Written by Wendy B. Sanchez and Nicole F. Ice
(News Bulletin, December 2004)
Accountability is currently a topic of much concern in schools. Teachers feel as though they are spending so much time preparing students for tests and giving tests that their actual time to teach mathematics is limited. Other teachers fear that if they do not spend the majority of their time helping students develop proficiency in skills and procedures, then their students will not perform well on accountability tests. In the online chat following her President's Message in the July/August NCTM News Bulletin, Cathy Seeley consistently addressed the importance of Standards-based teaching over excessive test preparation. For example, in one of her responses, Seeley wrote, "I honestly believe that if we teach a balanced, comprehensive program that combines facts, procedures, conceptual understanding, applications, and the development of problem solving and other processes as described in Principles and Standards for School Mathematics, students will do fine on just about any test they encounter." Tests can measure a variety of content and processes, covering the spectrum between procedural and conceptual understanding. Schoenfeld (2002) explains that current data support three conclusions about mathematics curricula that embrace the content and processes emphasized in Principles and Standards (p.16):
1. On tests of basic skills, there are no significant performance differences between students who learn from traditional or reform curricula.
2. On tests of conceptual understanding and problem solving, students who learn from reform curricula consistently outperform students who learn from traditional curricula by a wide margin.
3. There is some encouraging evidence that reform curricula can narrow the performance gap between whites and underrepresented minorities.
These conclusions support Seeley's belief that the key to accountability lies in sound teaching practices rather than in test preparation. If students are taught a rich, Standards-based curriculum, then they will do as well as their peers who are taught a traditional curriculum on tests that measure procedural knowledge. They will do better than those peers on tests that measure conceptual understanding, and as an added benefit, we may even narrow the achievement gap, which is annually monitored for each school under the No Child Left Behind legislation.
In our own work with teachers, we have found that many teachers want to teach by using hands-on, engaging, "discovery" teaching methods but they feel constrained by curricula that are too full to investigate topics deeply and tests that assess isolated skills and procedures. Cathy Seeley encourages teachers to become involved in writing state standards and participating in the development of state tests so that they measure the important mathematics content and processes that teachers value. In her President's Message, Seeley reminds us that "for many years now, American mathematics curricula have been appropriately labeled as 'a mile wide and an inch deep.'" An independent audit indicated that not only did Georgia's Quality Core Curriculum lack depth, but it also could not be reasonably accomplished. In an effort to address this problem, Georgia is in the process of implementing a new curriculum with a narrowed focus and reduced repetitiveness that will provide time for teachers to investigate topics more deeply. The curriculum was created through a collaboration process involving teacher teams, state and national experts, and Consultants. On its Web site, the Georgia Department of Education states that
the revised and strengthened curriculum will drive both instruction and assessment in Georgia's schools, providing guidelines for teachers, students, and test makers. We will now teach to a curriculum, not to a test or a textbook. Our statewide assessments will be aligned with the Georgia Performance Standards, taking the guesswork out of teaching and providing guidelines for our schools, students, and test makers— and those standards will be based on best practices that have proven to be effective in high-performing states and nations.
Georgia is turning its attention toward developing a high-quality curriculum that supports best-teaching practices. We would like to highlight how other states are addressing accountability issues, particularly how they are handling the conflict that many teachers feel when trying to strike a balance between following best-teaching practices and preparing their students for accountability tests. Send us information or insight into what is happening in your state or district to firstname.lastname@example.org.
Schoenfeld, Alan H. "Making Mathematics Work for All Children: Issues of Standards, Testing, and Equity." Educational Researcher 31, no. 1 (2002): 13–25.