Assessing students using the
KCASM/CCSSM
Minute-by-minute
Day-by-day
Katrina Slone, KDE Regional Math
Consultant – KVEC
Debbie Waggoner, KDE Regional
Math Consultant - CKEC
Kentucky Council of Teachers of Mathematics
Bowling Green, KY - October 8th, 2011
Today’s Targets
I can define formative assessment.
I can describe examples of formative
assessments.
I can classify formative assessments by their
types.
I can explain why each type of formative
assessment is critical to both assessment and
further learning.
Diagram #1
Listen to the following directions. Without talking to anyone, sharing work with anyone
or asking any questions, draw the figure described.
Diagram #2
Listen to the following directions and draw the figure
described.
List 3 examples
of formative
assessment….
Formative Assessment
Some things you may have identified as
Formative Assessments and are now
using:
bell ringers
THUMBS UP/DOWN
• Are these really Formative Assessments?
Answer: It depends!
Formative assessment can
and should be done BY
STUDENTS as well as by
teachers.
The key to improvement is
how students and teachers
use
assessment information.
Formative Assessment
Evidence of Learning
Formative assessment is a process used
by teachers and students during
instruction that provides feedback to
adjust ongoing teaching and learning
to improve students’ achievement of
intended instructional outcomes.
KDE, 2010
http://map.mathshell.org/materials/lessons.php
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Student Responses to Discuss
1. Describe the problem solving approach the student
used.
You might, for example:
Describe the way the student has colored
the pattern of tiles.
Describe what the student did to calculate a
sequence of numbers.
2. Explain what the student needs to do to complete his or
her solution.
15
Leon’s method
16
Gianna’s method
17
Ava’s method
http://map.mathshell.org/materials/lessons.php
http://www.insidemathematics.org/index.php/tools-for-teachers/problems-of-the-month
Formative Assessment
Shortcycle
Review the NCTM Research
Brief : What does research Say
the Benefits of Formative
Assessment Are?
Mediumcycle
Long-cycle
Typology of Kinds of Formative
Assessment
Type
Focus
Length
Long-cycle
Across marking
periods, quarters,
semesters, years
4 weeks to 1 year
Medium-cycle
Within and
between
instructional units
1 to 4 weeks
Short-cycle
Within and
between lessons
day-by-day
24-48 hours
minute-by-
5 seconds to 2
hours
minute
Why Now?
Lack of Engagement in
Math
• Lack of student engagement in learning
is the greatest problem in many math
classrooms.
• The Mathematics Practice Standards
present a way to leverage discourse.
• Formative assessment or Assessment for
Learning as learning activity for
teachers and students.
Traditionally Teachers Choose One
of Three Options
1. Go back and re-teach the topic with the entire
class.
2. Identify the students needing remediation and
find some time/opportunity to re-teach the
topic while the rest of the class continues on.
3. Feeling the pressure of the over packed
curriculum the teacher ventures on to the next
topic.
Re-teaching vs.
Re-engagement
Re-teaching
Re-engagement
Teach unit again
Revisit student thinking
Address missing basic skills
Address conceptual understanding
On the same or similar
problems
Examine task from different
perspective
Practice more
Critique student approaches
Cognition lower
Cognition higher
Generalizing Patterns: Table Tiles
Projector Resources
CLUSTER: Building a function that models a relationship between two quantities
CCSSM/KCASM ~ Content Cluster
CLUSTER: Building a function that models a relationship between two quantities
Knowledge Targets
Reasoning Targets
Define “explicit function” and “recursive
process”.
Write a function that describes a relationship between two
quantities by determining an explicit expression, a recursive
process, or steps for calculation from a context.
Combine two functions using the
operations of addition, subtraction,
multiplication, and division
Given a real-world situation or mathematical problem:
-build standard functions to represent relevant relationships/
quantities,
-determine which arithmetic operation should be performed
to build the appropriate combined function, and
-relate the combined function to the context of the problem
Evaluate the domain of the combined
function.
Identify arithmetic and geometric patterns Use given and constructed arithmetic and geometric
in given sequences.
sequences, expressed both recursively and with explicit
formulas, to model real-life situations.
Generate arithmetic and geometric
sequences from recursive and explicit
formulas.
Determine the recursive rule given arithmetic and geometric
sequences.
Given an arithmetic or geometric
sequence in recursive form, translate into
the explicit formula.
Determine the explicit formula given arithmetic and
geometric sequences.
Given an arithmetic or geometric
sequence as an explicit formula, translate
into the recursive form.
Justify the translation between the recursive form & explicit
formula for arithmetic and geometric sequences.
Performance
Skills Targets
Product
Targets
Assessing the Targets
Target
Formative Assessment
• Define “explicit function” and
“recursive process”.
• Determine the recursive rule
given arithmetic and geometric
sequences.
• Identify arithmetic and geometric
patterns in given sequences.
• Exit Slip: Define explicit
function.
• Entrance Slip: Find the
recursive rule for this
sequence.
• Thumbs UP if you think this is
an arithmetic pattern for this
this sequence. Thumps
DOWN if you think it is a
geometric pattern.
• Evaluate the domain of this
combined function on your
white board.
• Evaluate the domain of the
combined function
So…Do these assess the standard?
Standard Cake
CCSSM/ KCASM Learning
“I thought that if I taught them
all the bits, [students] could
put them together.”
FAL Trial
Teacher
Deconstruction was like sand-blasting to see each part: each
skill & concept students need to build on..,
Now we need students to make a Mosaiac seeing how the
targets & standards fit together to make clusters & BIG IDEAS in
mathematics…
Linking to Research:
The QUASAR Project
• Low-Level Tasks
▫ memorization
▫ procedures without connections to meaning
Martha’s Carpeting Task)
• High-Level Tasks
▫ procedures with connections to meaning
▫ doing mathematics
(e.g., The Fencing Task)
(e.g.,
Research – based
Conclusions
• Not all tasks are created equal -- they provided
different opportunities for students to learn
mathematics.
• High level tasks are the most difficult to carry
out in a consistent manner.
• Engagement in cognitively challenging
mathematical tasks leads to the greatest learning
gains for students.
• Professional development is needed to help
teachers build the capacity to enact high level
tasks in ways that maintain the rigor of the task.
Based on QUASAR & TIMSS Video Study
Formative Assessment Lessons, or
Mathematics FALs, are based on the
research about
formative assessment
and about
implementing high level tasks
Today’s Targets
I can define formative assessment.
I can describe examples of formative
assessments.
I can classify formative assessments by their
types.
I can explain why each type of formative
assessment is critical to both assessment and
further learning.
How Can We Support You?
Katrina Slone
KVEC Regional Mathematics
Content Specialist
Debbie Waggoner
CKEC Regional Mathematics
Content Specialist
Kentucky Department of Education
Kentucky Department of Education
Office of Next Generation Learners Office of Next Generation Learners
Debbie.waggoner@education.ky.gov
Katrina.slone@education.ky.gov
Thanks for your participation today.
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