The ultimate test of an educational system is whether it makes sure that every student, whatever their background, is exposed to the content they need to compete in today's society. U.S. schools are failing this most basic test, and in the process wasting the talents of millions of American children -- children from all backgrounds. The reality is that, for most students, the education they receive is largely based on chance, making academic opportunities into a kind of lottery -- one with profound consequences.
A central challenge in improving America's education system is to guarantee equal opportunity to learn the essential content, skills, problem solving, and reasoning abilities. Reformers on both the left and right have been consumed with equalizing resources, but they too often miss the core of schooling: the instruction of academic content by teachers to students. And it is precisely in the area of the coverage of instructional content that we find large inequalities, especially in mathematics and science -- key subjects for future job opportunities and U.S. economic growth.
I don't have the space here to delve into great detail; the full story can be found in my new book Inequality for All, written with Curtis McKnight. What I'd like to do here is highlight a few key points related to the extent and origins of inequalities in mathematics content coverage.
It should come as no surprise that inequality in opportunity to learn is related to the lower achievement of underprivileged students. Students in high-poverty districts are often exposed to less rigorous content. In fact, weak math instruction is so common in struggling districts that their instructional content has more in common with low-income districts in different states than they do with more affluent districts in the same state.
One of the reasons I wrote this blog -- and why we wrote our book -- was to dispel the myth that inequality in opportunity to learn is just a problem for poor and minority students. In fact the greatest variation in learning opportunities is among middle-income school districts. Parents can't assume that just because they live in a middle-class community that their child is getting an equal chance to learn important mathematics topics to the needed depth and in a coherent and focused way.
Unequal opportunity to learn is a threat to every student because it is the difference among classrooms that is the biggest source of variation. More than what state, district, or even school a student attends, their classroom assignment determines what math topics they have a chance to learn. Classes vary greatly in what topics are taught, for how long, with what rigor, and in what order. For example, students in different "algebra" classes could focus on basic arithmetic topics or cover more advanced mathematics, experiencing dramatically different learning opportunities despite sharing the same course title -- even at the same school!
What many don't realize is how widespread the practice of tracking, where students at the same grade are taught different mathematics content, really is. Students placed in classrooms with lower level topic coverage see their chances to move on and take more advanced courses in high school and college severely limited -- once placed in a lower track, it is very unlikely that they will ever catch up. This can also have longer term consequences. National statistics indicate that in eighth grade three-quarters of students are tracked in one way or another, as are roughly a third of fourth-graders. I challenge anyone to justify influencing a child's chances in life based on how well they are doing when they are only ten-years-old.
Before anyone rushes to conclusions, just because classrooms are where a lot of inequality originates, it does not mean that we should blame teachers. Too many teachers are inadequately prepared to teach mathematics, and are forced to pick and choose what to teach from the conflicting guidance of textbooks, state and district standards, and assessments. Too many mathematics textbooks give shallow coverage to too many topics rather than focusing on a few key topics at each grade, as is done in higher-achieving countries.
Despite the tremendous challenge of ensuring equal opportunity to learn matematics, I believe there is reason for optimism. The new Common Core State Standards in Mathematics, for example, presents an excellent chance for implementing high-quality standards. The Common Core represents a chance to reform the fragmented, incoherent U.S. math curriculum that makes mathematics education a product of blind chance, and to move toward a system that really does provide every child with an equal chance at an education. The American dream has always rested on the assumption that schooling provides the level playing field by which this is possible. The data presented in Inequality For All calls this assumption into question.
Ryan Hall: To Learn the Value of Algebra, Just Ask an Eighth Grader
The most important advice for parents: make sure your child is put into the honors classes. Even if your child is at the lower end of ability to be successful in an honors class, make sure your child is in that class. Otherwise, your child will waste time in school.
Second, enough with the "student-focused" learning. "Oh, our kids are so bright, they can teach themselves with just a bit of guidance from the teacher." Baloney. They don't know how to organize a project, prioritize information, or do research. What they're taught about research is often woefully out of date (remember physical notecards? Why are they STILL being used?) and out-of-synch with their development (asking 7th graders to make sense of the bureaucratese on .gov sites and academese on .edu sites...and they have no home access to plain old encyclopedias; plus, they're told to "use google books"--and how does one do that without guidance when you're 12?). Online learning is only for kids who become teen parents or kids whose parents squawk enough and threaten to pull out of the fundraising arm of the PTO. If you learn more quickly or more slowly than the classroom teacher teaches, tough luck. No online learning for you! No Khan Academy--as it's "unproven." Sit and listen to the teacher droning: that is your only choice in 2012 even in a top rated public school. It's appalling how far behind they are--and how much in denial they are!
Calculus for math majors - the course has a major focus on proofs
Honors calculus for science and engineering majors,
Calculus
Similar distinctions are made by the science departments as well.
Why is is wrong to do the same in public schools?
"...is exposed to the content they need to compete in today's society." Exposure is not the problem- learning is. Students who do poorly in school- and statistically go on to do poorly in life -have issues with learning the content. Not that they lack, "...an equal opportunity to learn..." The opportunity has been provided but has not been taken advantage of.
The education a student receives is not based on the "chance" of the school she or he attends, but on the chance of who the parents are. This is basic sociology- something ignored almost completely by education pundits and policy makers.
The solution is NOT in content but in creating effective ways of training the students to learn.
This author's "solution" - anti-ability tracking - actually creates more of the problem by creating the negative random chance situation- disruptions to learning by those who either have difficulty learning, causing the content pace to slow or who have anti-social behavior patterns, slowing the learning for everyone. Good tracking is matching instructional styles (and content) to the students.
Learning happens by building on what one already knows in a gradually expanding process with scaffolding and support- not by throwing content at everyone "equally," which is magically learned.
Until teachers and social scientist are more a part of the conversation, hot air will continue to create more heat than light in this discussion.
Tracking is here for a reason. Some of the kids are significantly ahead of others. Teaching to the slowest bores the more advanced. Teaching to the more advanced frustrated the less advanced. I pulled my 7th grade daughter out of classes that were moving to slowly and switched her to on-line classes so that she could more at a more appropriate pace.
My 6th grade son took 7th grade math (Algebra A) last year. One of his friends took 8th grade math instead.
The problem is the age lockstep that the schools are set in. Some students learn faster and more deeply than others - and this can be subject dependent.
As for my daughter, she finished 10th grade a month ago, turned 15, and is dropping out of high school. Instead, she is starting in the Honors program at the University of Washington with a cohort of other early admittance students.
One size does not fit all and the schools need to adapt.