I just read a journal that said, "Mr. Betz... preferred to consider some aspects of the present crisis in the teaching of elementary mathematics." If I didn't tell you the year, and you were aware of the history of mathematics education in the United States, you might think the paper was very current, or perhaps from the "math wars" in the late 80s and (is it still going on?). Or maybe you would think it was related to the "New Math" of the 60s. The actual paper was presented at the Twentieth Annual Meeting of the American Mathematical Association (1935) by Professor William Betz of the University of Rochester.
His concern was that high schools and universities were no longer requiring mathematics. "It appears that in seventeen states mathematics is no longer a required subject in high schools." He stated that in a survey of the state superintendents of instruction, they blamed poor teaching, poor textbooks, and "an unconvincing and ineffective formulation of the objectives of elementary mathematics." I wonder what the same type of survey would say today.
Later, he asks a question that could come, and frequently does, from many concerned educators today, "Does secondary mathematics... represent such a vitally essential educational element that it should be made mandatory in the curriculum of all normal pupils, even though many of them may never have occasion to use it for immediate, vocational use." How would you answer that question, and how would you justify your answer to someone who disagreed?
He goes on to give his answer to the question with three aspects of mathematics education that are most important, symbolic thinking, postulational thinking, and relational thinking. No "solving quadratic equations" or any other laundry list of "skills".
I recently wrote about the high number of college students who take remedial, not for credit, math courses in college. Many of them graduate with grade point averages of B or higher. This morning I searched around to see what I might find quickly about the present state of remedial courses... here are a few notes.
"An Arizona Community Foundation study released in January showed that half of Maricopa County's 2006 high school graduates who entered Arizona universities or colleges had to take a remedial math class and a quarter had to take a remedial English course." [By MIKE McCLELLAN, The Arizona Republic (Phoenix)]
In many areas of Arizona it was much worse. Higher education in the United States: an encyclopedia, Volume 1, By James J. F. Forest and Kevin Kinse reported that in Maricopa County Community College, "in 1997 up to 90% of entering freshmen required remedial mathematics courses".[pg 521] On the same page I read that the California State University System "which only admits students from the top one third of their high school class", regularly had over 40% of freshmen taking remediation courses in mathematics. The book also reported that in 1999 CUNY, after thirty years of a pro-remediation approach (following student protests in the 60s), began to deny entry to "underprepaired students". I am not sure what the current status of that policy is ten years later.
The two-semester remedial math program at LaGuardia Community College, City U. of New York, ... about 60% of entering students are required to take one or both of these courses.
From the Columbus (Ohio) Dispatch, "Statewide, 39 percent of about 52,000 first-year public college students took at least one remedial course in 2008, according to a state report released this year. Among all Ohio high-school graduates that year, more than two-thirds had taken a college-preparatory class."
Community colleges are struggling to solve the remedial math problem: How to get students who can’t find the lowest common denominator — or don’t know there is such a thing — to learn basic math skills and move on. For many, math is an insurmountable barrier, writes Elizabeth Redden on The Hechinger Report (and in Chronicle of Education).
"Only 31 percent of students placed into remedial math ever move beyond it, according to the Community College Research Center at Columbia University’s Teachers College.
Less than 25 percent of community-college students who take remedial or developmental courses earn a degree within eight years compared to 40 percent of non-remedial students
In her "Math Mama" blog, Sue VanHattum recently wrote about the start of her college course, "No one (3 sections, about 140 students total) passed the mastery test I gave on pre-algebra topics. (FIDO = fractions, integers, distributive property, and order of operations)."
Perhaps even more surprising was her discussion of having discipline problems with her college students. She has had more discipline issues in the first week of college classes than I have in a year of my advanced high school classes.
I admit I don't know where all these problems will take us. Many schools and states have started distance education programs where students don't even have to show up in person to take the final exam. Huge numbers of students are being home schooled, but I suspect they are getting a better than average education because of the selective sample who choose to raise their children this way. One more thing to look up...