By Stuart Shanker
This article was published as part of Reframed: The Journal of Self-Reg Volume 2, Issue 1 (2018)
Shanker, S. (2018). Reframing High Math Anxiety: Avoiding the Perils of a Victorian Paradigm: Stemming the Divide. Reframe: The Journal of Self-Reg, 2(1), 24-33
This paper reframes the Victorian view that the failure to succeed in math is due to a lack of perseverance. Instead the author explores the multiple stresses that lead to high math anxiety and how, by using Self-Reg, a student no longer sees math as a threat.
Keywords: Stress, cognitive stress, High Math Anxiety, self-regulation, self-control, hyperarousal, tension
Reframing High Math Anxiety: Avoiding the Perils of a Victorian Paradigm Stemming the Divides
A fascinating initiative was launched in the United States in 2017, encouraging scientists to run for public office so as to “Bridge the Divide between Science and Politics” (Kaplan, 2017). The goal is to ensure that government policy is based on current scientific knowledge, rather than what politicians tend – or would like – to believe. The Self- Regulation Institute could be said to be engaged in a similar mission: in our case, the goal is to bridge the divide between what science is learning about learning, and how educators teach. But then, to stem any divide we must first clarify why it exists. Is it simply due to a lack of knowledge, or are there deeper factors at play: a clash between paradigms?
There is an understandable fear that we are witnessing a revival in government circles of not just a denial of science but even an antipathy to it. Yet our concern is not with the latest clash between Flat Earthers and empiricists (for example, over environmental policy). Our brief vis- à-vis education concerns the divide between a teaching philosophy based on an ancient self-control paradigm, and an approach to teaching that is grounded in the modern science of self-regulation.
There have been major advances over the past decade in our understanding of the complex reasons why students find certain topics difficult to master and how to help them. It is never a lack of effort that is the problem but rather biological and sensory issues, processing constraints, and social-emotional challenges. Self-Reg is forever asking why a student is struggling in a particular area, and constantly seeking to identify and reduce the various stresses that are impeding learning. But those who believe that a child’s problems are due to a lack of character will never go down this path, for they have already decided on the answer.
In practical educational terms, the divide we are concerned with is between those who are succeeding in their schooling and those falling ever further behind. Educational stratification starts early. It is already evident by Grade 3, if not in Junior Kindergarten. And the question we need to address is to what extent the “achievement gap” is the child’s fault, or our own. Without an answer to this question, anxiety and frustration only grow – at every level: for students, parents, teachers, administrators, and policy- makers who must decide whether to turn to science or custom to address the problem.
The perfect illustration of this point can be found in the current debate over the decline in Grade 3 math scores on Ontario’s Education Quality and Accountability Office (EQAO) test. Here we are confronted with a divide that is not just frustrating but, in many quarters, alarming; for what we know about math instruction is already considerable, and yet results not only continue to disappoint, but are actually going in the wrong direction!
This slide has prompted the knee-jerk reaction that children – and perhaps their parents and teachers – need to work much harder. Complacency and lack of grit are seen as the heart of the problem. The unspoken conviction here is that “If students choose not to try harder, they must live with the consequences of that choice.”
This Victorian paradigm – the apotheosis of perseverance – is epitomized by what Samuel Smiles wrote in his highly influential Self Help (1859):
The maxim that “Labour conquers all things” holds especially true in the case of the conquest of knowledge. The road into learning is alike free to all who will give the labour and the study requisite to gather it…. In study, as in business, energy is the great thing…. It is astonishing how much may be accomplished in self-culture by the energetic and the persevering, who are careful to avail themselves of opportunities, and use up the fragments of spare time which the idle permit to run to waste. (p. X)
In other words, the State can offer all children an education, but it cannot force them to persevere. And if a 10-year-old has already fallen behind in math and doesn’t make the effort required to catch up, he has no one to blame but himself.
But no child chooses to be left behind, and if it seems that way, it is because you have not dug deeply enough. Those wedded to Victorian thinking find this principle deeply unsettling; for it highlights the need for an entirely new approach to teaching, based on self-regulation rather than self-control.
High Math Anxiety
The influence of inherited biases tends to wax and wane depending on how much stress an individual or society is under. The greater our anxiety, the more polarized and paralyzed our thinking becomes. Traditional nostrums suddenly become compelling.
Back in 1983, when Britain was undergoing a disturbingly high level of societal unrest, Mrs. Thatcher gave a speech celebrating the “Victorian values” on which she had been raised by her grandmother (Samuel, 1992). This attitude has surfaced again in the debate over the decline in math scores. Success in math, according to the perseverance doctrine, depends on hard work, discipline, and self-reliance: not mollycoddling (another classic Victorian term).
With the resurgence of this Victorian outlook, there has been a corresponding increase in the number of students with high math anxiety (HMA). HMA is used to designate a condition of acute emotional distress observed in a great many of the young students who are struggling with math; but it also describes a societal condition. In fact, the two phenomena are more than just correlated, and the crux of our Self-Reg Reframing of high math anxiety lies in unpacking the relationship between them.
There are many reasons why the decline in Grade 3 math scores has become a matter of great societal angst. To begin with, there is research showing how important the early years are for downstream math development, and how hard it is to catch up. There is also research showing the importance of competency in math for dealing with the demands of modern life and, not surprisingly, its impact on long-term socioeconomic status. It has become increasingly clear that math skills are a foundation, not just for later academic success in STEM, but for success simpliciter. But the major source of “societal HMA” is what The Economist dubbed The Other Arms Race: the international battle over math standings.
Children must now compete, not just with their peers at the local level, but also with children from around the world. Following his State of the Union address in 2013, then president Obama told the students at the P-Tech school in Brooklyn that in previous generations, America’s standing economically was so much higher than everybody else’s that we didn’t have a lot of competition. Now, you’ve got billions of people from Beijing to Bangalore to Moscow, all of whom are competing with you directly. And they’re – those countries are working every day, to out-educate and outcompete us.
In other words, children in the West have to compete with families in developing nations who see education as their only chance to escape from poverty and are willing to pay virtually any price to seize this opportunity.
In recent years, a number of important voices have warned about the perils of placing global competition in education ahead of children’s well-being (see Seth, 2002; Allison, 2013; Zhao, 2014). Math has become the battlefront in this massive international war. It is bad enough that the same countries keep dominating the Program for International Student Assessment (PISA) standings; to make matters worse, replicating these countries’ teaching practices does not produce the same results in different national settings.
Math education has been caught up in a violent stress storm, with mounting pressures coming from above and below: politicians and trustees inundated with reports about how we are falling behind; alarmist media reports; parents worried about their children’s future; teachers and administrators struggling to deal with the demands being placed on them, not least of which are the constant changes to the curriculum; researchers struggling to understand why the “fixes” aren’t fixing; and a constantly growing number ofyoung learners with HMA (Ramirez, Gunderson, Levine, & Beilock, 2013; Boaler, 2015).
It is this last factor that is the most worrying of all, insofar as HMA fuels itself. HMA seriously impairs a student’s comprehension and performance, leading to avoidance, which leads to further falling behind, and so on (Ashcraft, 2002; Hembree, 1990). But lack of effort is not the problem here; it is the lack of understanding as to when and why a student has HMA. The question is: to what extent is societal HMA a factor possibly pivotal – in student HMA?
The Cognitive Roots of HMA
Scientists have been looking carefully at the emotional, social, and prosocial causes of HMA: for example, negative math experiences, poor self-esteem and self-confidence, and gender and racial stereotypes. The biggest problem is that anxiety breeds anxiety. The more anxious the student, the more drawn to maladaptive coping strategies (for example, avoidance), which results in still greater anxiety down the road; the more anxious the adult trying to teach the child, the more anxious the child becomes, and vice versa; the greater the societal anxiety, the more all of the above are exacerbated.
HMA can occur in the absence of a generalized anxiety disorder, although the question of its impact on simmering anxiety, and the reverse, remains a significant issue. But what is most important about HMA is the fact that it is subject-specific (Rubinsten & Tannock, 2010). There is something unique about math that explains why we are seeing so many children developing HMA.
The root of the problem is that math is a cognitive stress. Indeed, it is a paradigmatic example of a cognitive stress. Western educators have intuitively known this fact for well over a thousand years, if not considerably longer (Friesen, 2010; see also Jardine, Clifford, & Friesen, 2006). But only recently have cognitive psychologists begun to understand why this should be the case.
Math makes considerable demands on working memory, and much more for some children than others. Common among students with HMA are problems in mathematical cognition: for example, number sense, counting, subitizing, and mentally comparing the magnitude of two numbers (Maloney, Ansari, & Fugelsang, 2011). These cognitive deficits have a direct impact on working memory and thus on math performance (Moore, Rudig, & Ashcraft, 2014).
According to the “dual-task” explanation, an HMA student’s working memory is divided between math task and intrusive thoughts. The contents of working memory are said to be “tainted” by worries (Stout, Shackman, Pedersen, Miskovich, & Larson, 2017). Stress in particular has been shown to exacerbate sensory issues and to reduce working memory–related activity in the DLPFC (Qin, Hermans, van Marle, Luo, & Fernández, 2009). Hence, the reason why reappraisal or mindfulness exercises improve math scores in older students with HMA – if and when they do – is that these practices reduce intrusive thoughts and thereby increase working memory capacity.
But none of this need bother those who believe that the student’s difficulties with math are caused by a lack of effort; on the contrary, “self-controllers” can argue that this only strengthens their point, which is that what is different today is simply that children are too lazy or unmotivated to tackle their problems. After all, as just noted, we have known for a long time that math is stressful, and there is nothing to suggest that we are seeing a jump in the number of children with impaired mathematical cognition. But what is different, according to those who emphasize the need for grit, is that children are much less willing to make the effort needed to overcome a challenge.
This reaction reflects precisely the point that Smiles makes in Self-Help and in Lives of the Engineers (1862). All of the cases that he cited were meant to show how highly successful individuals in all walks of life were able to overcome their obstacles “by dint of sheer industry and perseverance” (p. 112). This is the crux of the Victorian view of perseverance – and the point of intersection where it clashes with a paradigm based on the science of self-regulation.
The Self-Reg “Why?”
To say that math is a “cognitive stress” is simply to say that learning math burns energy. A lot of it. And to say that, for biological reasons, math is an intense cognitive stress for some children is to say that they expend inordinate amounts of energy compared to their peers.
In The Myth of Laziness (2003), Levine makes the point that when a young child “gives up” on a simple problem in arithmetic, this is a sign that he has been working far too hard (Shanker, 2017, May 10). A child with developmental dyscalculia – a numerical processing deficit that is not related to low IQ, sensory deficits, or social factors – presents just such a case. But what exactly does it mean to say that the child is “working too hard”?
There is some research that bears out the idea that “brain work” burns great amounts of glucose (Scholey, Harper, & Kennedy, 2001). But the findings in this area have been mixed (Kurzban, 2012). While the brain consumes an inordinate amount of glucose relative to its size (Swaminathan, 2008), the amount of additional glucose consumed in a challenging cognitive task is fairly negligible (Messier, 2004) – except when one especially pertinent factor is involved. That further factor is stress (Chaput, Drapeau, Poirier, Teasdale, & Tremblay, 2008).
The more stressful a task, the more glucose consumed (Baumeister & Tierney, 2011); and the child with poor numerical processing finds math stressful in much the same way that a child with poor motor control finds Phys Ed stressful. This is not simply a working memory – that is, a Blue Brain – issue, although, to be sure, the dual- task explanation has numerous cognitive-load studies to back it up (Moore et al., 2014). HMA introduces a further dimension into the mix in addition to the effect of intrusive thoughts on working memory: namely, the physiological costs of hyperarousal (Ashcraft and Krause, 2007).
Hyperarousal is the quintessential Red Brain phenomenon. Engaging in a difficult cognitive task when not hyperaroused (for example, working on a 1000-piece jigsaw puzzle) does not significantly affect blood glucose. Add in hyperarousal, however – as has been shown to happen in writing the SATs – and blood glucose can drop sharply: not because of the added cognitive load, but because the task triggers strong negative emotions, which elicits a powerful sympathetic nervous system response. We see a leap in tension, and thus, elevated heart rate and blood pressure, faster breathing, sweating, and higher levels of cortisol (Jabr, 2012).
This point is pivotal to understanding student HMA. A child with developmental dyscalculia quickly slips into Red Brain when trying to master the basics of arithmetic. This does not happen when asked how many objects are in a group of less than 5 items; but increase the group to 10 items and this triggers a limbic response as the child shifts from subitizing (perception) to counting (working memory). Other domains of stress are layered on top: emotional, social, and prosocial. The child is caught in a “math-centric” (Shanker, 2016) as he or she lags behind other children or fails to meet their teacher’s – or their own – expectations (Ramirez et al., 2013).
In short, the reason why children with problems in numerical cognition find math “a source of huge anxiety is because they must exert tremendous effort to understand what is obvious to their classmates” (Rubinsten & Tannock, 2010, p. 3). We think of math as a purely mental exercise (whatever that means). But what we learn from Porges’ (2011) “evolutionary lens” is that working on a mentally challenging problem triggers an ergotropic shift; for concentration is a full-body phenomenon.
We have adapted a primitive survival mechanism – one that involves tensing our muscles when hyper-focusing or striving to keep up with a group – to the task of learning math, which is far more demanding for children with numerical processing deficits. Facial and eye muscles, jaw, neck, shoulder, trunk, skeletal, and even leg muscles are strained much longer than occurs in the student for whom working on math is invigorating. The former child ends up in a very different arousal state from the latter. Because of differences in numerical processing, the one child finds the activity negative and aversive while the other finds it positive and rewarding (Maloney, Sattizahn, & Beilock, 2014). In terms of the Thayer Matrix (see figure 1), the struggling student sinks deeper and deeper into the bottom right quadrant, while the successful student swings effortlessly between top right and top left (Thayer, 1999).
But this explanation still leaves us with a triad of Self-Reg questions:
- Why should hyperarousal lead to HMA?
- What can we do about this problem before it reachesHMA proportions?
- What can we do about this problem once it hasreached HMA proportions?
Just why is it that a child – any child, and not just onewith developmental dyscalculia – should come to dread daily math class? What are we doing wrong? What do we need to do differently?
A Kindled Alarm
In a seminal article on HMA, Mark Ashcraft (2002) tells the story of an undergraduate in one of his studies who became so distraught while working on a simple problem in arithmetic that she burst into tears. But why would a problem such as “46 + 18 = ” cause anyone, let alone a university student, to have acute distress? The mere thought of doing math has been shown to cause the same neural response in HMA students as actual physical pain (Lyons & Beilock, 2012).Of all the discoveries that cognitive neuroscientists working in this area have made, the most remarkable is that HMA in children aged seven to nine is associated with hyperactivity in the right amygdala and anterior hippocampus and reduced activity in the frontoparietal systems associated with mathematical and numerical reasoning (IPS and DLPFC) and emotion regulation (vmPFC) (Young, Wu, & Menon, 2012). What this means is that HMA students exhibit a threat response to problems in arithmetic, with a corresponding reduction in working memory and numerical processing (Qin et al., 2009).
But why would a young child see math as a threat?Even more puzzling is when it is only math among school subjects that the child sees as a threat. Why does having trouble learning the basics of arithmetic render a child hypervigilant: even send a child into fight-or-flight, or indeed, freeze?
The Self-Reg answer to these questions lies in the consequence of persistently overriding a child’s limbic brakes. Ashcraft (2002) found that, on a test that becomes increasingly challenging (the basic IQ test design), university students with HMA often do well on the first part of the test, but as their anxiety mounts their accuracy begins to plummet, which further intensifies their anxiety. They reach a point where they suddenly stop. That is the point where their limbic brakes have kicked in.
The same thing is happening to the young child with a numerical processing deficit. The child is under a tremendous amount of tension trying to keep up with the rest of the class. The limbic brakes kick in at the point when blood-glucose drops below a certain threshold. And here is the critical point: if that child is then pressed to persevere – pushed past the peak of the inverted-V energy/arousal curve – the memory is registered (Shanker, 2017, April 24). The hippocampus and amygdala keep a meticulous record of experiences that exhausted energy reserves without a big compensating (neurochemical) payoff. The mere cues associated with that experience (for example, pulling out the math books) are then enough to trigger a state of “neuroceptive overdrive.”
A child in neuroceptive overdrive starts looking for and seeing threats everywhere, which we readily misconstrue as heightened distractibility. Startle reactions are misconstrued as heightened impulsivity. The anticipation of unpleasantness and the impact this has on concentration is misconstrued as poor attention. Halting mastery is misconstrued as limited “mathematical intelligence.” Limbic brakes kick in, which is misconstrued as oppositionality. This is the “dyadic nexus” that leads to math becoming an ongoing threat.
So, our Self-Reg reframing of HMA ultimately leads us to ask: Why are we pushing so many young children to override their limbic brakes – without realizing that we are doing so? How can we avoid or turn off a “kindled math alarm”?
The answer to the first question lies in the effect of societal HMA on our attitudes towards cases of “laboured learning.” Empathy turns off; old biases kick in. The answer to the second question lies in overcoming that reflex.
Bridging the “Unbridgeable”
The essence of the Victorian view of perseverance as articulated by Smiles is that when students fail it can only be because they did not try hard enough. Smiles was not denying the fact that some children have much more serious impediments than others. But he insisted that the greater the liability the greater the effort needed, because “there are no difficulties so great that the student of resolute purpose may not surmount and overcome them” (Smiles 1859, p. 384). To be sure, the obstacles that Smiles was thinking about were primarily physical, social, and economic. But it was no stretch to apply this way of thinking to cognitive deficits as well – as, for example, Winston Churchill (another of the great proponents of the Victorian view of perseverance) did when he suggested – misleadingly, as it happens – that he was able to overcome his cognitive deficits through sheer willpower (Churchill, 1977).
This Victorian outlook leads us to automatically assume that children lagging behind their peers for whom arithmetic comes more easily need to be pushed to make a greater effort lest they fall behind right at the start. The greater the societal angst around math, the more this Victorian mindset takes hold. When it does, we fail to read the signs that the child is rapidly approaching an energy/tension peak (for example, in pupil dilation, changes in prosody, facial complexion, restlessness, heightened “distractibility,” avoidance). We misread resistance as lack of effort, see anxiety as non- compliance. We persist in pushing or punishing when we should be pausing and probing: Why is this child, who is so active and interested in other school subjects, having so much trouble with math?
The first Self-Reg step in helping such a student is to reframe: where the Victorian paradigm sees straightforward misbehaviour, Self-Reg sees stress-behaviour in all its subtle forms. The hard part is the second step: identifying the reasons why math is such a significant cognitive stress for an individual student. This is where we need to be constantly asking “Why?” and reflecting on what we are learning about the student’s processing. Instituting such measures as a classroom makeover, mindfulness and exercise breaks, or providing stress-relieving manipulatives may help as a third step. But in the case of HMA this will never be enough. It will be essential to work on reducing the cognitive stress, not just through executive function coaching, but in some cases, through exercises that address underlying (for example, sensory-motor) deficits (infra).
It is no less essential that students become aware that and why they find math so stressful (the fourth step of Self- Reg). They need to internalize that this is not a reflection of “innate inadequacies,” but an example of the different kinds of processing deficits that modern science is learning how to address. (Bear in mind that there was a time, not so long ago, when myopia was seen as a weakness and wearing glasses a form of indulgence.) And finally, students need to develop “pre/post” strategies to maintain or restore balance in all five of the Self-Reg domains (the fifth step of Self-Reg). They need to learn how to self-regulate, not just in math class, but in all aspect of their lives; for the student who doesn’t know what “calm” feels like will find it impossible to remain calm when faced with a sharp stress, such as math.
The better we can understand math stresses and how they interact with the other stresses in a stress cycle, the better we can alleviate how hard a student must work. The techniques that Roman-Lantzy and the American Foundation for the Blind (2017) developed to enable students with cortical visual impairment to read are highly instructive in this regard. She experimented with making printed information more visually salient by adjusting font size, contrast, and colour (text and background); using coloured borders to highlight the text; and eliminating peripheral “visual noise” on the page (for example, illustrations). By enhancing the salience of visual information, she reduced the effort needed to process it, and the impact this has on energy and tension. Just consider how tense you become as you strain to absorb an important email that has been sent in a much smaller font than you are accustomed to reading.
We need to look at similar ways of reducing the effort required from HMA students by enhancing their numerical processing. We might begin with exercises that promote
kinesthetic, proprioceptive, and vestibular awareness ; or exercises that work on visualization (Brown, 2017). Abstract mathematical concepts need to be made personally relevant and meaningful (Sperber, Cara, & Girotto, 1995). Engaging ways to make executive function strategies more engaging should be explored (for example, card and board games). And it is essential to minimize temporal, social, and prosocial stresses (Barkley, 2012).
By enhancing the salience of the information and reducing the stress load, we reduce the physical strain that the HMA student is under. We soothe amygdalae. Only when a limbic alarm is turned off and the student is calmly focused and alert can we begin to increase the cognitive stress load: slowly, and incrementally.
But there is still a deeper divide that needs to be bridged here: namely, the idea that working on math skills is a completely different matter from working on a student’s social-emotional skills. The two are inextricably conjoined. Just imagine how empowering it must have been for Roman-Lantzy’s students once they understood the nature of their visual processing deficits and the manner in which they could take control of their reading: for example, by adjusting the layout of text on a handheld reader or using a multi-modal reading system to bootstrap. And, of course, by working on their self-regulation across the board: for when we talk about “restoring balance,” we are referring to all five domains and not just the one where problems in dysregulation stand out (for example, in the case of student HMA, emotion).
The anxiety that a child with HMA experiences may be subject-specific, but the ramifications are not. The fact that math plays such a big role in a child’s academic life – short- term as well as long-term – is all the reason that we need to take this issue so seriously. But to overcome an ingrained threat-response and the negative bias this evokes the student must feel safe. Math must cease to be seen as a threat.
A big problem with the Victorian paradigm is that it sees anxiety as a weakness that requires fortitude to be overcome (“With WILL one can do anything,” [p.7] as Smiles puts it). This attitude is definitely a major concern. But an even greater problem with the Victorian mindset is its fatalism: the divide between those who do and do not succeed is seen as fixed, either by the child’s character (Smiles, 1859) or genes (Galton, 1869). Neither is true. But just as we will never know how fast a car can go when it is held in check by a governor, so too we will never know what a student’s academic potential might be when that child is being held in check by limbic brakes.
If we truly believe that we need to stem the ever-growing divide in early math learners, we need to think hard about why a student has developed HMA and how we can change that trajectory. Where the self-control paradigm sees the problem as one of motivation, Self-Reg sees this issue as an opportunity to learn more about learning – and about ourselves! Our ultimate goal here, however, is not to raise the child’s scores, but to help the child discover (Strogatz, 2012). That is the greatest cost of all of societal HMA: namely that we turn into a penance what should be a source of personal pleasure and enrichment.
I am deeply indebted to Caitlin Gordon Walker for the remarkable work she did on an earlier draft of this paper. It goes without saying that the errors and omissions are mine; but without the thought and care that she put into this article there would have innumerably more.
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