The Current Dilemma
Over the past decade, states and schools have spent enormous sums of money in efforts to improve K-12 students’ proficiency in mathematics. A great deal of this money has gone into developing various annual standardized exams to measure student progress. Another large portion has gone toward various programs, including computerized “test-prep” programs, intended to help students raise their scores on these exams. At the same time, individual families have sought out tutoring and purchased computer programs to assist their children, often at considerable expense.
Unfortunately, most test-prep systems, like the standardized exams on which they are based, function primarily to determine students’ current levels of performance, while doing almost nothing to improve that performance. In other words, they are designed for assessment only, not for learning. This conventional approach to assessment means that the resources poured into standardized exams and test-prep programs have not, in fact, been used for mathematics instruction. No wonder test scores are not rising.
At the Distributed Learning Workshop, we believe assessment is a crucial part of mathematics learning and teaching, but that it must be part of an approach that we call “assessment-guided learning.” This approach has four key elements:
- Number, variety, and quality of assessment items. To help students prepare for standardized exams, states are required to publicly release bodies of items that are similar to those that will appear on the exams. These items are designed to measure proficiency across broad swaths of the curriculum, and to do so within the limited time frame of the exam itself. As a result, publicly released items are few in number, and each item is highly complex. To master the many intertwined strands of the mathematics curriculum, students need access to a much larger number and variety of standards-aligned items than states themselves are able to provide.
- Real-time feedback and progress reporting. Standardized exams are typically given at the end of the school year, and the results are released several months after that. This is far too late for either teachers or students to use these results to determine the areas of the required curriculum in which students need assistance. In contrast, when results are delivered in real time, teachers are able to continuously review their pedagogical strategies to better address students’ needs. The more assessments students take during the school year, the more data can be generated on their strengths and weaknesses, allowing teachers and students to focus on the precise content areas where students need improvement. Furthermore, students using the program, on their own or with a teacher or tutor, can use the data to better understand and take charge of their progress as mathematics learners.
- Worked-example solutions. There is a great deal of evidence that immediate feedback is even more effective when combined with “worked-example” solutions. Worked examples are a special type of instructional “exemplification,” designed to help students not only to understand the problem at hand, but to generalize and transfer that understanding to similar problems. Proficient mathematics learners benefit from worked examples because they help them pick up the underlying features of these relationships more quickly. Less proficient learners benefit because worked examples illustrate the relationships among mathematical elements in a deliberate, staged manner.
- Location-independent access. An important aspect of assessment-guided learning is helping students recognize their particular strengths and weaknesses as mathematics learners. When they can do that, they begin to take charge of their own learning, and their confidence and performance both increase. For this to happen, however, students need access to large numbers of item / worked-example pairs both inside and outside the classroom. Location-independent access empowers students to work at their own pace, on as many problems as they need to shore up areas of weakness.
The Workshop’s view of assessment thus stands in stark contrast to conventional approaches. In our view, assessment is a continuous, flexible, instructional process that accommodates individual students’ learning needs, helping them achieve a thorough and lasting understanding of mathematics.
We have developed Learning Conductor, an Internet-based suite of instructional technologies, to transform assessment into assessment-guided learning.
Learn more here