Creating Unified
TEKS-Based
Science/Math Projects
Through TC-STEM
Part II
CAST 2007
Austin, Texas
November 15–17
David Castro, science project manager
1
About the Dana Center
 Established during the early 1990s in the College of
Natural Sciences at The University of Texas at Austin to
support equity in mathematics and science education.
 Coordinated the development of the mathematics and
science Texas Essential Knowledge and Skills.
 Worked long-term with over 200 school districts to
support systemic change.
 Became a Texas Center for STEM (TC-STEM) in 2006.
 Provides ongoing research as well as support materials
and professional development for teachers and leaders.
2
Session Objectives
 Discuss the advantages and challenges of implementing
TEKS-based science/math projects.
 Define the characteristics of a successful T-STEM
academy.
 Learn three protocols for designing TEKS-based projects.
3
Why use project-based learning?
When implemented successfully, it
connects to the “real world.”
increases student engagement.
develops problem-solving skills.
promotes transfer of knowledge.
builds expert understanding.
is more effective than traditional instruction in
supporting TEKS implementation.
 creates productive citizens.
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4
Characteristics of a
Successful
T-STEM Academy
The Dana Center Perspective
5
,
A Successful T-STEM Academy:
 promotes interest in Science, Technology, Engineering,
and Mathematics.
 provides open access to all.
 embraces the small-school model.
 provides a rich problem-solving environment.
 produces college-ready graduates.
6
A Successful T-STEM Academy:

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
strongly supports implementation of the TEKS.
deliberately and methodically builds student skills.
promotes expert-level understanding of core content.
supports teacher collaboration and professionalism.
provides a guaranteed and viable curriculum.
creates structures for supporting and implementing
interdisciplinary project-based learning.
7
Supporting Project-Based Learning
To successfully implement science/math projects, teachers
must have . . .
 a guaranteed and viable curriculum.
 a common curricular vision.
 strong content knowledge.
 access to research-based pedagogy.
 a protocol for effective lesson design.
 commitment, high expectations, and accountability.
 leadership support.
8
Characteristics of Effective
Project-Based Learning
The Dana Center Perspective
9
Effective Projects …
are part of a guaranteed and viable curriculum.
are built around clear TEKS-based criteria.
use existing resources.
reinforce and extend process skills.
provide opportunities for integration and skill
transfer.
 are more effective than traditional lessons!
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11
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An effective curriculum must be both
guaranteed and viable.
Guaranteed
 Common understanding
of the TEKS
 Clear student
expectations
 Operational definition of
learning outcomes
 Mutual accountability
Viable
 In the available
instructional time,
essential content can be
taught by all teachers to
all students.
13
Student performance criteria transform the
TEKS into guaranteed and viable curricula.
14
15
16
The Need for Vertical Articulation
“Learning Line” diagram is taken from Robert J. Marzano,
Debra J. Pickering, & Jane E. Pollock. (2001). Classroom
Instruction that Works. Alexandria, VA: Association for
Supervision and Curriculum Development, page 67.
17
The TEKS Process Skills:
Grades 6–8
18
Vertically Articulated Process Skills:
Grades 6–8
19
The Science–Math Bridge
20
The Science–Math Bridge:
Overview

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Requires an investment of 3 to 4 days
Integrates science and math
Easy to plan
Easy to implement
Builds teacher and student capacity
21
The Science–Math Bridge:
Calendar
Day Science
1
Collect Data
2
3
Math
Analyze Data
Present
Present
22
The Science–Math Bridge
Design Protocol

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Collaboratively select TEKS
Determine student performance criteria
Select scenario
Design student work products
Identify necessary prior knowledge
Set implementation calendar
Analyze results
23
The Biology–Algebra I Bridge
Collaboratively
select TEKS
Biology
24
The Science–Math Bridge:
Biology–Geometry
Determine student performance criteria
25
The Science–Math Bridge:
Biology–Geometry
Select scenario
The scenario used in this example is based on AP Biology Free Response
Question No. 2 from the 2006 released test.
The graph featured in the problem depicts the effect of a newly introduced
species on the populations of two other species within the same biome.
Students are asked to describe the changes in population, suggest a
reason for the observed changes, and predict the relative populations at a
future date.
Students engaged in an integrated science–math project would be asked to
analyze the data either linearly (Algebra I), quadratically (Algebra II), or
exponentially (Precalculus), based upon their math course.
26
The Science–Math Bridge:
Biology–Geometry
Design student work products, such as…
–
–
–
–
–
–
–
–
posters
experiments
reports
simulations
“what if” scenarios
graphs
illustrations
design challenges
27
The Science–Math Bridge:
Biology–Geometry
Identify necessary prior knowledge, such as…
–
–
–
–
–
–
vocabulary
preconceptions
process skills
math skills
analysis tools (process)
other coursework (content)
In general, projects should extend prior
knowledge, not introduce new content.
28
The Science–Math Bridge:
Biology–Geometry
Set implementation calendar that is . . .
–
–
–
–
viable
flexible
guaranteed
realistic
A successful project provides structured
opportunities for students to share results and
create meaning.
29
The Science/Math Bridge
Design Protocol
Analyze results
1.
2.
3.
4.
5.
Engage in collaborative reflection
Analyze student work
Refine and modify criteria
Revise materials and activities
Incorporate into district curricular documents
30
UMTA
31
UMTA
(Understand, Model, Try, Apply)

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requires an 8-to-10-day investment
emphasizes problem solving
emphasizes direct experience and modeling
provides a structure for building knowledge
strongly supports STEM education
32
UMTA Instructional Model
 Understand
– Two days of observation, reflection, and guided conversation
 Model
– Two days of gathering data using real-time technology,
regression analysis, and equation building (math integration)
 Try
– Two days of carefully defined real-world problem solving
 Apply
– Two days of open-ended real-world application
33
UMTA Instructional Model
2 Days
2 Days
4 Days
Observe
Collect data
Confirm
understanding
Generalize
Create a
mathematical model
Apply in specific
contexts
Affirm
Test and apply
model
Apply in openended contexts
34
UMTA=STEM
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Science: Physics, Chemistry, Biology
Technology: Real-time data collection
Engineering: Real-world problem solving
Mathematics: Mathematical modeling
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STEM Physics: Introduction to Forces
Day
Lesson Title
Lesson Description
1
1.1 Understanding Models
Analyze scientific models for their strengths
and weaknesses.
2
1.2 Forces in Equilibrium
Use free body diagrams to describe the forces
on single objects in equilibrium.
3
1.3 Computer Modeling
4
1.4 Frictional Forces
Use Interactive Physics to construct computer
models that illustrate the forces on single
objects in equilibrium.
Investigate how frictional forces (kinetic and
static) determine the motion of single objects.
5
1.5 Modeling Friction
Use Interactive Physics to model and analyze
the transition between static and kinetic friction.
6
1.6 Problem Solving
Student groups solve problems focusing on ’s
1st law and vector notation.
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1.7 Project 1—“Where the Rubber
Meets the Road”
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1.8 Student Presentations—“Where the
Rubber Meets the Road”
Student teams design and conduct an
investigation to compare the effectiveness of
three different types of automobile tires.
Student teams present their findings.
36
The Project-Planning Protocol
(P3)
37
P3 . . .
 requires 7 to 10 days of science and math
investment.
 emphasizes integration, transfer, and real-world
problem solving.
 combines the best features of the science–math
bridge and UMTA.
 represents STEM-based education.
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The Alignment Issue
39
Project-Planning Protocol
Day
Science
1
Introduce New Content
2
Reflect
3
Gather Data
Math
4
Analyze Data
5
Model Data
6
Create Design Proposal
7
Refine Design Proposal
8
Conduct Experiment
9
Analyze
Analyze
10
Present
Present
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3
P
Sample
Project:
Video Analysis of Motion
Science
• Physics
Math
• Algebra 1
• Geometry
• Algebra 2
• Precalculus
41
Measuring Time
A video clip
plays at
30 frames
each second.
Δt = 1/30 s
42
Motion with Constant Speed
43
0/30
44
1/30
45
2/30
46
3/30
47
4/30
48
5/30
49
6/30
50
7/30
51
8/30
52
9/30
53
10/30
54
11/30
55
12/30
56
13/30
57
14/30
58
15/30
59
16/30
60
17/30
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18/30
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19/30
63
20/30
64
21/30
65
22/30
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23/30
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24/30
68
25/30
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Motion Transparency
70
Motion Grid
71
Motion Axes
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Motion Data
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Numerical Values
click
0
1
2
3
4
5
6
7
8
9
10
11
x position
-5.3
-4.2
-2.5
-0.1
1.6
2.7
4.2
5.2
6.6
7.8
9.2
10.5
click
13
14
15
16
17
18
19
20
21
22
23
24
x position
13
14.2
15.5
1607
18
19.2
20.5
21.8
23
24.2
25.4
26.4
74
Using “Real” Time Units
click
Since each “click” is 1/30
of a second, divide each
click by 30!
0
1
2
3
4
5
6
7
8
9
10
11
time (s)
0.00
0.03
0.07
0.10
0.13
0.17
0.20
0.23
0.27
0.30
0.33
0.37
75
Using “Real” Distance Units
Since there are 32 squares
in each meter, divide
each “x” value by 32!
x position x (meters)
-5.3
-0.17
-4.2
-0.13
-2.5
-0.08
-0.1
0.00
1.6
0.05
2.7
0.08
4.2
0.13
5.2
0.16
6.6
0.21
7.8
0.24
9.2
0.29
10.5
0.33
76
“Real” Numerical Values
t(s)
0.00
0.03
0.07
0.10
0.13
0.17
0.20
0.23
0.27
0.30
0.33
0.37
x (m)
-0.17
-0.13
-0.08
0.00
0.05
0.08
0.13
0.16
0.21
0.24
0.29
0.33
t(s)
x (m)
0.43
0.47
0.50
0.53
0.57
0.60
0.63
0.67
0.70
0.73
0.77
0.80
0.41
0.44
0.48
0.52
0.56
0.60
0.64
0.68
0.72
0.76
0.79
0.83
77
Graphed Data
x (m)
position (m)
1.00
0.50
x (m)
0.00
0.00
-0.50
0.20
0.40
0.60
0.80
1.00
time (s)
78
“Best Fit” Curve
1.00
position (m)
0.80
0.60
0.40
x (m)
Linear (x (m))
0.20
0.00
-0.200.00
0.50
1.00
-0.40
time (s)
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Equation for the Line
m = Δx/Δt
= (0.8 - 0.0)/(0.75 - 0.1)
= 1.23
b = -0.2
x = 1.23(t) - 0.2
80
A Closer Look at the Slope
Slope = (Δx/Δt)
= (Δ”m”/Δ”s”)
= 1.23 m/s
= speed
Note that the slope and, therefore, the
speed, is constant!
81
Tennis Ball Drop
 Given:
– Each frame is 1/30 second.
– Grid squares are 10 cm x 10 cm.
 Task:
– Plot and run regression analysis of position vs. time
and velocity vs. time.
82
0/30
83
1/30
84
2/30
85
3/30
86
4/30
87
5/30
88
6/30
89
7/30
90
Sample Position vs. Time
2
0
-2
-4
0
2
4
6
8
distance
Poly. (distance)
-6
-8
-10
91
Sample Velocity vs. Time
0
-0.5
0
2
4
6
-1
-1.5
velocity
Linear (velocity)
-2
-2.5
-3
92
Dropped Water Balloon
 Given:
– The balloon contains 10g of water.
– Each frame is 1/30 second.
– Grid squares are 10 cm x 10 cm.
 Task:
– Plot and run regression analysis of position vs. time
and velocity vs. time.
93
0/30
94
1/30
95
2/30
96
3/30
97
4/30
98
5/30
99
6/30
100
7/30
101
8/30
102
9/30
103
10/30
104
11/30
105
Sample Position of the Water Balloon
0
-2 0
2
4
6
8
10
-4
-6
-8
-10
Position
Poly. (Position)
-12
-14
-16
106
Sample Velocity of the Water Balloon
0
-0.5
0
2
4
6
8
10
-1
-1.5
Velocity
Poly. (Velocity)
-2
-2.5
-3
107
Comparison of Ball and Balloon
Sample Velocity vs. Time
0
-0.5
0
2
4
6
-1
-1.5
velocity
Linear (velocity)
-2
-2.5
-3
Sample Velocity of theWater Balloon
0
-0.5
0
2
4
6
8
10
-1
-1.5
Velocity
Poly. (Velocity)
-2
-2.5
-3
108
Contact information
David Castro, science project manager
davidcastro@mail.utexas.edu
www.sciencetekstoolkit.org
www.utdanacenter.org
109