Session 79 NCTM 2015 powerpoint for Secondary Mathematics Education

1. Assessing Problem
Based Learning
Relating Student Work to the Practice
Standards
Carmel Schettino, Ph.D
Deerfield Academy
NCTM 2015

2. Glacial Potholes of shelburne Falls

3. Overview
• Discussion of PBL Classroom
Practice – Definitions and
Distinctions (PrBL vs. PBL)
• Math Practice Standards and
Assessment
• My view of Assessments in PBL &
how PBL fosters the MPS
• Types of Assessments I do in my
Classroom Practice

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, grit,
risk-taking, innovation levels
• Become better collaborators with their
peers

6. PBL framework
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
A circle with radius 5 has an arc
from A(5,0) to B(3,4). Find the
angular size of the minor Arc AB
and then find the coordinates of
another arc with the same size.

10. 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?

11. How do the Tests Assess the Math
Practices?

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

13. Set the tone with clear expectations

14. Include Student reflections

15. Written Assessment
Formal
Written
Assessments
Problems for
Problem
Solving
Metacognitive
Journaling
Partner
Problem Sets
Quizzes for
Skill
Acquisition
Take Home
Parts of
problem Sets
Allow for
Corrections?
Hand-in
Homework

16. Purpose of Homework?
• Review material from past courses
• Trigger prior knowledge for an upcoming problem
• Inspire construction of new knowledge (give context
or connect)
• Introduce new technology use
• Practice new skill
• Challenge more able students
• Introduce new terminology/vocabulary
• See a familiar topic from a different perspective
• Concretize an abstract concept
• Have students summarize/generalize a new topic

17. Assessing Problem Solving

18. Think about main topic you want to assess
Connect with other topic?
What is your expectation of what they can
do on their own?
Put it in a different context

19. Homework Questions
Find two points that are 5 units away
from (0,0) on the line x=4.

20. Other perspectives

21. Change it up or ask students to
• Find two points that are 13 units
away from (1,3) on the line y=8.

22. Give it context

23. Then we assess...

24. 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

25. “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!”

26. Tech & Inquiry Projects

27. Table of Assessments
Type Rubri
c?
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

28. This Slideshow can be found at
www.carmelschettino.org
With all handouts

29. PD Opportunity
• PBL Math teaching summit
• July 16 thru 19
• Deerfield, ma
• Discussion, sharing and learning all about
pbl math
• Pick up a flyer

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31. Contact me
• carmel@carmelschettino.org
• @SchettinoPBL
• Slideshare.net/carmelschettino
(for this presentation)