1703 North Beauregard St. Alexandria, VA 22311-1714 Tel: 1-800-933-ASCD (2723) Fax: 703-575-5400
8:00 a.m. to 6:00 p.m. eastern time, Monday through Friday
Local to the D.C. area: 1-703-578-9600, press 2
Toll-free from U.S. and Canada: 1-800-933-ASCD (2723), press 2
All other countries: (International Access Code) + 1-703-578-9600, press 2
Summer 2008 | Volume 65 Thinking Skills NOW (online only)
Brent Loken
How can we push students to think for themselves?
How can we help students achieve what they need most—the ability to think for themselves and pursue their own learning? To facilitate this kind of learning, teachers need to rethink class design, instructional design, and curriculum design—and create structures that enable students to set their own pace for learning and assessment.
For several years while teaching math in Taiwan, I have successfully experimented with redesigning instruction and curriculum to help students take more initiative. I call my approach conscious differentiation.
I use an organizing strategy I call expeditions. Expeditions are long-term investigations of a core concept that feature much student choice and student-driven assessment. Students choose not only their own learning tasks but also their own schedule of assessments. For example, as part of a three-month expedition on linear functions, students explored how linear functions operate in the real world, an exploration that culminated in a multimedia presentation displaying their knowledge.
I set up three different pathways for each expedition, each reflecting a different ability level. Each pathway leads to mastery of the same benchmarks, but I provide more or less scaffolding—and assignments at different levels of difficulty—depending on the level.
In designing this structure, I drew on the Expeditionary Learning model (Expeditionary Learning Outward Bound, 2001). Organizing by expeditions helps cluster information around core concepts, one of the key ways that experts organize their knowledge. This approach takes students past superficial answers like "I'm studying Chapter 10" to deeper answers like "I'm exploring nonlinear functions" when asked what they are learning in math class.
Expeditions can spur student learning in any content area; in my current position at Hsinchu International School in Taiwan, I use this strategy to teach science and humanities courses. But I initially developed it while teaching a yearlong Algebra I course at Taiwan's Taipei American School. In this algebra course, students, broken into ability groups, moved through three expeditions: Linear Functions, Systems of Equations, and Nonlinear Functions. During the Nonlinear Functions expedition, I gave each group of students one of three digital portfolios to complete, depending on the group's level. Each portfolio required eventual mastery of the same benchmarks but was tailored to a different ability level. The portfolio pages, which I designed using Geometer's Sketchpad software, contained instruction, practice problems, and complex tasks such as building mathematical models.
Each student group chose its own daily tasks and pace as it moved through the portfolio. For example, one of the high-level groups decided to start the Nonlinear Functions expedition by building the mathematical models described in the later pages of that group's portfolio. These were complex tasks requiring students to use geometry software to, for example, build a model to calculate the optimal location for a warehouse that should be as short a distance as possible from three separate stores. These students spent a week trying to figure out how to build these models and finally realized they didn't have the knowledge to do so. So they went back to the first five pages of the portfolio and worked through the exercises until they had the skills necessary to build the models. Once the group members felt they were ready, they returned to the mathematical models, successfully completed these learning tasks, and passed the related assessments. Then they went back to complete the pages in the middle of their portfolio.
_{Photo courtesy of Brent Loken}
A group collaborates on chosen tasks as part of an expedition at Hsinchu International School.
This high-level group worked best by jumping back and forth through their portfolio and picking up the necessary information as needed. The students did not assign themselves any textbook problems or use the math book. They obtained all their information online or by asking other students, but they successfully completed their portfolio.
One of the mid-level groups doing the Nonlinear Functions expedition worked through its portfolio in a more systematic way. This group used class time to complete their portfolio task by task in sequence, take quizzes, and ask me questions. These students used their time at home to work on self-assigned homework problems from the textbook that would prepare them to do upcoming work in their portfolio. They assigned themselves homework every day. This group of students knew they did their best "figuring out" at home and their best "doing" at school.
These examples highlight the flexibility of expeditions. When students are given a chance to design their own learning experiences, they will design experiences that suit their learning needs.
Organizing expeditions—and the instructional year—around core concepts helps teachers carefully review standards and benchmarks and determine what they believe is worth teaching. To choose concepts, try using four filters developed by Grant Wiggins and Jay McTighe (2000) as part of their Understanding by Design framework:
In designing an expedition, I also consider which big ideas will incorporate the school's standards and benchmarks. My students now master as much or more math as they did before I introduced expeditions because they make deeper connections and retain information longer.
The next planning step is to work backward, choosing authentic summative assessments that will demonstrate students' mastery of the standards and benchmarks. For summative assessments, students initiate, for example, digital portfolios, original videos, and even pencil-and-paper tests.
Once I have selected summative assessments, I use formative assessment to continually measure each student's grasp of each objective or benchmark, typically through a combination of written and oral quizzes. Students receive immediate feedback on their understanding. Although I administer oral quizzes, students take written quizzes when they are ready and grade them themselves. A learner can take each quiz as many times as necessary to pass, and grades are not final until the end of the expedition.
Mr. Loken gives a student group an oral quiz, at their request.
Giving students the chance for retakes allows them to master content when they are ready. Many students who have a difficult time grasping a concept initially can master it at a later date.
I believe that each student should have the opportunity to receive an A in every class. In many classrooms, teachers target a more difficult interpretation of mastery, which makes it impossible for some students to earn an A. In this circumstance, the top tier of students is challenged, but the majority may be confused. In other classrooms, teachers lean toward a lower interpretation of mastery; more students master the standards, but a contingent of learners remains unchallenged. My approach challenges each student appropriately.
I use a color-coded grading system adapted from Clymer and Wiliam (2007) that clearly shows students which objectives they have mastered and which objectives they need to work on. In some expeditions, students progress through the objectives sequentially. In others, they can master objectives in any order they wish.
My last planning step is to design three different pathways students can take for the expedition. Students take a pretest to assess their knowledge, attitudes, and skills about key concepts. They then divide into three ability levels, each identified with a color to avoid stigma. Students group themselves into clusters of two to three students within their color level. Such choices give students ownership; 92 percent of the Algebra I students reported that grouping by ability helped their learning.
Students all master the same objectives, but the required tasks vary depending on each pathway's level. For example, the Nonlinear Functions expedition included the objective, "Be able to use mathematical models to solve real-world problems." The red group's assignment was to construct one model reflecting a real-world problem, the blue group completed two such mathematical models, and the white group constructed four models. This enabled the higher-level group to explore elementary calculus as well as parametrics.
Students write formal contracts in which they carefully describe their group's project and outline the objectives they must master. Before students begin the expedition, they discuss and propose a grading criteria for the whole class. Typically, students propose that the content portion of their grade be worth 75 percent of the overall grade and that the process (how students process the information and work as a group) be worth 25 percent.
Figure 1 shows a sample student contract developed for the Algebra I course at Taipei American School. Writing contracts takes time, but it's worth the effort because the resulting clear understanding of expectations increases student motivation. I help each group revise its contract if necessary and sign the final version. This agreement requires the teacher to pay the students with a letter grade upon successful completion of the contract, placing responsibility for the grade into the students' hands.
Next students plan the actions they will take in their expedition, particularly in three key areas:
Each expedition concludes with a different type of summative assessment project. For example, for the Linear Functions expedition, each group produced a 30-minute multimedia presentation demonstrating its knowledge of linear functions in the real world. I gave students a video camera and a motion detector and assigned them to discover how things move in the surrounding community. The video titled "Linear Is Everywhere" (see my Web site) is an example of the type of project students created to demonstrate their understanding of linear functions.
As the final assessment for the Nonlinear Functions expedition, students completed electronic portfolio templates showing the relevant mathematics, discussing how their work fulfilled the directions, and incorporating photographs or real-world examples of math. To see examples of student portfolios, videos, and assessments used with expeditions in various content areas, visit my Web site.
At Hsinchu International School, where I now teach, my colleagues and I use expeditions in many different content areas in the secondary grades. Although each expedition I have conducted or observed has unique content, and each discipline calls for a slightly different design, each one uses the general format and grading philosophy described here.
Besides learning content, students achieve other important goals through expeditions:
I have used expeditions at the International School of Islamabad, Pakistan; the Taipei American School; and currently at Hsinchu International School. Overwhelmingly, students at each of these schools have favored the learning environment created through expeditions. More than 85 percent of my students at Taipei American School reported that this learning environment helped them learn more than a traditional one, and 97 percent believed they had learned important life skills (for detailed student comments, see my blog). During 2007–08, the first year that teachers used expeditions at Hsinchu, average math grades rose between 5 and 10 percent compared to the two previous years. (The school has only existed for three years.)
The environment that expeditions create helps schools prepare students to not only pass examinations, but also to become the citizens our world needs. Expeditions provide fertile ground for differentiating instruction, curriculum, and assessment. I encourage readers to take the plunge and try using this approach.
Clymer, J. B., & Wiliam, D. (2007). Improving the way we grade science. Educational Leadership, 64(4), 36–42.
Expeditionary Learning Outward Bound. (2001). Evidence of success: Expeditionary learning in year eight. Garrison, NY: Author.
Wiggins, G., & McTighe, J. (2000). Understanding by design. Upper Saddle River, NJ: Prentice Hall.
This contract is entered between Mr. Loken and a student group of three from the Taipei American School concerning Expedition #3, Nonlinear Functions.
Overview: We are working to solve nonlinear equations using different resources. We will organize our own schedule to work toward mastering objectives. Every group member will get an A on every quiz and oral quiz if we score above 85%.
Objectives:
Resources: If we have any problems learning concepts, we will use or ask teammates and other classmates; the Internet; our textbook; Mr. Loken ("the Advisor"); or our tutors or parents.
Assessment: Students will earn the percentage below if they do the work as described below.
Process: 25% Students follow the schedule on their plans. Each group member contributes equally and shows teamwork.
Content: 75%Portfolio. Neat and organized but detailed. Quizzes. Students must get 85% or higher to earn an A. Oral GSP. Students should be able to explain the concepts clearly, showing in-depth thinking.
Portfolio. Neat and organized but detailed.
Quizzes. Students must get 85% or higher to earn an A.
Oral GSP. Students should be able to explain the concepts clearly, showing in-depth thinking.
Final Pledge: After all names have been signed to officially start this expedition, this contract will be valid from today, _________, until the project due date, ____.
Return to Article
Brent Loken is Director of Curriculum and Innovation at Hsinchu International School in Hsinchu, Taiwan.
Subscribe to ASCD Express, our twice-monthly e-mail newsletter, to have practical, actionable strategies and information delivered to your e-mail inbox twice a month.
ASCD respects intellectual property rights and adheres to the laws governing them. Learn more about our permissions policy and submit your request online.