Transcript Richard Woods, Georgia’s School Superintendent “Educating Georgia’s Future” gadoe.org Richard Woods, Georgia’s School Superintendent “Educating Georgia’s Future” gadoe.org Georgia Alternate Assessment Overview of High School Mathematics in 2015-2016 Session 2

Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Georgia Alternate Assessment
Overview of High School Mathematics in
2015-2016
Session 2
2015-2016 GAA
Purpose
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• The 2015-2016 webinars (Sessions 1-5) explain how
to prepare and submit GAA portfolios.
http://www.gadoe.org/Curriculum-Instruction-andAssessment/Assessment/Pages/GAAPresentations.aspx
• Information pertaining to the GAA can also be
found in the 2015-2016 GAA Examiner’s Manual.
http://www.gadoe.org/Curriculum-Instruction-andAssessment/Assessment/Pages/GAA-Resources.aspx
2
2015-2016 GAA
Looking Ahead
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• Additional sessions will be available for more indepth training on topics that will assist test
administrators.
• All presentations will be posted on the GaDOE
website at:
http://www.gadoe.org/Curriculum-Instruction-andAssessment/Assessment/Pages/GAAPresentations.aspx
3
Links to Presentations are on
the GaDOE website (shown below)
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
http://www.gadoe.org/Curriculum-Instruction-andAssessment/Assessment/Pages/GAA.aspx
4
Overview of this Presentation
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• This presentation will cover the following topics:
• Overview of HS Math content standards
• Coordinate Algebra (Math Entry 1) and Analytic Geometry
(Math Entry 2)
• Curriculum Access for HS students in Mathematics
• It is designed to inform:
•
•
•
•
•
High School teachers who administer the GAA
Peer Reviewers and Designated Trainers
Special Education Directors
Test Coordinators
Building Administrators
5
Requirements
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• States must ensure that all students, including
students with significant cognitive disabilities,
have access to challenging academic standards.
• The GAA ensures that all students have the
opportunity to learn.
6
Requirements for all GAA
entries
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• The GAA, designed with the assistance of Georgia
general and special educators, is a portfolio of original
student work that allows participants to showcase the
achievements and progress they have made in skills
aligned to the Georgia content standards.
• To document that progress, teachers collect student
work samples during two collection periods. The first
collection period provides evidence of the student’s
entry-level performance (initial/baseline performance
of the skill). The second collection period provides
evidence of the student’s achievement/progress to
date.
7
Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
GAA Blueprint and
Portfolio Components
8
2015-2016 GAA
High School Mathematics
Blueprint
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• The Blueprint outlines the requirements of the
2015-2016 GAA for High School math.
• The Blueprint identifies the content standards that
are required and eligible for assessment on the
GAA.
• The Blueprint, by grade, can be found in Appendix
D of the GAA Examiner’s Manual, 2015-2016.
Note: Do not use Blueprints from previous years
9
Content Standards
and Indicators
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• The state’s content standards are the goals for
instruction, learning, and assessment in each of the
content areas.
• Indicators are the specific concepts and skills that
make up the state’s content standards.
• The content standard and indicator descriptions, by
grade, can be found in Appendix E of the GAA
Examiner’s Manual, 2015-2016.
10
2015-2016 Blueprint
High School Blueprint, Math
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
GAA students in high school must submit two Mathematics entries.
Math Entry 1 must use one of the 11 Coordinate Algebra standards
shown here. Math Entry 2 must use one of the 12 Analytic Geometry
standards shown here.
11
2015-2016 Standards
GAA High School Standards, Coordinate Algebra (Math 1)
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
12
2015-2016 Standards
GAA High School Standards, Analytic Geometry (Math 2)
Math 2 standards continue on the next slide
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
13
2015-2016 Standards
GAA High School Standards, Analytic Geometry (Math 2) - continued
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
14
Coordinate Algebra
(Math Entry 1)
• Algebra and Functions clusters
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• Create equations that describe numbers or
relationships.
• Solve equations and inequalities in one variable.
• Understand the concept of a function and use function
notation.
• Interpret functions that arise in applications in terms of
the context.
• Build a function that models a relationship between two
quantities.
15
Coordinate Algebra
(Math Entry 1)
• Algebra Connections to Geometry cluster
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• Experiment with transformations in the plane.
• Algebra Connections to Statistics and Probability
clusters
• Summarize, represent, and interpret data on a single
count or measurement variable.
• Summarize, represent, and interpret data on two
categorical and quantitative variables.
16
Analytic Geometry
(Math Entry 2)
• Geometry clusters
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• Understand congruence in terms of rigid motions.
• Make geometric constructions.
• Understand similarity in terms of similarity
transformations.
• Understand and apply theorems about circles.
• Explain volume formulas and use them to solve
problems.
17
Analytic Geometry
(Math Entry 2)
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• Expressions, Equations, and Functions clusters
• Solve equations and inequalities in one variable.
• Interpret functions that arise in applications in terms of
the context.
• Statistics and Probability clusters
• Understand independence and conditional probability
and use them to interpret data.
• Use the rules of probability to compute probabilities of
compound events in a uniform probability model.
18
Alignment
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
• Alignment is the connection between the written,
taught, and tested curriculum.
• Alignment demonstrates the linkage of the activities
(student work) to the intent of the grade-level standard
and indicator on which the student is being assessed.
• In order for an entry to be scorable, all four (4) tasks
must align to the standard and indicator.
• Assessment tasks should be designed and task
descriptions written to specifically address the
standards-based skill being evaluated.
• Alignment is the subject of Session 4 on
Wednesday, August 26 at 1:00.
19
Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Coordinate Algebra
Math Entry 1
20
Coordinate Algebra samples
Math Entry 1
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Slides
Standard
22-23
A.CED.1
no Entry Sheet, one piece of evidence
24-26
A.REI.3
Entry Sheet, one piece of evidence
27-30
S.ID.1
no Entry Sheets, four pieces of evidence from
four different entries
31-33
S.ID.2
Entry Sheet, two pieces of evidence
34-37
F.IF.2
Entry Sheet, one piece of evidence
38-41
F.IF.2
Entry Sheet, one piece of evidence
42-47
F.IF.2
Entry Sheet, two pieces of evidence
21
Sample Evidence – Math Entry 1
Coordinate Algebra
Algebra and
Functions
(includes
Number and
Quantity)
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Solve equations and inequalities in one variable.
MCC9-12.A.CED.1 Create equations and inequalities in one
variable and use them to solve problems. Include equations
arising from linear and quadratic functions, and simple rational
and exponential functions.
22
The student is determining
which equation represents
the given equation. This is a
lead-in task for creating an
equation to solve problems.
The student moves to
creation deeper into the
same task (CP1 – Secondary)
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
23
Sample Evidence – Math Entry 1
Coordinate Algebra
Algebra and
Functions
(includes
Number and
Quantity)
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Solve equations and inequalities in one variable.
MCC9-12.A.REI.3 Solve linear equations and inequalities in
one variable, including equations with coefficients represented
by letters.
24
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
25
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
26
Sample Evidence – Math Entry 1
Coordinate Algebra
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Summarize, represent, and interpret data on a single
Algebra
count or measurement variable.
Connections
to Statistics
and
Probability MCC9-12.S.ID.1 Represent data with plots on the real number
line (dot plots, histograms, and box plots).
27
Coordinate Algebra
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Numerical data
28
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Numerical data have
been correctly
represented on the real
number line. The dots
represent the number
of students and the
numbers on the
number line represent
the number of toy cars
each student has.
29
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
30
Sample Evidence – Math Entry 1
Coordinate Algebra
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Summarize, represent, and interpret data on a single
count or measurement variable.
Algebra
Connections
to Statistics
and
Probability
MCC9-12.S.ID.2 Use statistics appropriate to the shape of the
data distribution to compare center (median, mean) and spread
(interquartile range) of two or more different data sets.
31
In this Collection Period 1
task, the student worked
individually with the special
education teacher to
complete this worksheet.
The student was given two
sets of data and was then
asked to calculate mean and
median and to compare the
means of the two data sets.
32
In this Collection Period 2
task, the student again
worked individually with
the special education
teacher and was given two
sets of data. The student
was then asked to calculate
mean and median of each
data set and to compare
the means and medians of
the two data sets.
33
Sample Entry – Math Entry 1
Coordinate Algebra
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Understand the concept of a function and use function
notation.
Algebra and
Functions
MCC9-12.F.IF.2 Use function notation, evaluate functions for
inputs in their domains, and interpret statements that use function
notation in terms of a context.
34
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
35
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
9/18
The student completes
function tables by using
function notation. The
teacher assisted the
student by using
manipulatives to help the
student visualize the
count.
36
9/18
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Function
notation is given
and the student
fills in the
input/output
tables.
9/18
37
Sample Entry – Math Entry 1
Coordinate Algebra
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Understand the concept of a function and use function
notation.
Algebra and
Functions
MCC9-12.F.IF.2 Use function notation, evaluate functions for
inputs in their domains, and interpret statements that use function
notation in terms of a context.
38
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
We have only included Collection
Period 1 Primary Evidence for this
screenshot.
39
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
The student’s task in Collection
Period 1 Primary Evidence was
to represent a function (her
eye color and the eye color of
classmates) on a worksheet
and to make a function table.
40
Rebecca
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Rebecca
Monica
41
Sample Entry – Math Entry 1
Coordinate Algebra
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Understand the concept of a function and use function
notation.
Algebra and
Functions
MCC9-12.F.IF.2 Use function notation, evaluate functions for
inputs in their domains, and interpret statements that use function
notation in terms of a context.
42
11/7/2015
43
11/7/2015
44
The student was
given a graph (see
previous slide) of
baseball players
and their batting
averages (one
input, one
output) and was
asked to find the
batting averages
of two players.
The function
notation is “b (_).”
11/7/2015
45
11/7/2015
46
In Collection Period 2
Primary Evidence, the
student was again asked
to use the table to find
players’ batting averages
but in this task there are
five questions.
The student is non-verbal
and communicates via
head movements, smiles,
and gestures.
11/7/2015
47
Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Analytic Geometry
Math Entry 2
48
Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Analytic Geometry samples
Math Entry 2
Slides
Standard
50-52
53-56
57-64
65-67
68-72
73-79
G.C.2
G.GMD.3
G.CO.6
G.CO.7
F.IF.4
A.REI.4
Entry Sheet, one piece of evidence
Entry Sheet, one piece of evidence
Entry Sheet, three pieces of evidence
Entry Sheet, one piece of evidence
Entry Sheet, three pieces of evidence
Entry Sheet, three pieces of evidence
49
Sample Entry – Math Entry 2
Analytic Geometry
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Understand and apply theorems about circles.
Geometry
MCC9-12.G.C.2 Identify and describe relationships among
inscribed angles, radii, and chords. Include the relationship
between central, inscribed, and circumscribed angles;
inscribed angles on a diameter are right angles; the radius of
a circle is perpendicular to the tangent where the radius
intersects the circle.
50
11/7/2015
51
Relationships are
essential for alignment
11/7/2015
52
Sample Entry – Math Entry 2
Analytic Geometry
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Explain volume formulas and use them to solve problems.
Geometry
MCC9-12.G.GMD.3 Use volume formulas for cylinders,
pyramids, cones, and spheres to solve problems.
53
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
The Analytic Geometry standard refers to cylinders,
pyramids, cones, and spheres, but it is not necessary for a
student to do tasks involving all aspects of the standard in
order to have aligned tasks. Tasks which focus on just one
aspect of the standard can be aligned. It is essential that
there is a consistent skill across both collection periods.
For example, do not choose to focus exclusively on cylinders
in the first task, pyramids in the second task, cones in the
third task, and spheres in the fourth task. An entry without a
consistent skill across both collection periods will receive a
“1” in Achievement/Progress.
54
11/7/2015
55
The student used eye gaze
to choose the numbers to
complete each step of the
volume formula.
11/7/2015
56
Sample Entry – Math Entry 2
Analytic Geometry
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Understand congruence in terms of rigid motions.
Geometry
MCC9-12.G.CO.6 Use geometric descriptions of rigid motions
to transform figures and to predict the effect of a given rigid
motion on a given figure; given two figures, use the definition of
congruence in terms of rigid motions to decide if they are
congruent.
57
11/7/2015
58
Rigid motions should be
used to determine if figures
are indeed congruent or
incongruent.
11/7/2015
59
11/7/2015
60
In the student’s Collection Period
1 tasks, she is given two answer
choices for each of the
questions. One choice is a
transformation (turn in one
instance, slide in the other) and
the other is the distractor “X.”
11/7/2015
61
62
11/7/2015
63
11/7/2015
64
Sample Entry – Math Entry 2
Analytic Geometry
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Understand congruence in terms of rigid motions.
Geometry
MCC9-12.G.CO.7 Use the definition of congruence in terms of
rigid motions to show that two triangles are congruent if and only
if corresponding pairs of sides and corresponding pairs of angles
are congruent.
65
11/7/2015
66
67
Sample Entry – Math Entry 2
Analytic Geometry
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Interpret functions that arise in applications in terms of
the context.
Expressions,
Equations
and
Functions
MCC9-12.F.IF.4 For a function that models a relationship
between two quantities, interpret key features of graphs and
tables in terms of the quantities, and sketch graphs showing key
features given a verbal description of the relationship. Key
features include: intercepts; intervals where the function is
increasing, decreasing, positive, or negative; relative maximums
and minimums; symmetries; end behavior; and periodicity.*
*intentional strikethrough
68
11/7/2015
69
70
11/7/2015
71
11/7/2015
72
Sample Entry – Math Entry 2
Analytic Geometry
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Solve equations and inequalities in one variable.
Expressions,
Equations
and
Functions
MCC9-12.A.REI.4 Solve quadratic equations in one variable.
b. Solve quadratic equations by inspection (e.g., for x² = 49),
taking square roots, completing the square, the quadratic formula
and factoring, as appropriate to the initial form of the equation.
Recognize when the quadratic formula gives complex solutions
and write them as a ± bi for real numbers a and b.
73
11/7/2015
74
11/7/2015
75
The student makes a model to
represent the square root of 4
and solves the equation using
numbered stickers. The
evidence (a 2-page worksheet) is
on the next slide.
11/7/2015
76
11/7/2015
77
The student makes models to
represent the square root of 4
and the square root of 9 and
solves the equations using
numbered stickers. The
evidence (a 2-page worksheet)
is on the next slide.
78
11/7/2015
79
IDEAS 2014 Handouts on
GaDOE website
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
http://www.gadoe.org/Curriculum-Instruction-and-Assessment/Special-EducationServices/Pages/IDEAS-2014-Handouts.aspx
80
Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Contact Information
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Questions About Test Administration
Call: GaDOE Assessment Administration Division
Toll free (800) 634-4106
Contact: Deborah Houston, Assessment Specialist (404) 657-0251
Email: [email protected]
81
Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Contact Information
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
For information about access
to the state-mandated content standards
for students with significant cognitive disabilities
Contact:
Call:
E-Mail:
Kayse Harshaw
Division for Special Education Services
(404) 463-5281
[email protected]
[email protected]
82
Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Contact Information
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Questions About Materials, Distribution or Collection
Call:
Questar’s GAA Customer Service
Toll free (866) 997-0698
Email:
Questar’s GAA Customer Service
[email protected]
83
Richard Woods, Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Richard Woods,
Georgia’s School Superintendent
“Educating Georgia’s Future”
gadoe.org
Questions & Answers
• Please use the link below to submit any questions
you may have related to Sessions 1 - 4.
2015 GAA Fall Training Questions and Answers for Sessions 1–4
84