A Review of Invictus The Movie Through Bible Literature

In his sermon, Jesus’ Inauguration Day, Samuel Wells Dean of Chapel Duke University tells us that Mark’s gospel describes three phases in the life of Jesus: Jesus the Messiah, Jesus the suffering servant and the cosmic Jesus.

This well crafted message of Reverend Wells teaches that some of Jesus’ followers tend to associate him with only one or two of these life phases. But Mark’s gospel clearly describes Jesus as a full participant in each of these life phases.

Professor Wells posits that these people mistakenly expect their lives to follow a similar abbreviated pattern. Continuing he says, when life presents them the life phase they eschew from Jesus’ life, they tend to experience spiritual disappointment.

In this message the Reverend Doctor Wells teaches that Jesus’ followers should fully embrace each of these three life phases because each phase prepares one for a deeper spiritual understanding, thereby positioning the person for a mature spiritual life.

The movie, Invictus, displays these three life phases in the life of Nelson Mandela, the political prisoner who becomes the first black president of South Africa.

Invictus does not followed Mark’s ordering of Jesus’ life phases but all are present.

The movie opens with Mandela ( Morgan Freeman) in the Messiah role.

His country suffers a deep racial divide from the now legally defunct apartheid.  Mark’s gospel presents Jesus driving out an evil spirit in his first healing.  Invictus presents Mandela at a community meeting preparing to drive out an evil spirit in his first public act.

In this scene, some black citizens prepare to vote in order to change the name and colors of the country’s rugby team. White South Africans had a passion for rugby. It was their game, their soul. To eliminate it or to change it was to cut deeply their soul.

Mandela stands against the action. He espouses a gospel against vengeance. Inclusion and forgiveness are to be his design to heal the racial divide and to forge a nonracial South Africa. His voice wins the action of the day.

Invictus presents to the moviegoer some of the stories and incidents that make the healing possible.

Click to read more.

Learning Mathematics with Disabilities in Higher Education

On January 1, 2009 Congress expanded the scope of the definition for a disable person in the American for Disabilities Act (ADA).

A disable person is defined by the ADA as an individual who:
Has a physical or mental impairment that substantially limits one or more major life activities;
Has a record of such an impairment; or
Is regarded as having such an impairment.

The phrase “major life activities” has been clarified by the explanation:  “major life activities include but are not limited to caring for oneself, performing manual tasks, seeing, hearing, eating, sleeping, walking, standing, lifting, bending, speaking, breathing, learning, reading, concentrating, thinking, communicating, and working.”

As the ADA domain includes colleges and universities, the new ADA provide higher education a means to offer accommodations to disable persons who pursue the study of a college class.

Unlike the situation in the K-12 grades where schools have the responsibility to determine student disability and work to accommodate it, in higher education the student is obligated to initiate the process by submitting the appropriate verification of the disability to the appropriate college administration in order to gain the requested  accommodation. If the accommodation does not place an “unreasonable” administrative or financial burden on the university, or if the requested accommodation does not substantially lessen the course academically then the requested accommodation is consonant with the intent of the new ADA.

Disable students who have had the benefit of course accommodations in K-12 should become aware of the accommodations many colleges and universities offer for success.

In many cases higher educational institutions offer accommodations to students experiencing challenges to learning mathematics. The wise student will seek those schools having the programs they are interested in and that zealously offer the  accommodations they seek then  present the required verification authorizing their disability to the appropriate administrator upon enrollment.

This note is not intended to exhaust the topics of mathematics disabilities in secondary education nor to offer legal advise. It is a beginning point for those having no knowledge of accommodations for students required to satisfy a mathematics course in higher education.

To gain an introductory feel for the legal aspects of this subject matter see Guckenberger vs. Boston University, a case often cited as validating the accommodation of disable students. For professional advice, see an attorney specializing in ADA.  Click this link to see the foundational paper of this note.[1]

[1 ] Kathleen Ambruso Acker. Mary W. Gary, Behzad Jalali, Accommodations of Learning Disabilities in Mathematics Courses, Notices of the American Mathematical Society, Volume 56, Number 9, October 2009

The Soloist: The Movie

My viewing of “The Soloist” recalled how cruel Fate can be to nice people. It placed the homeless, especially the mentally ill ones, in my face and forced me to deal with this unfortunate reality. Then it ushered me a quick glimpse of the world of classical music. “The Soloist” spins both topics as subplots around a remake of the Joseph story in the Book of Genesis. Undoubtedly, this movie will vibrate the full range of your emotions. Now recall the Joseph story.

Joseph had a special gift.  Subject to a grip of jealousy, his brothers sold him into slavery. While in service, Joseph endured and emerged a powerful ruler. Years later, upon confronting his brothers he said:

“Don’t be afraid. Am I in the place of God? You intended to harm me, but God intended it for good to accomplish what is now being done, the saving of many lives.  So then, don’t be afraid. I will provide for you and your children.” And he reassured them and spoke kindly to them. Genesis 46:19-21

“The principal characters in this engaging movie are Nathaniel Ayers, played by Jamie Foxx, and Steve Lopez, played by Robert Downey Jr.  Ayers is a modern-day Joseph. Fate plays the composite characters of Joseph’s brothers who sells him into mental illness.

Like the Biblical Joseph, the young Ayers is a very talented person. To carve out a life as a musician, he abandons the distractions of his world, elevates the great composers to prophets of the god he seeks, masters their techniques thereby developing his musical talent, to earn enrollment in the famed Julliard School of Music. To continue click this link.

A Multiplication Algorithm

Is your child is having difficulty learning the multiplication algorithm or multiplication tables.  Has he mastered addition? If your answer to both questions is yes, place value may be his stumbling block. Good new! A simpler method exists. It is easy to learn …  Click this link to read more.

Three Elementary Counting Problems

Part I

Three counting problems
In how many ways can a photographer pose seven students in shoulder-to-shoulder alignment?

Two of the seven students adamantly refuse to be photographed side-by-side. In how many ways can a photographer pose the seven students respecting the students’ wishes?

The partners of a second couple announced they do not wish to be photographed side by side. If a photographer honors these two couples wishes, how many ways can the seven students be posed?

Prologue
This tutorial discusses the solution of three counting problems. The techniques discussed exposes secrets that are useful to solve many counting problems.

Are there formulas to remember? Yes! And they should be memorized!

But unlike your past mathematics experiences, substituting numbers into a formula is not the best method to solve counting problems.

A promising approach to solving counting problems is to break the given problem into simpler problems whose solutions lead to the solution of the more difficult given problem. Two fundamental counting principles are discussed. They are helpful in breaking a given problem into simpler problems for solution to the givnen problem.

The first of the two fundamental principles is the addition rule.

The addition rule
If there are m tags in an urn and n tags in a second urn then the total number of ways of selecting a tag from the first urn or the second urn is (m+n).

The second fundamental counting principle is a multiplicative rule, hence it is called the product rule.

Example: A student must select one book from the library’s collection of complexity theory or one book from l collection of Mozart’s biographies. The library has 5 books in its complexity collection and it has 20 biographies of Mozart. The addition rule asserts there are (5+20) ways to select a book from one of these two library collections.

To apply the addition rule,  for each complexity book, put its title on a tag and place the tag in an urn. Into a second urn, place a tag containing the name of each biography. The addition rule asserts that the total number of ways to select a book from the first collection or the second collection is (5+20).

The addition rule can be used in a different way. Consider this example.

Mary registered her upcoming wedding with Stacy Department Store. Stacy’s supplies 147 different plate designs of which 94 of the designs have non-circular plates. Mary likes only circular plates. How many choices does Mary have available through a Stacy’s registration?

In this example a tag describes a plate featured at Stacy’s. There are 94 tags identifying a non-circular plate. Denote by “n”, the number of Stacy’s circular plates. By the addition rule, 147=94+n. Hence, there are (147-94) circular plates available to Mary through a Stacy’s registration. The two urns are those containing the tags of circular plate designs and containing the tags of non-circular plate designs.

The product rule
If an urn contains m tags and a second urn contains n tags then there are m*n ways to form a list of two tags, where the first tag in the list comes from the first urn and the second tag in the list comes from the second urn.

A list is a presentation of objects along a line. Lists are ordered. They have a first object, a second object, etc.

Example:
Urn 1 contains three tags, each tag bearing one of the digit 1, 2, or 3.
Urn 2 contains two tags. One of the tags is marked “a” and the other tag is marked “b” .

The product rule asserts that there are 3*2=6 two-tagged lists, where the first tag is from Urn 1 and the second tag is from Urn 2.
The six lists are: 1a, 2a, 3a, 1b, 2b, 3b, 1c, 2c, 3c .

A Reminder: The product rule prescribes order within the lists. The first tag of the list is from the Urn 1 and the second tag of the list is from Urn 2. This ordering must be honored.

The above reminder asserts that 1c and c1 are different in that two-tagged list. In fact, c1 cannot occur from the order imposed in the construction of the list.

The two counting rules can be extended to more than two conditions (urns).

Example
Given three urns U1 having three tags, U2 having 4 tags, and U3 having 6 tags. No two urns share a tag. The number of ways of selecting a tag from U1 or U2 or U3 is (3+4+6)=13.

The Extended Addition Rule
Given k urns: U1, U2, …, Uk. U1 contains n1 tags, U2 contains n2 tags, …, and Uk contains nk tags such that no two urns share a tag then the total number of ways of selecting a tag from U1 or U2, …, or Uk is (n1+n2+…+nk).

Here n1 is used to represent the number of tags in the first urn. n2, n3, etc. is similarly defined.

The Extended Product Rule
Given k urns: U1, U2, …, Uk. U1 contains n1 tags, U2 contains n2 tags, …, and Uk contains nk tags then the total number of lists of length k with the first tag from U1, the second tag from U2, …, and the kth tag from Uk is the product n1*n2*…*nk.

Suggestion: Memorize the counting rules. A helpful strategy that aids memorizing the counting rules is to recite them to yourself each time you use them. They are the means through which a problem will be broken into smaller problems that leads to the solution to more complicated problems.

Problem 1: In how many ways can a photographer pose seven students in shoulder-to-shoulder alignment?

For the solution, follow this link.

A Black History Commemoration

(The polite terms of the period are used in this article.)

Fannie Lou Hamer, Martin Luther King, Jr., Thurgood Marshall, Madame C. J. Walker, W. E. B. DuBois, Booker T. Washington, Benjamin Bannecker, George Liele are all noteworthy selections that should be cited during Black History Month. Their accomplishments were stellar in the History of Americans of African descent. Their stories are inspiring. Their commitment and fortitude are noteworthy models to be used in future struggles against injustice.

Notwithstanding their noble accomplishments, this writing focuses on a sisterhood that spanned more than 90 years of American history. Its members are linked by their common choice to relinquish what little joy life may have offered, in order to enhance the lives of family members and friends. They were the washwomen of the Negro race in America. The times were the early days of the Negro’s struggle for dignity and freedom in the United States of America.

Carter G. Woodson first called attention to them in The Negro Washwoman, a Vanishing Figure. Venerable saints – he called them. Saints they were; seldom venerated; more often forgotten. This note retells their story and calls for an annual remembrance of their life-struggles – especially their progenies and disciples of compassion.

Their Story: Pre-Emancipation
Their story began in the South during the ante bellum era. They were in service to an often-truculent plantation mistress. Their jobs were to keep their mistresses’ lives free of drudgery. At dawn, they left their hut to prepare their mistress’ meals, to toil with their mistress’ children, to wash and iron their mistress’ household clothes and to clean their mistress’ houses, while their home went unattended until they returned at dusk.

Upon their return, they found their children craving  mother’s love and attention; and their tired husbands resting from the drudgeries of fieldwork and the indignities of their life-status. Without regard for self, these ladies launched into the second half of their day’s toil. But this time, they were cooking and caring for their loved ones, thereby, stoking the flame that fueled their raison d’etre.

The final task of her day our saint devoted to her home enterprise; washing clothes for pay. From whence springs the term, washwoman. With this income, she purchased presents and clothes for her family, and sometimes, household items that turned her hut into a home. Amidst servitude, to become a washwoman was to surrender self for the good of others. It was a life commitment to elevate her family from mere existing, to a life with occasional joy. Our saint ended her day with less than a six-hours rest, ever knowing, the next weekday promised a rerun of the same.

The ante bellum system was taxing to the slaves, but to the female slave it was most agonizing. Slave marriages were prohibited by law, so masters encouraged their female slaves “to take up” with a man. Absent love, she refused, but the master’s will prevailed. Some of these “unions” were lasting. But their purposes were to enlarge the master’s slave inventory for auction and maintenance of his slave force for service. This made birthing a child into slavery tortuous, but it made separating from that child to support such an economic system an agonizing abomination.

In the North the freed colored woman fared better. She did not have to contend with the problems of slavery. But her economic plight was no different. If her husband had no trade, he worked menial jobs for low pay. Many able wives without artistic talent opted to supplement their husband’s low wages by “taking in wash” for pay.

Their Story: Post-Emancipation
Emancipation changed everything. Black men withdrew their wives and daughters from the fields to work at home. Many former slaves migrated to the North to seek a better life. The defeated South was in economic disarray. Returning soldiers were granted the skilled jobs, leaving the menial jobs with less-than subsistence pay to the emancipated. This prevalent scenario forced emancipated females to supplement their family income. Without education or artistic skills, washing clothes in her home was the choice of many: the washwoman.

To many of the emancipated, the North promised more than it delivered. Recently freed males were highly skilled from their trade experience on plantations. Unions closed their rolls to the emancipated to protect their members from these highly skilled competitors, leaving for them menial jobs with very low pay. Freedom in the North had changed the slaves’ social status, but it failed to impact their economic viability.

In the North, the emancipated female did not have to contend with the command  “take up with a man” nor did she have to see her child on an auction block. But her family experienced economic hardship equal to that of her Southern counterpart.  For her life’s trials merely changed its face from the demanding mistress or the dictating master, to that of economic reality in a cruel world: a nonworking husband or one with low pay.

After emancipation, the washwomen continued their sacrifices over 90 years. Then demand for their services gave way to modern wash machinery, modern laundries, and a more educated black people. Their sacrifices and courage during times of stress provided the foundation for the descendants of slaves to build a life position that was more stable than one built on only financial injections to the family. From this foundation, the family was fortified spiritually, civically and educationally. For from the experiences of her home business, the washwoman learned the know-how that ushered the Negro people into forming business enterprises to serve their communities. From the wisdom she gained from observing the American society, she supported building and maintaining organizations through which many emerged into the mainstream. From her zeal to overcome societies’ inequities, she embraced education as the optimal delivery system to a better life for succeeding generations. To that end, she funded causes that fostered education and societies that fought for her community. But equally important, she upheld the primacy of male leadership within the family as a cornerstone of a strong family unit. Upon that rock, the Black family met and fought the war for civil rights in the ’60s.

To read more click the link. Call to Remember

The Winning Attitude for Learning Mathematics

Watching a group of children – ages one to three years, is very entertaining. The little ones celebrate their freedom from adult’s grasps by running, jumping, stooping and peeking through their fingers.

This is a fun time for them. They never sulk. They dash here and there; often so fast they fall on all fours. With exuberant giggles, they climb to their feet and run again, attempting to press the envelops of the new capabilities.  This is also a time for learning. With each activity, the little ones develop muscles to run faster, jump higher, stoop lower and observe more. Mastering these activities is fun. But it is hard work and it requires a lot of practice.

Jesus of Nazareth, one of the great teachers ever to live, used imagery of child behavior to describe how to excel in a spiritual life. In Matthew 18:1 – 4, Scripture records:

[1] At that time the disciples came to Jesus and asked, “Who is the greatest in the kingdom of heaven?”

[2] He called a little child and had him stand among them. 3 And he said: “I tell you the truth, unless you change and become like little children, you will never enter the kingdom of heaven.  4 Therefore, whoever humbles himself like this child is the greatest in the kingdom of heaven.

Paraphrasing the great teacher, those who attain greatness in a spiritual life must come with enthusiasm to master the new life skills. But more importantly, they must enter the new life unencumbered and be ready to meet its challenges.

Learning and a New Life
Learning opens us to a larger set of truth. The new knowledge (truths) offers a hope of better decision-making, thereby promising a chance for a better life. Effective use of our new knowledge takes us from our past life, with all its mistakes, into the new life of promise.

In Matthew 18:2-4, Jesus announced that one attained greatness in a spiritual life by having the attitude of a child. This winning attitude is characterized by enthusiasm to master the new life’s skills, freedom from encumbrances of the past and openness to new possibilities.

The model that Jesus used to explain gaining “ the kingdom of heaven” holds for gaining proficiency in mathematics. If one substitutes “learning mathematics” for the phrase “enter the kingdom of heaven”, the previous consequences continue to hold. Those who seek – in wonderment and astonishment, the laws of mathematics and push themselves to a deeper understanding of its nature, gain the proficiency (skills) of a mathematician.

Mathematics Teachers
Likewise, that analogue holds for teachers of mathematics. They, too, must have the same childlike attitude. For only a teacher with conceptual knowledge of basis skills can lead a student beyond rote learning to understanding. Such teachers have laid bare the secrets of what they teach. Therefore they are not likely to say
“… that’s the ways it is…” , or
“… you must do it this way…”  or
any other statement whose frequent use impairs a student eagerness to know, when seeking a clear explanation from a teacher who is not able to provide it.

Conclusion: The willing attitude for success in mathematics is the attitude of a young child. It is characterized by inquisitiveness and the drive to master tasks.

Kloosterman & et suggest the following to build motivation in the elementary classroom. Also they help nurture the willing attitude for learning mathematics. Assess their value towards helping your child’s mathematical development.  Click the link to continue

Gran Torino: The Movie

Clint Eastwood’s Gran Torino is a delight. It flashes humor in parts while it seriously tells the story of salvation of an American Hmong family.

Eastwood is a retired Ford Motor Company worker and a decorated veteran of the Korean War living in a Hmong neighborhood that was created by white flight.  Click to read more…

Internet Risks and Your Child

The second half of the 20th century brought the Internet into our homes. Unlike television, the Internet is a virtual center of human activity ready for us to  participate in with a few keystrokes on a computer.

Swiftly the Internet traffic grew and attracted our children.  They go to it on school computers, on homes computers, at their friends’ house, on library computers and even at grandma’s house. They took to the new media like fish take to water. It is no wonder; the Internet is dubbed their new playground.

Playgrounds are places where fun rules. And playground activities are rehearsals of valuable life skills. The Internet activities are no exception. They provide educational, social, and analytical skills training. Thus the Internet is too valuable an experience for a child not to be involved in its educational promises.

Risks of the Internet

The threat of physical danger is rare on the Internet. But this new playground does host a small element that spreads hatred, pornographic material, and seeks to commercially prey.

Our young ones are not always the prime targets of these nefarious activities. But during an unsupervised first encounter, an innocent child can easily be ensnared within these amoral webs.  Such an encounter may prove life altering.

Our objectives are to discuss some risks and dangers our children are likely to face on the Internet, and to offer suggestions to strengthen them against those dangers.

The Rewards of the Internet

The rewards of the Internet are many: Entertainment, instant communication, expression of one’s thoughts via web pages or through chat room participation, communication via email, visits to resources of cultural, scientific, and current importance; all with a few computer keystrokes.

Surveys document our children use the Internet responsibly. They do homework, communicate by email, text message, send instant messages, go to chat rooms, make scrapbooks, swap music, play games, construct games, create websites, write stories and some present content.

These activities develop social skills, analytical skills, and research and presentation techniques. All are desirable skills for the electronic age.

Internet: A Peril to Society, Our Defense

Despite the positive boasts of  the Internet, this media provides cover for a small population that takes advantage of the innocent; in particular the young. This cover is unwittingly provided by free access and the unsupervised nature of the Internet. It is through these attributes that the dangerous ideas and amoral activities are easily disseminated.

Disseminating views that are consonant with the public good is desirable. Those that are in dissonance with the public good must be countered. Society’s best defense against this dissonance is provided by parents who have pass their values and beliefs to their children before others can imprint them.

To read more, click this link.

The Original Flaky Pie Crust Recipe

There are culinary experiences that delights the senses. This is one of them, a flaky pie crust that is easy to prepare, tastes good, melts in your mouth and humbles the preparer as well as those enjoying it. Try it as written and check our claim.Click to read more