Is Algebra Necessary? Of Course It Is!

Last week an op-ed piece--"Is Algebra Necessary" by a Poltical Sciences Professor Andre Hacker--was published in the New York Times (link here).  The thesis of this note was that schools should stop teaching algebra as a matter of course, that algebra is really not necessary for most careers anyway, and that poor performance in algebra is having a terrible impact on high school and college graduation rates.

This article went somewhat viral:  securing over 450 online comments at the NY Times site, and was noted in newspapers, online media, and radio/TV stations around the nation.  I must have gotten a few dozen emails about it and talked to quite a few of the local media about it.

I have two major points to share.  First, the idea of dropping algebra is one of the most foolish ideas I have heard in a long time.  Second, the fact that the media took this wacky proposal seriously says something about where we are as a nation...and I will let you judge whether that is good or bad.

Algebra is fundamental for virtually all technical subjects and careers:  engineering, science, medicine, and technology.  It is required for finance and business.  The list is a long one.

Now even if we made the huge assumption that the only use of algebra is for technical and math-oriented careers, there is an obvious reason why we need to teach this subject to virtually all our children:   we don't know in junior high or even high school which kids are going into such careers!   If we deny a child access to this subject we are determining that they NEVER will be able to go into a technical or financial subject.  Parents--would you accept this?   Would a student like their future circumscribed in such a way?  Of course not.   We live in an increasingly technological society and many of the careers of the future require math competence.  It is inconceivable that we would deny our children the ability to participate in this new world.   Our international competitors  (e.g., Chinese, Japanese, Germans, to name only a few) are pushing their kids to achieve in math--they laugh at the intellectual disarmament that hacker suggests.  Today, foreign nationals are taking over the technical and mathematical subjects...even in our own universities.  Folks, this is bad, real bad.  Because our nation will not be able to swipe the cream of the worldwide talent pool forever.

But algebra is more than a foundation for key careers of the 21st century.  It is one of the prime achievements of our civilization and one that has greatly contributed to our ability to describe mathematically the world around us.  It is no less important that Shakespeare or Homer.  (any yes...how often do we use classic literature in our daily lives...would anyone suggest dropping these subjects?)

Learning math and algebra is a central part of the education of every student.  Not only do they learn how mathematics can describe the world around them and can do so many useful things, but they learn to organize ideas in a logical, ordered way--extraordinary training for anyone, of any career direction.

Hacker makes a big point that a lot of students are not gaining mastery of algebra and for many it is a frustrating experience.   But that is more of a measure of the failures of the U.S. math education enterprise, not the inadvisability of teaching algebra.  The U.S. math education establishment decided, with no empirical evidence, to switch math education to a "discovery" approach roughly 15-20 years ago.  It has been a complete failure, with many schools now switching back to the direct instruction approach used by the nations best in teaching math.  Seattle is a prime example of the failure mode, with poor math curricula at all levels.  We need teachers who have deep knowledge of the math topics they teach, which is often not true in elementary and sometimes middle school.  In short, we need to fix the basics.   But the basics seems to be ignored by many districts and education boosters (like the Seattle Times, Wa League of Education Voters, Gates Foundation) who push quick-fix panaceas (charter schools, Teach for America, restricting teacher flexibility, etc.) that don't deal with the real problems.  Other major culprits are the education schools, who push trendy, theoretical approaches rather than making sure new teachers know their subjects and effective approaches to teaching.  


If students aren't learning algebra well, you can drop the subject--as Hacker suggests-- or learn how to teach it better...which would you prefer?

Heat Waves and the Thermal Trough

After a number of days with below-normal maximum temperatures, the Northwest is going to warm up for an extended stretch.  Several days in the 80s and even some hope of hitting 90F in portions of the west.  No, you are not dreaming.

But anyone wanting to be informed about northwest warm spells has to master the key feature of our warm periods:  the thermal trough.  I am very interested in thermal troughs...in fact, with support from the USDA Forest Service my student Matt Brewer and I have a research project on this topic.

If you look at a climatological pressure chart for the summer, it looks something like this.  High pressure over the Pacific Ocean and lower pressure over the HOT southwest deserts and Mexico. Hot air is less dense than warm air and this results in less pressure at the surface.  Yes, many of you think of low pressure being associated with cold, cloudy weather, but believe it or not, areas of very warm temperatures can be associated with low pressure as well.  Sometimes we call these features heat lows or troughs.

 In this kind of pattern, the coastal portions of the NW stay cool...higher pressure offshore and lower pressure inland forces onshore flow, and the ocean is cold.  Sorry, that is the way it is.  Natural air conditioning.

But sometimes..like this weekend...a miracle happens.  A lobe of high pressure extends inland of us, forcing offshore flow.   This offshore (easterly) flow starts over the heated interior of the continent and then gets even warmer when it sinks down the western slopes of the Cascades.   The result is that a tongue of warm air extends northwestward out of the southwest--generally northward from the interior valley of CA or the intermountain West---towards our region.   Each day it moves farther northward and strengthens.  And since warm air is less dense, a pressure trough (area of low pressure) extends northward with the warm air.  Want to see an example?  Here is one from a paper Matt and I have written (you can see the pressure lines and temperature--shading).

Now we call this feature a thermal trough, but we really should term it a thermally induced trough, but that would have a little too racy an acronym for conservative meteorological journals.

A thermal trough is about to develop over western Oregon and Washington.  Let me show you with the latest simulation.  Each figure will present sea level pressure (solid lines), surface winds, and lower atmosphere temperature (shading).

Today at 5 PM...the normal situation.

 Tomorrow at 11 AM.  High pressure building inland.  Easterly flow over Oregon...a thermal trough is starting!

 Saturday morning at 5 AM.  A nice thermal trough in western Oregon and its moving into western Washington.

Saturday at 5 PM.  WOW.  Huge, warm thermal trough extending into western Washington.  Heat wave.  Temperatures certainly in the upper 80s away from the water.

Thermal troughs don't last forever.  Eventually the supporting inland high pressure moves eastward and the trough jumps into eastern Washington.  This happens during the day on Sunday:

Don't worry, Sunday should be plenty warm--in fact, I expect it to be the warmest day...typically the day the trough moves across the mountains is the warmest day of the sequence.  Could well have lower 90s from Seattle southward.   Here is a model surface temperature  forecast map for 5 PM on Sunday. Close to 100F in southeast WA and of course Portland and the Willamette...isolated from the water...are much warmer than Seattle.  Water greatly moderates the temps over NW WA and the coast.

Thermal troughs not only bring warmth.  Often the heat results in poor air quality (high ozone), and thermal trough passage over the mountains can really rev up any wildfires that are smoldering.    Thermal trough passage causes big wind shifts that can play havoc with wind energy predictions.    You can see why we are studying these troughs...they are important for a number of reasons!

And to really warm your hearts, here is the latest 8-14 day forecast by the Climate Prediction Center.  Above normal over much of the west...except for the WA coast.

Climatologically, this is the warmest, driest time of the year...there is a reason SeaFair is this weekend.