So are all of the proportionality topics and all of the algebra topics. These results imply that the quality of learning opportunities surrounding many of the mathematics topics taught in 1st through 3rd grades was not likely to be high. They also suggest that there is large variability in self-reported content-specific knowledge. The other striking feature of the results was the large variability across districts.
For example, for fractions, in some districts all of the primary teachers felt very well prepared, while in other districts only about half of the teachers felt very well prepared.
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The results for districts for 4th- and 5th-grade teachers were quite different. For example, for eight different topics, all of the teachers in at least one district felt very well prepared academically for each of those topics. At the district level, the results for whole number meaning and operations were similar to those for 1st- through 3rd-grade teachers.
However, the variability across districts remains a striking feature for 4th- and 5th-grade teachers, particularly for decimals, percentages, and geometry basics.
These are all topics that were supposed to be introduced in these grades in Michigan and Ohio. For example, for decimals, in one district only one-fourth of the teachers felt well prepared, while in another district virtually all teachers indicated that they felt well prepared to teach decimals. We examined the pool of teachers from all of the districts taken together. Only two topics came close. Sixty-nine percent of the teachers indicated that they felt well prepared to teach the topic of data. This included the two topics just mentioned as well as nine others—negative, rational, and real numbers; exponents, roots, and radicals; number theory; polygons and circles; congruence and similarity; proportionality problems; patterns and relations; expressions and simple equations; and linear equalities and inequalities.
The Michigan and Ohio standards call for including many of these topics at the middle grades.
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For example, there has been a strong national movement to include elementary algebra topics in the middle school, particularly in 8th grade. The Michigan and Ohio standards reflect this, as do the Common Core State Standards , which are in the process of becoming the new Michigan and Ohio state standards. Adoption of the Common Core State Standards brings states more into alignment with international benchmarks of what is expected in the equivalent of middle school. The severity of the problems faced by these districts and, by inference, by the United States as a whole, was indicated by the fact that only about half of the teachers felt academically very well prepared to teach expressions and simple equations, as well as linear equalities and inequalities.
The story for high school teachers is rather different, which is not unexpected given their typically greater preparation in mathematics. The areas in which high school teachers indicated that they felt less well prepared were number bases, three-dimensional geometry, geometric transformations, logarithmic and trigonometric functions, probability, and calculus. These findings are, however, still cause for concern. For example, there is an increasingly strong push for the inclusion of probability and statistics in high school, as is found in the Common Core State Standards, yet less than half of the surveyed mathematics teachers felt well prepared to teach it.
However, there was still great variation across the districts, especially for geometry topics including transformations, three-dimensional geometry, polygons, and circles. There was similarly great variability in the percentage of teachers who felt that they had the coursework to make them well prepared to deal with calculus, probability, number theory, and logarithmic and trigonometric functions.
We have surveyed how well prepared in terms of disciplinary course work teachers at various levels felt for teaching various mathematics topics in what is a fairly representative sample of 60 districts. In general, we would summarize the findings by stating that many teachers felt ill prepared to teach mathematics topics that are in state standards and in the new Common Core State Standards for mathematics.
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Why did these teachers feel so ill prepared? There is perhaps a simple answer for the elementary and middle school teachers: They felt ill prepared because if we examine the coursework they studied during their teacher preparation, they were ill prepared. The new TEDS study results suggested this to be the case more generally, which clearly does not bode well for equality of learning experiences for students in these districts. In this section, we summarize what teachers have told us about their preparation in mathematics at the college level and as graduate students.
Teachers at this level are typically generalists—they must be prepared to teach many different subject-matter areas. They do not have adequate time in their preparation to get a major or a minor in each of those subject matters. At 4th grade, the international data paint a different picture. Unfortunately, the definitions are not precisely the same, but the data do provide us with a benchmark of sorts.
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Including those primary teachers with either a mathematics major or a minor in mathematics or science, around one-third of 4th-grade students on average had such a teacher in the countries that took part in TIMSS , [the Trends in International Mathematics and Science Study]. Curtis C. McKnight is emeritus professor of mathematics at the University of Oklahoma.
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Educational inequality - Wikipedia
Inequality for All makes an important contribution to current debates about economic inequalities and the growing achievement gap, particularly in mathematics and science education. The authors argue that the greatest source of variation in opportunity to learn is not between local communities, or even schools, but between classrooms.
They zero in on one of the core elements of schooling--coverage of subject matter content--and examine how such opportunities are distributed across the millions of school children in the United States. Drawing on data from the third TIMMS international study of curriculum and achievement, as well as a six-district study of over schools across the United States, they point to Common Core State Standards as being a key step in creating a more level playing field for all students.
Read more Read less. About the Author William H. Curtis C. McKnight is emeritus professor of mathematics at the University of Oklahoma. Free Returns We hope you are delighted with everything you buy from us. However, if you are not, we will refund or replace your order up to 30 days after purchase. Terms and exclusions apply; find out more from our Returns and Refunds Policy.