UPDATE: A similar exam was given in another big lecture class: Earth and Space Sciences 102. Here is the exam and results: http://www.atmos.washington.edu/~cliff/ESS%20102%20Math%20Assessment%20Solutions-1.pdf Unfortunately, there were very similar results, with poor performance on many questions. Thanks to James Prager of ESS for sharing the exam with us. This is a big problem faced by all professors at the UW.
As many of you know, I have a strong interest in K-12 math education, motivated by the declining math skills of entering UW freshmen and the poor math educations given to my own children. Last quarter I taught Atmospheric Sciences 101, a large lecture class with a mix of students, and gave them a math diagnostic test as I have done in the past.
The results were stunning, in a very depressing way. This was an easy test, including elementary and middle school math problems. And these are students attending a science class at the State's flagship university--these should be the creme of the crop of our high school graduates with high GPAs. And yet most of them can't do essential basic math--operations needed for even the most essential problem solving.
A copy of the graded exam is below (click to enlarge) and a link to a pdf version is at:
If you want a blank version to give your kids and friends, it is at:
Consider these embarrassing statistics from the exam:
The overall grade was 58%
43% did not know the formula for the area of a circle
86% could not do a simple algebra problem (problem 4b)
75% could not do a simple scientific notation problem (1e)
52% could not deal with a negative exponent (2 to the -2)
43% could not do simple long division problem with no remainder!
47% did not know what a cosine was.
I could go on, but you get the message. If many of our state's best students are mathematically illiterate, as shown by this exam, can you imagine what is happening to the others--those going to community college or no college at all?
Quite simply, we are failing our children and crippling their ability to participate in an increasingly mathematical world. I have even heard from carpenters complaining they are finding it difficult to hire new apprentices that can do the calculations needed to build a house. When I buy something, cashiers have difficulty making change. During the past several years professors such as myself have seen a progressive decline in math skills. Math remediation rates have soared at community colleges to the 50% level. The math tutoring industry has exploded (over 300% in the past decade and a half). Foreign nationals are filling our technical positions here in the U.S. We are in deep trouble. And it has to be fixed or our state and nation will slip into second class status.
This is a national problem--WA state is not the only place where math ability has floundered. But I am amazed how major foundations (e.g., the Gates Foundation) and big-time politicians are so clueless about what is going on, and how quickly major progress could be made.
Now why have things gotten so bad and what can we do about it? As in any disaster the causes are multiple. And let me say at the outset, it can be fixed. A lot can be done quickly with only modest resources.
One problem is curriculum and textbooks. Starting in the mid-90s colleges of education and "curriculum specialists" in districts become enamored with a new way of teaching math--called reform or discovery math. Instead of teaching the basics --followed by practice to mastery, the idea was that students could only learn math they "discovered" themselves. Working on problem sets was considered "drill and kill." Direct instruction by teachers and equations in books were out. Long division was out. Integrated math books where all topics were swirled together were in. Group learning and playing with objects (manipulatives) were in. Describing one's through process was considered more important than getting the right answer. Most of this proved to be a disaster, but those pushing it--professors in education schools and district curriculum types--were believers, even though there was no empirical proof that it worked. Many felt that the new reform math could serve social and political goals--helping the disadvantaged or those that traditionally could not "get" math. (as if minority groups were not capable of learning the same math as the privileged!) And it didn't work, as the exam below shows. (Ironically, their new approach hurt the disadvantaged more than others who could afford tutoring and private schools.)
Another problem is that many teachers are ill-prepared by colleges of education to teach math. Many elementary schools teachers have weak math knowledge and large numbers of middle school and high school math teachers do not have degrees in math or technical subjects. And of course the ill-founded reform and discovery math approaches are pushed into their heads. Now these weak teachers could function marginally if they had good textbooks and curriculum, but they don't. And the curriculum and books are so poor that students can't take them home to learn the material on their own or enjoy the assistance of their parents. It would be hard to design a worse system.
And, of course, there are a host of other problems--too much video games and Facebook at home--as an example. A lack of a sense of student responsibility by some. An out of control "self esteem" movement among the education community and some parenting experts. Larger class sizes don't help (although Asian countries seem to be able to do a good job with big classes) And more.
Now, all this can be fixed...some of it very quickly. But before I talk about that I should acknowledge some positive changes going on right now.
Terry Bergeson, an enthusiastic support of reform math and the ill-fated (and poorly constructed) math WASL, was voted out of office (Superintendent of Public Instruction). Randy Dorn, who does not share her ideological baggage, was voted in, and has already made some positive changes. Recently, his office made a major public announcement saying that the standard algorithms for addition, multiplication, subtraction, and division WILL be required and tested on the new exam his office is creating. (It shows you have far we have gone into the dumps when something like this is a major advance!) He has also recommended some excellent textbooks on the elementary and high school levels for acquisition by state districts. And he has begun to restrain the antics of some holdovers from the Bergeson era.
With support by the State Legislature (who got sick of Bergeson's shenanigans) and the State Board of Education state math standards have been enhanced (improved, but still not as good as they should be) . And several districts, like Shoreline and Northshore, are moving to excellent curricula and textbooks.
Importantly, parents have begun to understand how the past system has really ruined their childrens' math education.
But the battle is hardly won. Some districts are going backwards, not forwards. The Seattle Public Schools, has poor discovery math books at all levels; the Seattle School Board voted in the Discovering Math series last spring (4-3 vote), even though the State Board of Education found it "unsound." The math coordinator for the city does not have a degree in math or science and is a real discovery advocate. Recently, the Seattle Board has voted to spend hundreds of thousands of dollars for tutoring from Sylvan Learning (talk about admission of failure). If your child is in this district you have a real problem in this failing district. The irony is that this district has a large proportion of minority students and they picked the worst possible curriculum for them.
But not all disaster districts are underprivileged. Take Issaquah. Issaquah has a Superintendent (Steve Rasmussen) and curriculum staff that are determined to railroad discovery math through the district. Currently, Issaquah is using one of the worst elementary school textbook series (Everyday Math) and their handpicked Math Adoption Committee has voted unanimously for the "unsound" Discovering Geometry and Algebra series. They even hired an outside contractor that supported their decision (you would not believe the reasoning. For example, Discovering Math would fit better with their current middle school math, Connected Math. So because the students are so weak for the current offerings, they need a weak math curriculum in high school!). If I was a parent in that district, I would let these people know that their ideological math decisions are simply not acceptable. High tech parents will have to pay to get their kids properly educated by Kumon or Sylvan or see them flip burgers for the imported high tech employees of the future.
Anyway, my 101 exam and other assessments given throughout the U.S. has shown that our nation and state have been running an unfortunate experiment on our children that has failed. It will not cost much to change the curricula and standards and only a modest amount to switch out the textbooks. These change will have a major impact on our childrens' math education.
Some people (like the Seattle Times) are fixated on testing our kids with high stakes tests, but this doesn't make sense (and is even cruel) if we don't have reasonable educational material in places taught by teachers who know their material. I would offer it makes more sense to test the teacher first for a competent knowledge of math! It is a very American thing to think you can change everything with a test, when the whole foundation is rotten. Amazingly, some business groups, like the Business Roundtable, don't understand this and are fixated on the exams and not the underlying curriculum issues.
So fix the curricula and books first. Properly educate the teachers second (and allow technical people to easily get into teaching). It will be much harder to change the mindset of the education lobby and particularly schools of education and "curriculum specialists" who tend to have an ideological approach without empirical support. I am embarrassed to admit some of the worst of the worst are at the UW. But the disaster that is our schools of education or K-12 education specialists in the math dept should be reserved for a future blog.
Finally, if you are interested to learn more about this subject go to the website of a statewide group interesting in fixing this situation: