### A Vertical Look at Formative Assessment Lessons

```A VERTICAL LOOK AT
FORMATIVE
ASSESSMENT
LESSONS
Why is this any different from regular math “tasks”
or “quizzes?”
Dr. Cassie Rape
May 10, 2013
GACIS MDC Training
We don’t learn passively.
• People are active participants in their own learning.
• We construct bridges between what we are learning now and
• Misconceptions arise naturally as a result.
• http://youtu.be/JqDZqblvOn0
• FOR INSTANCE: A third grader constructs the following “rule”
for themselves based on their previous learning: I will get
larger number whenever I multiply two numbers together.
There is a BIG difference between a
Mistake and a Misconception.
MISTAKES
• Computational
Errors
• Lack of Attention
• Careless Errors
Handwriting
• Observed
Occasionally/
Infrequently
MISCONCEPTIONS
• Wrong applications of
Mathematical Rules
• Incorrect
interpretation of
mathematical
concepts
• Observed
consistently
Why is the consideration of misconceptions important?
•
Children construct meaning internally by accommodating
new concepts within their existing mental frameworks.
•
Thus, unless there is intervention, there is likelihood that
the pupil’s conception may deviate from the intended one.
•
Pupils are known to misapply algorithms and rules in
domains where they are inapplicable.
•
A surprisingly large proportion of pupils share the same
misconceptions.
Undiagnosed Misconceptions Become
Owned and Embedded
Misconceptions
Undiagnosed Misconceptions Become
Owned and Embedded
Misconceptions
Owned
Formative Assessment is Shown to be
more successful than direct instruction
alone.
Student does not understand
conceptually the relationship between
slope and speed
Student does not get all of the graph
right.
Student does not explain why the graph
is realistic
Student misinterprets scale (either
misplacing the x and y axis or
interpreting the units in the wrong
increments).
Does not know that speed is distance
(per) time
Student does not calculate speed
(incorrect descriptions of speed)
Student fails to mention specific
distance or specific time
Student interprets graph as speed vs.
time (acceleration)
Tricked by picture. Student interprets
the graph as a picture.
PRE-Test ERRORS ANALYSIS
PERCENTAGES
G
H
A(10%) B (25%) C (80%) D (95%) E (50%) F (5%) (90%+) (95%) J (10%)
H
G (10%+) (70%)
Student does not understand conceptually the
relationship between slope and speed
Student does not get all of the graph right.
F (less than
5%)
Student does not explain why the graph is
realistic
C
E
A (5%) B (5%) (30%) D (45%) (5%)
Student misinterprets scale (either misplacing
the x and y axis or interpreting the units in the
wrong increments).
Does not know that speed is distance (per)
time
Student does not calculate speed (incorrect
descriptions of speed)
Student fails to mention specific distance or
specific time
Student interprets graph as speed vs. time
(acceleration)
Tricked by picture. Student interprets the
graph as a picture.
POST-Test ERRORS ANALYSIS
PERCENTAGES (approximates)
J (5%)
A SIDE-BY-SIDE COMPARISON
PRE
• A(10%)
• B (25%)
• C (80%)
• D (95%)
• E (50%)
• F (5%)
• G (90%+)
• H (5%)
• J (10%)
POST
• A (5%)
• B (5%)
• C (30%)
• D (45%)
• E (5%)
• F (less than 5%)
• G (10%+)
• H (30%)
• J (5%)
Some Difficult Discussions
GET OUT OF YOUR OWN BRAIN!
• Recognize…the rest of the
world does not think the way a
math teacher thinks.
• …and that’s OK.
#mathteacherproblems
http://youtu.be/6LSOMiLMvAY
HOW WE THINK
HOW THE REST OF THE
WORLD THINKS
Things I Can Let Go….
• No Work=No Credit
• Pencil Only or No Credit
• Do it How I Told You To
• Show the Steps…no, not your steps…the ones I taught
you
• “MATH RULES”
A HORIZONTAL LOOK
AT FORMATIVE
ASSESSMENT
LESSONS
CONVINCING TEACHERS OF FAL VALUE
ENSURING FIDELITY IN SCALING ACROSS
SYSTEM
The Beliefs of Educated Educators…. A
Cycle
No Personal
Proof of
Effectiveness
Generated
Unwillingness
to Try
Because
Potentially
Ineffective
TRAINING FOR TEACHERS
• STRUCTURED FAL STUDY
• TEACHERS START AS STUDENTS
• DEMONSTRATE PROCESS
• NO-PRESSURE OPPORTUNITIES
TO RUN TRIALS
• USE LESSONS PERTINENT TO
PROVIDING for TEACHERS
• Lessons Provided by DOE
• Matched lessons to units
• Opportunities to Collaborate
• Materials to Implement
• Support for the Process
• Time to Analyze Student Work
MOTIVATING TEACHERS
• THE GAME IS CHANGING: Math is
no longer an exercise in choreography,
but in true understanding and
application
• PARCC
• SHELL
• CCGPS
• Standards for Mathematical Practice
OUR PLATES, as MATH TEACHERS
Gates Grant (Shell Centre) Formative Assessment,
Compared to Instructional Framework
PreAssessment
(NO HELP
from
teacher)!
Analysis of
Student Work
and
Understandin
gs
Creation of
/Probing/Gui
ding
Questions
Standard/Esse
ntial Question
Opening
Opening
Collaborative
Session
(Utilize
Questioning)
MiniLesson
Student Work
Session
(Utilize
Questioning,
Create
“Experts”)
Student
Work
Session
Plenary
(Summarizin
g) Discussion
Closing
PostAssessment
(Students
can have
their Probing
Questions
and Pre-Test
to use during
PostAssessment)
Why does an FAL matter?
CHECKING WHAT YOU EXPECT
• Make the Expectation Clear: “Non-
Optional” Formative Assessments
• Observe the Lessons
• Ask for Student Work Samples
• Ask to see Analysis of Student
Errors
Things to Learn from Our Successes and
Mistakes
• Make FAL’s an expectation.
• Set time aside to train every single teacher
• Re-Train Teachers
• Follow up with second time to train every single teacher in
•
•
•
•
•
ANALYSIS of STUDENT WORK
Video!!! Praise works better than force!
Provide Materials, Share Materials, House Materials
Centrally
Teachers provide (someone in leadership) dates of FAL
enactment