1. How to get students to think independently and critically
Presented by: Carri Carver
Woodward Academy
MathematicsTeacher

2.  Fall semester
 Take-home test
 1 real world
application problem
 2 of 14 students had
some success with
real world problem
 “Why can’t they do
ANYTHING by
themselves?”
A, 1
B, 1
C, 1
D, 5
F, 6
Take-homeTest Grades

3. How can I help my Precalculus students
become better:
 At solving real-world problems they have
never seen before?
 At figuring things out for themselves?

4. 1. Opportunities for problem solving
 Problem solving tasks
2. Strategies to improve problem solving ability
 Growth mindset
 Work Habits rubric (Habits of Mind Institute)
3. Assessment Reforms
 4.0 rubric (Marzano)
 Formative scores lead to summative grade (Marzano)

5. Level Description
2.0 / C Routine calculations, utilization of equations, solving equations.
3.0 / B Deriving equations, mathematical modeling.
4.0 / A+ Analyzing results, evaluating appropriateness of solutions.

6.  Pre-Survey & Introduction
 Task 1: Growth and Decay
 Task 2: Coffee Cooling
 Task 3: Case of the Cooling Corpse
 Corrections toTasks 2-3
 FinalTask: Choice of 3
 Rice on a Chessboard, Lillies on a Pond, orThe Big Melt
 Post-Survey and Open-ended Survey

7. A, 5
B, 6
C, 3
OverallTask Grades
April 2013
A, 1
B, 1
C, 1
D, 5
F, 6
Take-homeTest Grades
Fall 2012

8. Final grade assigned by
looking at best two
formative scores
Final average

9. From
Tasks
1-3
To
Final
Tasks
4&5
Improve-
ment
statistically
significant?
p-value
From
Task 1
To
Task 4
No
From
Task 1
To
Task 5
Yes p=.05
From
Task 2
To
Task 4
No
From
Task 2
To
Task 5
No
From
Task 3
To
Task 4
Yes p=.003
From
Task 3
To
Task 5
Yes p=.002
FormativeScore
Task number
 Not a strong positive correlation.
 Not statistically significant.

10. 6
6
3
-5
-2
2
-4
-2
2
-3
-1
8
-4
4
Growth mindset
Attitudes toward Math
NegativeAffects
Postive Affects
Independence
Number of
answers
improving
Number of
answers
regressing
Net gain
or loss

13.  Different rubric
 Scaffolding
 System for providing hints
 Checking student work in progress
 Growth Mindset
 Executive control and metacognition

14.  Food for thought…