1. Fixed or Fluid:
Understanding our Mindsets and
Learning Abilities
Norwalk Community College
Norwalk, Connecticut
Elizabeth Raver
Eraver@norwalk.edu
2. What We Will Cover
• How neurons form memories
• Working memory
• Stereotype threat
• The “math gene” myth
• Study habits
• Sleep and food
3. Basic Structure of the Neuron
• The human brain contains about 100 billion nerve
cells (neurons).
Dendrites
Axon
Dendrite
Neurons Connections
4. Synapse
–Each neuron
makes from one
thousand to ten
thousand
contacts with
other neurons.
–These
connections are
called synapses
5. –Synapses are always in a state of “on or
off”: excitatory or inhibitory.
–The number of permutations of the
number of brain states ...
• EXCEEDS THE NUMBER OF ELEMENTARY
PARTICLES IN THE KNOWN UNIVERSE.
6. When you First Learn Something New :
• Neuronal connections are very fragile.
• If you review what you just learned, the
connection strengthens.
• With each subsequent review/practice session
connections become stronger, faster and more
efficient.
7. Synaptic Firings
• The more you practice using the new
idea in your coursework:
– Increased synapses.
– Faster release of neurotransmitters.
– Faster and more efficient neuronal
communications.
• This can lead to
– Stronger memory
– Better understanding.
8. Long Term Potentiation
• Another name for long term memory.
• Involves how synaptic connections become
stronger as memory increases.
• http://www.youtube.com/watch?v=sTPa2rvq
DWs
9. Like a muscle, the more you use your
brain the stronger it will be.
• Practice makes perfect:
– Sports, Ballet, Music, Writing, Singing, Painting…
• What would happen if you played football
without practicing?
10. Working Memory
• Working Memory: To be able to mentally hold
information while doing something else:
– A type of short term memory.
– Our brains use working memory to problem
solve, including mathematics.
– Working memory can account for between
50% to 70% of people’s ability to think
abstractly, i.e., fluid intelligence.
– A large component of IQ.
11. • Working memory examples:
– Remembering a phone number while cooking.
– Remembering traffic directions.
– Picturing how to place a new sofa in the living
room.
– Remembering the grocery shopping list.
12. Working memory may be hindered by:
• Distractions: music, noise, television, text
messaging, competition from other visual
sources, worries, siblings, children, etc.
• Sleep deprivation.
• Poor eating habits.
• Too much stress.
13. Working Memory and Mathematics
• People who compute slowly run the risk of
losing track of their thoughts.
• Working memory is necessary when learning
new mathematical concepts.
– Practice, practice, and more practice.
14. • Most mathematics require a lot of working
memory.
• Strong proficiency in basic mathematics skills
frees working memory for reasoning and
higher-level problem solving.
• Basic mathematics skills: multiplication tables, rules for
dividing fractions, order of operations, etc.
15. Many cognitive abilities are correlated
with mathematical ability:
– Intuition
– Flexibility
– Memory
– Verbal and Reasoning Skills
– Persistence and Interest
16. Stereotype Threat
• When a social group attempts to perform a
task but its ability is undermined by negative
stereotypes.
• Used to explain academic underperformance
in minorities and women.
• Can be induced in all social groups including
white males.
17. • This is a video on stereotype threat in which
the researcher who uncovered this
phenomenon, Claude Steele, is interviewed.
• https://www.youtube.com/watch?v=tS2Bv8Yh
1oU
18. • The following slide is a synopsis of one of
many experiments regarding stereotype
threat.
• Pay special attention to time differences
between the two different conditions.
• Question: What do you think caused this
difference?
19. First Condition Second Condition
Subjects Were Told Males Did Subjects Were Told Genders
Better on Past Tests Did Equally Well on Past Tests
Males 817 seconds Males 697 seconds
Females 609 seconds Females 659 seconds
Males obtained higher scores Genders did equally well
20. • Here is another experiment on stereotype
threat.
• It provides a “hint” as to how students and
faculty can lessen or remove the effects of
stereotype threat.
• What do you think the hint is?
22. Priming Experiment With Vandenberg
3-D Rotational Test
Gender Private School North East
Emphasized Emphasize Residency
Emphasized
Female 13.8 (2.2) 16.7 (2.1) 15.3 (2.47)
Male 21.6 (2.6) 19.4 (2.38) 18.5 (2.03)
23. Studies on Stereotype Threat
• White males and Asian American males
• Stereotype Lift
• Arousal
• Working Memory
• Plus many, many more.
24. Decreasing Stereotype Threat
• Understand that difficulties in school occur to
everyone.
• Understand that intelligence is not rigid and
innate.
– It is flexible and like a muscle that when exercised
becomes stronger.
25. • Academic struggles are part of the learning
experience and are not unique to your social
group.
• Simply be aware of the phenomenon of
stereotype threat.
• Understand how the brain forms memories by
creating synaptic connections created through
practice.
• Develop a sense of humor.
26. • Reflect on values outside of school that
are important to you.
• First write down 3 values most important
to you, for example:
»Family relationships, friendships,
religion, spirituality, music, poetry,
reading, history, etc.
• Next, write a brief paragraph on why
these values are so important to you.
27. Math Gene Myth
• The idea that only some people are born with
the ability to learn math is a myth.
• Anyone can learn mathematics if they are
patient and persistent!
• Math is difficult for everyone.
• If you look closely at so called “math
geniuses”, most have been exposed to a lot
more math than the general population.
28. Research has Indicated:
• Students who believe that intelligence is
malleable will not give up trying to understand
a new concept even if they are struggling.
– This attitude results in higher grades.
– A self-fulfilling prophecy of success.
29. In Contrast:
• Students who believe intelligence is fixed tend
to give up quickly if they do not immediately
understand a new concept.
– This attitude results in lower grades.
– A self-fulfilling prophecy of non-success.
30. MYTH: People are Right or Left Brained
• Therefore, one’s ability to learn math depends
on whether one is a right or left brained
person.
• TRUTH: People are “whole-brained.”
31. Brain Functions Important for Mathematics
are Found in Both Hemispheres
Left Hemisphere Right Hemisphere
• Controls the right hand • Controls the Left hand
• Spoken language • Nonverbal
• Written language • Visual-spatial perception
• Mathematical Calculations • Music and artistic processing
• Emotional thought and
• Logical Thought Processes
recognition
• Analysis of Detail • Processing of the whole
• Reading • Pattern Recognition
• Facial Recognition
32. If People Were Right or Left Brained
Then the Following Could not be
Possible:
– Michelle M. who was born with only ½ a brain, the
right side.
– Because of neuroplasticity her right hemisphere
has both right and left brain functions.
33. Study Habits
• When introduced to a new math concept the
initial synaptic connection is weak:
– Most forgetting occurs within one hour of
learning something.
• Later that day take twenty minutes to review
your math notes.
– This will strengthen your synaptic connections.
34. • Your brain works on the unconscious level
during sleep to process new memories.
• Look over notes before falling asleep.
• If you are struggling with mathematical
concepts:
– Look over the math problem that you “don’t get”
before falling asleep.
– When you wake up the next morning, try the
math problem again.
35. Do Not Cram
• Do not cram mathematics at the last moment.
• Cramming will not give your brain enough
time to form strong synaptic connections.
• Pace yourself each day and take breaks.
– For some 30 minutes is their maximum, others 60
minutes.
36. • Each credit hour requires a minimum of 2
hours of homework each week.
• A 3 credit hour algebra course requires a
minimum of 6 hours of studying each week.
• Work with your brain, not against your brain.
37. Study in Groups
• Have you ever heard the following:
– Just buckle down and study.
– Use adversity to motivate you to study harder and
longer.
– Get out there and prove yourself.
• What if there is more to how this works?
• What if it is possible to “over study” to the
point of diminishing return?
38. • Philip Uri Treisman conducted an
anthropological study at the University of
Berkeley on mathematics students.
– He followed his students around campus, outside
of class, in the library, dorms, social life, etc.
– He looked at how, where and with whom they
studied.
39. Treisman Found:
• Asian students
– Studied in formal and informal groups, more often
than White and/or African American students.
– Made little distinction between their academic
and social lives.
– Saturday night at the library working on math
counted as a social event.
– Received the highest mean math grade.
40. • White students
– Studied more in groups than African Americans
but less in groups than Asians.
– Talked about math outside of class, compared
notes on difficult problems.
– Sought help from teaching assistants and other
students.
– However, had a greater tendency to separate their
social lives from academics.
• Not likely to be found studying math in the library
Saturday night.
41. • African American students
– Studied in greatest isolation.
– Intensely independent and private.
– Studied longer hours than Asians or Whites.
– Often had no one to talk to, no one to check their
answers with (except the back of the book.)
– Greatly separated their academic from their social
lives.
42. • Being so isolated, they could not see how
their classmates also were struggling with
mathematics.
• They believed that their difficulties reflected
their abilities, even though not true.
• This kept them from seeking help from faculty
or others.
43. Benefits of Group Studying
• You get to check your answers with your
classmates, not just the answer key.
• You see first hand how normal it is to struggle
when learning mathematics.
• If you are hung up on a problem, your
classmates can help you.
44. • This frees up your mind to concentrate on
new concepts.
• By helping others, those who know the
material well have an opportunity to obtain an
even deeper understanding.
• Those who do not know the material well,
have an opportunity to obtain immediate help
instead of waiting to see a tutor or instructor.
45. • You will become better at gauging your
mathematical proficiency.
• If you have to go to faculty for help you will go
with
– Greater confidence.
– Greater understanding of what you do not know.
– You will receive greater benefits from seeking
help.
• Higher grades!
46. Sleep and Food
• Most college students:
• Do not get enough sleep:
– How many of you slept at least 8 hours last night?
• Do not eat right:
– How many of you had breakfast this morning?
47. Sleep
• Minimum of between 7 and 8 hours each
night.
• Teenagers need more sleep than adults.
• During sleep the brain processes what you
learned in class.
• Without enough sleep it is more difficult to
learn new concepts.
• Greater vulnerability to getting sick.
48. • The darker the room the better.
• Maintain consistent sleep patterns.
• Quietly watch television or read 45 minutes
before expecting to fall asleep.
• Falling asleep by 10 pm is more in rhythm with
your circadian cycles.
49. Food
• Your brain needs energy from food to properly
function.
• Without enough food you will be sleepy and
not able to concentrate on mathematics.
• Best combination: carbohydrate, protein and
fat (of the right kind).
