A VERTICAL LOOK AT FORMATIVE ASSESSMENT LESSONSWhy is this any different from regular math “tasks” or “quizzes?” Dr. Cassie RapeMay 10, 2013GACIS 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 what we already know

• 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• Misreading Own

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.

PRE-Test ERRORS ANALYSIS PERCENTAGES

A(10%) B (25%) C (80%) D (95%) E (50%) F (5%)G (90%

+)H

(95%) J (10%)

Tricked by

picture. Student interpret

s the graph as a picture.

Student interprets graph as speed vs.

time (accelerat

ion)

Student fails to

mention specific distance

or specific time

Student does not calculate

speed (incorrect descriptio

ns of speed)

Does not know that speed is distance (per) time

Student misinter

prets scale (either

misplacing the x and y axis or interpreting the units in

the wrong

increments).

Student does not explain why the graph is realistic

Student does not get all of

the graph right.

Student does not understa

nd conceptually the relations

hip between

slope and

speed

POST-Test ERRORS ANALYSIS PERCENTAGES (approximates)

A (5%) B (5%)C

(30%) D (45%)E

(5%)F (less than

5%) G (10%+)H

(70%) J (5%)

Tricked by

picture. Student

interprets the graph

as a picture.

Student

interprets

graph as

speed vs.

time (acceleration

)

Student fails to

mention specific distanc

e or specific

time

Student does not

calculate speed (incorre

ct descriptions of speed)

Does not

know that

speed is

distance

(per) time

Student misinterprets scale (either

misplacing the x and y axis or interpreting the

units in the wrong

increments). Student does not explain why the graph is realistic

Student does

not get all of the

graph right.

Student does not

understand conceptuall

y the relationship

between slope and

speed

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.

#mathteacherproblemshttp://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 LESSONSCONVINCING TEACHERS OF FAL VALUEENSURING FIDELITY IN SCALING ACROSS SYSTEM

The Beliefs of Educated Educators…. A Cycle

No Personal Proof of

Effectiveness

Unwillingness to Try

Because Potentially Ineffective

No Results Generated

TRAINING FOR TEACHERS

•STRUCTURED FAL STUDY•TEACHERS START AS STUDENTS•DEMONSTRATE PROCESS•NO-PRESSURE OPPORTUNITIES TO RUN TRIALS

•USE LESSONS PERTINENT TO THEIR GRADE/SUBJECT

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

CCGPS New CurriculumFAL

TASKSDifferentiated

Instruction

(D.I.)

Response to

Intervention (R.T.I.)

Flexible Grouping

Lunch Duty

PDF is Bookmarked

for Easy Access

Min

i-Les

son

Standard/

Essential Question

Opening

Mini-Lesson

Student

Work Session

Closing

Pre-Assessment (NO

HELP from

teacher)!

Analysis of

Student Work and

Understandings

Creation of

Leading /Probing/Guiding

Questions

Opening

Collaborative

Session (Utilize

Questioning)

Student Work

Session (Utilize

Questioning,

Create “Experts

”)

Plenary (Summarizing)

Discussion

Post-Assessment

(Students can have their

Probing Question

s and Pre-Test to use during Post-

Assessment)

Gates Grant (Shell Centre) Formative Assessment, Compared to Instructional Framework

Sum

mar

yWhy does an FAL matter?

Through Course Assessments

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

There will be some initial resistance…

Expect that.

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• Ask for feedback from teachers!• Ask for feedback from students!

Questions?• Dr. Cassie Rape • cassie.rape@hcbe.net

@DrCRRape