1. Everybody Loves Math
How can we enhance learning
experience
for advanced learners
and capture the interest of students
not inclined toward math?

2. Why focus on advanced
learners?
“Without a science-literate population
[including the mathematical sciences],
the outlook for a better world is not
promising.”(AAAS, 1985)
In order to prepare the scientists of
tomorrow, it is important to recognizing
different learning needs of advanced
learners as they are likely to be the
scientists of tomorrow.

3. Why focus on advanced
learners?
The central function of the educational
system is providing each and every
student, regardless of his/her social and
economical status with learning
opportunities that match their potential
and promote it to the maximal extent.
“Learning opportunities are the most
critical factor for the realization of
human intellectual potential.” (Leikin,
2010)

4. Also timing is very important
“If suitable learning-stimulating tasks are
not given at the right moment [research
suggest by middle school the latest],
then some intellectual abilities may not
have the chance to
develop.”(Sierpinska, 1994)
Also if their learning needs are not met
students may be frustrated and
consequently they become disruptive or
aggressive elements in the classroom
environment. (Fetzer, 2000)

5. Who are advanced
learners?
Students who are intrinsically motivated,
persistently work hard, and achieve top
grades, but may not qualify as "gifted.”
Gifted students without an adequate
educational plan in place.
Gifted students who are for whatever
reasons not recognized as gifted.

6. Providing enrichment for
advanced learners will
require:
Willingness to focus on the learning needs
of advanced learners.
Ability to recognize advanced learners.
Providing teachers with adequate support
Including the wider learning community
to support teachers, parents, and
students.

7. Is there a willingness to
focus on advanced learners?
Teachers are teaching classes that are too
big and have challenging compositions.
Through their own schooling teachers
have learned to prioritize supporting
students with low math skills.
Math enrichment resources are plentiful
yet disorganized and appear limited.

8. Reasons that advanced
learners are overlooked
For example Leikin (2011) claims that
people’s views about education of gifted
[or advanced learners] is strongly
dependent on their personal experience
and histories related to the education of
the gifted.
While Al-Hroub (2010) points that there
are students, who are gifted along with
having learning difficulties, whose
abilities in mathematics are easily
overlooked by teachers and parents.

9. First reflection point
Teachers pause to reflect about the
composition of their classes.
What is the composition of your
present and/or past classes?
Can you think of examples of
students who you have known who
may have been advanced/gifted?

10. Our hidden censor. (Keith
Payne, 2013)
Is it really possible that we are constantly
failing to notice things right in front of
us?
Yes, hundreds of studies have backed up
the idea that when attention is occupied
with one thing, people often fail to
notice other things.
What we do or do not see depend on the
biases of “unconscious selective
attention” of our mind.

11. How to identify advanced
learners?
Advanced learners should be seen as
potentially gifted.
Parents and teachers are important allies
in the identification of students who
need gifted programming.
Research indicates that parents are best
suited to identify gifted behaviours in
young children.

12. How to identify advanced
learners?
But, if parents have not initiated setting
of an adequate educational plan then it
is the teacher’s responsibility to
advocate for the child.
Teachers can provide an important
perspective by indicating how a student
performs compared to other students of
the same age.

13. How to identify advanced
learners?
Teachers who see students needing a
higher level of challenge in the
classroom have an obligation to
document their findings and provide
appropriate learning opportunities.
It is advisable that teachers look for
support of a trained gifted education
specialist in the school or the district.

14. Obstacles to identifying
advanced learners/ gifted
Race/Culture/Ethnicity
Socio-economics
Instructional Practices
Gender Inequality
Sexual Orientation
Asynchrony
Student Behaviour
Hiding Gifts and
Talents
Affective
Characteristics
Other
Exceptionalities

15. Twice-exceptional
students
Among all others, gifted students
who also have learning disabilities
are the most frequently overlooked
because their exceptionalities
mask each other and for that
reason they are most frequently
“hiding” in our classrooms.

16. Twice-exceptional
students
It is even harder for students if only
one of their exceptionalities is
recognized. Usually it is students’
disabilities that are noticed and
frequently education plans do not
address their talents. This can
cause further emotional distress.

17. Twice-exceptional
students
While it is important to address
students’ academic needs,
recognizing and supporting the
social and emotional needs of
twice-exceptional students can be
even more important.

18. Twice-exceptional
students
Because “students with the potential
to be high achievers are showing a
rate of dropout that approximates
low achievers” (Phillips 2008) it is
important that teachers learn the
characteristics of twice-exceptional
students.

19. Possible characteristics of
twice-exceptional students
Discrepancy between
verbal and written
work
Creativity
Excel on tasks
requiring abstract
concepts
Difficulty on tasks
requiring
memorization of
isolated facts
Anxiety
Depression
Acting-out behavior
Poor organization
Poor motivation
Active problem solvers
Analytic thinkers
Strong task
commitment when
topic is personally
meaningful
Withdrawal/shyness
Discrepancy between
out-of-school talents
and classroom
performance

20. Second reflection point
In your experience as a teacher were
there students that were overlooked?
What could be done differently?
What did work?
What kind of support do teachers need in
order to provide better learning
opportunities for advanced learners?

21. S. M. Baum’s guidelines for
teaching twice-exceptional
students
Focus attention on developing
students' talents and
strengthening their abilities
through enrichment activities.
Provide a nurturing environment in
which students feel valued and
their individual differences are
respected.

22. S. M. Baum’s guidelines for
teaching twice-exceptional
students
Teach compensation strategies after
efforts to remediate skill deficits
have helped students reach a level
of proficiency.
Encourage students' awareness of
their individual strengths and
weaknesses.

23. Math specific guidelines by
Nisbet
Talking aloud
Cognitive apprenticeship
Analysis of the processes of
argument
Cooperative learning
Socratic questioning

24. Al-Hroub’s and Nevo’s
approaches
Al-Hroub distinguishes between
acceleration and enrichment.
Similarly, Nevo distinguishes
between acceleration, broadening
and deepening.

25. Who needs enrichment?
The feedback that Phillips (2008) has
received from educators at all levels,
parents, and indeed students, is that
“we have sacrificed the learning
potential of highly motivated students,
preventing them from breaking away
and advancing in selected subjects -
especially math and sciences - beyond
grade level expectations”.

26. Who needs enrichment?
Many would argue that all students need
enrichment.
Gamoran and Hannigan’s (2000)
investigation supported the benefits of
algebra training for all students, rather
than just those who show aptitude
through grades or testing.
Students who were low achievers gained
more from algebra instruction than
similar groups exposed only to general
math.

27. Enrichment for all
students?
Taking a developmental point of
view, Sheffield (2009) suggests a
continuum of mathematical
proficiency through the
development of creative ability in
mathematics: innumeraters,
doers, computers, consumers,
problem solvers, problem posers,
and creators.

28. A new risk group
Research shows that students feel social
pressures to "dumb down" in high
school to fit in socially (Colangelo et al.,
2004).
This begs a question “Have American
[and Canadian] schools, on the whole,
created a new risk group by applying
disproportionate time and resources to
another?”
(Phillips, 2008)

29. Enrichment or Meeting
Requirements
There are highly motivated students
who achieve top grades, but may
not qualify as "gifted".
Focusing only on meeting grade
level requirements neglects the
needs of many highly motivated
students (Colangelo et al., 2004;
Davidson & Davidson, 2004).

30. Courage to advocate for
enrichment
Enrichment and advanced information are
academically beneficial for all students.
Raising the bar of excellence will not
leave students behind, it will challenge
students to reach up instead of out.

31. What do teachers need?
Teachers have to be provided with
multiple opportunities to advance their
knowledge about advanced learners’
learning styles and the importance of
mathematical challenges for meeting
advanced learners’ academic and
emotion needs.

32. Also
Teachers should feel safe
(mathematically and pedagogically)
when dealing with this type of
mathematics (Holton et al., 2008).

33. Resources for teachers
Teachers need to be helped with the
enrichment task by providing them
with appropriate learning material,
making a large number of
challenging tasks available to
them, and providing multiple
opportunities to advance their
knowledge, be mentored by math
professionals.

34. Third reflection point
What is your reaction to the suggested
supports?
What other supports would help you to
better accommodate advanced or
twice-exceptional students?

35. Developing students’ math
potential needs additional
support from
Parental support (not pressure) –
intellectual, emotional and financial
Availability of special settings and
frameworks for highly capable students
in schools and out of schools.
The necessity of involving technological
tools that promote mathematical
creativity in students and support
teachers' attempts to scaffold students
mathematical inquiry

36. Other components of
support
Mathematical challenges as a central
characteristic of a learning environment
that develops creativity and promotes
mathematical talent;
Teachers' proficiency in choosing and
managing mathematical challenges.
Other activities such as math clubs,
competitions, and student conferences
found both in school and out of school.

37. Old stories about math need to
change.
Frequently math is seen as hard,
boring, and never needed after
high school.
It still causes anxiety in parents and
some teachers which is then
imparted on children / students.

38. In the media
Math is presented as a stumbling
block for all kinds of people.
Only rarely are there programs, like
Numb3rs, that show math in a positive
way.

39. Students’ attitudes can
change
Students not inclined toward math
usually also suffer from math
anxiety, while advanced learners
find math too easy and repetitive.
Providing enrichment to support
advanced learners would enhance
math learning experiences for all.

40. Public attitudes can
change
Accomplished students could change the
public feeling about math.
Kids might start waking up early not only
for hockey but also for math clubs.

41. Changes in media
When the public perception of math
changes, the media will cover math
related research and discoveries more
often, e.g. one about 'number sense'
that is universal to all animals not only
humans.

42. Ideas for math lessons
Margo Kondratieva (2011) suggests
interconnected problems.
Angela M. Smart (2011) suggests
cryptology and modular arithmetic,
symmetry and the art of Escher, and
Roman numeral arithmetic.
Smart also suggests using ideas and
resources designed for gifted students.

43. Everybody Loves Math?
Not yet but with joint efforts we will
get there soon.
Also, my “Everybody Loves Math” blog
houses enriched Math Magic lessons
and other resources.
http://beyondrequired.blogspot.ca/

44. Bibliography
See the resources page in my blog