Presentation on theme: "The role of math anxiety in cognition, and what you can do about it"— Presentation transcript:
1The role of math anxiety in cognition, and what you can do about it Too Afraid to LearnThe role of math anxiety in cognition, and what you can do about itCristina Post, Ed.M.MathAffectAs math teachers, we are perennially aware of the problems that math anxiety causes in the classroom. Recent research in affective neuroscience reveals the large role that emotion plays in learning, and as a result we better understand how math anxiety interferes with cognition. Understanding the problem gives us strategies to combat it, and alleviating math anxiety is associated with an achievement gain of over twenty percentile points. This presentation will cover the causes, ages of onset, and prevalence of math anxiety, a review of the research surrounding its effects on cognition, how to assess the level of math anxiety in your classroom, and alleviation strategies broken down by grade level. Special attention will also be paid to the distinction between math anxiety and stereotype threat, which influences how girls (and other stereotyped groups) perform in math class.
2Research in Affective Neuroscience Learning, attention, memory, decision making, and social functioning are all controlled by emotionPeople whose emotional centers are damaged cannot make “rational” decisionsEmotional ThoughtPhysical ReactionsHigh ReasonThe emotional center referred to in the slide is the ventromedial prefrontal cortex.Basically, emotion helps children apply what they learn in school to the rest of their livesImmordino-Yang and Damasio, 2007
3What is Math Anxiety?State anxiety (vs. trait anxiety) only present when doing mathDifferent components of math anxiety:Affective - general fear of or dislike of mathSocial/performance - board work in front of class, small group work with peersTest anxietyNot correlated with IQ or verbal aptitude, Mild positive correlation with trait anxiety, Strong negative correlation with math achievementTest anxiety not differentiated before 6th grade - that is not to say that tests don’t make them anxious, just that they can tell the difference between feelings about math and feelings about a math test. After that point, however, separate interventions are necessary to eliminate anxiety around tests and anxiety around math. Dew, Galassi, & Galassi, 1984
4Math AnxietyMath Anxiety: Decreased performance stems from conscious worry over an expectation of high performance levelStereotype Threat: Decreased performance due to unconscious negative effects from an expectation of low performance levelI chose the calm blue sea slide b/c seemed appropriate for a presentation on anxiety , but actually relaxation training does little for decreasing anxiety. Still pretty though.You often hear parents or teachers say that math anxiety occurs only in girls. In reality, it affects both genders, and we think of girls because of the prevalence of stereotype threat in female math learning.Repeated exposure to stereotype threat will cause math anxiety to develop, so they are related.
5Ages of Onset93% of American adults self-identify as being bad at or disliking mathThree major ages of onset (Hembree, 1990):Grades 1-3 are more likely to present with stereotype threat (Beilock et al, 2010)4th – 6th9th – 10thCollegeStarts in 4-6th grade (due to teachers and demands on working memory) and increases linearly with a peak at grades 9-10 (demand is higher, novel learning situation), and again in college (demand is higher, novel learning situation, teachers with accents) and then leveling off to the point where 93% of American adults in one study identified as being bad at or disliking math. Affects boys and girls equally. The onset of math anxiety is usually around 4-5th grade, peaking in 9-10th grade, and the onset of negative performance due to stereotype threat seems to be due to teacher modeling and occurs as early as 1st grade (Beilock, UChicago). Math anxiety does not affect performance until around grade three: Krinzinger, Kaufmann, and Willmes (2009)
6Causes of Math AnxietyMath anxious teachers in elementary (and sometimes middle) schoolsTeaching techniquesAnxiety modelingIncreased demand on working memory, beginning in fourth gradeA vicious cycle of poor learning and heightened anxietyHowever, studies show that 72% of the negative math experiences that arise in early-middle primary school are attributable to the teacher, rather than math content, family attitudes, or peers (Uusimaki & Nason, 2004). THIS LAST SENTENCE NEEDS CLARIFICATIONOne of the most common ways for math anxiety to develop in the elementary or middle school classroom is by teacher modeling of math anxious behaviors (Gresham, 2007; Tobias, 1998; Vinson, 2001). Anxiety is a background emotion, which we exhibit unconsciously through body posture and movements, minimal changes in amount and speed of eye movements, and the degree of contraction of facial muscles (Damasio, 1999). These minimal changes are what children pick up on and react to, creating a learning environment where math is depicted as a subject to be avoided at all costs. Indeed, elementary school teachers who score higher on measures of math anxiety spend less time preparing for math lessons and less time teaching math, modeling this math avoidance (Brady & Bowd, 2005). Math-anxious teachers also tend to focus on teaching skills, rather than concepts (Norwood, 1994), an important part of teaching for understanding.
7How does MA affect learning? Math anxiety interferes with verbal working memory, the phonological loopWorking memory is the system in the brain that keeps things in mind while performing complex tasks: reasoning, comprehension, learning (Baddeley, 2010)
8Visuo-spatial sketchpad Working MemoryCentral ExecutivePhonological LoopEpisodic BufferVisuo-spatial sketchpadThe capacity of the phonological loop is about 10 seconds, and can be tested (rough and dirty) using digit span. To be more accurate, remember backward.2 9Experiments: Do simple math problem:Then a problem involving carrying: (write horizontally)(vertically)Then hold in head while doing 6 + 5Then hold in head while doingLong term MemoryAdapted from Baddeley, 2010
14Working Memory and Math Working memory is taxed by mental arithmetic: carrying, borrowingHighly anxious people do worse on tasks that require working memory capacityControlling for anxiety and taxing working memory reveals the same effectWM is NOT involved in rote memory tasks like retrieving simple math facts(Ashcraft, 2002)It takes high-anxious students about three times longer to solve a problem involving carrying than a low-anxious student. Under time pressure, anxious students will sacrifice accuracy for speed (3 + 4 = 12).Research shows that giving college students simple whole number addition problems to solve in untimed, low stress conditions found no difference between low and high anxious learners, but giving the same problems under time pressure showed worsened performance in the high anxious group (Faust, Ashcraft, & Fleck, 1996).No anxiety effects were found on performance of whole number arithmetic problems solved on paper (though mentally there were effects), but fractions, percentages, factoring, and equations with unknowns all showed performance deficits in the high-anxious group (Ashcraft, 2002). All these skills arise around 4th grade.
15Why do we care?STEM careers: fastest growing jobs, & 78% of growth over the last decade was in computer and math fieldsAccountability (Ashcraft & Moore, 2009): after anxiety onset in 4-5th grade, standardized tests are no longer an accurate measure of math abilityRemediation of math anxiety is associated with over a twenty percentile point gain on standardized tests (Ma, 1999)People with math anxiety do poorly in math, take fewer math courses, do not enter math careers. Each additional year of math study has been shown to correspond to a $2K salary raise.Since up to 6th graders can’t differentiate between math anxiety and test anxiety, testing below 6th grade just contributes to the problem
16What can we do about it? Pre-K – Grade 3 An ounce of prevention…Preservice teacher training to reduce math anxiety in teachersHarness positive emotion toward math learning through storytelling and gamesFemale math teachers who model math anxious behaviors results in lower math achievement of girls (Beilock et al. 2010), so need for teacher interventions to help alleviate anxiety among elementary school teachers.Right now locus of “blame” is on the student. However, studies show that 72% of the negative math experiences that arise in early-middle primary school are attributable to the teacher, rather than math content, family attitudes, or peers (Uusimaki & Nason, 2004).Teacher behaviors that contribute: cold manner, too much emphasis on memorization, or calling students up to the board to perform in front of the class.Using alternative methodology and innovative practices (discovery math, teaching for understanding) can prevent math anxiety from forming in the classroom but is ineffective at remediating anxiety
17What can we do about it? Grades 4 – 8 The Mathematics Anxiety Scale for Children (MASC; Chiu & Henry, 1990)Begin each year with a traditional transmission style classroom before beginning more unfamiliar techniquesGroup interventions are not effectiveTeachers as counselors (Furner & Duffy, 2002)Use math mentors – older students, tutorsIronically, if you inherit a class that is math-anxious, the best thing to do is a transmission style classroom as you build confidence and trust, then you can switch to more alternative methodologies (small group work, discovery math). In a traditional classroom the teacher is at the front of the classroom transmitting information to relatively passive learners. This method is not ideal for engendering a high level of math understanding, but it lessens discomfort for students who suffer from lack of confidence, as a strong positive teacher presence, an emphasis on cognitively simple rules, and a clear class structure can help students feel safeClassroom interventions, whether pedagogical (innovative curricula, such as discovery math) or psychological (relaxation training, such as positive visualizations), were not effective at reducing math anxiety. Group counseling was not effective, and Furner & Duffy (2002) suggest that teachers act as counselors to individual students to help them overcome math anxiety.Systematic desensitization combined with anxiety management training
18What can we do about it? Grades 9 – 12 The shortened Math Anxiety Rating Scale (sMARS; Alexander & Martray, 1989)Systematic desensitization combined with cognitive restructuringRephrasing negative internal dialogueSupport with post-exam appraisalsConvert feelings of anxiety from threat to challengeTraditional talk therapyEffective interventions were one-on-one, and the most effective strategy was systematic desensitization, especially when combined with cognitive restructuring (Hembree, 1990), a technique of cognitive behavioral therapy aimed to help students rephrase negative internal dialogues or pessimistic post-exam appraisals (Ma, 1999).Since math anxiety is usually correlated with lower achievement levels, the temptation is to remediate content in all cases. However, even with no math content remediation, anxiety reduction alone can return student scores into the normal range (Hembree, 1990)
19Teaching Techniques Model a positive attitude towards math Emphasize that everyone makes mistakes, which are just opportunities for learningUse varying types of assessment, and do not assess too oftenUse methods that are fun and engage positive emotion, like storytelling and gamesAcknowledge that this is biased towards middle school math, since that is what I teach.
20Teaching Techniques Provide clear goals and feedback Offer choices between tasks whenever appropriateScaffold challenge carefully to improve student confidenceWhen using social interaction to teach, ensure that it is cooperative, not competitive
21Resources for using storytelling in the classroom Schiro, M. (2004). Oral Storytelling & Teaching Mathematics. Thousand Oaks, CA: Sage Publications.Zazkis, R. & Liljedahl, P. (2009). Teaching Mathematics as Storytelling. Rotterdam: Sense Publishers.
22Resources for using games to teach math Grades 1-3: Kaye, P. (1987). Games for Math. New York: Pantheon Booksiplaymathgames.comAudience probably has far more resources than I do for the varying grade levels – I would LOVE to hear about the best ones – please go online to mathaffect.com and let me know, either through blog commentary or direct contact.
23Math Anxiety Resources Post, C. (2010). Too Afraid to Learn: The role of math anxiety in learning and what you can do about it. Available online soon at mathaffect.comTobias, S. (1993). Overcoming Math Anxiety. New York: Norton & Company.Zazlavsky, C. (1999). Fear of Math: How to Get Over It and Get On with Your Life. New Brunswick: Rutgers University Press.
24ReferencesAlexander, L., & Martray, C. (1989). The development of an abbreviated version of the mathematics anxiety rating scale. Measurement and Evaluation in Counseling and Development, 22,Ashcraft, M. (2002). Math Anxiety: Personal, Educational, and Cognitive Consequences. Current Directions in Psychological Science, 11(5),Ashcraft, M., & Moore, A. (2009). Mathematics anxiety and the affective drop in performance. Journal of Psychoeducational Assessment, 27(3),Beilock, S., Gunderson, E., Ramirez, G., & Levine, S. (2010). Female teachers’ math anxiety affects girls’ math achievement. Proceedings of the National Academy of Sciences, 107(5),Chiu, L., & Henry, L. (1990). Development and validation of the mathematics anxiety scale for children. Measurement and Evaluation in Counseling and Development, 23(3), 121.Hembree, R. (1990). The Nature, Effects, and Relief of Mathematics Anxiety. Journal for Research in Mathematics Education, 21(1),Immordino-Yang, M. H., & Damasio, A. (2007). We feel, therefore we learn: The relevance of affective and social neuroscience to education. Mind, Brain, and Education, 1(1), 3-10.Ma, X. (1999). A meta-analysis of the relationship between anxiety toward mathematics and achievement in mathematics. Journal for Research in Mathematics Education, 30(5),
25The role of math anxiety in cognition, and what you can do about it Too Afraid to LearnThe role of math anxiety in cognition, and what you can do about itCristina Post, Ed.M.MathAffectAs math teachers, we are perennially aware of the problems that math anxiety causes in the classroom. Recent research in affective neuroscience reveals the large role that emotion plays in learning, and as a result we better understand how math anxiety interferes with cognition. Understanding the problem gives us strategies to combat it, and alleviating math anxiety is associated with an achievement gain of over twenty percentile points. This presentation will cover the causes, ages of onset, and prevalence of math anxiety, a review of the research surrounding its effects on cognition, how to assess the level of math anxiety in your classroom, and alleviation strategies broken down by grade level. Special attention will also be paid to the distinction between math anxiety and stereotype threat, which influences how girls (and other stereotyped groups) perform in math class.