After a long and frustrating homework session with his 2nd grade son one day last school year, Jeff Severt dashed off a letter to the teacher.
鈥淚 have a bachelor of science degree in electrical engineering. ... Even I cannot explain the common-core mathematics approach, nor get the answer correct.鈥�
A word problem about a fictional student named Jack had put Mr. Severt, of Cary, N.C., over the edge. It asked students to look at Jack鈥檚 鈥渘otes,鈥� including a number line with arcs indicating he鈥檇 skip-counted backward, and figure out where he went wrong in calculating 427 minus 316. 鈥淲rite a letter to Jack telling him what he did right and what he should do to fix his mistake,鈥� the problem said.
Mr. Severt鈥檚 wife snapped a picture of the 鈥渃ommon core鈥� math problem and the note to the teacher, and put them on Facebook. The post went viral.
Reactions to the problem ranged from angry aspersions cast at the federal government (the supposed purveyors of the Common Core State Standards) to strong defenses of the teacher and the task. Many people sympathized with Mr. Severt鈥檚 frustration that the problem made a simple subtraction task into a complicated, multistep production.
The response from the lead writers of the common standards for math was perhaps the most interesting: The problem wasn鈥檛 part of the common core, said mathematicians William G. McCallum and Jason Zimba. It was simply the product of a badly written curriculum.
The episode serves to illustrate the complex challenges and competing demands that schools and teachers face as they work toward implementing the new math standards.
As detailed in this report, part of a series of special reports by 91制片厂视频 Week that identify and explore high-priority issues in schools, the common standards for math differ from most previous state standards in significant ways. They are fewer in number, connect more broadly across grade levels, and emphasize conceptual understanding along with the procedural skills that schools have traditionally taught.
A recent survey by a research team at the University of Arkansas, in Fayettville, led by education professors Jason Endacott and Chris Goering found that 62 percent of the 191 math teachers who responded said they 鈥渁gree鈥� or 鈥渟trongly agree鈥� that the common-core standards are 鈥渕ore rigorous鈥� than their state鈥檚 previous standards. An additional 19 percent said they 鈥渢end to agree.鈥� (The survey was not nationally representative, though it drew on responses from teachers in all but one state that adopted the common core.)
Curriculum Confusion
The new standards include more granular changes as well. Students learn fractions by the use of number lines, a way of emphasizing their relation to whole numbers. They learn proportions as the relationships between two varying quantities, not as problems to be solved through cross-multiplication. And they鈥檙e asked to explain and justify their solutions, which involves increased use of academic language鈥攁 particular challenge for English-learners and students with below-grade-level literacy skills.
In addition to the content expectations, the common core includes eight Standards for Mathematical Practice. Those expectations describe the habits and methods exhibited by proficient math students, including perseverance, attendance to precision, and the ability to critique others鈥� reasoning.
Some of the changes can be hard to tease out of the standards themselves, so it鈥檚 understandable that many people have relied on social media and word-of-mouth accounts about what鈥檚 happening in math classrooms. Unfortunately, that tendency has led to what some see as critical misunderstandings about the common core鈥攑erhaps the most fundamental and widespread of which is that the standards are a 鈥渃urriculum.鈥� The standards are intended to be benchmarks for what students should know and be able to do. Curriculum, on the other hand, as Tom Loveless, a nonresident senior fellow at the Washington-based Brookings Institution鈥檚 Brown Center on 91制片厂视频 Policy, wrote in a recent blog post, 鈥渋s the 鈥榮tuff鈥� of learning, the content of what is taught in school鈥攅specially as embodied in the materials used in instruction.鈥�
A University of Arkansas survey asked 191 math teachers whether the common standards are more rigorous than the standards previously used in their states.
SOURCE: Jason Endacott and Chris Goering, University of Arkansas, 2013
But the distinction between what students should know by the end of the year (standards) and the specifics of how they should learn it (curriculum), can be blurry. For example, the common core doesn鈥檛 say 3rd grade students have to draw pictures when solving word problems involving multiplication. But it does require them to 鈥�use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings.鈥� Many teachers and textbook-writers will inevitably interpret picture-drawing as a key element, and some may go on to require it with every problem鈥攅ven though a separate 3rd grade standard states that students are also expected to memorize their multiplication tables.
Not surprisingly, as this report details, math-education experts see the development of more tailored and authoritative curriculum resources, along with improved professional-development opportunities for teachers, as critical to making the new standards work in classrooms.
Political Pushback
On top of the confusion about what鈥檚 in the new standards, the common core has been the subject of heated political battles across the country. When the new standards were introduced in June 2010, they were adopted in rapid succession by nearly all of the states. In many states, however, the standards have since encountered significant opposition. In the past year, Oklahoma and Indiana have bowed to political pressure and repealed their adoption of the framework.
The political debates have often been less about the content of the standards than the process by which the common core was adopted. Case in point: Indiana has since adopted standards that are very similar, if not identical, to the common core in many areas. Some opponents of the common core continue to regard the standards as an unprecedented federal intrusion into schools. In fact, the federal government was not involved in writing the standards, but it did provide financial incentives for states to adopt them.
The common-core-aligned tests, scheduled to debut this spring in many states, have also heightened anxieties about the standards. The Partnership for Assessment of Readiness for College and Careers and the Smarter Balanced Assessment Consortium received a total of about $360 million from the federal government to develop the new computer-based tests. Those assessments are expected to be more difficult than previous state tests, with the math sections including complex performance tasks. That has raised concerns for many teachers, especially those in states that plan to link educators鈥� evaluations to students鈥� scores.
Mr. Severt, of Facebook renown, eventually replied to the barrage of comments on his son鈥檚 math problem. He explained that his son, who has autism spectrum disorder, 鈥渒new the math answer immediately in his head. But this problem required a narrative answer utilizing a number line. While he knew the math, he balked at the answer being a writing assignment鈥攈is greatest anxiety.鈥� Mr. Severt decried the focus on 鈥渘ext-level critical thinking鈥� over basic operations with such young students. At the same time, he defended the assignment to a point, calling it 鈥渃reatively valid.鈥�
Indeed, the new math landscape in schools is marked by hard questions and daunting instructional shifts. This report aims to shed some light on the terrain by looking closely at the standards themselves and how they are changing math classrooms. The articles explore how schools and teachers are adjusting their practices to the new math standards and, perhaps more importantly, where there are gaps in support and understanding.
