Math's Need for Speed

Professor Jo Boaler, of Stanford’s Graduate School of Education, says, “Mathematics education in the United States is broken.” I can’t get her recent Atlantic Magazine article, “The Stereotypes That Distort How Americans Teach and Learn Math” off my mind. It has been sitting in an open tab on my browser since it was published in mid-November. 

In the article, Professor Boaler goes on to write that math classes have focused too much on “procedure execution” instead of embracing a far broader curriculum including making connections, working visually, and problem-solving. Boaler even challenges the idea that there is such a thing as a “math person.”

However, the part of the article that resonates the most for me is at the end of the article:

“Another problem addressed by the Common Core is the American idea that those who are good at math are those who are fast. Speed is revered in math classes across the U.S., and students as young as five years old are given timed tests—even though these have been shown to create math anxiety in young children. Parents use flash cards and other devices to promote speed, not knowing that they are probably damaging their children’s mathematical development. At the same time mathematicians point out that speed in math is irrelevant. One of the world’s top mathematicians, Laurent Schwartz, reflected in his memoir that he was made to feel unintelligent in school because he was the slowest math thinker in his class. But he points out that what is important in mathematics “is to deeply understand things and their relations to each other. This is where intelligence lies. The fact of being quick or slow isn't really relevant.” It is fortunate for Schwartz, and all of us, that he did not grow up in the speed- and test-driven classrooms of the last decade that have successfully dissuaded any child that thinks deeply or slowly from pursuing mathematics or even thinking of themselves as capable. " 

"The U.S. does not need fast procedure executors anymore. We need people who are confident with mathematics, who can develop mathematical models and predictions, and who can justify, reason, communicate, and problem solve. We need a broad and diverse range of people who are powerful mathematical thinkers and who have not been held back by stereotypical thinking and teaching. Common Core mathematics, imperfect though it may be, can help us reach those goals.”

Why must content-driven high school courses force students to demonstrate what they know quickly? Why do teachers insist on writing tests that challenge students’ ability to complete them? How does a child’s ability to move quickly demonstrate her academic skills?

In all fairness, math is not alone in subjecting students to speed testing. Many disciplines do it. However, it seems to accompany those subject areas that want kids to memorize facts, formulas, or procedures. From a Bloom perspective, it is always the lower level thinking skills of knowing, remembering, and applying that are the focus of these kinds of “objective” tests. What about evaluating, synthesizing, creating, or analyzing? Yeah, those don’t work as well on multiple choice Scantron tests. 

Do you work well when you are forced to move quickly? Do you do your best when the amount of work you have to do will not fit in the amount of time you have to do it? Want to be judged on the tasks you had to rush through? Why make kids do that?

When my children have struggled on tests, it is often not about the material or their preparation that has been the issue. It has been about finishing the test! Is that one of the targets of the course: be able to regurgitate at warp speed?

When a test is so long and difficult that kids must rush to finish, it a set up for failure.  Is it a realistic or reasonable assessment of their learning? What would we lose and what would we gain if students could take as much time as they needed to complete these tests and even had time to double check their responses?

We’d get a much more accurate measure of what they have learned!

A Bad Pick Up Line

I walk to school. When I arrive in the morning, a steady stream of cars drop off kids for early class, meetings with teachers, and other activities. When I leave in the afternoon, the line of cars is so long that it encircles the parking lot. Parents will sit in their car for a half hour or more waiting for their children to come out.

I am baffled. Why are they there? Why are they picking up their children as soon as school lets out?

The line is long at 3:15. The line disappears by 3:30 or 3:35. Why sit and wait that long? For that matter, why not let your child take the bus, walk, or ride a bike home?

Of course, sometimes there is a doctor appointment, skating lesson, or other obligation. But the number of cars waiting at the end of the day is far too many for those kind of periodic tasks.

Our school has over ninety clubs and sixty sports. Some of these require auditions or try outs, but a vast majority of them are open to all students. A handful meet in the morning before school starts, but a most activities and teams meet between 3:15 and 6pm after the class day has ended.

I want to knock on windows as I walk past the row of cars and ask, “Why are you here? Why are you picking up a child who should be able to find his or her own way home? Why isn’t your child involved after school?”

As a teacher of freshmen, I work hard to connect my students to our school’s co-curricular program of activities and athletics. Although there are no grades or transcripts for what happens in the afternoon, for many of my students, and many of us, sports, performing arts, clubs, and other activities were the real reason we went to school. They were also where we learned lessons that we carried into adulthood. The people with whom we spent time after school became our closest friends.

This is what the students who leave school at 3:15 are losing. Do they know how much they are missing? Are their parents who facilitate their departure aware of this price?

Yes, yes, yes: I play a spring sport, so in the fall I go home and several times a week, I work out or play with a club. I have a job. I go to youth group. That’s great. I don’t believe that the enormous line of cars is filled, even partially filled with these kids. The line is way too long.

High school is about more than classes. For many kids, classes are the gateway to the fun and wonderful things that happen after the final bell rings and the real love of learning begins. To deprive a student of this opportunity, even under the guise of helping them get home, sparing them bus embarrassment, or making their life easier, is to deny them a key component of their development.

Don’t pick your kids up after school! Don’t make it easy to get home. Do help them find their after school home. Do push them to join a club, be on or backstage, play a sport, or help with the countless events that occur all afternoon and into the evening at most high schools.

One my favorite aphorisms from Robert Heinlein’s Time Enough For Love is “Don’t handicap your children by making their lives easy”. Here is my corollary: Don’t pick them up after school!

Fun With Guns: Guns for Everyone!

The solution to the problem of mass shootings and even the threat of terrorist attacks is to make sure that there are enough guns that a shooter would be stopped by an armed citizen. The reason so few mass shootings have actually been prevented this way is that there just aren’t enough guns out there.

It is clear what we must do: give everyone a gun – or two! A shooter would have to be crazy to attempt to cause a massacre because each victim is also a potential shooter!

But what if the shooter has an automatic weapon? What if the shooter goes into a school?

The solution is simple: teachers should be permitted to carry automatic weapons and their students should be armed, just in case. Weapons should be as important an item on the school supply list as crayons, smocks, and paste. Perhaps students should purchase ammunition for their teachers just as they now bring in boxes of tissue paper.

Consider the possibilities: This would not only protect our schools from mass shootings, it could also be the ultimate solution to the problem of bullying. You’d have to be out of your mind to bully a kid you knew was packing a pistol.

Since everyone is going to have a gun, this would resolve a host of social issues. No more domestic violence or armed robbery. It would be insane to drive by and shoot someone when the person around the next corner could shoot back! Who would do that?

Frankly, there is a lot out there to fear. There are bad guys (and even some bad gals) around every corner. People who do bad things, say bad words, and think bad thoughts, This is endangering our right to live the lives we want. If we all had guns, those people would have lots of good reasons to change their evil ways!

Think about it: that person texting in the movie theater, cutting you off on the highway, budging in line at the store, or putting up idiotic signs on his lawn would be stopped in his tracks! This is democracy in action!

It would be the end of crime. Should someone be stupid enough to actually step out of line, BANG! No one would make that mistake more than once!

We would have a renaissance of civility. People would treat each other well again. They would think about what they did or said because it could have serious consequences. Would they make fun of people who believed that vaccinations cause autism? I don’t think so. Would they criticize politicians who want to ban gay marriage but end up having gay affairs? Not in public, they wouldn’t!

No more name-calling! No more silly questions. People would do good things, say good words, and think good thoughts - or they would have to face the wrath of those who disagreed! We’d be perfectly confident that no one would offend! We could call it that: perfect confidence or PC for short!

Laurie Anderson said it best. In United States Live, she noted that “to be really safe you should always carry a bomb on an airplane. Because the chances of there being one bomb on a plane are pretty small. But the chances of two bombs are almost minuscule. So by carrying a bomb on a plane, the odds of your becoming a hostage or of getting blown up are astronomically reduced.” Now that is logical! Why can’t our politicians think this way?

If every man, woman, child, and pet had a gun, the odds of being shot or being a victim of a crime would greatly reduced. Why aren’t we doing this right now? That is the great question! Talk to your congressmen right way – or better yet…

Thoughts and Prayers Are Not Enough – We Must Take Action!

While it may bring us some comfort to say we are thinking or praying for those in Paris and Beirut, it is not enough. Although statements of solidarity may be comforting to the victims and their families (and to us), we must also take action.

What can we do? What more do we have to offer than our condolences and outrage? Quite a lot! We can work to change our communities, countries, the world, and ourselves. We can add our voices to our prayers and thoughts, our contributions to worthy causes, and then roll up our sleeves and do something!

Through the products we purchase, the politicians we support, and charities we fund, and the actions we take, we make a difference. People all over the world are living in conditions that breed terrorism. Poverty, disease, unemployment, and brutal circumstances are far too common throughout much of the developing world. How do we benefit from their suffering? We must work to find ways to rectify the conditions that create extremism. In addition to giving to causes that work to end these deplorable conditions, we must also examine how our behaviors, both individually and as a community and country, contribute to and perhaps even profit from this sad state.

Because of natural resources like oil, strategic locations, or political expediency our government has supported regimes that value neither human rights nor human dignity. We have valued our prosperity and comfort over the well-being of very poor people. Whether we approve or disapprove – or even if we know about these issues – our country acts on our behalf and in our names. Our well-being is intertwined with the well-being of people all over the world. If we prosper at the expense of those far away, we (or those we love) will pay for that abuse later. In this global age, we must work to make sure that all people live in safe, secure, and sustainable conditions.

Learning about the causes and issues surrounding terrorism feels selfish if it's only for our own edification. Using that knowledge to demand that our legislators and government officials change the role our country is playing internationally is a step toward addressing the larger pieces of this very complicated puzzle.

Terrorism is about fear. It is about fomenting hate and division. Another way we can take action is to actively fight the fear, and build bridges between people with different ideas, beliefs, backgrounds, and values. It is by creating the kind of world the terrorists are trying to destroy!

Starting with thoughts and prayers is fine. Ending there is copping out. Go further. Make some contributions. Learn about the larger issues. Engage in policy discussions. Change your consumer choices. Actively work for peace.

Yes, we all have important tasks. Yes, we all have jobs, families, and communities, which require great amounts of time and energy. Is all you can spare a few thoughts? Is that all that this is worth? We must go further. It is our responsibility and obligation. The fate of our world rests with our choices. Get out there and do something!

Things We Can Do to Stop The Shootings!

The time for debate on whether or not we should put controls on guns is over. The debate is moot. The question is rather, how do we stop the shootings? What do we do to end the blood bath of gun violence that is raging out of control? The problem seems large and overwhelming, especially when we are painfully aware that wealthy and powerful forces are enjoying, benefiting, and supporting the carnage.

We must take action. Talk is not enough. Debating your neighbors will change nothing. We (you and me) must DO something! The purpose of this blog entry to provide two simple and clear things we can do: write legislators and give money to organizations working to end gun violence.

Write or call your legislators. 

Common Cause has a page that will list all of your elected officials. Click here and enter your address and you will get a list of your federal and state legislators and their contact information.

Here is the email I sent. Feel free to use it or make it your own:

Subject: What are you doing to stop the shootings?

Dear Lawmaker,

What are you doing to stop the shootings and end gun violence? It is painfully clear that whatever measures are in place, they are inadequate. Both mass shootings like the recent events in Roseburg, Charleston, Washington DC, Newtown, Aurora, Fort Hood, and shootings in urban areas are all the more tragic because of our failure to prevent them. The debate is over. No sensible person can argue that more guns can solve this problem.

I am asking you to do two things:

1. Pass legislation this year to regulate the sale, distribution, and use of guns and end these shootings. Like so many other products that have caused safety issues, guns users should be required to have a license, training, and be liable if weapons that they purchased are used for murder.
2. Begin a process to address the problems with the second amendment that have put us in this terrible place. Whether it is another amendment or another solution, there must be a longer and more far-reaching solution that will end both this debate and the killings.

The way we will know these laws are effective will be when there are no more shootings. Other countries have solved this problem; we must do so as well.

I implore you to bring legislation to a vote this year,

Yours truly,

David A. Hirsch

Next, support organizations that are working to end gun violence. Those who oppose common sense gun regulation are very wealthy. We must chip in to create a voice that can be heard over the moneyed loonies who fund the opposition to sensible gun laws.

In researching organizations, I found that the Brady Campaign was an excellent organization. Click here and make a donation!

Other organizations you could explore are:

The Coalition Against Gun Violence

The Illinois Council on Handgun Violence

Parents Against Gun Violence

Gabby Gifford’s organization: Americans for Responsible Solutions

If you want more information, here are three articles, one from the New Yorker, a second from the New York Times and a third from the Boston University of Public Health which may help to put the issue in context.

While guns are unregulated, no one is safe. If children in an elementary school, audiences in movie theaters, and military personnel at an army base can be victims, we are all at risk. Let’s act to prevent anyone else from being senselessly killed.

One more thing: please keep this issue on your mind as you vote in November.