Precise Mathematical Language: Exploring the Relationship Between Student Vocabulary Understanding and Student Achievement

In this action research study of my classroom of fifth grade mathematics, I investigate the relationship between student understanding of precise mathematics vocabulary and student achievement in mathematics. Specifically, I focused on students’ understanding of written mathematics problems and on their ability to use precise mathematical language in their written solutions of critical thinking problems. I discovered that students are resistant to change; they prefer to do what comes naturally to them. Since they have not been previously taught to use precise mathematical language in their communication about math, they have great difficulty in adapting to this new requirement. However, with teaching modeling and ample opportunities to use the language of mathematics, students’ understanding and use of specific mathematical vocabulary is increased.

The Critical Reception of Beethoven’s Compositions by His German Contemporaries, volume 2

The volumes in The Critical Reception of Beethoven's Compositions by His German Contemporaries bring to light contemporary perceptions of Beethoven's music, including matters such as audience, setting, facilities, orchestra, instruments, and performers as well as the relationship of Beethoven's music to theoretical and critical ideas of the eighteenth and nineteenth centuries. These documents, most of which appear in English for the first time, have been compiled from German-language periodicals published between 1783 and 1830. They present a wide spectrum of insights into the perceptions that Beethoven's contemporaries had of his monumental music. This is the second in a projected four-volume series. It begins with Opus 55, the Eroica, and ends with Opus 72, Fidelio.