Alternative Geometry

1.  Sacramento tests students during their ninth, tenth, and eleventh grades in math.  If students are not enrolled in a standards-aligned math class, the school earns the gift of 200 (a very low score) for each of those students from an API perspective.  All students get a score.  It is assumed that all students taking a math class will score better than 200.

2.  The third year test is called "High School Math."  It combines Algebra 1, Geometry, and Algebra 2.  Only three other tests are available: Algebra 1, Geometry, and Algebra 2.  As a result, only the tested Sacramento standards-aligned math classes matter to schools concerned about API.

3.  Sacramento only requires two years of math.  Schools have to encourage students to take a third year to get past the gift of 200.  It is assumed that this is also in the best interest of students; since it is a UC requirement.

4.  Normally, Mathematical Analysis (aka Pre-Calculus and Trigonometry) follows Algebra 2.  Statistics is the alternative for third year students.  It allows a "warm Mathematical mind" for those students so that scores above 200 can be achieved.  Linear Algebra is the remaining standards class.

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1.  Schools have exerted strong efforts to get some students through Algebra 1. At-risk students in Geometry frequently confuse perimeter with area. The burden of getting them through a conventional standards-based Geometry course is extreme on all parties.  It  is highly likely that many students may have to take Algebra 1 for two years and Geometry for two years in high school, that is, if they don't drop out.

2.  It is not clearly known if the dropout rate has been exacerbated by rigorous Algebra 1 and Geometry, when a generation ago, Algebra 1 wasn't even a requirement, but the difficulty of getting at-risk students through math in high school cannot be understated.

3.  Many advocate a second year of Consumer Math or some form of Applied Math for at-risk students.  This may or may not be wise for the students.  However, it certainly hurts the API of the schools.

4.  As a result, a standards-based Geometry course, that is more accessible, may balance student needs, state law, and school API's best.

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1.  Topics are covered in neither a Power Standards, nor blueprinted, nor conventional order.

2.  The exploratory nature of Geometry would be stressed.  For example, three dimensional surfaces could be explored first and translations/symmetry second.  Building the geometric and mathematical intuition of the students is the primary objective.  They need to enjoy the class, not hate it.

3.  Aids such as NCTM's Geometry Navigations or Euler diagrams would be used extensively.  Students would also construct nets of 3-D objects.  In this listing, 30 lessons exist at least.  Add complex constructions with compasses and miras for another 4 lessons.  If TI graphing calculators with Cabri Jr are used, another 5 - 15 lessons would be available.  Using spreadsheets to show how changes in dimensions affect area and volume would occupy at least 3 lessons.

4.  It is assumed that the course would evolve quickly over time.  For example, if ALEKS (see below) were used two days a week in a low-cost computer lab, then 100 -120 lessons would be needed, plus 5 STAR preps.  The lessons would be updated or deleted as more currently-available exploratory devices such as Java applets are incorporated.

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1.  Students still need practice in procedural Geometry and test-taking.  Many software programs could be used.  ALEKS should be strongly considered for it's "accelerated learning" capability, and gap filling.  It may be possible to simply assign ALEKS for homework once or twice a week, or two days a week in a computer lab may suffice.  It is a complement to the exploratory Geometry of the classroom.  ALEKS has an exceptional proof component.

2.  Geometer's Sketchpad or Geometry Expressions would be used in the computer lab for more exploratory work.  These have costs of over $100 per copy, and ALEKS has a charge of $35 per student.

3.  It is assumed that an alternative geometry classroom would have a LCD projector (e.g. Epson S4 at $700).  This would allow online Geometry applets or PowerPoints to be displayed on a screen.  It is not necessary to have a "smartboard."  A Wacom Graphire input device would be helpful.

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1.  If a software program could be considered a text, from a Williams perspective, then the software charge may be achievable within a reasonable budget.  There is no standard text for this class at this time.  If a text is required, a classroom set of the district-adopted Geometry book may suffice. However, a sequence of lesson plans becomes the text!

2.  Home Internet access would greatly benefit students.  This applies to almost all coursework.  It is necessary to achieve, if we want schools to reach a higher level of instruction.  This issue needs a task force to implement with perseverance.

3.  The course could be named Standards Geometry or Visual Geometry.  It should be vibrant and not "Basic Geometry," because it's not.