nor
to one country. International comparisons of high school
students show that some students in every country are
anxious about math. It is perhaps unsurprising that
there is an inverse relationship between anxiety and efficacy:
countries where kids are less proficient in math (as
measured by the Program for International Student
Assessment, or PISA) tend to have higher levels of math
anxiety. In the United States, an estimated 25 percent of
four-year college students and up to 80 percent of
community college students suffer from a moderate to
high degree of math anxiety. Most students report having at
least one negative experience with math at some point during
their schooling.*