This resource offers a groundbreaking effort to make mathematics education research on ratios and proportions readily accessible and understandable to preservice and in-service teachers of grades 6 to 8. Using extensive annotated samples of student work and based on research gathered in the Ongoing Assessment Project (OGAP), A Focus on Ratios and Proportions teaches readers how students develop understanding and fluency involving ratio and proportion concepts. Special features include: A close focus on student work, including 150+ annotated pieces of student work, to help teachers improve their ability to recognize, assess and monitor their students’ errors and misconceptions, as well as their developing conceptual understanding. A focus on the OGAP Ratios and Proportions Progression, based on research conducted with hundreds of teachers and thousands of pieces of student work. Sections on how Common Core State Standards for Math (CCSSM) are supported by math education research. Student work samples and vignettes to illuminate the research, as well as end of chapter Looking Back questions and Instructional Links, which allow teachers to analyze evidence of student thinking and strategies and consider instructional responses. An accompanying eResource, available online, offers an answer key as well as extensive explanation of the Looking Back questions. Like A Focus on Multiplication and Division and A Focus on Fractions, this book is designed to bridge the gap between what math education researchers know and what teachers need to know in order to better understand evidence in student work and make effective instructional decisions.
TEAN-LOUIS LUCHE A French poet of this eentury, Pierre Mae Orlan, wrote "Adventure does not exist, it is only in the mind of he who is pursuing it, and, as soon as it is at one's finger tips, it vanishes to come back to life, far away, in a different shape, at the frontiers of imagination". This sentence could be used to define the adventure that many sonochemists experienced. Most of them did not even suspect that the "laboratory trick" they were using was the first contact with a considerable amount of science. If a personal note is allowed here, it ean be interesting to mention the part played by chance in my involvement in sonochemistry. Almost 20 years ago, we had to perform an apparently simple Grignard reaetion with n-butylmagnesium bromide and geranial, but the results were repeatedly unsatisfactory. The one-pot Barbier technique was attempted, also without success. From my studies at the University, I imagined that the failure of the latter reaction could be caused by a common phenomenon known by solid state chemists as passivation, which in some cases can be overcome by ultrasonication. By chance, an ultrasonie bath was sitting on the next beneh, borrowed to clean some equipment. We clamped our reluctant reaction mixture into the bath, the reaction proceeded vigorously, and ... the adventure started. Without knowing anything about cavitation, high energies, ete., we had an illustration of Goethe's word "Am Anfang war die Tat" (at the Beginning was the Act).
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