loves math 5

Everybody Loves MathEverybody Loves Math

How can we enhance learning experience

for advanced learners and capture the interest of students

not inclined toward math?

How can we enhance learning experience

for advanced learners and capture the interest of students

not inclined toward math?

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.

“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.



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)

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)

Also timing is very importantAlso 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)

“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)

Who are advanced learners?

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.

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.

Providing enrichment for advanced learners will

require:

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 supportIncluding the wider learning community

to support teachers, parents, and students.

Willingness to focus on the learning needs of advanced learners.

Ability to recognize advanced learners.Providing teachers with adequate supportIncluding the wider learning community

to support teachers, parents, and students.

Is there a willingness to focus on advanced

learners?

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.

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.

Reasons that advanced learners are overlookedReasons that advanced learners are overlookedFor 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.

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.

First reflection pointFirst 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?

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?

Our hidden censor. (Keith Payne, 2013)

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.

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.

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.

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.



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.

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.



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.

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.

Obstacles to identifying advanced learners/ giftedObstacles to identifying advanced learners/ gifted

Race/Culture/EthnicitySocio-economicsInstructional Practices Gender InequalitySexual OrientationAsynchrony

Race/Culture/EthnicitySocio-economicsInstructional Practices Gender InequalitySexual OrientationAsynchrony

Student BehaviourHiding Gifts and

TalentsAffective

CharacteristicsOther

Exceptionalities

Student BehaviourHiding Gifts and

TalentsAffective

CharacteristicsOther

Exceptionalities

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.

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.



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.

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.



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.

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.



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.

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.

Possible characteristics oftwice-exceptional studentsPossible characteristics oftwice-exceptional students

Discrepancy between verbal and written work

CreativityExcel on tasks requiring

abstract conceptsDifficulty on tasks

requiring memorization of isolated facts

Anxiety DepressionActing-out behavior

Discrepancy between verbal and written work

CreativityExcel on tasks requiring

abstract conceptsDifficulty on tasks

requiring memorization of isolated facts

Anxiety DepressionActing-out behavior

Poor organizationPoor motivationActive problem solversAnalytic thinkersStrong task commitment

when topic is personally meaningful

Withdrawal/shynessDiscrepancy between

out-of-school talents and classroom performance

Poor organizationPoor motivationActive problem solversAnalytic thinkersStrong task commitment

when topic is personally meaningful

Withdrawal/shynessDiscrepancy between

out-of-school talents and classroom performance

Second reflection pointSecond 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?

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?

S. M. Baum’s guidelines for teaching twice-exceptional

students


studentsFocus 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.

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.


students


studentsTeach 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.

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.

Math specific guidelines by Nisbet

Math specific guidelines by Nisbet

Talking aloudCognitive apprenticeship Analysis of the processes of

argumentCooperative learningSocratic questioning

Talking aloudCognitive apprenticeship Analysis of the processes of

argumentCooperative learningSocratic questioning

Al-Hroub’s and Nevo’s approaches

Al-Hroub’s and Nevo’s approaches

Al-Hroub distinguishes between acceleration and enrichment.

Similarly, Nevo distinguishes between acceleration, broadening and deepening.

Al-Hroub distinguishes between acceleration and enrichment.

Similarly, Nevo distinguishes between acceleration, broadening and deepening.

Who needs enrichment?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”.

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”.

Who needs enrichment?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.

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.

Enrichment for all students?

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.

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.

A new risk groupA 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)

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)

Enrichment or Meeting RequirementsEnrichment 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).

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).

Courage to advocate for enrichment

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.

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.

What do teachers need?

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.

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.

Also Also

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

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

Resources for teachersResources 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.

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.

Third reflection pointThird reflection point

What is your reaction to the suggested supports?

What other supports would help you to better accommodate advanced or twice-exceptional students?

What is your reaction to the suggested supports?

What other supports would help you to better accommodate advanced or twice-exceptional students?

Developing students’ math potential needs additional

support from

Developing students’ math potential needs additional

support fromParental support (not pressure) –

intellectual, emotional and financialAvailability 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

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

Other components of support

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.

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.

Old stories about math need to change.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.

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.

In the media 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.

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.

Students’ attitudes can change

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.

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.

Public attitudes can change

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.

Accomplished students could change the public feeling about math.

Kids might start waking up early not only for hockey but also for math clubs.

Changes in media 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.

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.

Ideas for math lessonsIdeas 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.

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.

Everybody Loves Math?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/

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.












BibliographyBibliography

See the resources page in my blogSee the resources page in my blog

loves math 5

Education

gifted students

exceptional students

supporting students

students disabilities

identification of students

examples of students

students academic needs

education of gifted