assessing mathematical understanding · goals of assessing mathematical understanding promote...
TRANSCRIPT
Assessing
Mathematical
Understanding
Lori Williams, Ph.D.
K-12 Math SpecialistManitowoc Public School [email protected]
Independent Mathematics [email protected]
Learning Intentions for This SessionI will understand that:
Data from AMU can guide instructional
decisions made by kindergarten and first
grade teachers.
I will know I understand when I can:
Name the components of the AMU and what
data they provide.
Describe how data from the AMU might drive
Tier 1 core instruction
Describe how data from the AMU might drive
Tier 2 intervention/enrichment decisions
To Get Started:
http://educationnorthwest.
org/register-download-
amu-materials
Goals of Assessing
Mathematical Understanding
Promote student learning in
mathematics
Enhance teachers’ ability to
meet individual student needs
Facilitate teacher collaboration
around student learning
p. 2
AMU:
MPSD’s K-1 Universal Screener
http://dpi.wi.gov/sites/default/files/imce/rti/pdf/rti-roadmap.pdf
Components
Guide book
Two Grade Level assessments:
Kindergarten Items for Assessing Mathematical
Understanding
First Grade Items for Assessing Mathematical
Understanding
Comprehensive diagnostic assessment
Diagnostic Items for Assessing
Mathematical Understanding
http://educationnorthwest.org/resources/assessing-mathematical-understanding
Content of the Assessment
9 concept areas
51 corresponding learning
goals
Aligned to the CCSS &
Wisconsin Math Standards
p. 2
Learning Intentions for This SessionI will understand that:
Data from AMU can guide instructional
decisions made by kindergarten and first
grade teachers.
I will know I understand when I can:
Name the components of the AMU and what
data they provide.
Describe how data from the AMU might drive
Tier 1 core instruction
Describe how data from the AMU might drive
Tier 2 intervention/enrichment decisions
Grade Level Assessments
One-on-one interviews
EdNorthwest provides:
Student prompts
Teacher directions
Scoring sheets
Manitowoc developed:
Partial credit guidelines for Kindergarten
Scoring cut lines
Student & Teacher Prompts
MPSD’s Scoring DiscussionsResponse Codes (Provided by EdNorthwest)
Use the following codes to categorize the
student’s response to each item:
c correct answer given quickly with
confidence (3 points)
C correct answer (2 points)
P partially correct answer (1 point)
X incorrect answer, no response to the
problem or “I don’t know” (0 points)
S skipped based on skip criteria (0 points)
MPSD’s Scoring DiscussionsResponse Codes (Used by MPSD)
Use the following codes to categorize the
student’s response to each item:
Correct answer (2 points)
Partially correct answer (1 point)
Incorrect answer, no response to the
problem or “I don’t know” (0 points)
Skipped based on skip criteria (0 points /
blank)
**Try to record what you can about
student thinking.
Instructions for Interviews Preparation
Introduction to students
Administration
Read each item as printed and elaborate,
if necessary.
Give neutral feedback
Record student responses
Follow the “moving through assessment”
directions
Scoring
Scoring Prompts
MPSD Example
MPSD Scoring Discussions
Learning Intentions for This SessionI will understand that:
Data from AMU can guide instructional
decisions made by kindergarten and first
grade teachers.
I will know I understand when I can:
Name the components of the AMU and what
data they provide.
Describe how data from the AMU might drive
Tier 1 core instruction
Describe how data from the AMU might drive
Tier 2 intervention/enrichment decisions
AMU:
MPSD’s K-1 Universal Screener
http://dpi.wi.gov/sites/default/files/imce/rti/pdf/rti-roadmap.pdf
MPSD Scoring Discussions
Data Wall Categories Based on Points from Section 1 Problems ONLYKindergarten: Beginning-of-Year September
Minimal Basic Proficient Advanced
0 - 5 6 – 8 9 – 21 22 - 26
Data Wall Categories – Grade 1: Mid-Year January
Minimal Basic Proficient Advanced
0 - 17 18 - 23 24 - 31 32 - 42
Mid-year Expectations: Sections 1 & 2 Points Only
• Based on the experience of the first grade teachers and an analysis of our current math
resource (Math Expressions), most students who are “on target” at this point in the year will
score 24-31 points.
• Students scoring 17 or less may be at greatest risk and should be assessed for learning gaps
using the First Steps diagnostics, and then be provided with the appropriate small group /
individual interventions.
• Students who score from 18-23 are moderately below grade level expectations. Additional
data (unit tests, formative assessments/exit cards, observation checklists and/or First Steps
diagnostic tasks) should be used to determine learning gaps, followed by corresponding re-
teaching and/or intervention.
• Students who score from 32-42 should also be given Section 3. These students will benefit
from extension/enrichment interventions throughout second semester.
Tier 1: Core Instruction Considerations
Beginning of the Year
How many of my students are coming in where I
expect them to be?
Do I need to add anything to my first unit?
What universal design pieces do I need to
concentrate on?
Do I need to contact the Gifted & Talented
coordinator and consider additional data
collection and subject acceleration?
Tier 2: Interventions & Enrichments
Beginning of the Year
Who is not coming in with the knowledge I
expect?
Are they just a little behind and I should watch
them?
Are they far behind ? Would they benefit from early
intervention?
Do I need diagnostic data in order to determine
targeted interventions for specific concepts?
Did anyone surprise me? Do I need to consider
pre-testing and compacting a few students?
Tier 1: Core Instruction Considerations
Mid-year
Have all of my students made the progress I
want?
Have I missed anyone in my Tier 1 or 2 intervention
groups?
Did anyone surprise me? Do I need to
incorporate more challenge problems to my daily
instruction?
Should I review any concepts with my whole class
before moving forward? Or, should I build reviews
into some of the lessons coming up?
Tier 2: Interventions & Extensions
Mid-year
Have all of my students made the progress I want?
Have I missed anyone in my Tier 1 or 2 intervention
& extension groups?
Do I need diagnostic data in order to determine
targeted interventions for specific concepts?
Did anyone surprise me?
Do I need to encourage a few more students try the
extentions?
Should I be pre-testing more students to see if more
compacting is needed?
New Considerations
Math Expressions Scope and Sequence
Grade 1 Switch Sections 2 & 3
Additional Professional Development
Kindergarten: “Too much time!”
Accurate Data
Compare administration strategies and finding
time
Deeper diagnostic data – AMU or First Steps?
Learning Intentions for This SessionI will understand that:
Data from AMU can guide instructional
decisions made by kindergarten and first
grade teachers.
I will know I understand when I can:
Name the components of the AMU and what
data they provide.
Describe how data from the AMU might drive
Tier 1 core instruction
Describe how data from the AMU might drive
Tier 2 intervention/enrichment decisions