tag:blogger.com,1999:blog-56097856470119635332017-09-25T08:36:41.596-07:00Math AnxietyDavid Mills, Ph.D., M.A.http://www.blogger.com/profile/13115000746728769229noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-5609785647011963533.post-22355326613266876982010-12-08T05:27:00.000-08:002011-07-24T10:42:29.232-07:00<div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><a href="http://www.mytutorsandiego.com/"><b>David Mills, Ph.D., M.A.</b></a><b> </b></span><br /><br /><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><b>Negative feelings about math, </b>not lack of ability or preparation, can directly interfere with learning math. These negative feelings include hating or disliking math, nervousness, fear, anxiety, worry, and/or tension when learning math or taking math tests. </span><span style="font-size: small;"> The presence of any such feelings, <i>if</i> they interfere with taking or learning math, can be termed "math anxiety." </span><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-k0ux8pmpfaw/TgIqdbbBH8I/AAAAAAAAAi4/FJEwxjPyUHY/s1600/MathTeacherMed.jpg" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img border="0" src="http://1.bp.blogspot.com/-k0ux8pmpfaw/TgIqdbbBH8I/AAAAAAAAAi4/FJEwxjPyUHY/s1600/MathTeacherMed.jpg" /></a></div><span style="font-size: small;"><b>Such feelings are often a result</b> of an earlier bad experience with math, poor instruction or a critical teacher, experiences which may or may not be consciously remembered. Negative feelings about math which result from a specific difficulty learning math, such as dyscalculia, or poor preparation, are not considered math anxiety <i>per se</i>, by the definition here.<b> </b></span><br /><br /><span style="font-size: small;"><b>Math anxiety</b> as defined interferes with learning math, being tested on math, and/or taking math courses, resulting in difficulties in the manipulation of numbers and solving of mathematical problems in a wide variety of academic and real world settings. It can be considered a phobic response, in that the person avoids math (or particular aspects of it) and avoids situations where such aspects might be encountered, and feels anxious when such situations cannot be avoided.<b> </b></span><br /><br /><span style="font-size: small;"><b>In academic settings</b>, students with high math anxiety tend to do poorly in math classes, and tend to take the absolute minimum math courses required. <b>Most importantly, they avoid choosing careers</b> in which any use of math would be required, even careers in which they may be otherwise quite interested. This is the most unfortunate consequence of math anxiety, because 1) more than half of all careers, the better-paying half, require math knowledge, and the fraction is increasing; and 2) it is possible to overcome math anxiety and resume normal learning of math, as explained below. That is, <b>math anxiety <i>per se</i> should not be a reason to avoid a career in which math is important</b>.<b> </b></span></div><div style="font-family: Georgia,"Times New Roman",serif;"><br /></div><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><b>In ordinary life, people with math anxiety may also</b> have difficulty making change, may avoid tipping or tip too much because they are unable to calculate the appropriate amount, may not check their bank balances or credit card statements, and may avoid checking a potentially incorrect bill, paycheck, etc. More seriously, they typically have trouble comparing investment opportunities, evaluating their retirement benefit and medical insurance options, and have in general difficulty estimating probabilities and probable outcomes in a variety of real life situations.<b> </b></span></div><div style="font-family: Georgia,"Times New Roman",serif;"><br /></div><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><b>In school, math anxiety is essentially unknown in the first few grades. </b>It begins to emerge as a problem around sixth grade, at a time when students typically encounter problems involving fractions, long division and "unknowns." The number of students affected by math anxiety continues to rise through adolescence, then levels off. By adulthood, about 60% of people are reported to have negative feelings about math.</span><br /><br /><span style="font-size: small;"><b>Unfortunately, the individual reasons</b> for the initial onset of the anxiety are not well studied. Many students report that their anxious feelings began when they were asked to work out a problem on the board in front of the class (i.e., as performance anxiety). Other students report that their anxiety began when they were first asked to learn a new and complicated math topic, e.g., fractions. Some students do not remember what specific event may have caused the onset of their math anxiety.</span></div><div style="font-family: Georgia,"Times New Roman",serif;"><br /></div><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><b>As is suggested</b> by the above examples, research <i>has</i> shown that an individual's math anxiety tends to focus on one of two areas: 1) taking math tests and similar math performance issues; or 2) learning math concepts and procedures. Research has also demonstrated that math anxiety is <i>not</i> associated with general anxiety disorders, nor is there any association with low intelligence. On average, females are found to be slightly more likely than males to report problems with math anxiety.</span></div><div style="font-family: Georgia,"Times New Roman",serif;"><br /></div><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><b>Math anxiety interferes</b> with learning math or succeeding in taking math exams in the following way. Anxiety from any cause is treated by the brain as an alerting signal to danger, to a "flight or fight" response. In particular, anxiety causes the release of cortisol in the blood, which causes the frontal lobes to focus on the anxiety, to be alert for danger. With too much cortisol, the mind does not have sufficient additional resources available in working memory to learn new material nor can it focus successfully on exam questions when being tested.</span><b> </b></div><div style="font-family: Georgia,"Times New Roman",serif;"><br /></div><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><b>While very disruptive, m</b><b>ath anxiety is NOT a math learning disability </b>as defined here. There are several important ways that math anxiety differs from a math learning disability, or developmental dyscalculia: 1) Math anxiety is an <i>acquired</i> emotional response, <i>not</i> due to a genetic/neurological dysfunction. 2) Its specificity, and non-correlation with general anxiety disorders, is evidence that math anxiety is triggered by a specific event involving math, even if the event may not be consciously remembered. 3) Math anxiety may be general to math or may be specific to particular topics. Especially, people may react with anxiety to problems involving fractions, long division and algebra. 4) The late onset of math anxiety also contrasts sharply with dyscalculia, signs of which can often be detected in kindergarten. 5) Most importantly, math anxiety, as with other specific phobic responses, <b><i>can in general be successfully overcome</i></b>.</span></div><div style="font-family: Georgia,"Times New Roman",serif;"><br /></div></div><div style="font-family: Georgia,"Times New Roman",serif;"><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"></span></div><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;">In contrast, people with <a href="http://www.mathdisabilities.blogspot.com/"><b>dyscalculia</b></a> can learn to cope with their math disability, but at present there is no successful approach that will remove its effects entirely.<b> </b> The disassociation between math anxiety and dyscalculia is further demonstrated by the finding that students with math anxiety have difficulty with counting but <i>not</i> with <b><a href="http://www.mathdisabilities.blogspot.com/">subitizing</a></b> (Maloney et al., 2010) , where dyscalculics have significant difficulty with both, <i>especially</i> with subitizing, compared to normals.<b> </b></span></div><div style="font-family: Georgia,"Times New Roman",serif;"><br /></div><hr width="100%" /><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><b>Do you have math anxiety? </b> If you do, you probably already suspect it. But if you wish to have a useful analysis of your math anxiety characteristics (or a youngster's) you may wish to take (or administer) the short questionnaire below. This short survey was originally developed by Hopko, <i>et al.</i>, and evaluated in a study of college freshmen. Statements in the questionnaire below have been modified so that it can be used for high school students as well as for adults. For some adolescents, and certainly for younger children, an adult should preferably read and score the questions, suitably rephrasing questions with the age and experiences of the youngster taken into account.</span></div><div style="font-family: Georgia,"Times New Roman",serif;"><i><br /></i></div><div style="font-family: Georgia,"Times New Roman",serif;"><span style="font-size: small;"><i>In most browsers, the questionnaire can be printed by clicking on it once and using "File/Print."</i><b> </b></span><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/_vRsObFw-TN0/TSS0FvVZS_I/AAAAAAAAAeQ/qxCHJ6Vqyho/s1600/AMASmod.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="640" src="http://1.bp.blogspot.com/_vRsObFw-TN0/TSS0FvVZS_I/AAAAAAAAAeQ/qxCHJ6Vqyho/s640/AMASmod.jpg" width="502" /></a></div><br /><span style="font-size: small;"><b>The average score</b> for college freshmen is 21, with most students falling between 14 and 28. If your score falls above 28 points, you are in the group of people who are the most math anxious. This group comprises 16%, or 1 in 6, of the total number of all students.<b> </b></span></div><br /><span style="font-size: small;"><b>If you add up the subscores</b> as noted above, you can also establish which aspects of math are the most anxiety-provoking for you. This is potentially important, as it can help determine the main area to target for the relief of the math anxiety.<b> </b></span><br /><br /><span style="font-size: small;"><b>The relief of math anxiety</b> is certainly indicated for a student if it has serious consequences; if, for example, it interferes with learning math, getting good grades in math, taking additional math courses, or if math anxiety unduly influences the choice of a career. If the math anxiety is relieved, normal learning of math can resume. Additional study or tutoring, of course, may be required to make up for lack of adequate understanding of earlier math concepts.</span><br /><br /><span style="font-size: small;">A return to normal math learning, of course, is possible only if the anxiety is not due to an underlying math learning disability. Even in this case, at least unnecessary anxiety can be reduced even if math learning cannot become completely normal.</span><br /><br /><span style="font-size: small;"><b>Mild to moderate math anxiety</b>, especially when the anxiety is focused on learning specific material, can be overcome using the following approach. Motivational issues are explored, and the relevance of the material is established in terms of the student's needs and interests. The affected material is re-learned under conditions so that anxiety is kept minimal. Conceptual understanding is the important focus, with rote practice following to solidify understanding and to provide practice for use in homework and exams. The success rate is kept high in order to minimize negative reactions. If the main issue is math test anxiety, the approach is similar but includes desensitization to test situations using an incremental, step-by-step sequence.</span><br /><br /><span style="font-size: small;"> <b>Severe cases</b> of math anxiety can be treated like any specific phobia, and like specific phobias, the chances of a successful outcome are high when proper treatment is employed. Cognitive-behavioral therapies have so far had the highest success rate in treating specific phobias. In such cases, a professional with training and experience in treating specific phobias is recommended. Some resources with further information are listed below. Further discussion of the treatment process is outside the bounds of this posting.</span><br /><br /><b>We value your input:</b> If you would like to post information or pass on experiences helpful to others, add a comment or ask a question, please open the <a href="http://034053c.netsolhost.com/comment.htm" target="_blank"><b>comment form.</b></a><br /><br /><hr width="100%" /><span style="font-size: small;"><b>REFERENCES AND RESOURCES</b><b> </b></span><br /><br /><span style="font-size: small;"><b>The views above </b></span><span style="font-size: small;">are those developed by the moderator based on his training and experience. Other information and opinions on math anxiety can be found in the review chapter, "Is Math Anxiety a Mathematical Learning Disability?" by Ashcroft <i>et al.</i>, in "<i>Why is Math So Hard for Some Children</i>," Berch and Mazzocco, Eds (2007).</span><br /><br /><span style="font-size: small;">The questionnaire above, AMASm, was modified from that published by Hopko <i>et al</i>, "The Abbreviated Math Anxiety Scale (AMAS): Construction, Validity, and Reliability," <i>Assessment</i>, <b>10</b>, </span><span style="font-size: small;">178-182 (2003).</span><span style="font-size: small;"> The main modification was to simplify wording, e.g., replacing the word "algebra" with "math," to make the assessment more applicable for younger students while leaving it valid for undergraduate students (upon whom it was normed). The order of two questions was reversed to make it easier to count up the subscales.</span><br /><br />A good web resource is the Math Academy site, <a href="http://www.mathacademy.com/pr/minitext/anxiety/index.asp">Dealing with Math Anxiety</a>.<br /><br /><span style="font-size: small;">Maloney, <i style="font-family: Georgia,"Times New Roman",serif;">et al.</i>, "Mathematics anxiety affects counting but not subitizing during visual enumeration," Cognition, 114, 293-297 (2010).</span><br /><br /><span style="font-size: small;">A relevant discussion of the treatment of severe math anxiety (suitably interpreted) can be found under the Wikipedia entry on <a href="http://en.wikipedia.org/wiki/Specific_phobia">specific phobias</a>. The <a href="http://en.wikipedia.org/wiki/Cognitive_behavioral_therapy">cognitive-behavioral approach</a> is reported to have successfully relieved symptoms in 90% of cases involving specific phobias.<u><b></b></u></span><br /><br /><span style="font-size: x-small;">Note: All original material on this and linked websites © D. Mills 2011.</span> </DIV>David Mills, Ph.D., M.A.http://www.blogger.com/profile/13115000746728769229noreply@blogger.com2