I’m re-releasing my course on How To Learn Math. Please visit this link for more details.
My article in The Atlantic:
We need to change the way we teach math in the U.S., and it is for this reason that I support the move to Common Core mathematics. The new curriculum standards that are currently being rolled out in 45 states do not incorporate all the changes that this country needs, by any means, but they are a necessary step in the right direction.
My article in Education Week:
Mathematics education is in crisis: A third of all schoolchildren end up in remedial math courses, and the level of interest in the subject is at an all-time low. This is a result, in part, of schools in the United States heading down a fast-moving track in which the purpose of math has been reduced to the ranking of children and their schools. Math has become a performance subject. Children of all ages are more likely to tell you that the reason for learning math is to show whether they “get it” instead of whether they appreciate the beauty of the subject or the way it piques their interest. The damage starts early in this country, with school districts requiring young children to take timed math tests from the age of 5. This is despite research that has shown that timed tests are the direct cause of the early onset of math anxiety.
Timed math tests have been popular in the United States for years. Unfortunately, some of the wording in the Common Core State Standards may point to an increased use of timed tests. From the 2nd grade on, the common standards give math “fluency” as a goal. Many test writers, teachers, and administrators erroneously equate fluency with timed testing.
It is critical that we take a moment to review the emerging evidence on the impact of timed testing and the ways in which it transforms children’s brains, leading to an inevitable path of math anxiety and low math achievement.
The personal and educational consequences of math anxiety are great. Math anxiety affects about 50 percent of the U.S. population and more women than men. Researchers know that math anxiety starts early. They have documented it in students as young as 5, and that early anxiety snowballs, leading to math difficulties and avoidance that only get worse as children get older. Researchers also know that it is not related to overall intelligence.
Until recently, we have not known the causes of math anxiety and how it affects the brain, but the introduction of brain-imaging research has given us new and important evidence. Sian Beilock, an associate professor of psychology at the University of Chicago, for example, has found that when children are put under math stress, they are unable to execute math problems successfully. The stress impedes their working memory—the area of the brain where we hold math facts. Beilock found that stressful math situations cause worries that compete for the working memory, causing it to be blocked. She also found that math anxiety has an impact on those with high, rather than low amounts of working memory—the very students who have the potential to take mathematics to higher levels.
In Beilock’s recent research conducted with children in 1st and 2nd grade, she found that levels of math anxiety did not correlate with grade level, reading level, or parental income. For the most capable students, the research confirms, stress impedes the functioning of their working memory and reduces achievement. Research conducted at Stanford revealed that math anxiety changes the structure and workings of the brain.
When I moved to the United States from Europe a few years ago, I was shocked to learn that many school districts give children, as early as 1st grade, 50 math problems to solve in three minutes. For many students, it is not an exaggeration to describe this experience as torturous. When teachers of 2nd and 4th graders in one elementary school I visited asked students to write down how the test made them feel, responses showed that the test prompted anxiety in one-quarter of the students in each class, but that anxiety was not correlated with test success. Indeed, some of the students with the highest levels of success were those who indicated the greatest anxiety and made comments such as “I feel nervous. I know my facts, but this just scares me.”
It should not come as a surprise that the highest achievers displayed the greatest anxiety; in fact, neuroscience tells us that these students experience the greatest degree of cognitive dysfunction. But this anxiety does not only affect high-achieving students. Second graders from across the achievement spectrum described the tests as making them feel “upset” and “unhappy” and that they are “terrible at math.”
Timed tests have been given to young children in school districts in the United States with the best intentions, but with negative consequences for many years. The brain research that has emerged recently could be the impetus for shifting the momentum. But the inclusion of the word “fluency” in the common standards may mean that educators will continue to use these tests, and that they will even be included as part of the new common-core assessments.
There are many good teaching strategies for encouraging fluency in math, but the ones that are effective are those that simultaneously develop number sense—the flexible use and understanding of numbers and quantities—without instilling fear and anxiety. Strategies that involve reasoning about numbers and operations, such as the pedagogical approach called “number talks,” are ideal for developing fluency with understanding.
Beyond the fear and anxiety, timed tests also convey strong and negative messages about math, suggesting that math ability is measured by working quickly, rather than thinking deeply and carefully—the hallmark of high-level mathematical thinking. The ideas students develop about math in elementary school are critical for their future in the subject.
Policies in education rarely draw from research knowledge. But I would argue that this particular policy—of giving young children timed math tests—is one of the clearest ways schools damage children, and we now have evidence of the extent of the damage.
The United States faces a serious problem with widespread underachievement in mathematics, and insufficient numbers of students available to continue mathematical, scientific, and technological innovations. Educators and policymakers share an important goal: to create math classrooms where students are excited to learn the subject, rather than being stressed and worried about their performance under pressure. There is no disagreement about the goal, but policies that require the testing of young children under timed conditions may be inadvertently achieving the opposite. Assessments for the common core could break or perpetuate this cycle of damage. Let’s hope they do the former.
I have a guest post on the Washington Post’s blog, co-written with Vicki Abeles, describing the effects of standardized testing on our students:
And the pressure is harsh, indeed. At a high school in the Bay area, the principal announces whether his school has performed better or worse than neighboring schools over the PA system. And the statewide test scores appear on students’ transcripts — an inclusion that’s prompted some teachers to remark to students that the scores will “follow you for the rest of your life.” Such public anxiety is found across grade levels. At a screening of the film, “Race to Nowhere,” held at the California Teachers Association, several educators volunteered that the state of California has developed an official protocol for what to do when a young child vomits on a standardized test. Enough said, no?
The personal and educational consequences of math anxiety are great, including fear and worry about math, low achievement and math avoidance. Math anxiety impacts a large proportion of the US population and the consequences of this stress-induced state of mind are well documented in the literature (see, for example Hembree, 1990). One of the most important consequences of math anxiety is math avoidance with math anxious individuals ceasing math study as soon as they are able, thus diminishing their future career and life choices. This declining interest in higher-level math courses in the US – the number of math majors in four year colleges has dropped by 19% in the last ten years – also has consequences beyond individual’s lives, as it threatens the future of the economy, and of scientific and technological developments in the US (Boaler, 2008).
Math anxiety has been well documented in middle and high school children, and is known to lead to lower math achievement, avoidance of math, and worry and stress about math failure (Richardson and Woolfolk, 1980). In the last two years researchers have extended their work to young children and not surprisingly have found that very young children show the same dangerous and damaging symptoms of math anxiety as older children and adults (Ramirez, Gunderson, Levine, & Beilock, in press; Young, Wu & Menon, 2012). Importantly, recent studies have also shown that timed tests exacerbate the effects of math anxiety and that students experience stress when taking timed tests that is absent when they work on the same mathematics in untimed situations (Ashcraft, 2002).
Until recently the causes of math anxiety and the ways it impacts the brain have not been precisely known. Fortunately we are now entering a new age in which brain imaging is providing critical evidence that tells us how math anxiety works. We now have an understanding of the relationship between math anxiety and the functioning of the brain, which tells us something important about the conditions that create math anxiety and about how math anxiety works to undermine math performance. In this short paper I will summarize some of the research that has emerged from neuroscience over recent years as well as classroom data on the ways students in 2nd and 4th grade experienced timed math tests in a US school district.
Findings from Neuroscience
Researchers know that math anxiety is not related to overall intelligence. Individuals who show math anxious behavior, such as increased heart rate when faced with math problems, show no reaction when faced with complex problems in other domains (Faust, 1992; Aschcraft, 2002). Researchers have also shown that math anxiety starts early – it is documented in children as young as five – and that early anxiety snowballs, leading to math difficulties and avoidance that accentuates as children get older.
Neuroscientists study the ways math anxiety affects individuals by conducting brain scans and Sian Beilock has led the field in recent years with careful studies to show the ways math anxiety works when individuals are put under stress (see, for example, Beilock, 2011). She and her colleagues have found that when children are put under math stress, they are unable to successfully execute math problems because the stress impedes their working memory.
Working memory is involved in the control, regulation, and maintenance of information. When children need to compute math facts such as 17 + 8, they hold the different steps in their working memory. The more working memory an individual holds the better their capacity for academic work (Engle, 2002). Beilock and her colleagues have found that stressful math situations cause worries that compete for the working memory. Importantly, they have also found that math anxiety impacts those with high rather than low amounts of working memory – exactly those students who have the potential to take mathematics to high levels.
In an important recent study that is yet to be released Beilock and colleagues extended their work to 1st and 2nd grade children (Ramirez, Gunderson, Levine, & Beilock, in press). They worked with 150 young children and measured the children’s levels of math anxiety. They found that children as young as first grade reported math anxiety and that levels of math anxiety did not correlate with grade level, reading level, or parental income. Importantly, they again found that math anxiety did not impact the achievement of all students, but only those with higher levels of working memory. For the most capable students, stress impeded the functioning of their working memory and reduced their achievement.
In a Stanford study released this week (3/20/12) Vinod Menon also worked with young children showing the impact of math anxiety on the brain. He and his colleagues analyzed brain imaging data from forty-six 7-9 year old children which they obtained while children worked on addition and subtraction problems. A series of scans showed that those students who ‘felt panicky’ about math had increased activity in brain regions associated with fear. And when those fear areas were activated there was decreased activity in parts of the brain involved in problem solving (Young, Wu & Menon, 2012).
Math anxiety is an important and widespread phenomenon, it impacts the performance of the working memory (one of the building blocks of I.Q.), and it interferes with the brain’s ability to process information needed to succeed in school. It is critical that we understand better and act upon the causes of math anxiety in young children, and if we find causes of math anxiety in schools, that we work to eliminate them.
The Causes of Math Anxiety
There are many known causes of math anxiety, including the presence of math anxious elementary school teachers, an effect that is known to particularly impact girls (Beilock, Gunderson, Ramirez & Levine, 2009), and the use of classroom strategies that exert pressure upon students (see also Aschcraft, 2002; Seeley, 2009). One of the clearest and most significant causes of the early onset of anxiety is the use of timed math tests. Ashcraft (2002) for example, found that timed tests revealed math anxiety, whereas untimed versions of the same math problems did not. Thus it was not the work on math problems that induced anxiety but working on math problems in timed conditions.
It could be argued that at some ages students need to work on math problems under timed conditions, a practice that could reasonably be developed during the secondary school years. But in a school district which we recently visited, and many other school districts across the US, children as young as first grade are required to complete 50 math fact questions in 3 minutes.
The district in question requires the tests to be given once a term, although researchers found that some teachers chose to prepare students for the district test by administering the tests on a weekly basis. The teachers explained that they needed to prepare their students because the first time they gave out the test some of the students cried.
In a study of the impact of the tests we asked the teachers of 2nd and 4th graders in one of the elementary schools in the district to administer a survey to students after taking one of the timed tests (n=42). The survey asked the students how the test made them feel. This was a small study that should be repeated with more students, but the responses showed that the test prompted anxiety in approximately one-quarter of the students in each class, and that anxiety was not correlated with test success. Indeed some of the students with the highest levels of success were those who indicated the most severe anxiety, with comments such as “I feel nervous, I know my facts but is just scares me”. And “Nervous. I know my facts well, it just scares me that I might get a bad score”. It should not be surprising that the highest achievers were displaying the most anxiety – neuroscience tells us that it is these students who experience the greatest amounts of cognitive dysfunction, and it is these students who are probably aware that they are not able to perform as well as they could. But anxiety affects students from across the achievement spectrum. The second graders described the tests as making them feel “upset” “unhappy” and that “they are terribul at math” (original spelling retained). The quarter of the students in each class who expressed anxiety is probably a minimal estimate of those who actually experience anxiety as many students are unable to express such complex emotions at this age.
Some students are unaffected by timed tests, but for a significant number of high and low achievers the timed tests induced fear and stress – these are not emotions that we want students to associate with math. In addition to the powerful, negative emotions caused by the tests, the tests give students a very strong message about math – that it is a performance subject, the main purpose of which is to order and categorize students, rather than an interesting and accessible subject that could empower them to solve problems in their lives (see also Boaler, 2008). The ideas students develop about math in elementary school are critical for their future in the subject, we know that the attitudes that students adopt about various subjects early on are often maintained throughout schooling.
Timed tests are given to young children in school districts with the best intentions – generally because policy makers want students to develop automaticity with math facts. Automaticity is helpful and it is developed through practice of math facts but not practice under stress, indeed it is the timed aspect of the tests that causes harm to young children. Importantly, there are many good strategies for encouraging automaticity that also develop ‘number sense’ – the flexible use and understanding of numbers and quantities. Number sense is so critical to young children that it is known to distinguish high achievers from low achievers in mathematics (Gray & Tall, 1994; Boaler, 2008). Strategies that enable students to practice facts and to understand quantity and number, without stress, develop strong and important foundations for all students and they should replace timed tests, as a matter of urgency (see also Seeley, 2009).
The US faces an education crisis with widespread mathematics underachievement and insufficient numbers of students available to continue the mathematical, scientific and technological innovations, that the future requires. Educators and policy makers share an important goal – to create math classrooms where students are excited to learn math, rather than stressed and worried about their performance under pressure. There is no disagreement about the goal, but policies that require the testing of young children under timed conditions may be inadvertently achieving the opposite of this goal and need urgently to be reconsidered in the light of new scientific evidence that is now available to us.
Ashcraft, M. (2002). Math Anxiety: Personal, Educational and Cognitive Consequences. Current Directions in Psychological Science. 11, 5, 181-185.
Beilock, S. (2011). Choke: What The Secrets of the Brain Reveal about Getting it Right When You Have To. Simon & Schuster, Free Press: New York.
Beilock, S., Gunderson E., Ramirez, G., & Levine, S. (2009). Female Teachers’ Math Anxiety Affects Girls Math Achievement. Proceedings of the National Academy of Sciences February 2, 2010, Vol 107, 5, 1860-1863.
Boaler, J (2008). What’s Math Got To Do With It? Helping Children Learn to Love Their Least Favorite Subject – and Why It’s Important for America. Penguin: New York.
Engle, R. W. (2002). Working Memory Capacity as Executive Attention. Current Directions in Psychological Science, 11, 19-23.
Faust, M.W. (1992). Analysis of Physiological Reactivity in Mathematics Anxiety. Unpublished doctoral dissertation. Bowling Green State University, Bowling Green, Ohio.
Gray, E. and D. Tall. (1994). Duality, Ambiguity, and Flexibility: A “Proceptual” View of Simple Arithmetic. Journal for Research in Mathematics Education, 1994. 25 (2), 116-140.
Hembree, R. (1990). The Nature, Effects, and Relief of Mathematics Anxiety. Journal for Research in Mathematics Education, 21, 33-46.
Ramirez, G., Gunderson, E. A., Levine, S. C., & Beilock, S. L. (in press). Math anxiety, working Memory and Math Achievement in Early Elementary School. Journal of Cognition and Development.
Richardson, F. C, & Woolfolk, R.L. (1980). Mathematics Anxiety. In I.G. Sarason (Ed), Test anxiety: Theory, research and application (pp 271-288). Hillsdale NJ: Erlbaum.
Seeley, Cathy (2009). Faster isn’t Smarter (2009). Sausalito, CA:Math Solutions Publications
Young, C.B., Wu, S.S. & Menon, V. (2012). The Neurodevelopmental Basis of Math Anxiety. Psychological Science Online First. March 20, 2012. doi:10.1177/0956797611429134