Integrating Math Tools
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All-Year-Summer-School allows short (less than five credit) courses, basic skill enhancement, and aspects of core course debugging to occur under a low risk environment.  It serves as a prototype of a data-driven curriculum that could make the administration famous; especially if a few students can get summer lab work as a result.  The following classes suggest themselves:

Start all year summer school with a computer lab open after school offering iPass and ALEKS courses as Miscellaneous Elective - Math.  The classes do not have to be five credits.  This supports students in mastering the basics while taking standards-based courses concurrently.  Fasttmath would also be available. 

There are enough activities available to get a short course in use of TI Graphing Calculators going.  It would primarily be an on-your-honor course with a simple demonstration test for elective credit.  This could be followed by a Vernier demonstation course for familiarity with the instrument and data acquisition.

Similarly, short courses in Geogebra and Geometers Sketchpad could be offered.  This would allow a more rigorous Honors Geometry to take place.

Miscellaneous Elective - Science, less that 5 credits, can be offered to have students perform statistically-based, data-driven exercises. This would allow labs and software to be debugged, and when a critical mass is achieved and money available, implemented into the classroom as part of a standard course.  Teachers would learn how to use the products.

Miscellaneous Elective - Biology Lab could be comprised of Bio-Rad or equivalent exercises.  Again, this would allow labs and software to be debugged, and when a critical mass is achieved and money available, implemented into the classroom as part of a standard course.

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1.  Online software that satisfies the main needs for procedural math instruction is available from several suppliers, such as Carnegie Learning or ALEKS.  The most useful criteria include:

    a.  Adaptive Assessment - through AI student knowledge levels are identified, which allows faster learning with less fatigue.

    b.  Randomized Values - if problems are identical to problems offered earlier or known to other students, only practice in sharing answers will be given.  This is a defensive need.

    c.  Easy database maintenance and reporting to reduce teacher fatigue.  This must be very fast to handle hundreds of students.  If a teacher takes minutes to drill down, then usage will decline.  This is a defensive need.

    d.  Student choice in selecting work allows coping with frustration.  It allows them to work longer and also minimize teacher facilitation time.

2.  Smartboard instructional software is available.  HeyMath! is the leader.

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1.  As the simple review diagram suggests, the lack of adaptive instruction is the primary reason that math software lags.  It's hard enough to tutor one-on-one. Getting software to recognized different learning styles so that graphics routines, or complex text, or audio can be brought to play automatically is the holy grail of this business.

2.  Acceptance of using math in English classes, for example, or English in math courses is lacking.  Math teachers should know that language is the primary driver for real learning of mathematics.  Focusing on doing problems is a dead end.  It is easier for science teachers to use math problems and it is reasonable for math teachers to use science examples.

3.  Putting tools together has been and can be done for inter-class integration.

4.  The tools approach has embedded a high-end reform math perspective that many fine unsettling.  It is data-driven math: concepts with real values.  To put it differently, in traditional geometry, right triangles with Pythagorean triples for sides and the extreme emphasis on 30-60-90 triangles is mathematically trivia, but the lack of real numbers in courses force problems in this area.

    Data-driven elementary approaches and problem/activity-based learning is acknowledged for superiority, then it is tossed in middle/high school.  This cultural issue is not a mathematical one.  In short, Fathom and InspireData should be the center-piece of an integration effort, but enthusiasm for this is low.

5.  Graphing calculators are difficult to use and dramatically obsolete.  Any computer has software that duplicates them better; for example, Microsoft Math.  If it wasn't for the fact that the SAT and ACT only allow graphing calculators, they would be disappear.

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