Mathematics education in the United States has never been more exciting. New content and pedagogy, enhanced and spurred by technological advances, have grabbed the public's attention. NCTM has led the way to inform and rally professionals to address this renaissance in how we approach the learning of mathematics. Educators are tackling the jobs of dealing with new curricula and keeping up with professional development to align their school district's goals with the NCTM's Standards. Educators are also seeking ways to keep parents more informed and involved. One such effort was to develop a guide to be used by teachers and principals to provide unified responses to the questions most commonly asked by parents.
Next we give a couple of examples to illustrate the procedure given above. Example I: Let S = 7 263 025 = 5 2 x 7 4 x l l 2. Here N = 2 4 x 3 2 x 5 2 = 3600. Note that d(S) = d(N) = 5 x 3 x 3 = 45. We can take M = 2 3 x 3 2 x 5 x 7 = 2520 and d(M) = 4 x 3 x 2 x 2 = 48. Note that M < N < S and while each of S and N has 45 divisors M has 48 divisors. Example II: Let S = 148 225 = 5 2 x 7 2 x 11 2. Here N = 2 2 x 3 2 x 5 2 = 900 and N < S. We can take M = 2 4 x 3 2 x 5 = 720. Now M < N < S. Note that d(M) = 5 x 3 x 2 = 30 and d(S) = d(N) = 3 x 3 x 3 = 27. So M has more divisors than N (and so than S). I thank the referee for his suggestions.
One of the Japanese mathematics lessons reported in the Third International Mathematics and Science Study (TIMSS) involves the concept of the area of a triangle. On the first day, students explore the area of triangles obtained by using the same base but translating the vertex opposite the base along a path parallel to the base, thus keeping the height constant. The next day the students are reminded of that property and are given a challenging problem that applies the property.
Safemap is an acronym for the Santa Ana/Fullerton Elementary Mathematics Project, a partnership between the Santa Ana Unified School District and California State University at Fullerton and is cofunded with the National Science Foundation. Teachers of grades K–5 meet on weekends once a month to study mathematics content, complete homework assignments, and prepare to implement lessons in their classrooms, all of which are shared and discussed at the next monthly meeting. Regularly scheduled monthly meetings allow for networking and bonding among teachers that have not previously been evident in summer institute. Every participant in SAFEMAP is also trained in Family Math courses and conducts six Family Math sessions for students and their parents.
The Calculators and Mathematics Project, Los Angeles (CAMP-LA) (NSF Grant #MDR-8651616)1 has produced mathematics lessons for grades K-6 that make use of the basic four-function calculator. Experiences at mathematics education conferences where these lessons were shared, indicated that there was interest among middle school mathematics teachers to develop similar lessons appropriate for that level. We decided to explore this interest by sampling from a larger and more diverse audience before expanding the project to include middle school materials. In addition, it was decided that the new materials should consider using newly developed calculators that could compute with fractions. Thus, the following questionnaire was developed to determine the most current information on the use of calculators in middle school mathematics classes. The questionnaire was designed to ascertain 1) how often and in what ways calculators are being used; 2) teachers' opinions on the impact calculators should (could) have on the mathematics curriculum; 3) how familiar teachers are with various so-called “fraction” calculators; and 4) what types of curriculum materials (if any) should be developed if students used a fraction calculator.
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