CwiC Session at Anja Greer Math and Technology Conference 2019

1. Assessing Problem
Based Learning:
Devalue the answer & Value the process
Carmel Schettino, Ph.D.
Avenues: The World School
ASG Conference 2019 http://bit.ly/PBLCwiCs

2. “The concept of assessment
in PBL focuses on what
learners achieve – not what
teachers provide”
R. E. PURSER

3. Overview
1. Learning Goals of PBL Math
Classroom
2. Types of Assessments & How
they meet those learning Goals
3. Framework for thinking about
Assessment & Rubric

4. What is PBL?
An approach to curriculum and pedagogy where
student learning and content material are co-
constructed by students and teachers through
mostly contextually based problems in a
discussion based classroom where student
voice, experience, and prior knowledge are
valued in a non hierarchical environment.
Schettino, 2013

5. Learning Goals of PBL
Master mathematical content
Help students become better problem solvers
(WDYDWYDKWTD?)
Become better mathematical communicators
(oral, written, digital, different representations,
etc.)
Improve perseverance, creativity, risk-taking,
innovation levels
Become better collaborators with their peers

6. Cschettino 2013

7. PBL Classroom
Attribute of PBL Classroom MP Standard
Connected Curriculum
Decompartmentalized problems, focus on
the why
Make sense of problems and persevere in
solving them
Scaffolded problems Reason abstractly
Dissolve traditional hierarchy, Construct viable arguments
discourse moves that improve equity,
valuing risk taking, multiple perspectives
Critique reasoning of others
Mutliple perspectives Look for repeated reasoning
Scaffolded problems Use appropriate tools
Student presentation, use of prior
knowledge
Model with mathematics
What are the measures of the
angles in a triangle that have a
base the same measure as its
height?

8. Key Questions
How do you keep assessment
authentic and consistent with the
values of the pedagogy?
How do you ensure that your
assessment measures the learning
goals?

9. Table of Assessments
Type Rubric How
Often
Type of
Feedback
Learning Goal
Assessed
Class
Contribution
Yes Ongoing Student self-
assessment, teacher
feedback, self-
evaluation
Communication,
Persistence,
perseverance
Quiz No biweekly Numerical grade Content Mastery
Individual
Problem Set
No 2-3 weeks Numerical grade,
written feedback
Content mastery,
problem solving
Partner
problem Set
No 1-2 a year Numerical grade,
written feedback
Communication,
collaboration
Journal entries Yes biweekly Extensive written
feedback, letter grade
Communication,
problem solving
Daily
homework
Yes Daily Oral Persistence, problem
solving, content
mastery
Homework
Hand-in
Yes biweekly Written feedback Content mastery,
communication

10. Oral Assessment
Ongoing
monitoring
of Classroom
Discourse
Harkness
Diagramming
Student Self
Assessment
Class
Contribution
&
Presentation
Student-
Authored
Norms
Teacher feedback
Class Contribution
Rubric Discussions

11. “Reflective thinking
compels to inquiry”
JOHN DEWEY

12. Self-assessment of classwork

13. Gather student reflection

14. Written Assessment
Formal
Written
Assessments
Problems for
Problem
Solving
Metacognitive
Journaling
Partner
Problem Sets
Quizzes for
Skill
Acquisition
Take Home
Parts of
problem Sets
Feedback
before Grades
Hand-in
Homework

15. What good are journals?
Communication form not usually practiced in math classroom,
but still a standard (reflection and communication)
Some teachers give prompts – open ended or direct
Some teachers are very clear about the structure other leave it
more open i.e “free writing” vs. discussing a problem vs. “the
journalist’s questions” vs. “learning log”
Response to other students solutions
Present your initial error/view and reflect on that perspective –
describe why it was wrong and correct it.
Mid-continent Research for Education and Learning, 2009 , http://files.eric.ed.gov/fulltext/ED544239.pdf

16. “I assumed I needed to do a straight line. I then saw ‘three units’, so I
put a point on (5,1), and drew the line y=1. If (5,1) was 3 away, I
thought, shouldn’t all the points on the line be 3 away?”
“Only 1 point on each of the lines was actually 3. The rest of the
points were actually all further than 3 units from the point.”
“This, I thought, would cause all points on the line to be 3 units away from point
(5,4). However, I was again wrong. The blue line on the diagram shows a point on
one of my lines that was more than 3 units from (5,4). The red line shows a point on
one of the lines that is less than three units from (5,4). The green lines are points
that are 3 units away from point (5,4). I have effectively created a range of lengths
from (5,4) opposed to what the question was asking for which was 3 units from
(5,4).
“It made perfect sense!…Any point from the centerpoint
of a circle to any point on the circle was the same length
(the radius). I immediately drew the connection. 3 was
the radius and (5,4) was the center. the distance between
the middle point and any point on the circle was 3!”

17. Problem Set Assessment
• Measures content knowledge and mastery
• Not your typical test
• How to assess problem-solving skills
• How to study for these types of
assessments
• Value creativity, synthesis and risk-taking
• Journals are allowed

18. Feedback before Grades

19. Feedback allowed for:
•Time to study what they felt they took risks on
•Similar questions in their notes
•Feeling as though their second attempt mattered, as well
as their first (simulates classwork more closely)
•Their creativity was important

20. Avenues world elements
http://awe.avenues.org/table.aspx

21. Math Elements
(Interdisciplinary)

22. Rubric for our elements

23. “Feedback should be
more work for the
recipient than the
donor”
DYLAN WILIAM

24. Contact/follow me
cschettinophd@gmail.com.
carmelschettino.org
@SchettinoPBL
CarmelSchettinoPhD
Slideshare.net/carmelschettino