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Differentiating Math Instruction: Project EQUAL Ongoing Assessment. What teachers need to know…. How are my students responding to mathematics instruction?. In order for students to be successful in Mathematics, each of these intertwined strands must work together, so… - PowerPoint PPT Presentation
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Differentiating Math Instruction:
Project EQUAL
Ongoing Assessment
What teachers need to know…
How are my students responding to mathematics instruction?
Adding it Up, National Research Council, p. 117, 2007
In order for students tobe successful in Mathematics, each of these intertwined strands must work together, so…
What do we measure to determine if they are making progress?
Continuously Assessing LearningEducators should evaluate what students know
and can do before, during and after instruction
Before Instruction: evaluate student prerequisite knowledge, skills, experiences and interests that relate to the target concept. Know where to begin instruction.
During Instruction: Are students gaining understanding? Are they able to use knowledge and skills proficiently? Results allow for immediate adjustment, if necessary.
After Instruction: Where are students in terms of their conceptual learning and skill proficiency? Assessing for the purpose of answering this question will help in planning future instruction.
Types of Assessment:Mathematics
Before: Screening
During: Formative
Diagnostic
(if necessary)
After: Summative
Pre-Assessment
Formative
Assessment
Summative
Assessment
Adapted from: Allsopp, D., Teaching Mathematics Meaningfully, 2007
Making mathematics
accessible through responsive teaching
Understanding & teachingThe big ideas in math ANDThe big ideas for DOING math
Understanding learning characteristics/ barriers
for students with difficulties In mathematics
Continuously assessing learningTo make informed instructional
decisions
Model for Meaningful Mathematics Instruction
Pre-Assessme
nt
Formative
Assessment
Summative Assessment
Big Ideas of Mathematics~Number & Operations~Algebra~Geometry~Measurement~Data analysis & probability
Processes for Doing Mathematics~Problem Solving~Reasoning & Proof~Connections~Communications~Representation
Responsive Teaching Framework for Differentiating Mathematics Instruction
Most Intensive
Few
Some
ALL
• Daily or Weekly, precise
• Graphically represented
EX. : Precision Teaching Great Leaps CBM probes
Least Intensive
• Weekly or Bi-weekly, more precise• Graphically
representedEX: CBM Probes
The more intensive the instruction…
the more intensive the monitoringshould be!
• District math benchmark assessments (as indicated)• Curriculum embedded assessments• Flexible student
interviews• Error Analysis• Student Work Samples• Rubrics for Problem
Solving (Applied Math)
MonitoringProgressorProgress Monitoring?
ProgressMonitoring
Monitoring Progress for
How can I measure student knowledge levels?Thinking Differently…
CRA Level of Understandin
gMethod Criterion
Abstract 1-5 minute timings(depends on nature of
target concept)
Fluency (Rate & Accuracy)
Representational(Drawing) 8-10 tasks Accuracy
90-100% 3 times
Concrete 3 tasks Accuracy100% 3 times
Start
INVESTIGATE!Review the continuous, formative assessment tools you have at your table.
As a Table Group, prepare to explain what it is, & how it might be used.
Think in terms of the intensity equalizer. Is it more intensive, or less intensive?
Progress Monitoring Probe
Abstract Level
Procedural:
See/Write 2 digit addition without
regrouping (sums < 20)
Measure:# of digits correct
Examples of Concrete and Representational/Drawing Probe Tasks
Use circle pieces and string to solve the following equations.
1. 3 x 4 = 12
Concrete
Representational/ Drawing
Making Instructional Decisions
Create a visual display of student performance data• Chart• Graph• Think of this visual display as a
“picture” of your students’ learning
Evaluate what the learning picture reveals about student learning
“goal line”
Visual Display
“corrects”
“incorrects”
What does this learning picture show?
Allsopp, 2008
Problem Solving Learning Picture Example: Student Use of Strategies
Allsopp, 2008
Algebraic Thinking Standard: Represent, describe, and analyze patterns and relationships using tables, graphs, verbal rules, and standard
algebraic notation.
NCTM Process: Representation
NCTM Process: Communication
0 1 2 3
Algebraic Thinking Standard: Represent, describe, and analyze patterns and relationships using tables, graphs,
verbal rules, and standard algebraic notation. Allsopp, 2008
Some General Guidelines for PM
Incorporate at concrete, drawing & abstract levels
Use short, easy to evaluate “probes”
Pinpoint key concepts for monitoring
Teach students to chart their learning
Use as a way to engage students in setting learning goals
At least 2-3 times weekly, more often if needed
CELEBRATE SUCCESS!!
Learn More About Continuous Progress Monitoring
at the MathVIDS Website:
http://fcit.usf.edu/mathvids/
Other Ongoing Monitoring Resources include:www.interventioncentral.org www.aimsweb.com
A Word About Follow Up
Choose an instructional practice you learned about in Project EQUAL
Implement in your Classroom
Join our Project Equal Wiki
Post a reflection about your action research.
With Gratitude…
Dr. David Allsopp
University of South FloridaFor his
Insightfulness andCollaborative Spirit
Thank You!
Contact Information:Donna Crocker 407.217.3679 [email protected] Geisel 407.317.3681 [email protected] Levy 407.317.3677 [email protected]
