Math Curriculum Alignment

Transcription

1 AGENDA ath Curriculum Alignment Friday February 12, 2010 (10am-2pm) Valencia Community College, West Campus Building 11, Room 106 I. Welcome and introductions. II. Review of past meeting. III. Calculus II IV. Calculus III V. Best Practices for Calculus VI. Best Practices Conference for STE Field at UCF VII. Conclusion and next steps. a. Include high schools in process? i. How? ii. What makes most sense or what is most needed? iii. Recommended schools in your service area? b. Next meeting c. Date and location

2 ath Curriculum Alignment Workshop inutes Valencia Community College, West Campus February 12, 2010 In Attendance: Linda Parrish (BCC); ichael Jamieson (CFCC); Randall Allbritton, arc Campbell, Natalie Weaver (DSC); Steve Boast (LSCC); Tony alaret (SCC); Lori Dunlop-Pyle (UCF); Lisa Cohen, Lynn Hearn, James Lang, Nathan Baker (VCC); Craig Tidwell, Carol Watson (UCF). embers welcomed at 10:10 am by Craig. Everyone then introduced themselves and shared what courses they teach. inutes from the ctober meeting were reviewed and approved. Question was raised about calculator use in Calc I and for testing purposes. Short discussion ensued on calculator use the pros and cons were debated. DSC stated that they were moving to a no calculator environment (except basic scientific model) for testing purposes, which UCF does for some of its courses below Calc II. Reviewed the discussion from the last meeting from Calc I on the coverage of transcendentals (early vs. late). The group discussed the idea of a best practices conference for the fall of All in attendance were in favor of such a conference. Focus on cross communication between subject areas such as biology and engineering to math. Have other subject matter areas share what they need from math. Include public school science teachers from the 4 subject matter areas (biology, chemistry, math, and physics). The group then spent the majority of the time covering the major topics and sub-topics for Calculus II and III. The topic list was reduced and combined to make a shorter and more relevant list (see next two tables).

3 AC2312 Course Content AC2312 Course Topics - Calculus II Course Topics = andatory, =ptional, R=Review, V=verview The algebraic definition and basic properties of the logarithmic and exponential and inverse functions R Calculus of logarithmic and exponential functions Integral definition of the natural logarithm function Derivatives of exponential and logarithmic functions Integrals of exponential and logarithmic functions of exponential and logarithmic functions The derivatives, integrals and graphs of the inverse trigonometric functions Hyperbolic functions Definition Derivatives Inverses Integrals L Hospital s Rule Indeterminate forms Integration techniques of Integration Parametric Equations Integration by parts Trigonometric integrals Trigonometric substitution Partial fraction method Improper integrals Approximation techniques Arc length Surface area Center of mass, centroids Work problems Volumes of revolution Fluid force Slope of a tangent line Arc length Graphs,R

4 Polar coordinates Definition and rules for infinite sequences and series Power series Introduction to Differential equations Area Length Graphs Conics Convergence Divergence Geometric series Alternating series Telescopic series Divergence test Integral test Direct comparison test Limit comparison test Ratio test Root test Alternating series test Absolute/Conditional convergence Interval and radius of convergence Representations of functions as power series Taylor and aclaurin series Taylor remainder theorem Derivatives and integrals Binomial series Separable differential equations Direction fields Euler's method

5 AC2313 Course Content Vectors 3D Coordinate Systems and Functions of 2 or 3 Variables Vector-valued functions of 1 variable Functions of several variables Double and triple integrals Vector analysis AC2313 Course Topics - Calculus III Algebraic and geometric Dot and cross products Definitions and interpretations Scalar triple product Equations of lines and planes in space Graphs of quadric and cylindrical surfaces Cylindrical and spherical coordinates Contour plots Level curves and surfaces Definitions, properties, continuity. Calculus of vector-valued functions. Arc length and curvature Unit tangent, normal, and binormal vectors Acceleration and velocity Definition Limits, continuity, and partial derivatives of functions Graphs Chain rule Tangent and normal planes Directional derivatives and gradients Linear approximations and differentials aximum and minimum values. Lagrange multipliers Definitions Evaluation of iterated integrals in cylindrical, rectangular and spherical coordinates Change of variables and The Jacobian Vector fields Line integrals Conservative fields Fundamental theorem of line integrals Green's theorem Curl and divergence Course Topics = andatory, =ptional, R=Review, V=verview

6 Topics to cover at the next meeting. Possibly discuss liberal arts math, and statistics. Implementation of what has been done in the math area. Include the public schools, but invite the math specialists from the district offices, not necessarily the teachers. Include biology, and engineering faculty at the next meeting to get their feedback on what they expect from math courses. Involve the state in this work to see if they will adopt and try to solve the common course numbering system dilemma. At next meeting in September, invite other faculty for the afternoon portion of the session (wrap up math from 10am-12pm, and then from 12-2pm include other faculty and public schools). The next meeting will be held on September 10, 2010 tentatively at UCF Partnership II Building (on Research Parkway and Technology Drives in rlando).