It's time for another exegesis of an article in Edweek, this one on what the Common Core is doing for algebra students:
Under the Common Core State Standards, Algebra 1 is a much tougher course than what was taught previously in most states, teachers and standards experts say, in part because many of the concepts that historically were covered in that high school class have been bumped down into middle school math.Actual Common Core-inspired algebra problems tell a different story.
Some say those changes could complicate efforts around the country to put 8th graders in Algebra 1—a still-debated trend that's grown over the past two decades.And thus the Common Core, besides all the other fashionable K12 practices it endorses, has become yet another excuse not to accelerate students, but rather to impose a one-size-fits-all on everyone based on their calendar age.
And while that kind of move can disappoint some parents, educators point out it doesn't mean 8th graders aren't learning algebra.Well, that depends on what you mean by "algebra."
"There's big confusion between the Algebra 1 course with a capital A and algebra, the mathematical subject," said William G. McCallum, a mathematics education professor at the University of Arizona, in Tucson, and one of the lead writers of the common standards. "If you follow common core, there's now tons of algebra content in the 8th grade."Well, that depends on what you mean by "algebra."
"Traditionally in Algebra 1, a lot of time was spent looking at linear functions," said Diane J. Briars, the president of the Reston, Va.-based National Council of Teachers of Mathematics. "But a lot of that work now has been moved into 8th grade common core."Right. Kids in 8th grade (and younger) are filling in input and outputs on function charts, guessing and checking and plotting points on grids, and solving for x in simple equations involving minimal mental (or algebraic) manipulation. Then there's ratio and proportion.
"The common core… built much higher expectations for conceptual understanding regarding ratio and proportional relationships [in 8th grade] to prepare students to understand the ideas of slope and rate of change."It sounds pretty impressive:
Simultaneous linear equations and functions and their graphs—concepts also typically taught in Algebra 1—are now also taught in 8th grade under the common core.The catch is that those simultaneous equations never have more than two variables in them, even in today's Algebra 2, and that they require little in the way of symbolic manipulation.
The idea is that by the time students get to Algebra 1, they will have developed deep understanding of some basic algebraic concepts, and can dive into more complicated coursework.The "complicated coursework," though, is about applying these concepts to "real-world" situations, not to situations of mathematical complexity:
Students are focused on applying the algebra they're learning, rather than seeing it as a series of procedures and algorithms.
For instance, rather than doing a set of problems from the textbook, Mr. Ryan said, students in Algebra 1 might collect data on the weight of students' backpacks, plot them on a graph, and model them with an algebraic function.What's challenging about math, however, often isn't the concepts themselves. How hard, after all, is the concept of a function, or a slope, or an algebraic "model" of a simple, real-world situation like the weight of students' backpacks?
What's challenging about math, rather, is the mathematical complexity and abstraction that emerges from applying functions, slope, and algebraic models, not to real-world situations, but to mathematically complex situations, with layer upon layer of abstractions, abstract patterns, and symbolic manipulations. What students need practice mastering is this emergent property of complex, abstract math, and not the building-block concepts themselves--or their real-world applications. Yes, students need to engage with the concepts in action, but most especially in an abstract, mathematical way that few are seeing today.
Here are some examples of what they are missing, and will miss--throughout their years of Common Core-inspired high school math:
--simultaneous equations involving more than two variables.
--simultaneous quadratic equations.
--equations involving abstract quadratic patterns.
--real-world situations that take some real mathematical thinking to model mathematically.