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(continued) Online Practice AP Testing in Calculus and Statistics (info at Online Practice AP Chemistry Testing (Beginning Spring 2009) Online Materials (see UTeach Replication ( teach HOUSTON )
Citation preview
Your Students…Where Are They Headed?
What Do They Need?(with your help) Jeff Morgan
Chair, Department of MathematicsDirector, Center for Academic Support and
AssessmentUniversity of Houston
Shameless Advertising
• High School Mathematics Contesthttp://mathcontest.uh.edu
• Houston Area Calculus Teachers Association AP Calculus Workshopshttp://www.HoustonACT.org
• EatMath Algebra I Teacher Workshopshttp://www.EatMath.org
(continued)
• Online Practice AP Testing in Calculus and Statistics (info at http://www.HoustonACT.org)
• Online Practice AP Chemistry Testing(Beginning Spring 2009)
• Online Materials (see http://online.math.uh.edu)
• UTeach Replication (teachHOUSTON)
Technology Tool Tips
• PDF Annotator• Mimio Notebook• WinPlot• Bamboo Tablet
Back to Business…
Interesting Trends and Observations
Fall Freshmen Math
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07
Fall Calculus I, II and III
Math 2433 enrollment: Summer 06 = 62, Summer 07 = 106.
0
200
400
600
800
1000
1200
1400
F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07
M1431M1432M2433
Fall Math Below Calculus
0
500
1000
1500
2000
2500
3000
F96 F97 F98 F99 F00 F01 F02 F03 F04 F05 F06 F07
1300 Fundamentals ofMathematics1310 College Algebra
1311 Elementary Math.Modeling1312 Intro. To Math.Reasoning1313 Finite Math
1314 Elements of Calculus
1330 Precalculus
Concerns• Prerequisite Knowledge
– Arithmetic
– Graphing Knowledge
– Algebraic Skills
• Student Performance
– Independence
– Responsibility
Previous Attitude
They are adults. Let them find their own way.
Current Attitude
Force them to work hard.
2003 - Actions In MathematicsBelow Calculus I
• Improved Placement Testing - Fall 2007• No Adjunct or Graduate Student Instruction• Mandatory Attendance• Daily Class Grades• Daily Written Homework• Weekly Online Quizzes• Online Course Materials• Increased Tutoring Availability• Common Exams and Common Grading• Improved Instruction and Course Coordination
2007 - Actions In Calculus I
• Improved Placement Testing – Fall 2007• Mandatory Attendance (40%)• Daily Class Grades (40%)• Weekly Written Homework (75%)• Weekly Online Quizzes (100% 2005)• Online Course Materials (100% 2005)• Increased Tutoring Availability (2003)• Common Exams and Common Grading (2005)• Improved Course Coordination (2005)• Peer Pressure
Performance Data - College Algebra
1310 Fall 06 A B C D F W
Number 662 409 313 212 247 242
Cumulative 662 1071 1384 1596 1843 2085
% 32 20 15 10 12 12
Cum. % 32 51 66 77 88 100
Improved performance with increased standards.
Performance DataPreCalculus
1330 Fall 06 A B C D F WNumber 206 156 127 101 111 146Cumulative 206 362 489 590 701 847% 24 18 15 12 13 17Cum. % 24 42 57 69 82 100
Maintained performance with increased standards.
Performance DataCalculus I
1431 Fall 06 A B C D F WNumber 215 290 229 181 258 248Cumulative 215 505 734 915 1173 1421% 15 20 16 13 18 18Cum. % 15 35 51 64 82 100
.
Time will tell…
The Bottom Line
Students will only work as hard as you require them to work.
If you want more from your students, then demand more.
Which Missing Skills Are Crippling Students in College?
(…the same ones that cripple them in your classroom…)
• Simple Arithmetic• Simple Algebraic Manipulation• Graphing and Understanding Basic
Shapes• Simple Geometry• Critical Thinking• A Sense of Responsibility
Simple Arithmetic
Example – Basic Fractions
872
31
Example – Integer Manipulation
14138
Solutions
• Restrict calculator usage.• Encourage drill and kill arithmetic for 5
minutes each day.
Simple Algebraic Manipulation
Example – Facts Through Experimentation
11
false?or True
2
22
xx
baba
baba
Example – Facts Through Experimentation
cos2cos2cossinsincoscos
false?or True
(if they are proceeding to calculus)
Comments
• Not everything has to be memorized.• Encourage students to experiment.• We expose students to so much of the
forest, that they don’t know the difference between an oak and a pine.
• Students need to be able to organize their work.
Example – Lines 1
A line with slope 3 / 2 passes through the point 2, 3 . Give the equation of the
line in slope-intercept form.
Example – Lines 2
form.intercept -slopein line
theofequation theGive .14,2point he through tpasses 3 slope with lineA
aaa
Example – Lines and Quadratics
?9,1
throughpass alsoit Can .14,2point he through tpasses 3 slope with lineA
aaa
Graphing and Understanding Basic Shapes
Please…
2
3
Make sure students can graph
2 6
2 3
1
y x
y x x
y x
yx
y x
More…
Make sure students can graph
sin
cos
tan
y x
y x
y x
You Can’t Keep Yourself From Reading “Stop”
2
Give the Basic Shape of
3 2
2 3 11
cos
y x
y x x
yx
y xy x
(this is a different drill)
Example – Why Shape Is Important?
A line with slope 3 passes through the point 2 , 4 1 . Are there any points that
this line can not contain? Explain.
aa a
Example - Growth
xy
xxy
xxy
xxy
xxy
x
2
20100
10
252
310
? of valueslargefor larger isWhich
5
3
2
Notes
• Your students will be required to create simple graphs without a calculator, and also think about the shapes of simple graphs.
• Your students should know everything about lines and parabolas (except foci), square root, 1/x, sine and cosine.
• Your students should have seen an asymptote.
Simple Geometry
What Geometric Concepts are Important?
• Pythagorean Theorem• Areas of triangles, rectangles and circles.• Circumference of rectangles and circles.• The sum of the angles in a triangle.• The facts associated with isosceles and
equilateral triangles.• Triangle trigonometry (if they are
proceeding to calculus).Honestly, that’s it!
Combining Arithmetic, Algebra and Geometry
In General, We Are Happy If Students
• Can do simple arithmetic and basic algebra.• Know everything about lines.• Know everything about parabolas (except foci).• Can solve linear and quadratic equations.• Can factor simple quadratics, complete the square and
use the quadratic formula.• Have seen an asymptote.• Know the shapes of basic functions (nothing tricky).• Know the area formulas for circles, rectangles and
triangles, and know the perimeter of a circle and a rectangle.
• *Know the trig functions at the special angles.• Can organize their work.
Critical Thinking
Can your students find the error in an argument?
Can your students combine ideas without seeing a previous example?
Do your student know the difference between a definition and an example?
Example – Simple Critical Thinking
Determine what lead from the initial equationto the subsequent equations, and find the error.
3 2 1 0
3 2 13 2 1
2 21
x
xxxx
A Sense of Responsibility
This Is The #1 Employer Requirement!