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"BY: Yassmina T.G. & Tina A.

Brain Areas Involved in Mathematics

  Different brain areas are specialized in carrying out various mathematical tasks.

  Thus, the aim should not be to focus on just one particular area of the brain.

Study of Brain-Damaged Patients

  Researchers found that:

  certain patients confused components of numbers (ex. reading 9 as 5), whereas others confused the decimal quantity of a number (ex. reading 46 as 460).

  Damage to the left vs. right visual cortex

  What does all this information suggest?

Split-Brain Patients

  The two hemispheres of the brain are connected to one another through a mass of fibers called the corpus callosum.

  Patients whose right and left hemispheres are no longer connected are of special interest to researchers. This is the case for individuals who suffered from intractable epilepsy, where back in the day, their corpus callosum was surgically removed to reduce epileptic seizures.

  Although these patients no longer suffered from seizures, it resulted in the loss of communication between the left and right hemispheres of the brain.

  In order to investigate the two hemispheres working in isolation, scientists conducted experiments where an object was presented to one side of the body.

YouTube video: http://www.youtube.com/watch?v=ZMLzP1VCANo

  Comparison between quantities does not rely on language; therefore it can be processed by both hemispheres as long as the digits are presented to the same visual field. 

Quantity Comparisons

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Guestimates Brain Imaging Studies and Mathematics

  Parietal lobe is activated while engaging in mathematical tasks.

  Lower parietal lobe in the right hemisphere is activated when participants compare numbers as well as adding and subtracting.

  Positive correlation between mathematical ability and spatial ability.

  Exact calculations occur predominantly in the left hemisphere, whereas comparisons activate both hemispheres with a slight preference to the right.

Gender Differences

  Study by: Doreen Kimura and colleagues

  Looked at spatial abilities in women during hormonal cycle.

  Found that: women’s spatial ability was inversely related to the level of estrogen (female sex hormone).

  More recent study found that testosterone (male sex hormone), improves spatial memory and increases hippocampus size in males and females.

  In sum: gender differences are at least partially socially induced and there is little agreement as to what these differences really mean.

  Video by Brian Butterworth

  Cited in this chapter because he has been studying dyscalculia for many years.

  Found that Dyscalculia can runs in families.

  Numeracy fails despite excellent teaching and rich environmental input.

  Often causes frustration and anxiety in children.

Developmental Dyscalculia Can Arise From

  Lack of innate number sense.

  Brain damage or genetic disorganization of underlying neural circuitry.

  Parietal lobe lesions caused by strokes can lead to dyscalculia and therefore lack an intuition of quantity.

  Connections between quantity and exact number concepts may fail to develop properly.

Teaching Dyscalculic Children

  Based on psychological and neuroscience studies of number based processing.

  Remedial teaching – teaching with a lot of patience and slow repetition of the core elements that are normally taken for granted.

  Make the implicit explicit.

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Siegler and Ramani (2008) Playing linear numerical board games promotes low-income children’s

numerical development

  Two Hypothesis:

1.  Low-income preschoolers’ poor mathematical performance has to do with less frequent use of numerical magnitude.

2.  Playing numerical board games can bring about greater use of appropriate representations and improve low-income children’s numerical competence.

Experiment # 1

  Examining the initial numerical estimates of low and middle-income preschoolers.

  Children met individually with an experimenter who asked them to mark the location of a number on a line that started with 0 and ended with 10.

  Results indicated that middle-income preschoolers correctly ordered more (81%) of their estimates than low-income preschoolers (61%). This reflects low-income preschoolers’ poor understanding of numerical magnitude.

Experiment # 2

  Examining the effects of playing numerical board games on low-income preschoolers’ representations of numerical magnitude.

  Low-income preschoolers were randomly assigned to either play a board game where each space included a number or a color. Children met individually with an experimenter for four 15-minute sessions for 2 weeks.

  Results show that children who played the numerical board game ordered correctly the magnitude of more numbers on the posttest than pre test (81% vs. 62%). Children in the color version showed no pretest-posttest change.

Significance of the Study

  Playing numerical board games offers an inexpensive means for reducing the gap in numerical knowledge that separates less and more affluent children when they begin school.

Boyle et al. (2005) Mathematically gifted male adolescents activate a unique brain network during

mental rotation

  3D mental rotation tasks involve the use of two cognitive processes: the creation and manipulation of mental images. The later capacities are thought to be very useful when applied to high-level mathematical thinking and reasoning.

  Neuroimaging studies have demonstrated mental rotation to be mediated primarily by the parietal lobes, particularly on the right side.

  6 mathematically gifted adolescents and 6 average ability adolescents were presented with mental rotation tasks and matching tasks.

Results

  The two groups of participants did not differ in mental rotation accuracy and their mean processing times were similar.

  During the mental rotation tasks, average math ability adolescents’ brains showed activation in the right superior parietal lobe, the left inferior parietal lobe, and bilateral activation in the premotor cortex.

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Results Continued…

  Mathematically gifted participants had more brain regions activated, when there was overlap in brain areas used by average math ability participants, these regions were activated bilaterally.

  Greater activation in right anterior cingulate, left superior temporal gyrus, and the left premotor cortex. The greater cortical activation is suggestive of heightened processing power and better imagery capacities.

Significance of the Study

  In the mathematically gifted, their bilateral engagement of the parietal lobes is complemented by selective activation of the anterior cingulate and frontal cortex on both sides of the brain. The enhanced involvement of these regions, taken in conjunction with extensive engagement of the parietal lobes, may be related to the emergence of their mathematical giftedness.

  Activation of these anterior areas, particularly the cingulate, is virtually absent in those of average math ability. This may be interpreted as reflecting a relatively more immature state of brain specialization, one that is potentially less developed in terms of executive processing capabilities.

Halberda and Feigenson (2008) Developmental Change in the Acuity of the

“Number Sense”

  Ability to nonverbally represent number is shared across species and across development.

  The foundational Approximate Number System (ANS) that underlies this ability produces abstract number representations (Barth, Kanwisher, & Spelke, 2003) that support arithmetic computation across the life span.

  No research to date has explored the full developmental trajectory of its representational acuity.

  ANS acuity in 3-, 4-, 5-, and 6-year-old children and in adults was tested using psychophysical modeling to determine the finest numerical discriminations possible at each age.

Methods/Procedures

  Participants:

  Five age groups with 16 participants per group: 3-, 4-, 5-, and 6-year-olds and adults.

  On each trial of the numerical discrimination task:

  two arrays of between 1 and 14 items appeared side-by-side on a large video screen.

  Items varied in size, and were randomly chosen from 46 possible images of familiar objects.

  Each array appeared within a background frame “Big Bird’s Xs” on the left side of the screen and “Grover’s Xs” on the right.

Results

  Significant age group effect, with participants performing better with increasing age, and a marginally significant effect of sex, with girls and women performing slightly better than boys and men overall.

  Significant trial type effect was observed. Planned t tests revealed that all age groups performed significantly above chance on both trial types, but performance was slightly better on area correlated trials.

Significance of the Study

  Although children between 3 and 6 years old have already begun formal instruction in mathematics, the present results show that the acuity of the ANS is still developing during this time.

  Sharpening of the ANS does not appear to be complete until early adolescence.

  This protracted period of development highlights the importance of coming to understand the effects of changes in ANS acuity on math learning and achievement.

  Implications both for math education and for our understanding of the interplay between individual experience and the “number sense.”

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Significance of the Study

  What causes the ANS to increase in acuity?

  Some of the sharpening of this system may be due to simple maturation of the neural circuitry subserving the ANS.

  However, recent evidence suggests that experience can also affect its development.

  Practice at numerical discrimination appears to increase acuity in children with math learning disabilities (Wilson, Revkin, Cohen, Cohen, & Dehaene, 2006).

A case study of computer gaming for math: Engaged Learning from Gameplay?

  Question: Does mathematical video game playing improve students’ math learning outcomes?

  The study took place at a math camp for 4th and 5th graders, which was held three times a week, where children played eight ASTRA EAGLE (series of web-based games) math games over 10 2-h sessions. Each session participants were assigned to a different math game. The games specifically targeted 4th and 5th graders, and focused on skills such as comparing whole numbers, and mapping X and Y coordinates.

(Ke, 2008)

Game Examples

  Cashier: students played as a cashier that needs to do math calculation of money.

  Treasure Hunt: students needed to perform the task of locating X and Y coordinates on a map in order to dig for treasure.

  Up, Up, and Away: game players had to answer a list of math questions before they could continue with the game play – traveling by balloon.

  Immediate feedbacks were provided upon students’ actions, but these feedbacks only involved marking the answer correct/incorrect. Each game had score keeping and employed progressive difficulty levels.

Procedures

  Game Skills Arithmetic Test (GSAT): measured cognitive math skills that the computer games were designed to reinforce. The test comprised 30 multiple-choice questions.

  Five-point Likert-scaled inventory: a 40-item survey, investigating students’ feelings toward mathematics

  Metacognitive skill was measured by the Junior Metacognitive Awareness Inventory (Jr. MAI) Version A: A 12-item self-report questionnaire about the way students learn.

  All participants did all three tests as a pretest. They then played eight ASTRA EAGLE math games during 10 two-hour sessions for five weeks. After five-week gaming treatment, all participants retook the three tests in the posttest.

  Direct observation of the participants was conducted during every game-playing session. Concurrently, participants were asked to do think-aloud that helps to reveal their emotional situations and cognitive processes when interacting with game features, and strategies to handle math problems in the games. The computer game program recorded participants’ on-task time (the time when they logged-in the games), the numbers of math questions they had tried to solve, the questions they had solved correctly, and the gaming scores they earned.

Results

  The results indicated that students developed more positive attitudes toward math learning through five-week computer math gaming, but there was no significant effect of computer gaming on students’ cognitive and math test performance.

Other Research

  Mario Math with Millennials: The Impact of Playing the Nintendo DS on Student Achievement (Gelman, 2010)

  This quantitative study examined the impact of Brain Age 2 for the Nintendo DS on seventh grade achievement in math and on student attitude towards school. A sample of eighty seventh graders from the same school played the Nintendo DS daily for fifteen minutes over nine weeks. No significant difference was found in math achievement after using the game. Students who played the Nintendo DS daily reported a more positive attitude towards math, their teachers, classes, and school than those that did not play the Nintendo DS.

  Mathematics and S.cience Achievement: Effects of Motivation, Interest, and Academic Engagement (Singh, Granville, Dika, 2002)

  Purpose: To examine the effects of 2 motivational factors; attitude, and academic engagement in 8th grade students’ achievements in math and science. Results supported the positive effects of attitude and academic engagement on math and science achievement.

  Therefore, playing mathematical games leads to a more positive attitude towards math, and a positive attitude towards math leads to better math achievement. As a result, we can say that mathematical computer games indirectly lead to better mathematical achievement.

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Young, Wu, & Menon (2012) The Neurodevelopmental Basis of Math Anxiety

  Math anxiety is a negative emotional response that is characterized by avoidance as well as feelings of stress and anxiety in situations involving mathematical reasoning.

  This study is the first to identify the neural basis of math anxiety in young children and demonstrate its impact on brain functioning and connectivity at one of the earliest stages of formal acquisition of math skills.

Participants

  Sample (n = 46) consisted of 28 boys and 18 girls in the second and third grades.

  All but 4 children were right-handed.

  None of the participants had a history of psychiatric illness, neurological disorders, or learning disabilities.

  Used the Mathematics Anxiety Rating Scale (MARS), to create the Scale for Early Mathematics Anxiety (SEMA).

Method

  Obtained data while children determined whether addition and subtraction problems were correct (e.g., “2 + 5 = 7”) or incorrect (e.g., “2 + 4 = 7”).

 

Neuropsychological Assessment

  Wechsler Abbreviated Scale of Intelligence used to measure IQ.

  Wechsler Individual Achievement Test used to assess performance.

  Working Memory Test Battery for Children used to determine working memory capacity.

  Parents of study participants also completed the Child Behavior Checklist for Ages 6–18, and trait anxiety was determined using the DSM-Oriented Anxiety Problems subscale of the CBCL.

Functional Brain Imaging

  Each child completed two runs in the fMRI scanner: the addition run and the subtraction run.

  Two task conditions: (a) complex arithmetic problems, and (b) simple arithmetic problems.

  Both conditions, full equations were given, child indicated via a button box whether the answer shown was correct or incorrect.

Results: Math anxiety and behavior

  HMA group greater activation in the right amygdala extending posteriorly into the anterior hippocampus.

  HMA group less activation in multiple cortical and subcortical areas, including the intraparietal sulcus and superior parietal lobule, the right dorsolateral prefrontal cortex and adjoining premotor cortex, and the bilateral caudate and putamen nuclei of the basal ganglia.

  HMA group greater deactivation of the ventromedial prefrontal cortex regions than did the LMA group.

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What does this mean

  HMA and LMA groups did not differ on measures of trait anxiety, suggests that the observed behavioral and brain differences arose from math anxiety rather than from general anxiety.

  Children as young as 7-9 years of age, math anxiety is associated with hyperactivity and abnormal effective connectivity of the amygdala.

  Demonstrate that math anxiety in 7- to 9-year-old children is associated with significant differences in activation of brain areas that mediate affective and cognitive information processing.

Significance of the Study

  Findings suggest that math anxiety is associated with aberrant activity in the right amygdala.

  Identified the basolateral nucleus as the most prominent site of hyperactive amygdala response. Plays an important role in learned fear, as demonstrated by classical conditioning studies in healthy adults (Delgado, Nearing, & LeDoux, 2004).

  These findings not only emphasize parallels between math anxiety and other anxiety disorders but also validate math anxiety as a genuine type of stimulus and situation-specific anxiety.

Significance of the Study

  Math anxiety is associated with reduced cognitive information-processing resources during arithmetic task performance in the developing brain.

  One mechanism by which anxiety is thought to influence performance is through reduced capacity for working memory, attention, and cognitive-control processes engaged during math problem solving (Beilock & Decaro, 2007).

  These identifications can, in turn, be used to design remediation strategies based on treatments that work on other phobias.

Discussion Questions

  Why is it important to assess math anxiety at a young age?

  How can math anxiety at a young age have implications on an individual’s long-term academic and professional success?

  How can we integrate mathematical computer games in the school and preschool system in order to help children grow a more positive attitude towards math?