1 Aligned for Success: Creating Vertical Teams! Developing a Vertical Perspective John W. Staley, Ph. D. [email protected] Secondary Mathematics Coordinator Baltimore County Public Schools
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1
Aligned for Success:
Creating Vertical Teams!
Developing a Vertical Perspective
John W. Staley, Ph. D.
Secondary Mathematics Coordinator
Baltimore County Public Schools
Baltimore County Public Schools– Wraps around but does not
include Baltimore City
– Approximately 800,000 residents
– Suburban, rural, and urban
neighborhoods
– 27th largest school system in the
U.S., 3rd largest in Maryland
– 173 schools, programs, and
centers
– 103,832 students
(2009-2010)
Baltimore County Public Schools
Baltimore County Public Schools (2009-10)
– 39.3% eligible for free/reduced price meals
– 52.2% minority enrollment
– 8,850 classroom teachers
– More than 7,400 graduates annually (85% of
graduates immediately pursue higher education)
– Average of 17 Advanced Placement courses at each
high school; one-third of all high schools offer 20 or
more AP courses
Blueprint for Progress
1.2 All Grade 10 diploma-bound students will participate in the PSAT.
1.3 All students scoring a 55 or above on critical reading/mathematics PSAT will enroll in honors or gifted and talented level courses.
1.13 All high schools will meet or exceed the national average of a 7.0% participation rate on the Advanced Placement (AP) examinations.
1.14 All high schools will have at least 70.0% of their students who take Advanced Placement (AP) examinations achieve passing scores.
1.17 All high schools will meet or exceed the national average for participation in the SAT or the ACT.
1.18 All high schools will meet or exceed the national average for critical reading, mathematics, and writing scores on the SAT or the ACT.
Performance Goal 1: By 2012, all students will reach high standards, as established by the Baltimore county Public Schools and state performance level standards, in English/reading/writing, mathematics, science, and social studies.
Developing a Vertical Perspective
1. Why develop a Vertical perspective?
2. How did we develop a Vertical perspective?
3. What is the impact on Teaching and
Learning?
4. What are our next steps?
5. What lessons have we learned?
1. Why develop a Vertical perspective?
Thoughts to ponder…
I’m not sure what my students learned in
the grade… before or after me.
Why do my students have such a wide
range of ….?
I have to teach them how to solve “One-
step” equations, they didn’t learn that in
middle…elementary school?
If they learned that (Geometry Concept) in
middle school why does it seem as if they
never saw it before?
2. How did we develop a Vertical
perspective?
CollegeBoard Vertical Teams Workshops
Summer Workshops, Academies, Institutes
Mathematics Leadership Team
CollegeBoard Workshops
2005-2007
All Schools
Select Schools
Workshops, Academies, Institutes
Middle School Geometry
Algebra 1
PreCalculus
Technology
A Glimpse Into Slope Fields
(2005FR6 – AP Calculus)
1. Consider all lines whose slope, m, is 2
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a) Sketch eight lines that have a slope of m.
b) Let bmxy be the particular line which passes through the point 4,6 . Write
an equation for the line, and use it to find the value of y when 1.1x
c) Find the equation of the line perpendicular to the line in part (b) and passes
through the origin. Graph both lines in the grid above. Be sure to label your
lines.
Sugar
(2008FR1 – AP Statistics)
To determine the amount of sugar in a typical serving of breakfast cereal, a student
randomly selected 60 boxes of different types of cereal from the shelves of a large
grocery store. The student noticed that the side panels of some of the cereal boxes
showed sugar content based on one-cup servings, while others showed sugar content
based on three-quarter-cup servings. Many of the cereal boxes with side panels that
showed three-quarter-cup servings were ones that appealed to young children, and
the student wondered whether there might be some difference in the sugar content of the
cereals that showed different-size servings on their side panels. To investigate the
question, the data were separated into two groups. One group consisted of 29 cereals that
showed one-cup serving sizes; the other group consisted of 31 cereals that showed three-
quarter-cup serving sizes. The boxplots shown below display sugar content (in grams) per
serving of the cereals for each of the two serving sizes.
Use the box plot to answer to questions below.
1. What is the median sugar content for each serving size?
_______ for 1 cup _______ for ¾ cup
Based upon these medians, which serving size appears to be more healthy?
Which size was liked by children more?
MHEC Pathway Summer 2008
Bridging the Way from
Algebraic Thinking to BCPS Algebra 1
Algebra 1 and Algebra Data/Analysis
9th
Grade High School Teachers
A Stipend is available
$$$
DETAILS
Session 1: 7/21- 7/24 Towson High 1-4 pm
Session 2: 8/4-8/5
Deer Park Magnet 8am-3pm
Session 3: 8/6-8/7
Deer Park Magnet 8am-3pm
Spaces Limited: 30 High school
Teachers per session
The Institute is designed to provide insight into the middle school Algebraic Thinking program
and connections to the BCPS Algebra I curriculum. Participants will be immersed in the
curriculum as it pertains to content, teaching strategies, and technology. In addition, participants
will learn strategies for differentiating instruction based on student’s prior knowledge and
experiences, learning preferences and styles and exchange ideas that support students who have a
history of struggling with math. High school Algebra 1 teachers will also increase content
knowledge and pedagogy in order to better prepare their students for success on the High School
Assessment, algebra final exam and county assessments 9-12.
To Register
Link to Professional Development’s website http://www.bcps.org/apps/registration
From this link enter your BCPS e-mail user name and password and select
“Workshops and Meetings-Registration” from the Catalog drop-down menu.
After logging on, select “Catalog” from the Menu at the left side of the screen
Locate the section “Mathematics PreK-12 Workshops and Meetings”
Select the professional development opportunity and register for the session
Verbal
Representation
Algebraic
Representation
Numeric
Representation
Graphic
Representation
Algebraic
Thinking
Unit A: Applications of Real Numbers Algebra 1 Objectives Algebraic Thinking/KEAS
A1 1-2 Order of Operations Evaluate numerical expressions by using the order of
operations.
Evaluate algebraic expressions by using the order of
operations.
Part I: Lessons 17, 18, 19, 20
Part II: Lessons 1 and 3
A2 2-1
2-7
Rational Numbers on the Number
Line
Square Roots and Real Numbers
Graph real numbers on a number line.
Find absolute values of rational numbers.
Find square roots.
Classify and order real numbers.
Part I: Lessons 21, 22 and 105
Part II: Lessons 20 and 58
(Imbedded throughout several concepts)
Part II: Lesson 5 Appendix #1
A3 2-2 Adding and Subtracting Rational
Numbers
Add rational numbers.
Subtract rational numbers.
Evaluate algebraic expressions.
Part I: Lessons 13-16, 23-27, 32, 34, 35 - 38
Part II: Lessons 6, 7, 12 and 13
KEAS: 2, 3
A4 2-3
2-4
Multiplying Rational Numbers
Dividing Rational Numbers
Multiply and divide rational numbers.
Evaluate algebraic expressions and formulas.
Part I: Lessons 29, 30, 31, 39 and 40
Part II: Lessons 8-10, 14 and 15
KEAS: 4, 5
Unit A Snapshot Bridge to Algebraic Thinking
A1 stresses the learning of the graphing calculator for HS students
when evaluating expressions. MS students are required to evaluate
numerical expressions without a calculator.
“Where Do I Belong” in A2 allows the students to review the
classification of real numbers.
Using the graphing calculator to evaluate expressions with fractions
is crucial. Students are introduced to the Math feature to convert
decimals to fractions and vice versa.
“Expressions pairs” in A4 includes several examples of real-world
problems that the students may see on the HSA. Teachers are
encouraged to extend this worksheet with other real-world
examples.
Key Mastered Skills from AT: Order of Operations, Integer Operations
and Square Roots of Perfect Squares.
Students used a foldable of an inverted pyramid to reinforce order of
operations.
Students played Touchdown in both courses to reinforce ordering and
comparing integers.
Students used red/yellow counters to model perfect squares in AT 1 and to
find approximations for square roots in AT2.
Students used red/yellow counters or algebra tiles to model all integer
operations in both courses.
Students built fraction kits and used them to model all fraction operations
in both courses.
Students created a graphic organizer for relating words to operations in
order to write and evaluate expressions.
Students learned in AT2 to use calculators to convert decimals and
fractions.
Teaching Mathematics with Technology
Summer 2009
Taking it to the Next Level with TI and Technology
TI- NSpire
Getting Started with TI- Navigator
Using Real Data in the Math Classroom
Getting Ready for Algebra With Virtual Manipulatives
Summer 2010
Building Student Understanding with e-Mathematics Resources (Safari Montage, Lure of the Labrynith, Math by Design, NCTM Illuminations, National Library of Virtual Manipulatives,...)
"New" Tools for the Mathematics Classroom -Promethean Tools
TI- NSpire
Mathematics Leadership Team
Middle and High Department chairs
– Monthly
– Prime Leadership Framework
DO Math
– Division, Perimeter and Area, Rich Tasks
– Geometry
Professional Learning Community
– Communication: E-M-H
– Content
– Special Topics: PI Day , Math Month
3. What is the impact on Teaching
and Learning?
Know and be able to do
Curriculum and Instruction
Know and be able to do
Elementary to Middle
Middle to High
Same grade level
Different grades
3. What is the impact on Teaching and Learning?
Curriculum and Instruction
– Algebraic Thinking Program (Grades 6-8)
– High School Algebra 1
Current Curriculum Guides
– Mathematics 6
– Gifted and Talented Grade 6
– Geometry
– PreCalculus, College Algebra,
Trigonometry with Analytic Geometry
4. What are our next steps?
Bridge– Elementary to Middle
– Middle to High
– Connecting mathematical experiences across the grades
Technology– Building and enhancing student understanding
– Engages students in the learning process
Transition to Common Core Standards
– Professional Development that focuses on Grade bands vs isolated grades
– Mathematical Practices
5. What lessons have we learned?
Developing a Vertical Perspective
CollegeBoard Vertical Teams Workshop
– Build Foundation
– Small vs All
Curriculum
– Prior Knowledge
– Explicit Connections
– Instructional Strategies
Professional Development
– AP Calculus and Statistics
– Content and Strategies
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Aligned for Success:
Creating Vertical Teams!
Developing a Vertical Perspective
John W. Staley, Ph. D.
Secondary Mathematics Coordinator
Baltimore County Public Schools
26
Aligned for Success:
Creating Vertical Teams!
Questions
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