Using MARS assessments
Overview
Understanding student performance
CST – Released Items Algebra 1
The design of scaffolded
performance assessment tasks
Top
Core
Core
Ramp
Access
Apprentice
Task
Performance Assessments
To Inform Instruction And Measure Higher Level Thinking
Top
Task Design
Core
Access
Ramp
Entry level (access into task)
Core Mathematics - (meeting standards)
Top of Ramp (conceptually deeper, beyond)
•
•
The Mathematics Assessment Resource Service (MARS) is an NSF
funded collaboration between U.C. Berkeley and the Shell Centre in
Nottingham England.
The Assessments target grades 2- Geometry and are aligned with the
State and NCTM National Math Standards.
Performance
Exams
40,000 – 70,000
students per year
since 1999
Students in grades 2
through 10th/11th grade are
administered performance
exams (5 apprentice tasks
per exam).
Student results are
collected, analyzed,
and reported by an
independent data
contractor.
Random sample of student
papers are audited and
rescored by SJSU math & CS
students. (Two reader
correlation >0.95)
District
scoring
leaders are
trained in
using task
specific
rubrics
Student tests are hand
scored by classroom
teachers trained and
calibrated using standard
protocols.
MAC vs. CST 2012
Silicon Valley Mathematics Initiative
Mathematics Assessment Collaborative
Performance Assessment Exam 2012
MAC vs CST 2012
2nd Grade
MAC Level 1 MAC Level 2 MAC Level 3 MAC Level 4
Far Below
Basic
Below Basic
Basic
Proficient
Advanced
2nd Grade
CST Below
CST At/Above
Total
1.0%
1.9%
1.3%
0.4%
0.3%
MAC Below
0.3%
2.4%
4.8%
3.5%
0.9%
0.1%
1.2%
5.5%
17.7%
23.4%
MAC At/Above
0.0%
0.0%
0.3%
3.4%
31.4%
Total
11.7%
7.1% 18.8%
5.1% 75.9% 81.0%
16.8% 83.0% 100%
Elementary Grades
3rd Grade
CST Below
CST At/Above
Total
4th Grade
CST Below
CST At/Above
Total
5th Grade
CST Below
CST At/Above
Total
MAC Below
15.9%
13.7%
29.6%
MAC Below
16.9%
20.3%
37.2%
MAC Below
20.6%
18.7%
39.3%
MAC At/Above
5.2%
65.4%
70.6%
MAC At/Above
2.8%
60.0%
62.8%
MAC At/Above
3.8%
56.9%
60.7%
Total
21.1%
79.1%
100%
Total
19.7%
80.3%
100%
Total
24.4%
75.6%
100%
Middle School
6th Grade
CST Below
CST At/Above
Total
7th Grade
CST Below
CST At/Above
Total
Course 1
CST Below
CST At/Above
Total
MAC Below
37.2%
25.1%
62.3%
MAC Below
33.3%
27.4%
60.7%
MAC Below
34.5%
30.3%
64.8%
MAC At/Above
1.4%
36.5%
37.9%
MAC At/Above
2.1%
37.1%
39.2%
MAC At/Above
3.6%
31.5%
35.1%
Total
38.6%
61.6%
100%
Total
35.4%
64.5%
100%
Total
38.1%
61.8%
100%
8th Graders Taking HS Geometry
Course 2
MAC
Below
CST
Below
3.1%
MAC
At/Above
Total
0.8% 3.9%
CST
At/Above
51.3% 44.8% 96.1%
Total
54.4% 45.6% 100%
Use of Formative Assessment
Research suggested that attention to the use of
assessment to inform instruction particularly
at the classroom level in many cases
effectively doubled the speed of student
learning.
Five elements of using assessment to
inform learning
• The provision of effective feedback to
students
• The active involvement of students in their
own learning
• The adjustment of teaching to into account
the results of assessment
Five elements of using assessment to
inform learning
• The recognition of the profound influence
assessment has on the motivation and selfesteem of students, both of which are crucial
influences on learning
• The need for students to be able to assess
themselves and understand how to improve
The teacher’s job is not to transmit knowledge. It is to engineer
effective learning environments for students. The features of
effective environments are that they create student engagement and
Allow teachers, learners, and their peers to ensure that learning is
Proceeding in the intended directions.
Bell and Swan study
An important technique for helping students
understanding learning intentions and
success criteria is asking them to look at
samples of other students’ work and to
engage in a discussion about the strengths
and weaknesses of each.
Students are much better at spotting errors
and weaknesses in the work of others than
they are in their own.
Putting Principals into Practice
Mathematical Practices
• Attend to precision. -use clear definitions
• Construct viable arguments and critique the
reasoning of others.
Briefly: Think of a definition for perimeter. Share
with a neighbor.
Marco thinks
Plan C has a
larger perimeter
than Plans A
and B. Explain
why Marco is
wrong.
Look at sample work and engage in
discussion about strengths and
weaknesses
“Marco probably counted. But he
counted wrong.”
“How could this explanation be improved?
What is missing to make it convincing?”
Getting students engaged
“Plan A and B have bigger areas,
so they have bigger perimeters.”
Do you agree or disagree? Is this sometimes
true, always true, or never true?
Understanding Learning Trajectory and
a Variety of Strategies
Jade sold only Peanut Butter Cookie
Dough. She raised $32. How many
Tubs did she sell?
What do you think the student is doing?
What do the lines represent? What do
the numbers represent? Does it make
sense?
This helps lay the foundation for
proportional reasoning at later grades,
for understanding input/output tables,
for making graphs.
Understanding Learning Trajectory
Situating the mathematics of the task in the learning
trajectory for number and data: At earlier grade
levels students have been learning about data
collection and representation in the form of bar
graphs. At this grade level students are extending the
ways of displaying data to include line plots. In second
and third grade students have been successfully
thinking about most and least and using comparison
subtraction to find the how many more. Also at third
grade students have started to expand their ideas
about number to include fractions, as parts of a
whole, and use rulers to measure with fractions.
Understanding Learning Trajectory
At this grade level students are starting to
decompose a fraction into a sum of its parts
and add and subtract fractions. At later grades
students will learn algorithms for adding and
subtracting fractions. Students will perform
more complex analysis of data to look at
mean, median, mode and range.
Asking a Question that gives Insight
into learning
Promote learning/ push thinking
“As teachers we are not interested in our
students’ ability to do what we have taught
them to do. We are only interested in their
ability to apply their newly acquired
knowledge to a similar but different situation.”
Asking a Question that gives Insight
into learning
How much longer was the longest wingspan from the shortest?
Understanding Place Value and
Subtraction
What does a student need to understand to use this process?
What principals remain in place from subtraction with whole
numbers?
Understanding Place Value and
Subtraction
What principals about subtraction doesn’t the student understand?
Understanding Place Value and
Subtraction
What is going on in the diagram? Where do the numbers come
from? Does this make sense?
Use of Formative Assessment
Research suggested that attention to the use of
assessment to inform instruction particularly
at the classroom level in many cases effective
doubled the speed of student learning. So, I
sincerely hope that you take what we’ve
learned, the tools we developed, and use the
tasks this year to inform instruction.
Suggestions for Getting Started
• Have staff try some former tasks in classrooms
and use staff meetings to use the “Tools for
Teachers” to think about implications for
instruction and design re-engagement lessons.