Monday, December 29, 2008

How Did You Remember How to Tell Your Right From Your Left?

I recently asked a six-year-old how she remembered right from left. She told me that she just "used her brain and thought about it". So, I asked her how she learned it. She told me that her mother told her one day when she was brushing her hair and then she just remembered. She doesn't use any special technique to remember. She just knows.

What does this have to do with math? Not much except... The way that I learned my right from my left is similar to the definition of "even" and "odd".

The definition of even: Divisible by two.
The definition of odd: Not even.

I remembered which was my right hand because it was the one that I used to write with. My left hand therefore was the one that wasn't right.

The only flaw: I was ambidextrous and could never remember the hand I supposed to use (my mom and the kindergarten teacher had rules about such things).

How did you remember? Take the poll in the left column.

Monday, December 22, 2008

From the Ministry of Silly Walks

A very interesting video from T.E.D.

Steven Strogatz: How things in nature tend to sync

Friday, December 12, 2008

Trends in International Mathematics and Science Study Report

The 2007 TIMSS report was just released on the internet. The good news: Math scores have increased for fourth and eighth grade students in the U.S. The U.S. is now scoring above average compared to 35 countries at the fourth grade level and 47 countries at the eighth level. All 5 countries, that scored measurably higher than the American 8th graders, are in Asia.

Saturday, November 29, 2008

The Algebra Project

After reading the report from the Brown Center, November 16th blog post, I decided to look into the Algebra Project founded by Robert Parris Moses.

I had visited Algebra Project web site previously and upon reviewing it remembered why I had discarded it to the trash bin of my mind. The website piques one's interest with titles such as, "Raising the Floor: Algebra Project National Conference", "Connecting Community and Schools", and "Building Excellence in Teaching", but is disappointing because it doesn't answer many pertinent questions. I wasn't able to find any definitive information, on the site, describing the program for teachers or data showing the Project's outcomes. Since the Project was founded in 1982, isn't it logical to expect to see data on its website to show that it is working? In other words, the site didn't answer any of my questions about what the Project actually DID, and even the blurbs about its philosophy weren't clear.

I found a paper, The Road Coloring Problem, written by Gregory Budzban, Department of Mathematics, Southern Illinois University, that gives a hint to the impetus of the Algebra Project. In the paper, Dr. Budzban describes a project that Dr. Moses did with one of his high school algebra classes based of the Road Coloring Problem.
"Over the next several months, together with other members of the Algebra Project, we put together a proposal to write a new 9th grade curriculum based in part on the RCP (Road Coloring Problem) and also drawing from Moses' and others work on curriculum based on 'mathematically rich' experiences."
I'm skeptical... a curriculum based on the Road Coloring Problem? Dr. Budzban, however,
does answer my question about where I can find information on how the Algebra Project works,
"A detailed explanation of the Algebra Project "Five Step Process" is contained in Radical Equations, and any serious discussion of it would require an article in itself."
There is one important point that I gathered from the Algebra Project's website, and Dr. Budzban's paper: Community involvement is very important in order to change the way we think about mathematics .

I completely agree. To further improve student outcomes in mathematics, in the U.S. we need to change the way we think about math education.

I am not swayed to believe that access to mathematics education is entirely an equal rights issue, in terms of race, as implied on the Algebra Project's website. It may be better argued that mathematics education is a class issue, but that doesn't tell the full story either. Although access to quality education can be argued to be a class issue, availing oneself to math education seems to be a cultural issue.

Children who are born into families inculcated in education will be better prepared to maneuver through the educational system than other children. They will have advantages in understanding the importance of attendance, being able to organize their binders and backpacks, getting help from tutors when needed, preparing for SATs, and slogging through the paperwork for applying to colleges, loans, and grants. For many students, this translates into an advantage in mathematics, but not always.

Mathematics apathy is cultural, specifically American in nature. Just as children born into families that are familiar with the ropes and red-tape of the educational system have an advantage, children inculcated into math-wise families will think of math as a natural part of a comprehensive education. If a parent works in a job that requires mathematics (surveyor, bank clerk, bookkeeper, machinist, chemist, engineer, physicist, actuary, accountant, computer programmer), white collar or blue collar, the child will be more likely to think that mathematics is important. Many highly educated Americans, and frighteningly too many school teachers, don't know a thing about mathematics and many let it be known that they don't care.

Therefore, I agree with Robert Moses that changing the way the community thinks is essential to changing the way math education is viewed in the United States. The National Mathematics Advisory Panel even mentioned the problem in their report published earlier this year.

Gregory Budzban, contributor to the Algebra Project, and who's paper is cited previously, responds to how he views mathematics education in the U.S.:
"Any curriculum process of this sort (referring to his curriculum collaboration with Robert Moses) must be aware of the 'math wars'. Students need both conceptual understanding and the ability to perform (without the aid of technology) the algorithms and procedures that we refer to as symbolic manipulation. Students must be prepared for the various state and national tests that have become increasingly important for their educational careers. There is no other short term option.
"For me, another part of the motivation for the work is to give students a sense of the
creative and aesthetic nature of mathematical research. Much of what passes for math curriculum at the K-12 level is the equivalent of grammar and vocabulary in a natural language. Imagine if, for twelve years, all you were taught was grammar and vocabulary in your native language. Imagine that you never had the opportunity to read anything other than the 'grammar book' and all you did was diagram sentences and write definitions. This is the equivalent of what we do in mathematics education at the K-12 level, in my opinion.
"For a true national mathematical literacy effort an important question is, 'How does one keep students involved and motivated?' For this, it is imperative that we display to students the creative and aesthetic nature of our beautiful subject. Jerry P. King wrote eloquently concerning this in his book, The Art of Mathematics. Yes, I understand students need the basics and a good foundation. My response to those who would emphasize only the basics, only the three 'R's' above all else is, 'Two of the three R's are misspelled.'"
Gregory Budzban's point is beautifully stated and I love Jerry King's metaphor.

The concept of Algebra for all 8th grade students, the impetus of my last post, was not addressed in any of the information I found regarding the Algebra Project.

Sunday, November 16, 2008

Algebra Plan in California Halted

On Tuesday, October 28, 2008, a Sacramento Superior Court judge ordered the California State Board of Education to postpone its plan to test all 8th grade students in Algebra.

The last minute decision for the test, made by the board in July, had been pushed by Governor Schwarzenegger and was opposed by California Superintendent of Public Instruction, Jack O'Connell.

The History of the Trend

In 1990 only about a sixth of eighth graders were enrolled in an algebra course. The Clinton administration, in response to America's poor showing in math relative to other developed nations, made enrolling all students in an algebra course by the 8th grade a national goal. Robert Moses, founder of the U.S. Algebra Project, added to the movement by claiming the issue to be "The New Civil Right".

The campaign continued and the enrollment of eighth graders in algebra rose from 16% in 199o to 24% in 2000. The trend proceeded into the next decade and by 2007, 31 percent of all 8th graders were taking advanced math (algebra or above).

According to a recently published Brown Center report, the push for universal enrollment of eighth graders in algebra, is based on an equity argument and is not based on empirical evidence. From the point of view of the equity movement, "democratizing eighth grade algebra promotes social justice", advancing students who had not been able to previously take advanced math, particularly students of color and students from poor families.

The Brown Center of Education Policy, part of the Brookings Institution, used NAEP data (National Assessment of Educational Progress) to investigate the ramifications of increasing the percentage of students enrolled in advanced math classes by the eighth grade.

The Findings of the Brown Center Report

The typical eighth grader knows more math today than in 2000, but the typical eighth grader in advanced math knows less.

The Brown Center decided to look at the students scoring in the 10th percentile and lower on the NAEP math test. In 2000, 8.0% of these "low-achieving" students were enrolled in advanced math courses. By 2005, the rate of low-achieving students had risen to 28.6%. The report calls these students "the misplaced students". In the same time period "high-achieving" students, enrolled in advanced math courses, dropped from 27.0% to 20.0%.

The phenomenon "has been viewed as an accomplishment, not a cause for worry". The low achieving 8th grade students score an average of 211 on the NAEP math test. This is 27 scale points below the national average for fourth grade students. Since 11 scale points on the NAEP test is equivalent to approximately one grade level, the misplaced students are functional at a second grade level, about 7 grade levels below fellow students in the same courses.

Fractions and are a particular problem for the misplaced students. Knowledge of fractions, an elementary school subject, is essential for success in advance level math courses.

Misplaced students are more likely to come from poor families and are overwhelmingly black and Hispanic. The schools with higher percentages of misplaced students tend to be large and urban. The schools with higher percentages of misplaced students also tend to shun tracking (placing students by ability). The teachers of misplaced students are more likely to have taught for less than five years, are less likely to hold a regular or advanced teaching certificate, and are less likely to have majored in mathematics.

Referring to these schools, the report states, "Let us not forget the hundreds of thousands of well-prepared students-who are also predominately black, Hispanic, or poor-sittting in the same classrooms as the misplaced students and equally deserving of a good education. Well-prepared students need a real algebra class, not a fake one teaching elementary school mathematics".

It falls to the teachers to make up for the skill deficiencies of the misplaced students. The system put the burden on the algebra teacher to find a way to fix the problem of unprepared students. Recall from above: In 2007 31% of students were performing in the lowest 10th percentile. The average of these students were performing at about a second grade level... and it is up to the algebra teachers to fix the problem.
Many of the advocates for 'algebra-for-all'
"do not believe that students must learn basic mathematics in order to successfully tackle higher-level mathematics. They will argue that keeping remedial math students out of algebra in eighth grade denies these students the opportunities that good math students take for granted".
What is commonly overlooked is that the burden of such an idealistic view falls on the classroom teacher.

Another irony: The mathematics required on the California High School Exit exam is far below the level of the test proposed for all eighth graders in California.

The Recommendations of the Brown Center Report:
  1. Get the goal right.
  2. Teach and assess prerequisite skills.
  3. Early intervention.
  4. Collect data, conduct research.
When students are misplaced, they get lost in the curriculum and pay the price. Their classmates, who are ready for advanced math, also pay a price. "The students who already know arithmetic and are ready for algebra are the losers".

We, as a country, ranking 24th of 29 developed nations in mathematics, also pay the price of such education policy.

Saturday, October 25, 2008

Using Schematics to Teach

The Flower Design
I've used this lesson in middle school and high school to help students learn how to manipulate the compass tool.

At home, start as early as third grade. Precocious kids might be able to do this in kindergarten or first grade.

Knowing how to read is not required.

The flower design is a great exercise for developing spacial sense, mastering the compass tool, and practicing precision.

The use of schematics for directions appeals to children.
Use schematics to teach small children how to draw five-pointed
stars, six-pointed stars, octagons, etc.

A five-year-old, inspired by the idea of schematic directions for five-pointed stars, made a colored schematic for drawing a picture of Pikachu. Then she followed her own schematics to create the Pikachu out of colored Play-Doh.

Thursday, October 16, 2008

Taking Action Against Cheating

Hats off to Dr. Jason Stephens of the University of Connecticut. He is embarking on a project to curb cheating by fostering a culture of ethics in school. It sounds so obvious!

Might his techniques, to emphasize a code of honor in schools help to foster a culture of ethics in our nation?

Let's start at the top and use the Trickle Down Theory. I suggest that the next administration hire Dr. Jason Stephens to help implement his code of honor in all of the branches of our government. The executive and legislative branches are particularly in dire need of assistance.

With effective oversight, the honor code will filter down to Wall Street. The ethical mindset will certainly, eventually, trickle down to the common people of America. Americans and the rest of the world, will be more at peace when the nation can make inroads on the abatement of the 'It's All About Me' Syndrome.

Teachers to Be Measured Based on Students’ Standardized Test Scores

If you are following education issues your interest was surely piqued when it was reported this month that nation's largest school district, New York City Department of Education, is starting to measure teachers' performance by looking at student test scores.

At one time, in the recent past, I was completely against the idea. In the hands of an incompetent, not very intelligent, or politically driven, administrator this could be a dangerous tool. On the contrary, in the hands of a visionary and competent administrator, looking at student performance can be a wonderful aid to help a teacher tweak his or her practice.

We need a method for evaluating administrators, superintendents, and school boards.

See the NYT article.

Monday, October 13, 2008

Sunday, October 5, 2008

Best Math Joke of the Week; Unfortunately it is a True Story

A high school math teacher asks his students if they know what the number 144 represents. Of course they don't know (there are numerous answers, but this is 2008).

He informs them that 144 represents a quantity called 'a gross'.

So then he asks, "What does the number 288 represent?"

They don't know that either, but he tells them it is two gross to mention.

The only person laughing is the 73 year old T.A. in the back of the class.

Sunday, September 28, 2008

46th Mersenne Prime discovered at UCLA

Mersenne Primes are named after Marin Mersenne, a 16th century theologian, referred to as the 'father of acoustics', but known for his discovery of a special set of prime numbers. Mersenne Primes are in the form of 2^n +1. In the case of the 46th Mersenne Prime, n = 43,112,609.

Every once in awhile a new Mersenne Prime is found. When in college, a fellow student printed, what was probably the 30th Mersenne Prime, on a dot-matrix printer, and hung it up on a wall in the math wing of the university. It took pages of paper to print the entire number.

In contrast, the 46th Mersenne Prime, found this month by a group at UCLA, is over 13-million digits long and would take about 10 weeks to write down, a digit at a time. It took 75 PCs running Windows XP to generate the prime number. It is the 8th such prime discovered at UCLA.

Wednesday, September 24, 2008

The Edible Schoolyard

Why I did not know about the Edible Schoolyard project, I cannot say. It is just a few miles away in Berkeley, CA. There are acres of beautiful garden on a school campus in the San Francisco Bay Area. The garden is stunning: tomatoes, corn, kiwi, berries, chard, mint, mulberry, pears, apples, quinoa, beans, lettuce, sage, borage, and other plants that I cannot recall.

But, when I saw the gloves with all the lefts and rights paired-up on a rack near the garden shed door, upside-down pairs of muddied rubber garden boots on racks, the garden shed, neat as a pin, with the wheelbarrows lined up against the wall, the composting pile, the green house with its seedlings, the chicken coop (with the movable mini coop (hmmm) that is used to fertilize the garden patches), the pergola, with its hay bail benches and the not-so-ready-to-pick kiwi hanging from vines woven through its rafters, the only thought that kept striking my mind was, This is the most civilized approach to schooling that I have seen! Ever!

The students, at this PUBLIC URBAN middle school learn about the value of healthy eating by growing the food themselves. The lesson, on the day that I toured the garden, seemed centered around the taste of freshly picked corn. The instructors brought corn from the local store, the students picked corn from the garden and they had a compare and contrast taste test seated at wooden benches in front of an old brick fireplace on one side of the garden. The students also learn how to prepare and cook the food they harvest.

The healthy-eating theme is carried throughout the school environment. The students 'commune' in the beautiful dining hall for half an hour (no books or backpacks allowed) and then play and mingle on the grounds for half an hour. There is a kitchen garden of herbs (ever seen one of those in English period films?) right outside the door of the dining hall kitchen, where students are free to wander. After an hour of lunch, the students spend, a half hour in silent reading before returning to their core classes.

Imagine if every urban and suburban school board, throughout the country, could implement a program like this in their schools? Just imagine!

Sunday, September 7, 2008

What to do about bullying in school?

Michael Bloomberg, NYC mayor, recently announced regulations meant to combat bullying in schools. I don't think legislating rules is the best way to combat this universal problem.

Bullying happens. Unfortunately, some teachers are unaware of it even when it is happening right in front of them. My theory, untested, is that anyone, having been the victim of bullying in school, is more aware of it than other people.

Teachers need to be made aware of the signs of bullying and be given tools that they can use in the halls and classrooms to help mitigate bullying. The other side of the equation is student training. School administrations should be running programs in the schools that help students 'buy into' a school culture of kindness, equity, and of course, non-violence. A former colleague used to say, "Those kids need to be paper trained." Kidding aside, the students often do need to be trained and the adults in the school environment need to recognize the seeds of harassment.

And violent students should be removed from the schools.

D.C. Schools to Pay Some Students

Fourteen middle schools in the D.C. area will be paying students up to $100 every two weeks. The criteria:
Academic Performance

The program costs, $2.7 million, will be split between D.C. and Harvard University.

The trend seems to be sweeping across the country. Five states experimenting with cash-for-grades programs.

I once read a story about Ivana Trump. She described how when she was young and not working very hard in school, her father sent her to work in a shoe factory that he owned. It did not take long for her to decide to return to school and do well.

The tax payers in D.C. are paying about $24,600 per pupil, per year for students in public schools, which is more than twice as much as the average private school tuition in the area. If students are not working hard, and especially if they are misbehaving, maybe they should be required to do some work service, perhaps with the Conservation Corps, or picking up litter around the monuments, raking leaves in the parks, etc. to earn a minimum wage. I bet it wouldn't be long before they wanted to return to school.

Tuesday, September 2, 2008

The School Year Starts Again

School has begun and the education buzz starts anew.

Judy Mousley - Ed., President of the Mathematics Education Research Group of Australasia [MERGA], was a guest writer this week for the Mathematics in Australia blog.

From reading her post it sounds like the issues with mathematics education in Australia (or more widely 'Australasia') are similar to the issues in the U.S. They have MERGA and we have the NMAP [National Mathematics Advisory Panel].

It occurs to me as I read her post, that we are all looking for better ways to teach mathematics: We need better trained teachers, we need to force all students in the 8th grade to take Algebra, we need to teach concept, we need to teach algorithms, we need to teach students to memorize their time tables in elementary school, we need to stop teaching rote mathematics, on and on.

I have written about some of these issues in this blog. But several recent events in my daily travels have forced me to rethink these issues.

I saw a friend, and former colleague, recently. He is one of those dynamic teachers that engages people old or young. His field is history and he is brilliant. Because of his intellect and quick wit he might be better suited to teaching high school or junior college, but at the time we worked in the same district together, he was teaching 7th grade social studies. Then he moved out of the area and I didn't see him again for several years. When we reconnected, he told me a sad story. Last year he taught in a district that shall remain unnamed. Here is his story as I recall it:
The teacher upon reaching the second floor saw a girl hanging a boy out of the window by his ankles. Not wanting the girl to panic, lest she drop the kid on his head, the teacher said something to the effect of, "What the heck are you doing? Bring that kid back in the building." And she did. Then he wrote her a referral.

That night the girl went home and raked something sharp and cutting, like barbed wire, across her forearm. The next morning she came marching into the school with her parents, making accusations that the teacher had mauled her.

When the administrators looked up the incident report they couldn't find one because the girl had lied about her name. The parents left. No charges against the teacher were filed. My friend quit his job and left the teaching profession at the end of the term.

He didn't think it was safe to teach anymore. Not because he was afraid for his physical well-being, but because it is so easy for a child to bring a false accusation against a teacher, ruining his or her ability to seek employment, or worse, landing a teacher in jail.

What a loss to the teaching profession and to all of the students who could have benefited from the talent of this teacher.

The next story...

I recently purchased something on Craig's List and drove out of town to fetch the item. It turned out that the seller was also a teacher; high school English.
Although he was a new teacher this year, recently credentialed, he quit the profession.

He is planning to return to college to perhaps get his PhD., so that he will be qualified to teach at the college level.

Why did he leave the profession after just one year? Because he was utterly devastated at having to fail so many students because the students were not up to the task, or refused to work.

And then of course we have the recent story of the teachers in Harold, TX being able to carry guns. Why? Because of the fear of a Columbine-like situation occurring at the school.

So while we are looking to tweak the education system, which is nothing new, the teenage culture has changed immensely making it more difficult every year for teachers to do their jobs.

The findings of NMAP in the U.S. (and probably MERGA in Australia) are not going to change mathematics education significantly because the report does not address what is at the root of the problem.

Ethics Have Eroded

A man without ethics is a wild beast loosed upon this world.
Albert Camus

Values have changed and people are more self-absorbed than ever. This is devastating, especially for teenagers who, as a group, tend to be self-absorbed to begin with. It's all about you!

If a child is failing in school, it is the teacher’s fault… and all of these reports are pointing in that direction since much of the focus is on what teachers need to do to improve. However, children are failing in math, in large part, because math takes work and kids don’t want to work that hard to think. On a broad cultural level, children are not being made to think.

If a teacher offers a challenging course and some students fail to get good grades, the teacher is put at risk because parents complain (of course it couldn’t be the child’s fault). The shameful irony being that since standardized test scores have become the measure of a teacher's success, the rigorous teacher, the one with the highest performing students, will also be the teacher most scrutinized.

Children have been empowered and will threaten teachers with language such as, ‘I will get you fired’, falsely implicate a teacher such as described above, or even falsely claim that the teacher has made sexual advances. Kids lie. Good teachers are fleeing the profession because of these risks and attitudes. There is even an organization in the U.S. called NAPTA (National Association for the Prevention of Teacher Abuse) which was founded for these very reasons.

When the culture changes to one that expects children to be respectful and responsible, to one that values telling the truth instead of getting away with lying, to one that thinks that math is important and praises the teachers that work hard to help students understand math, then we will have students that are more successful in math. I am not optimistic.

The time is always right to do what is right.
Martin Luther King, Jr.

Sunday, August 24, 2008

Teach for America - What is the Goal?

This weekend I attended the memorial service of my cousins' grandmother who lived to be 106 years old. She could play Scabble, until her last days, usually winning by all accounts. She had such a keen mind that she strategized a design to cheat during her last game, hiding a U in the bedsheets until the desired high-pointed Q arrived on the scene. (The family found the U after her death.)

At lunch I sat across from the nice couple who sang at the service. During a brief discussion of education, they told me that their niece had joined Teach for America and did the required two years of teaching so that she could put it on her resume, which then helped her to be accepted to Med School. I was stunned and didn't really believe that they could be recounting the story correctly. But, I was utterly wrong.

How did I find out? When I arrived home from the memorial service, in a twist of irony, I stumbled upon a blog post, in my google alerts, entitled Why I Hate Teach For America. Blogger Anna, a New York City Teaching Fellow, writes a scathing, yet interesting article, comparing the NYCTF and TFA programs. From Anna's article:
"They [TFA] don’t require teachers to take the steps to become permanently certified because there is no expectation that their teachers will stay in teaching once their two-year resume-building experience is over. How do I know? Because it’s on their website!"
She's right! The TFA website even has a tab labelled, "After the Corps", where teaching is implied to be an entry level job to building another type of career.

But TFA purports to be so much more. No wonder a friend and former teacher/nun/administrator used to refer to Teach for America as "Teach for the Universe". I'm not usually so naive, but I didn't get the full extent of the joke. From the Teach for Ameica Website:

"What we do

Teach For America aims to end educational inequity—the reality that in our country where a child is born determines his or her educational outcomes and, in turn, life prospects. Our mission is to build the movement to eliminate educational inequity by enlisting our nation's most promising future leaders in the effort. Our vision is that one day, all children in this nation will have the opportunity to attain an excellent education."

That is a lofty mission for an organization that encourages its members to teach for two years, (without a credential), in order to leave that entry level job for a better position!

Some Background
In California, to earn a teaching credential, college graduates are required to go through a certified teacher credential program, at a teaching university, for a year, or a year-and-a-half. During that time, they are required to observe credentialed teachers in several environments including a semester of observation in at least one school. The credential candidates are also required to student teach for a semester, under the guidence of a master teacher. The candiates do all of this while paying exhorbitant amounts of tuition to the teaching institution and not getting paid a dime for the work they do.

In stark contrast, the Teach for America program gives young college graduates some summer training (5 weeks). At the end of the summer, the TAF candidates start teaching in urban schools. They take some teaching courses during their two year commitment, usually in the evening. They are required to work toward a credential, but are not required to get one. They get credit for their teaching and paid for their work at the regular salary rate of the district where they work. TFA is part of Americorp, thus the TFA teachers also receive an Americorp stipend [award].
From the TFA website:
"Teach For America is currently a member of AmeriCorps, the national service network. Through this relationship, our corps members who have not previously received AmeriCorps awards receive an education award of $4,725 at the end of each year of service (a total of $9,450 over the two years). Corps members are also eligible for loan forbearance and interest payments on student loans."
While earning my credential, I was told that the first two years of teaching would be rough. It was estimated that it took at least 7 years to get to a point of mastery. They were correct.

A last thought: The more that education is corporatized, the less valued are teachers who have spent years mastering their art, their craft. It is, after all, fiscally efficient to maintain a young staff earning entry level salaries.

Thursday, August 21, 2008

Reality TV Goes to the Principal's Office

I don't watch television. Who has the time? I know... some of my relatives have already told me that makes me a freak*. So I love gathering evidence for my side of the argument. One such bit of evidence is Reality T.V. As a genre, I don't get Reality T.V. My position? Go out and live your life instead of spending time watching others live theirs.

I was a little dumbfounded (and I shouldn't have been) when I saw a little article in the Times,
The Cops Who Keep Fifth-Period Math Safe and Sound. Apparently, reality t.v. goes into the principal's office and records the disciplining of students. There is even one such instance, at Booneville High School in Arkansas, where a student receives 3 whacks (although the actual whacking is not shown on t.v.).

It gives No Child's Left Behind new meaning. In California, the principal would be arrested and stripped of his/her credentials for such action.

*In my defense: I do rent films, peruse newspapers, read articles on the internet, and listen to the radio.

P.S. I had a poll on the side: Corporal Punishment in School: OK, or not OK.
Google deleted it... very interesting.

Monday, August 18, 2008

Teachers in Harold Texas can carry guns!

I was wondering when this was going to happen. See the New York Times article of August, 16.

If the schools are so violent, that the teachers need to carry guns, what about the children who are attending those schools to learn? How are they to cope with the violence?

Chalk up a point for home schooling in Harold, Texas.

Wednesday, August 13, 2008

Homeschooling OK in California

With the excitement over the opening of the 2008 Summer Olympics in Beijing (wasn't that amazing!), enjoying the last days of vacation, and getting ready for school to start, you may have missed the announcement of a California state appellate court's 08/08/08 ruling, permitting home schooling "as a species of private school education". Is 'species' a legal term? Wouldn't 'sub-category' have been a better description?

In February, the court, in a child protection hearing, ruled that parents must have a teaching credential to home school their children. The irony of the ruling being that private school teachers, in California, are not required to have a teaching credential. Score 1 for home schools.

Governor Schwarzenegger, who had sided with the home schoolers, praised the decision. Even Jack O'Connell, State Superintendent of Public Instruction admitted that home schools have a place in California education.
"As head of California's public school system, it would be my wish that all children attend public school, but I understand that a traditional public school environment may not be the right setting for each and every child."
According to the Home School Legal Defense Association (the only resource I could find on the topic), home schools out-perform public schools by 30 or more percentage points.

See the LA Times article.

Wednesday, August 6, 2008

Sir Ken Robinson: Do schools kill creativity?

My friend and colleague, Lee, sent this video to me. Sir Ken Robinson speaks some truths about education. The video comes from the TED website.
TED stands for Technology, Entertainment, Design. It started out (in 1984) as a conference bringing together people from those three worlds. Since then its scope has become ever broader.
The video is about twenty minutes long but Sir Ken Robinson is an entertaining speaker and you will find yourself enjoying the talk.

Thursday, July 24, 2008

Algebra in 8th Grade Revisited

First, a fictional story about children in the state of Californialand
In Californialand swimming is a big deal. All children are expected to learn how to swim.

Some children start learning to swim when they are young. Maybe they have swimming pools in their back yards or the family has a beach house. Maybe they belong to the swim club. Some of these children even get to take swim lessons. They become very proficient swimmers and may even be on a swim team.

Other children don't have the same exposure to pools and beaches. But maybe the grandparents or the neighbors down the block have a pool. These children get intermittent exposure so don't have the same developed abilities as the children previously mentioned. They usually learn to tread water and dog paddle but they don't have developed swim strokes.

Other kids have minimal exposure to pools and beaches. Sometimes their parents are even afraid of the water and that fear is passed on to their children. Although these children may wade in shallow water, they really are not skilled swimmers and would not be considered "water safe".

Then a new law is passed in the state. All kids aged 12 years 9 months to 13 years 8 months must be thrown in the deep end of the pool to be tested for their ability to swim. They will either pass or fail.

It does not take an expert to predict what happens. The kids on the swim team, those with pools in their back yards, and those who take swimming lessons pass the test at an advanced level. They are ready for scuba lessons, ocean surfing, or the synchronized swim team.

Others, who get some exposure to pools and beaches, do fairly well. They do not have the stamina to swim 10 laps or do rigorous water sports but at least they are ready for the next level swim lesson.

Some kids can barely dog paddle to the side while their parents nervously watch with vicarious spasms of fear. No one can really say these are proficient swimmers and alas they fail the test.

And then there are still the few kids who have to be rescued while they panic and are not even able to tread water.

It is too bad that the Californialand Board of Swimming Proficiency, does not think to make sure that all kids are at least proficient swimmers before throwing them in the deep end of the pool.

But the state's rationale, according to the Governor, it that not exposing all children to the deep end of the pool by 8th grade, creates an equity issue. All kids should have the exposure to swimming in deep water by 8th grade otherwise, in their way of thinking, they won't be able to be on the swim team or learn to surf, and how fair would that be? So, throw the kids in the deep end and give them the exposure. No one could ever accuse the Governor of not providing education equity to all students.

The flaw in logic is that equity does not start in the eighth grade. To throw kids who do not know how to swim into the deep end is not equitable. It is trying to fix the problem with the wrong tool.
Back to Reality

Most thinking and compassionate people do not throw their children in the deep end of the pool to teach them to swim. But the State Board of Education, with the Governor's urging, has decided to throw all eight graders into Algebra.

Here is what some of the people on the National Mathematics Advisory Panel had to say about California's new policy, taken from the article entitled, Math Experts Question Wisdom of Calif. Algebra Rule, in Education Week:

Tom Loveless, Ph.D. in education, M.A. in special education, and an A.B. in English, senior fellow at the Brookings Institution, Director of the Brown Center on Education Policy, classroom teacher for 9 years -
“It’s a shortsighted policy that confuses taking a course with learning. The state has not been serious about preparing kids for algebra—they’re just throwing it on the schools. It’s absolutely far-fetched." Also, policymakers there [California] were wrongly assuming that simply enrolling students in 8th grade algebra will result in more of them becoming proficient in the subject. An examination of students’ math course-taking and test performance shows that premise to be false.
Vern Williams, B.S. math education, teacher for 37 years, Math Counts Coach, teacher of the year Virginia 1990 -
California schools, when faced with the reality that many of their 8th graders are not ready for Algebra 1, will simply water down those courses and craft classes that are Algebra 1 “in name only.” Some students, even motivated ones, are not ready for algebra until 9th grade. By forcing students into that class early, schools risk not only discouraging struggling learners, but also holding back higher-achievers, who have to wait for classmates to catch up.“Sometimes, it’s strictly the [lack of] math preparation, but also, there are just kids, even bright kids who ... need to be exposed to a bit more math in 8th grade, or to a pre-algebra course.”
Skip Fennell, President of NCTM, B.S., M.S., PhD (bio did not mention subject), classroom teacher, Maryland outstanding mathematics teacher of the year 1997 -
“I’m all about raising standards, but I wouldn’t want to legislate that every 8th grader take a course in Algebra 1." When it comes to that course, we need to provide access—to kids who are ready.” The math panel’s final report recommended that schools move more students into 8th grade algebra—but only if they had received thorough preparation in whole numbers, fractions, and other concepts.
Russell M. Gersten, Executive Director of Instructional Research Group, PhD special education, nationally recognized expert in both quantitative and qualitative research and evaluation methodologies, with an emphasis on translating research into classroom practice -
California officials would be better off focusing on math preparation at early grades and making sure that courses called “algebra” offer authentic algebra. “The reality is that a lot of kids fail algebra. If anything, [that] makes them math-aversive.”

From the other point of view:

Theodore R. Mitchell, President of the California Board of Education, PhD history of American education, M.A. history, B.A. economics and history, college professor and administrator, congressional adviser -
“The research has been pretty clear that Algebra 1 is a gateway course. We wanted to make it clear we’re going to give all kids the opportunity to go through the gateway. We will not have a two-tier system in middle schools. We’ve been doing a terrific job of getting more kids into algebra. We see this less as a hammer than as urging the state to get across the finish line. The good news is we’ve never heard this level of conversation about what it will take.”
Matthew M. Gardner, the president and chief executive officer of BayBio, an association representing more than 400 Northern California life-sciences companies with 60,000 employees -
“The industry’s view is that California’s science and math education is falling behind. We should expect more from the kids in our school system and from the system itself.”
Arnold , Governor of California, actor, body builder (was unable to find details of education) -
“To do otherwise, would lower our expectations and continue to divide our children between those we believe in and those we leave behind."
I think the Governor is using rhetoric to scare people. The whole notion of "no child left behind", at its foundation, has little to do with school or curriculum. The number one indicator of how children do in school is zip code: where kids live and the wealth of their families.

If we want to ensure that kids are going to be prepared to compete in the global market we need to address inequities such as: Two parents working full time at Wal Mart do not make enough to live in the community where they work. They do not have enough money for the rent, the car, car insurance, car maintenance, clothing, good nutritional food, basic medical care, putting money away for retirement, let alone the computer so that the kids can do their school reports, or the internet so they have the same access to information that their wealthy counter parts have. Yet the CEOs of big companies receive severance packages, after only a few years of work, that blow my mind. THAT is inequity.

Until that kind of inequity is addressed, the poor kids will do poorly and the wealthy ones will be just fine.

Related posts: California requires Algebra 1 for all eighth-graders
California Dropout Rate and Money

Friday, July 18, 2008

California Dropout Rate and Money

California has a 1 in 4 Dropout Rate

California has a new system for accounting for students as they move from one school district to another. For the first three years the system will cost more than $33 million. The initial results indicate that California has a 24.2% dropout rate, far higher than the 13.9% reported last year using the previous method.

Although a 24% dropout rate is dismal, the good news is that California has a better way of tracking students. Previously, when a student stopped attending class, a truancy officer might check on the student if alerted by a conscientious teacher. But if a student checked out of school, there was little to no follow up to the whereabouts of the student.

It's Really About the Money

In a related editorial in the LA Times, the author states
"The Los Angeles Unified School District put its numbers [dropout rate] at about a third... Despite some of the rhetoric in the accountability movement, the dropout rates are not entirely the fault of public schools. Teachers cannot put an end to gangs or mend troubled families or solve poverty; yet all of these are elements of academic failure. The job of preparing a new generation is daunting; it will require a comprehensive approach that addresses health and welfare issues as well as educational ones.

But schools can and in some cases do make a big difference. San Jose Unified School District, for example, is an urban district with a 13% dropout rate. Yet despite the common wisdom that higher standards prompt more teenagers to drop out, San Jose pushes all of its students to complete a college-prep curriculum. Its Latino students are nearly twice as likely to do so as their counterparts across California, and their dropout rate, at 19.5%, is more than 10 points lower than the statewide figure and 15 points lower than L.A. Unified's."
The author is explaining that, because of the higher standards, the dropout rate is less in San Jose than it is in Los Angeles, especially for Latino students.

What the author doesn't mention, is that the median family income in San Jose, last year, was $87,941, while it was $44,713 in Los Angeles, (according to That is more than double!

In one of my recent blogs I mentioned that Marin County has the top schools in the country by SAT scores. In California, Marin has the highest median income and Santa Clara ranks second (San Jose is the county seat of Santa Clara County).

To give readers perspective: I recently visited a Marin middle school that had gardens and lawns, and every student had a MacBook (an Apple laptop) that they could bring home. In the same week, I visited a Middle School in Oakland, situated in the middle of a field of asphalt, not a tree in sight, and the building had paint peeling from the ceilings. Where would you want to stay in school?

The mathematical equations:
higher median income = better school materials and facilities
higher median income = more rigorous curriculum
higher median income = higher SAT scores
higher median income = fewer dropouts

Saturday, July 12, 2008

California requires Algebra 1 for all eighth-graders

Wednesday, the California Board of Education voted to require Algebra 1 for all 8th grade students. The decision was made after a last minute push by Governor Schwarzenegger. Superintendent of Public Instruction, Jack O'Connell, vehemently disagreed with the Board's decision. Only one Board member, Jim Aschwanden, sided with the Superintendent.

Alas... Call me a pessimist, but I don't think there will be enough "highly qualified"* middle school math teachers to cover the increase from the 34% of students currently taking Algebra 1 in the 8th grade, to the 100% of 8th grade students who will be taking that course three years from now. And that is the tip of the iceberg.

Before I continue to rant, I want readers to know that Algebra 1, in the 8th grade, was the hardest math course I ever took. Compared to Algebra 1, calculus was a piece of cake. Suffice to say that there was weeping over homework (and I like math).

The Algebra Story

More than ten years ago, the California educrats (the ones in Sacramento - I'm feeling snarky), decided to make Algebra part of the California Mathematics Standards for 8th grade. For plenty of students, the opportunity to take algebra in the 8th grade makes sense. Many students are even ready to take algebra in the 7th grade, and a few special students are ready in the 6th grade. But, about half the students in California (and that is probably a conservative estimate) are not ready for algebra until sometime in high school.

Did the Governor or the Board of Ed ask for the opinions of the teachers that teach these courses? The teachers will tell you that even students who are somewhat successful in algebra are most likely not proficient in fractions, decimals, and percents, let alone more basic arithmetic. Or how about the public? The voters? At least eight out of ten adults tell me that they either hated or were not good at math when I tell them I am a math teacher or majored in math in college. It is almost like a confession or an apology,
"Oh, I was terrible at math. It was my worst subject."
"Don't worry about it. I promise I won't make you solve fractions or train problems."
Fantastical Thinking

If I were the Goddess of mathematics education in California (thankfully I'm not), I would opt for introducing basic algebraic, geometric, and measurement concepts in elementary school, then going into more depth in middle school. I would also insist upon mastery of fractions, decimals, and percents by 8th grade.

Continuing with that fantasy... The students who are particularly adept at mathematics could pursue the higher levels in high school and those that have not mastered the basics by then could take courses that ensured mastery by graduation from high school. The California Exit Exam could be weighted toward testing for the math that everyone needs to know: arithmetic (including fractions, decimals, and percents), measurement (standard and metric), problem solving (including solving basic equations), and estimation.

In my imaginary world we need to be able to compare prices on gallons of milk or liters of pop, to figure out our income tax, our checking account, and our 401k, to know if the sale price of the tires is correctly calculated and if we receive the correct change, to tip the waiter appropriately, to make certain we are not being cheated on our bill, to estimate the cost (including tax) of the car we want to buy or the new carpet we need in the den.

Jim Aschwanden, the descenting California School Board member mentioned earlier, was quoted as saying,
"Not all children are developmentally ready to take algebra in the eighth grade."
Many people think this way. I believe, however, that with a homogeneous culture (which we don't have), rigorous mathematical training in the early grades (which we don't have), and a cultural consciousness that we can all do math well (which we also don't have), most students would be developmentally ready to take algebra in the eighth grade and thus nearly 100% would be adequately proficient in algebra by the completion of middle school.

Back to Reality

Unlike California children, most 8th grade students in Singapore and Japan seem to be developmentally ready for algebra by eighth grade. This may have been a motivating factor for the School Board's decision. I applaud the kind of thinking that encourages Californian/American children to be prepared to compete in the world market. A one-shoe-fits-all plan isn't going to work in California.

My predictions:
  • Math teacher shortage in middle school
  • A compounded education funding crisis
  • Watering-down the algebra curriculum to avoid failing huge numbers of students
  • More parents will be paying for math tutors in middle school
  • Eventually 9.5 out of 10 people will tell me they hated math or were not good at it in school

See AP articles California to require algebra taught in 8th grade, Calif. mandates algebra for all eighth-graders and an excellent article by Dave Ellison of, Requring eigth-grade algebra makes no sense

*No Child Left Behind Act

Monday, July 7, 2008

What You Know About Math?

Math geeks rapping... What can I say?

America's Best Places to Raise a Family

This Forbes article surprised me. It lists the best 20 counties, in the country, to raise a family. Marin County came in at number 15. Apparently Marin would have been higher on the list except for the gnarly $901,900 median home price. Keep in mind that is median (the middle valued house), not average.

What surprised me? Marin County tops the nation in education. I'm getting a clearer picture of the education crisis when Marin tops the list. I am a Marin native, and a Marin teacher, and I have seen education, specifically math education, decline in the last 30 years.* (I write about the unsettling fact that the U.S. ranks 25th out of 29 developed nations in Math education for high school students, so my thinking might be a bit skewed compared to the average American.)

Forbes gives the average SAT score in Marin as 1,133. For those of us older than 30, the College Board added 100 points to the score in 1994 - so that average score should look more like 1,033 to us. 1033 does not seem that great to me. The average score was designed to be a combination of 500 in English and 500 in math, in 1941 when the test began. But, since the average combined score had decreased to about 850 by 1994** the College Board raised everyone's test score by 100 points, making the student average 950, closer to what it was when the test was designed.

In other words... our children in Marin, averaging 1,033 are not doing significantly better than the average student in 1941. Oh but, we must take into account that more students are taking the test these days because more students are going to college. But still...

15. Marin County, Calif.

Population: 248,742

If money were no object, Marin would be tops on our list. It offers the best education in the country, with a 97% graduation rate and a list-topping average SAT score of 1,133. Marin is filled with picturesque bay-side communities like Tiburon and Sausalito, and outdoor attractions include Point Reyes National Seashore, Muir Woods Redwood Forest and Mount Tamalpais. Good luck finding a place to live: The median home price is a staggering $901,900, the most expensive on our list.

* Of course it is also declining in the rest of the country and in other developed countries - England and France are having trouble urging their teenagers to study math.
Dumbing Down Our Kids : Why American Children Feel Good About Themselves but Can't Read, Write, or Add

Sunday, June 29, 2008

Poll: What Does the Nation Think About Education

The poll was funded by the Bill and Melinda Gates Foundation.
About half of the Nation thinks that schools are not preparing kids adequately for college and the work force.

Education is trying to function at cross purposes. I keep reading about how all students need algebra in the 8th grade. "Algebra is the gateway to college". But, since when does everyone in the work force need college or choose the college path? Is college the new high school? Is it recommended for everyone? Solving linear equations, the essence of algebra, is not going to help huge numbers of people in the Nation's workforce. Being able to handle fractions and percents, which many students have not mastered, including students in higher level courses such as advanced algebra, would serve to better prepare students for the work force and life.

If we need to do a better job training kids for college and the work force then we might want to think of offering different kinds of high school education. A student might want to prepare for college. Others might want to prepare for business, a trade, or the arts. If we start offering appropriate training in high school, then we will have appropriately trained students entering college and the work force.
Sixty percent of adults think that teacher pay should in some way be tied to student results on standardized testing.
I have taught honors level math courses. Good! My salary will reflect the fact that my students are doing well on standardized tests. I have taught remedial math. Woe is me! A salary cut because many of the students in my class speak English as a second language, a large percentage of them have learning disabilities, are economically disadvantaged, or any other number of reasons that cause students to have trouble learning math. The remedial students are much more difficult to teach than the honors level students. The quality of the teacher is more crucial at the remedial level, yet the test scores won't show how capable that teacher is.

An analogy: One person has an automobile that is an engineering wonder. It performs well with little service and the service that it does need is straight forward and simple. The other person has a car that was manufactured with questionable engineering. It is made of plastic parts that break down and need to be replaced often. It is always in the shop due to its poor quality construction. The cars are repaired at two different repair shops. The first car goes to a shop that is spotlessly clean. Any replacement parts are readily available and are of top quality. The second car goes to a shop that is falling apart. It is filthy. The parts have to be ordered and take days to get to the shop. When they arrive at the shop, they are of poor quality because the clients can't afford better parts. Yet the mechanic is able to keep the car running despite the poor circumstances of the shop. The first car always runs better than the second car in all tests.

The second mechanic risks his life everyday to get to work because the shop is in a crime ridden neighborhood. He is in fact a much better mechanic than the first. When a part can't be found, he is able to fashion one to suit the purpose, in order to get the car back on the road. He does work for free sometimes because his clients can't always pay.

The way that 60% of our Nation thinks is that the first mechanic should get paid more because the car he works on always performs better in all tests.

For anyone who thinks this way, be clear on what you really mean. If teacher pay is to be based on testing outcome, then you are advocating that teachers who teach in schools that have everything they need, for kids who want naught, should be paid more than teachers who work with students who have little, in schools that are falling apart. Testing outcomes are directly related to the zip codes of the homes of the students.

The Brain: Understanding How it Functions and the Impact on Our Teaching Practice

Reading and studying about how the brain works had more of an impact on my teaching practice than any course required by the teaching credential program I undertook.

When I encounter former students, they reminisce about the information I presented on the functioning of their brains, metacognition, and the metaphors I used to help them understand how to use their brain to boost their learning. There is no mention of geometry or algebra (the subjects I taught) during these encounters.

As is especially appropriate for their age group (teenage/young adult), they were thirsty for knowledge of themselves, especially when compared to learning the quadratic formula or the Pythagorean theorem.

The following videos are about two amazing people sharing their experiences, helping to give us insight into how our brains work.

Josh Waitzkin, The Art of Learning

Josh Waitzkin was a chess prodigy, the subject of "Searching for Bobby Fischer". He then became a Tai Chi champion. Watch him talk about his insights on learning. Thanks Lee, for sending me this clip.

Jill Bolte Taylor: My Stroke of Insight

Jill Bolte Taylor had a stroke in the left hemisphere of her brain. She is a neuroanatomist and was able to document her experience from her professional perspective. It is fascinating. Thanks Dyan for sending me information about Ms. Taylor.

Wednesday, June 18, 2008

Closing the Achievement Gap - An Impossible Feat

The Fordham Institute released a new study today: High-Achieving Students in the Era of NCLB. The study consists of two parts:

Part 1 - An Analysis of NAEP Data
(The National Assessment of Educational Progress)
Part 2 - Results From a National Teacher Survey

Part 1 finds that although the rate of achievement has increased for the lowest 10% of students, the rate has remained virtually flat for the top 10% of students. Part 2 finds that the majority of teachers report that "low-achieving students receive dramatically more attention" than their high-achieving counterparts, yet the majority of teachers "believe that all students deserve equal attention". The majority of teachers (especially those in the nation's lowest-income schools) recommended that advanced students be in homogeneous classes, or magnet schools that bring advanced students together. ( much for the concept of "de-tracking", ubiquitously taught in teacher training programs!)

According to the report summery, the pattern of bigger gains for low achieving students and lesser gains for high achieving students is "associated with the introduction of accountability systems". The term "accountability systems" refers to student testing "regimes" in general, and specifically to the accountability system of NCLB.

A New York Times article cited Amy Wilkins, a vice president at Education Trust, an education lobbying group:
“My concern is that this report makes it seem like we have to choose between seeking equity and excellence,” she said. “We need to strive for both.”
What? Of course we need to strive for both. The report is saying that it is not occurring, and it does not occur in the "high stakes" testing environment of NCLB.

From the Education Trust Web Site (italics added):
Mission Statement

The Education Trust works for the high academic achievement of all students at all levels, pre-kindergarten through college, and forever closing the achievement gaps that separate low-income students and students of color from other youth. Our basic tenet is this — All children will learn at high levels when they are taught to high levels.

What We Do

The Education Trust advances its mission along several fronts, from raising its voice in national and state policy debates to helping teachers improve instruction in their classrooms. Regardless of where it occurs, our work maintains a relentless focus on improving the education of all students, and particularly those students whom the system has traditionally left behind.
Closing the achievement gap is impossible (see explanation below). The gap can only be practically decreased by helping the lower achieving students, intensively, from birth. The achievement gap is a massive cultural problem that will not be solved by putting pressure on teachers to improve.

Closing the Achievement Gap

These graphs are hypothetical representations of learning achievement. They are for elucidation purposes only and do not represent actual data.

The assumptions are that at birth (age 0) children know virtually nothing and by the time they are age 15 there is an achievement gap between the upper 10% of students and the lower 10% of students.

Graph 1 is a baseline representation. The top 10% of students are achieving at at faster rate (steeper slope) than the bottom 10% of students. The distance between the two graphs at age 15, represents the "achievement gap".

In graphs 2 and 3, the achievement gap has narrowed from the base line graph. In graph 2 the top students' achievement rate remained constant, but the lower 10% of students achieved at a faster rate than in the base line graph. In Graph 3, the the achievement rate of the lower 10% of students remained constant, but the achievement rate for the top 10% of students declined.

In graph 4, the rate of achievement for both groups increased. The rate of increase doubled (increased by 100%) for the lowest students but only increased by 50% for the highest students. Even though the rate of achievement was twice as much for the lower students, the gap remained the same.

A major problem with the NCLB act, is that it is narrowly focussed. It assesses student achievement with testing, then focuses on overall school performance and teacher improvement. This has put an impossible burden on teachers. Administrators come under scrutiny by the public when test scores indicate that a school needs to improve. They, in turn, put pressure on the teachers? It would be interesting to see if the NCLB correlates with an increased number of teachers fleeing the profession.

Tuesday, June 17, 2008

Planting the Seed in Kindergarten

Germany is suffering from a shortage of engineers. According to this article in Money, there are 90,000 positions to fill and only 40,000 trained engineers to fill them. German companies, like their American counterparts, find themselves looking to Asia to fill those vacancies. A few prominent German corporations have decided it would be a good idea to convince six-year-olds that engineering is a good career choice. Why not? As one German representative who was interviewed on NPR explained (loosely quoted),
"There are doctors and lawyers on the soaps, but when is there ever an engineer? Teenagers are using their ipods, their computer games, and a lot of other technology, without realizing the engineering behind those products."
I think the U.S. should look into borrowing this idea.

Wednesday, June 11, 2008

Anecdotes and Rationale About Why Math is Important, cont.

Anecdote #2 – Panic Attack at the Deli! What Happens When the Customer Wants 1/3 of a Pound of Salami?

When I was a young mom, on my way to a picnic with my two small children, I stopped at the deli and ordered a 1/3 of a pound of salami. I suppose that seems absurd, but ½ a pound was too much and ¼ pound wasn’t enough, so there you have it.

It occurred to me that it was taking a long time to get my order and I wondered where the clerk was. I found her standing in front of the electronic scale in a daze.

In the olden days, when televisions had knobs and phones had dials, the scales at the deli were marked with ounces and fractions of pounds. The clerk would put slices of meat on the tray until the correct number of ounces or the correct fraction of a pound was indicated. (Back then, I would wager that most clerks knew that 1/3 of a pound was close to 5 ½ ounces or thereabouts, but that is the topic for a different post).

Back to the deli clerk… She was standing in front of the relatively new digital scale, frozen in a mild panic attack. It took me a moment to realize that she didn’t know the decimal equivalent of 1/3 and was too embarrassed to ask anyone. So, I helped her out with 0.33 (or so), and we were on our way.

Anecdote #3 - How Does One Make a ½ Sandwich?

Fast-forward twenty years into the future. I was teaching high school one summer and a student of mine, who coincidentally worked in that very same deli from the last anecdote, shared the following story:

One day a customer came into the store and ordered half a roast beef sandwich and half a turkey sandwich (the deli sold half-sandwiches). So, the teenage, soon-to-be-off-to-college coworker of my student made a whole turkey sandwich, and a whole roast beef sandwich, cut them in half, and gave one of each half to the customer.

My student told this story in class and got the desired laughs from most of his classmates, especially when he told the part about asking his coworker what she was planning to do with the left-over halves. Apparently, having been embarassed by the question, she told him exactly where she thought they should go and included some colorful explatives. The class thought that was hilarious.

Both of these stories have several points in common. The problems involve parts of wholes. They, when juxtaposed with each other, illustrate the importance of numeracy, particularly with fractions and decimals, as well as mathematical thinking. It is striking to realize that one young woman was a recent high school graduate and the other, would be off to college within a year. The skills involved in the deli tasks should have been mastered by the 6th grade, and that is a generous estimate.

In his recent testimony before the Congress, Dr. Skip Fennell, member of the National Mathematics Advisory Panel, stated the following regarding conceptual understanding of mathematics:
"As students learn mathematics they need to have the mutually reinforcing benefits of conceptual understanding, procedural fluency, and the opportunity to solve problems applying and extending the mathematics learned."
Regarding fractions he stated:
Some would argue that fractions may be the most critical of the Panel's Critical Foundations for algebra. Fractions are defined here as fractions, decimals, and percent, leading to work with ratio and proportion. Several of the Panel's task groups, as well as the Panel's teacher survey, substantiated that difficulty with fractions is pervasive and an obstacle for far too many students to success in algebra."
And on the abysmal state of our cultural thinking (actually Dr. Fennell called the section "Effort Matters"):
"So, once and for all, we need to stop the parent conference that begins with the phrase, 'Well, you know I was never good in math either.' Math is important - for our children and for our country."


Anecdote #4 – The Geometry Teacher has the Last Laugh

If you don’t teach math, try for a moment to put yourself back in your high school fill-in-the-blank math class. One of the questions students repeatedly ask is, “What am I ever going to use this for?” This particularly happens in Geometry class. I was delighted to see one such student behind the counter of the carpet store, using geometry everyday no less, only several years after he had left my class. Ironic!

The moral to these stories is that it is a good idea to pay attention in math class. One probably does not have 20/20 foresight to know whether or not he/she will need to know given mathematical concepts at some point in the future.

Tuesday, June 10, 2008

Anecdotes and Rationale About Why Math is Important

Anecdote #1 – The Curtain Ring Problem

A couple I knew, college educated I might add, needed to make a curtain for a closet opening. Curtain rings come in packages of 12. This might seem very practical, 12 being a dozen and all.

So, the couple divided the fabric into 12 spaces, easily done by folding in halves and thirds.  When they attached the rings, they found that they were one ring short, thus no ring for the end.  They discovered that they needed 13 rings when the curtain has 12 spaces.  Alas, they just left the curtain flapping.  See the diagram. 

Clearly they were using a mathematical approach, but unfortunately, it wasn’t the best one.

Using 12 rings means the curtain needs to be folded into 11 spaces, and 11 is a prime number, meaning it has no other factors except itself and 1. Therefore the folding method to determine the spacing of the rings is impractical. The curtain needs to be measured, then the measurement number needs to be divided by 11 or alternately multiplied by 1/11.

Example: Let us say that the fabric is 5ft. wide.

Yes, I used the frightening "fraction" to help solve the problem. The result: A curtain that doesn’t look ridiculous, lot of money saved. And some say that math isn’t practical and they have no use for it!

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