An examination of existing research indicates that an increase in classroom thinking may improve student mathematics achievement. The 1999 TIMSS (Trends in International Mathematics and Science Study) found cognitive demand to be a key difference between mathematics instruction in the countries posting higher scores. The American Educational Research Association (AERA) explains in its fall 2006 Research Points that two types of cognitive demand are associated with student performance on achievement tests. The first has to do with the number and kind of mathematics courses taken. The second relates to how much thinking is called for in the classroom. In both cases, more is better.
Steps to improve K8
mathematics programs The National Research Council concluded in 2001 that many elementary and middle school teachers have only a shaky grasp of mathematics themselves and often are unable to clarify concepts for students or solve problems that involve more than basic calculations. Professional development for K8 teachers may be a prerequisite to the council's recommendation of a coordinated and systematic approach to K8 mathematics education.
Greater program coherence and in-depth coverage of selected content, from preschool to eighth grade, is the apparent goal of recommendations released in 2006 by the National Council of Teachers of Mathematics (NCTM). NCTM's Curricular Focal Points identifies key skills or concepts per grade level, such as quick recall of addition and subtraction facts in the second grade, and quick recall of multiplication and division facts in the fourth grade.
Only about a fourth of all students nationally take algebra in the eighth grade, but several studies have shown that students who take this gateway course are more likely to continue taking high-level math classes through high school. The Southern Regional Education Board (SREB) finds that students entering college are less likely to need remediation if they have completed challenging academic courses in high school, including a high-level mathematics course in their senior year.
AERA reports that a common practice is to sort students by perceived ability and assign them to fast or slow speeds of learning. Students taking a "slow track" course will most likely not cover as much by the end of the school year and may not be adequately prepared for high-level mathematics courses.
When Robert Dixon and colleagues (Review of High Quality Experimental Mathematics Research, 1998) reviewed findings from 110 experimental research reports, they concluded that effective mathematics lessons do not require students to apply new knowledge independently until they have demonstrated an ability to do so successfully.
Research supports the idea that students benefit academically when teachers frequently check for understanding and use a variety of strategies to engage students' thinking. Effective strategies can include reflective journals, cooperative learning, and whole-class discussion, especially when used to share, explain, and examine a variety of approaches to solving a problem.
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