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This engaged the whole class, regardless of their previous comfort level with mathematics. Graphing was also helpful for students to visualize what things really 'meant' in terms of the numbers they were studying.
Communication
Solving word problems as a class in a hands-on fashion forced all students to communicate with one another about mathematics. This increased student comfort levels and generated a collective interest in the mathematical solving process.
Students were given stories that illustrated mathematical concepts to read and asked to tell their own 'stories' to show they could understand mathematical concepts in a qualitative fashion. They were often asked to interpret graphs using verbal descriptions.
One of the most popular activities was the use of online research. Students were asked to research concepts on the web, such as examples of fractions, proportional rectangles, or the use of certain calculation techniques, and report back on their independent research the next day. This also fulfilled the need to encourage students to communicate...
Using visual representations to understand abstractions proved essential, such as finding a 'mistake' on an Oriental carpet that was not consistent with a numerical patterning sequence. For some students, being allowed to describe concepts such as variables in words or representing them in pictures was an important learning step before they could understand more conventional numerical representations on the page.
Standards-Based Assessment Across the nation, states are setting tough new education standards, defining what students should know and be able to do. To help students meet these standards -- and to measure their progress in doing so -- states are also designing and implementing new standards-based assessment systems.States and districts use two types of interrelated standards: those that specify the content (what students should know or be able to do at
Students should be able to reflect on the process of problem solving. Reasoning and Proof Students should recognize that proofs are a fundamental aspect of mathematics. Within that understanding, they should develop the ability to select and use various types of mathematical reasoning. Communication The standard calls for students to communicate their mathematical thinking in a coherent and clear way to teachers, peers, and others. Students should be able to express their ideas
24). In order to speak specifically to grade level, the process standards were broken down by grade spans. The middle school grades were represented by standards 5-8, as these are commonly the grades that represent middle school. This presentation of process standards specifically presented by grade levels were called content standards. These were updated in 2000 as well. The 1989 content standards included the following ten standards: number and number
This has had the unintended consequence of increasing the dropout rate, as students who fail to perform and to be promoted leave the schools altogether. Many good, creative teachers also drop out, frustrated with the stringent controls placed upon their teaching style. ELL (English Language Learner) students are at a particular disadvantage for taking standardized tests, given the frequently arcane wording of the exams. The tests are often poorly written,
Use the appropriate representations to model problems in the physical and social sciences (Ibid.) Numeration Systems and Number Theory -- Number theory is a basis for all areas of mathematics. Number theory and sense are precludes to computation, to estimate, and to have an understanding of the ways numbers are represented and interrelated. Fluency of also understanding the way positive and negative numbers can be visually represented on a line,
relearn several mathematical concepts and learn how to instruct other about them. It also became necessary to learn the different components of educating students on math based upon their current knowledge and abilities and how the teacher will evaluate the students to make that determination. Not only did I learn how to teach the subject, but I was also instructed on how to submit and fulfill standards. In short,