The February 2004 issue of Educational Leadership on “Improving Achievement in Math and Science” raises an essential question—How can we improve curriculum and instruction to provide all students with a strong foundation in mathematics and science? The topic is especially important in light of U.S. students' somewhat dismal performance in these two content areas.
The Curriculum—A First Step?
Improvement in mathematics starts with the curriculum, according to William H. Schmidt (“A Vision for Mathematics,” p. 6). He looks to effective curriculums already in place in countries whose students showed outstanding performance in the Third International Mathematics and Science Study (TIMSS). Standard curriculums, coherent curriculums, challenging curriculums—only these, he contends, have a chance of boosting U.S. students' mediocre performance in mathematics.
Do you agree? Or do you feel that the teacher or pedagogy is more important than the curriculum in improving student achievement? Schmidt also challenges student tracking—a practice, he points out, that is unique to the United States for middle grade math. What is your school's experience with tracking in mathematics? Do you think tracking is effective? Is it equitable? What supports would you require to effectively provide all students with one rigorous mathematics curriculum? See Carol Burris and colleagues' account of a successful universal accelerated math program, in which high achievers' performance improved and more students became high achievers (“Math Acceleration for All,” p. 68).
Or Is It About Improving Instruction?
According to the Inside the Classroom study, less than 15 percent of science and mathematics classrooms deliver high-quality lessons (“What Is High-Quality Instruction?” p. 24). Authors Iris Weiss and Joan Pasley assessed 364 lessons on the basis of a number of sample indicators (see article sidebar). With your colleagues, read over and discuss the 12 indicators. Where do your classes measure up? Where do they fall short? What steps can you take to provide higher-quality lessons?
James Stigler and James Hiebert (“Improving Mathematics Teaching,” p. 12) agree that the pathway to student achievement is through excellence in instruction. They look to the proverbial fly on the wall: The TIMSS video studies of 1995 and 1999, which capture close-up pictures of instruction in 8th grade mathematics classrooms in several countries throughout the world. What do high-achieving countries seem to have in common? The answer, the authors write,does not lie in the organizations of classrooms, the kinds of technologies used, or even the types of problems presented to students, but in the way that teachers and students work on problems as the lesson unfolds.
The authors suggest that even when the curriculum includes “rich” problems that focus on concepts and connections among mathematical ideas, U.S. teachers generally turn the problems into procedural exercises or simply supply the answers. Do you find that this is the case in your classroom? What kinds of problems do you think students should work on during a mathematics lessons? And how should they be presented—as procedural exercises or as making connections problems? How can teachers create a successful blend of both? See Reys and colleagues' article on “Why Mathematics Textbooks Matter” (p. 61), in which the authors show an instructional approach adopted by some recent mathematics textbooks that challenges students to discover mathematical relationships. The lesson in question—at the 7th or 8th grade level—tackles the volume of cylinders and cones. Compare the traditional lesson (fig. 1) with the updated standards-based approach (fig. 2). Which most closely parallels your method of instruction? Which do you find the most effective?
Tom Loveless and John Coughlin (“The Arithmetic Gap,” p. 55) look at the problem from a different perspective, arguing for increased emphasis on computational skills, which they contend have fallen by the wayside in the wake of poorly prepared teachers, increased reliance on calculators in the early grades, and various math reforms. Do you agree that instruction should focus on honing students' computational skills? What role should calculators play in the early grades? In middle and high schools?
Richard Strong and colleagues (“Creating a Differentiated Math Classroom,” p. 73) suggest that teachers can facilitate student learning by using a variety of teaching strategies that take into account the four different mathematical learning styles that students bring to the classroom. Instruction can focus on step-by-step demonstrations, concepts and reasoning, real-life applications, or visualization and exploration. With your colleagues, discuss the four learning styles and the teaching strategies best suited to each. Do you use a variety of teaching strategies to explore mathematical topics? What new strategies might you incorporate in your lessons to include students with different learning styles?
Teachers can only improve classroom practice if they are aware of how their day-to-day teaching affects student learning. Do you and your colleagues regularly engage in such analysis? Does your school encourage classroom observation by fellow teachers, mentors, or lesson study partners to provide teachers with productive instructional feedback? For a look at a successful lesson study program, read Catherine Lewis and colleagues' article, “A Deeper Look at Lesson Study” (p. 18).
Make It Meaningful
Students often see little connection between their lives and what goes on in the physics or chemistry classroom. And students who don't see that connection are often reluctant to learn.
Several authors in this issue suggest strategies that can make science meaningful for students. Ginorio and colleagues (“The Rural Girls in Science Program,” p. 79) show how long-term research projects that connect directly to student concerns can increase student interest. In “The Dangerous Intersection Project...and Other Scientific Investigations” (p. 30), Conn suggests sparking student interest by presenting the class with real-world problems—such as how to fix a dangerous intersection. With your colleagues, brainstorm some real-world problems that would pique your students' interests. What long-term research projects might suggest themselves? What real-world problems—the more local and close-at-hand, the better—might you address in the classroom? Informally survey your students: What issues would they like to tackle; what problems would they like to research? Do you feel adequately prepared to successfully deploy inquiry-based instruction in the classroom? Is this an area where professional development might provide some needed support?
