Education Week - December 3, 2014 - (Page 10)

Word Problems Should Be Given At the Start of Lesson, Studies Say Earlier exposure found to boost learning By Sarah D. Sparks Fort Worth, Texas If Ms. Smith's 8th grade algebra class works through 10 word problems in an hour, and Ms. Jones' class works through 10 equation problems during the same time, which class is likely to learn more math concepts by the end of class? Please show your work. Word problems are often considered one of the most challenging tasks in a beginning algebra class, with students likely to stumble over the move from the clean, basic formula to applying it in a real context. Now, however, evidence from an ongoing series of experiments with students from middle school through college suggests that word problems might be easier and more beneficial for students when presented at the beginning, not the end, of a mathematics lesson. "Early on, symbols are barriers to learning," said Mitchell J. Nathan, an educational psychology professor at the University of Wisconsin-Madison. "Even with no context, word problems provide powerful informal problemsolving strategies, and language itself provides an entry point to mathematical reasoning that is highly superior to the algebraic equation." Mr. Nathan is one of a group of researchers who want to rescue word problems from the back of the textbooks. In an ongoing series of experiments he described at a symposium at the International Mind, Brain, and Education Society conference here on Nov. 6, Mr. Nathan and his colleagues are finding word problems may be most helpful for students just starting to learn algebra, rather than being saved until after they have "mastered" the formulas. Mr. Nathan, his University of Wisconsin-Madison colleague Martha W. Alibali, an educational psychology professor; Kenneth R. Koedinger, a professor of human-computer interaction and psychology at Carnegie Mellon University in Pittsburgh; and others are developing an intervention called "Bridging Instruction" to help students and teachers use word problems more flexibly. New Starting Point? In a prior study by the same group, high school teachers predicted students would have more difficulty with math problems presented as stories or non-narrative word problems than with those presented as symbol SYMBOLIC Solve for n: n x 6+66=81.9 equations. Moreover, the researchers found that teachers with a higher background in math-those who had majored in mathematics or physics, for instance-were more likely to think students would struggle more with math word problems than equations. Teachers with a lower math background and those who struggled in math themselves were more likely to believe students would struggle with stand-alone equations. "Maybe one's knowledge of math gets in the way of your ability to predict what your math students will do," Mr. Nathan said. "These highknowledge math and science teachers hold this theory about how students should learn math, and it doesn't match up to the student behavior." In a series of experiments-five separate high school studies, as well as some trials with middle school and college students-researchers, including Mr. Nathan, found students more accurately solved word and story problems than symbolic problems in both arithmetic and algebra. In each group, students were randomly assigned to solve different versions of the same problem: a symbolic equation, a story problem using that equation, or a non-narrative word problem of the equation. From the get-go, students were more likely to even try to answer a word problem than an equation. EXPRESSING MATHEMATICS Algebra problems can be presented in different formats, and a series of experiments suggests well-timed word problems may help students learn new concepts. NON-NARRATIVE WORD PROBLEM Starting with a number, if I multiply it by 6 and then add 66, I get 81.9. What number did I start with? STORY PROBLEM "When Ted got home from his job as a waiter, he multiplied his hourly wage by the six hours in his shift, and added the $66 he had made in tips. He found he had earned $81.90. How much does Ted make per hour?" SOURCE: Mitchell J. Nathan Working through narrative problems also made students feel more empowered to explore different methods of solving a problem, rather than following a single sample process. For example, a student might "guess and test" a variable in a word problem, using clues in the text to suggest a potential variable and then writing out the equation to test it. Or, the student might "unwind" a story problem to figure out the proper order of operations in the equation; for example, a mother sharing money with three daughters would divide by three, because subtracting three wouldn't make sense in that context. "When we asked students how they solved a problem when they had done informal reasoning, they said, 'I cheated'-because they hadn't done it the way the teacher had taught," Mr. Nathan said. Looking across the different variations of the problems, the researchers found 91 percent of students could solve a given math problem in a story- or word-problem form, while only 62 percent accurately answered the symbolic equation. Further, more than one-third of students could solve the problem only in verbal form, compared with only 7 percent of students who could solve symbolic equations but not word problems. Bridging Instruction In a more recent project, the researchers piloted their intervention, Bridging Instruction, with 90 7th and 8th graders in four math classrooms in a middle-class school district in the Midwest that used the Ed. Dept. Tapping Principals' Expertise for Policy CONTINUED FROM PAGE 1 standards-that put principals in the driver's seat for making such initiatives work in schools. "This effort might be a way to pinpoint the key agent of change, which in many cases is the school-the school as the unit of change and the principal as the key agent of that change," said David A. Gamson, a professor of educational theory and policy at the Pennsylvania State University College of Education. The federal initiatives focus primarily on school improvement and professional development and training for selected principals. They include the School Leadership Program, which awards competitive grants to districts to recruit, train, and mentor principals and aspiring principals; the Teach to Lead Initiative, a partnership with the National Board for Professional Teaching Standards that promotes teacherleadership opportunities in schools; and the Turnaround School Leaders Program, which disburses grants to train principals to lead low-performing schools slated for turnaround under the department's School Improvement Grant program. Those initiatives, among others, are seen as signs of progress by principals' groups and some school leaders who have long lamented that principals are often absent from the policymaking process or included as an afterthought. Some of the efforts, such as a "principal shadowing week," in which Education Department staff members spend part of the day observing principals on the job, appear to be photo-ready opportunities. However, both administration officials and principals' groups say the shadowing program can have impact-by putting department aides who make policy in direct contact with principals who are tasked with putting those policies into practice. Real-World Advisers Another effort, known as the Principal Ambassador Fellowship, installs in the department working principals who bring real-world experience and expertise into the policymaking process. Three ambassadors -two part-time and one full-time- play an important role in ensuring that principals' voices remain part of the discussion, and they provide insight on how the policies are likely to play out in school buildings. "I think it's easy for people to dream up big ideas and to go with what a textbook would say, in terms of what might work, but when it actually trickles down to the school level, we have to have people in the room who can say, 'Yes, this is practical; 10 | EDUCATION WEEK | December 3, 2014 | this is something that can actually happen in a school and can actually work,' " said Jill Levine, the full-time ambassador fellow. The fellowship program was revived two years ago-it first appeared when Richard W. Riley served as education secretary for President Bill Clinton-as a direct result of the principal-shadowing program. The federal focus on principals is not coming just from the administration. Those who work in leadership say they are also seeing an intentional inclusion of principals by congressional leaders while crafting legislation. The two largest principal associations say the new focus is heartening, but more action is needed. The National Association of Elementary School Principals and the National Association of Secondary School Principals have asked for more funding for the School Leadership Program, which received $25.8 million in fiscal 2014. Increasing funds would expand professionaldevelopment opportunities that address critical areas of the job, the associations argue, including conducting effective teacher evaluations and improving school climate. The groups also want a specific designation for principal-professional-development programs in Title II of the Elementary and Secondary Education Act, or esea. While districts can use Title II money for principals' professional development, most use the bulk of that aid for teacher-centered training programs. "With the implementation of college- and career-ready standards, [and] the new evaluation systems that are in place, [principals] definitely need additional training," said Amanda Karhuse, the director of government relations at the nassp, based in Reston, Va. More Action, Less Talk Kelly Pollitt, the associate executive director of policy, public affairs, and special projects at the alexandria, Va.-based naesp, praised the department for emphasizing the importance of principals, but said that federal education officials' talk about principals hasn't translated into policy initiatives that support the vast majority of the workforce. "They have talked a lot more about principals, ... but it's somewhat within the context of other initiatives," Ms. Pollitt said. "It's not about truly building the capacity of this particular role in education directly." Ms. Pollitt argued for more robust research-based professional-development and mentoring opportunities for principals. She also called on the department to redirect some of its discretionary funds to the School Leadership Program. Some point to Deborah S. Delisle's appointment in 2012 as the assistant secretary for elementary and secondary education as the pivotal moment for the department's emphasis on principals. "She was a teacher, she was a principal, she was a superintendent, she was a state chief, and that definitely brought a different perspective because most of the policy staff at the department came from [congressional offices]. They didn't come from education," said Ms. Karhuse. Ms. Delisle doesn't take credit for the shift, but said she's purposeful about including principals in serious policymaking discussions. (Mr. Duncan is fond of saying that he has yet to see a great school without a great principal.) "I am very aware that while a school or a school district may adopt higher standards, for example, that unless there is a school culture in which the principal and teachers share a common vision that all students can succeed, then the standards won't really mean anything at all," Ms. Delisle said. "It's not just to have an awesome staff, but it's certainly to have a visionary, courageous leader at the helm." Ms. Delisle and Ms. Levine are convening a working group of Education Department staff members who will continue to work closely with principals. They will invite principals to the department to talk

Table of Contents for the Digital Edition of Education Week - December 3, 2014

Education Week - December 3, 2014
Rules Aim to Heighten Ed. School Monitoring
Parents Get Schooled On New Math Standards
Principals’ Central Role Gets New Attention at Ed. Dept.
Districts Press Publishers On Digital-Content Access
Consortium Sets High Bars For Its Common-Core Tests
Table of Contents
News in Brief
Report Roundup
New Teacher-Licensing Exams In N.Y. Lead to Subpar Results
Obama Grants Deportation Relief To Immigrant Parents
Kindergartners Found to Benefit From ‘Tools of the Mind’
Blogs of the Week
Word Problems Should Be Given At the Start of Lesson, Studies Say
Tech. Vendors Cloudy On K-12 Buying Needs
New Guidance Offers States Roadmap to NCLB Waiver Renewal
Achievement, Dissension Marked Tennessee Chief’s Tenure
States Get Federal Running Room On Teacher-Equity Plans
Blogs of the Week
JOHN CESCHINI: STEM + Art: A Fruitful Combination
KIP ZEGERS: A Teacher, Students, and Poetry in Motion
JEAN HENDRICKSON: Why Not Art for Children’s Sake?
TopSchoolJobs Recruitment Marketplace
JEFF DEKAL: A Brief Portrait of a Young Artist

Education Week - December 3, 2014