Transcript Administrator’s Guide - Kansas State University

Fewer, Clearer, Higher . .
What Exactly Does That Mean?
3÷½=
What “Knowledge” is
needed to solve this
problem?
½ ÷¼=
How might you get your students to “reason
why”?
“Yours is not to reason why, just invert and
multiply” is all about memorizing a procedure.
Multiplying across the numerators and
denominators (never mind why that works in
multiplication but not in addition!), you get the
answer 4/2 or 2. Reasoning why was not part of
the equation.
It is easy to reason through that question by
asking, “How many fourths are in a half?” You
might illustrate the question by creating a
diagram of a whole square, and then shading
in one half of it (Figure 3.6).
How many fourths are inside that half? It’s easy
to see that there are two of them.
A good teacher
makes you
think
even when you
don’t want to.
-Fisher, 1998 Teaching Thinking
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bring greater rigor to standards driving
instruction and expectations for ALL students,
focus curriculum and instruction on deeper
student understanding of a few critically
important areas rather than skimming a
multitude of topics,
provide clearer direction to teachers on what
American students should know and be able to
do as they leave high school for college or career
purposes.
Before we begin . . .
Take a couple of minutes to write your
personal definition of “cognitive rigor” as
it relates to instruction, learning, and
assessment.
At your table, discuss the following:
• Your definition of cognitive rigor?
• What does “rigor” look like in the classroom?
Be prepared to share your group’s definition.
Reflect on your definition of RIGOR as we discuss
this morning . . . .
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Quality Instruction:
Students achievement is more highly
correlated with the nature of classroom
instruction- HOW the content is taught
and HOW teachers use the curriculum-rather than with WHAT curriculum is
used.
The
♥ of the matter
is the Depth of Knowledge
Challenging Tasks
There is no other decision that teachers make
that has a greater impact on students’
opportunities to learn and on their
perceptions about what mathematics is than
the selection or creation of the tasks with
which the teacher engages the students in
studying mathematics.
(Lappan & Briars)
The Bottom Line . . . .
Our students won’t learn
What they need to learn,
if we don’t give them
opportunities to learn it.
Different states/schools/teachers use
different models to describe cognitive rigor.
Each addresses something different.
•Bloom – What type of thinking (verbs) is
needed to complete a task?
•Webb – How deeply do you have to
understand the content to successfully
interact with it? How complex is the
content? (What follows the verbs?)
Webb’s Depth of Knowledge (DOK):
scale of cognitive demand
There are 4 Levels of Cognitive Complexity
Depth of Knowledge refers to the cognitive demand
required for the task or problem or the “type of thinking”
required. It is the depth and complexity of the task or
problem, not difficulty level.
The intended student learning outcome determines the
DOK level. What mental processing must occur?
While verbs may appear to point to a DOK level, it is what
comes AFTER the verb that is the best indicator of the
rigor/DOK level.
Depth of Knowledge is the degree of depth or complexity of
knowledge.
DOK is NOT.....
about Verbs - Verbs are not always used appropriately.
about "difficulty" - It is not about the student or level of difficulty for the
student - it requires looking at the assessment item not student work in order
to determine the level. DOK is about the item/standard - not the student.
DOK is....
about what FOLLOWS the verb. What comes after the verb is more important
than the verb itself. It’s about the complexity of mental processing that must
occur to answer a question.
Remember DOK...
Descriptive, not a taxonomy
Focuses on how deeply the student has to know the content in order to
respond.
Not the same as difficulty.
 DOK-1 – Recall & Reproduction - Recall of a fact, term, principle,
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concept, or perform a routine Procedure
DOK-2 - Basic Application of Skills/Concepts -Use of information,
conceptual knowledge, select appropriate procedures for a task,
two or more steps with decision points along the way, routine
problems, organize/display data, interpret/use simple graphs
DOK-3 - Strategic Thinking - Requires reasoning, developing a plan
or sequence of steps to approach problem; requires some decision
making and justification; abstract, complex, or non-routine; often
more than one possible answer
DOK-4 - Extended Thinking - An investigation or application to real
world; requires time to research, problem solve, and process
multiple conditions of the problem or task; non-routine
manipulations, across disciplines/content areas/multiple sources
Cognitive Rigor Matrix
Depth +
Thinking
Level 1
Recall &
Reproduction
Remember
Recall conversions, terms,
facts
Understand
Evaluate an expression
Locate points on a grid or
number on no. line
Solve 1 step problem
Level 2
Basic Skills &
Concepts
Level 3
Level 4
Strategic Thinking Extended
& Reasoning
Thinking
Specify, explain
relationships
Make basic inferences
Use concepts to solve nonroutine problems
Use evidence to justify
conjectures
Relate mathematical
Concepts to other
content areas, other
domains.
Apply
Analyze
Evaluate
Create
DOK Handout
Cognitive Rigor & Implications for
Examining Resources & Assessments
• Assessing only at the highest DOK level will
miss opportunities to know what students do &
don’t know—go for a range and end “HIGH” in
Critical Areas.
• Performance assessments can offer varying
levels of DOK embedded in a larger, more
complex task.
Individually:
Write a mathematics word problem
for which 3 ÷ ½ would be the method
of solution.
NAEP, 8th grade-2011
Student A:
Student B:
66% Incorrect
14% Correct
20% Omitted
What is …
½x½÷½=?
Justify your answer with
the Twizzler.
¼
(half of one-half)
How much of the
¼
½ fits into ¼?
½
½ of the ½ fits into ¼
This is why ½ is the answer.
1.
2.
3.
4.
5.
6.
7.
8.
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
Use appropriate tools strategically
Attend to precision
Look for and make use of structure
Look for and express regularity in repeated reasoning
Implications for Depth of Knowledge?
How does this relate to your knowledge package?
You’ve heard new information about the CCSS
-DOK Levels
-Expectations
-Examples, etc.
In your team
1. Analyze SBAC of KS Assessment item for rigor
2. Use DOK Poster to Justify your choice for DOK
Level
3. Reach Consensus
4. Show your DOK Analysis (1, 2, 3, 4)
5. You MUST defend your choice!
Math 4th Grade (KS State Assessment)
 Each day that Jasmine turns in her homework on time, she earns
5points. Jasmine has turned in her homework on time for the
last 8 days. How many points has Jasmine earned altogether?
a)30
b)35
c)40
d)45
Math, 3rd Grade
Look at the number below:
6,593
Which digit is in the tens place?
a. 3
b. 9
c. 6
d. 5
6th Grade , Math Sample, SBAC
8th Grade, Math Sample SBAC
HS Math Sample, SBAC
3rd Grade
Diego buys a greeting card that costs $1.29. He pays for the
card with two $1.00 bills and receives the correct amount of
money as change. Which group of coins could Diego have
received as change?
3rd Grade, SBAC
6th Grade SBAC
High School
SBAC
THINK FOR A MOMENT . . .
Do ALL of your sudents
have the opportunity to grapple with
challenging tasks, everyday?
 Do you have resources that embed the Habits of Mind in every
lesson?
 Are the tasks you choose for your students cognitively
challenging?
 Are ALL students exposed to rich tasks that promote higher
order thinking?
 Are at least 80% of your test questions (Formatives &
Summatives) written at “higher” DOK levels?
Putting it all together . . . . .
1. Revisit your definition of “rigor”
and what this looks like in the
classroom– have your ideas
changed? If so, in what ways?
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