Developing Analytical
Thinking in K-2 Learners
How do I implement rigor,
relevance, and the Common Core
into my overall instruction?
Session Objectives:
• Define analytical thinking.
• Describe observable behaviors that analytical
thinkers display.
• Examine student work products to identify
analytical thinking.
• Research and evaluate strategies for
promoting analytical thinking in K-2 learners.
What is Analytical Thinking?
The student demonstrates an ability to….
•Discern components of a whole
•Solves more difficult problems
•Strive to determine more complex, abstract
relationships and patterns in procedures,
experiences, ideas, and/or objects
•Organize and plan events and procedures in a
thoughtful and logical way with attention to
details
Kingore, 2001
Let’s connect analytical thinking
to the Common Core Standards
Analytical Thinking:
Rigor and Relevance
• Analytical thinking is woven into the
Common Core Standards.
• Approaching lesson planning with Analytical
Thinking in mind will make sure you are
scaffolding your lessons to include the
highest levels of thinking.
Common Core Connections- Math
Kindergarten
First Grade
Second Grade
K-CC.4 Understand the
relationship between
counting to cardinality.
K-CC. 6, 7 Compare
numbers.
n/a
n/a
K.OA 2- Solve addition
and subtraction word
problems.
K.OA 3- Decompose
numbers in more than
one way.
K.OA 4- From any
number 1-9, find the
number that makes 10.
1.OA1, 2- Solve word
problems using addition
and subtraction, up to 3
numbers for addition.
1.OA 3,4- Understand
and apply properties of
operations and the
relationship between
addition and subtraction.
1.OA. 6 Decompose and
use the relationships
between addition and
subtraction in order to
add and subtract.
1.OA. 7- Understand the
meaning of the equal sign
and determine if
equations are true or
false.
Analytical Thinking
Connection
•
•
2.OA1- Use addition and
subtraction within 100 to
solve one and two-step
word problems.
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•
•
•
•
•
Represents
numbers abstractly
Compares numbers
as numerals
Analyze and break
apart word
problems into
relevant parts.
Attentive to
important details
when solving
problems.
Shows logical
thinking.
Problem solving
strategies are sued
effectively.
Analyzes
alternative
solutions.
Can think
abstractly about
numbers and
Common Core Connections- Math
Kindergarten
First Grade
Second Grade
K. NBT 1- Compose and
decompose numbers to gain
foundation of place value.
1.NBT2,3- Understand place
value and compare two digit
numbers.
1.NBT 4,5,6 Use place value
to add and subtract.
2.NBT 1- Understand place
value up to hundreds.
2.NBT 4- Compare numbers
based on place value using
appropriate symbols.
2.NBT 5, 6, 7, 8, 9- Use
place value understanding
and properties of operations
to add and subtract.
•
2.MD All StandardsMeasure and estimate
lengths in standard units,
relation addition and
subtraction to length, work
with time and money,
represent and interpret
data.
•
2.G 1, 2, 3- Reason with
shapes and their attributes.
•
K. MD 1, 2- Describe
measurable attributes of
objects and compare and
contrast them.
K.MD 3- Classify objects into
given categories.
K.G. 1 Describe objects in
the environment based on
shape.
K.G. 4,5,6 Analyze, compare,
create and compose shapes.
1.MD 1- Compare and order
length.
1.MD 4- Organize, represent
and interpret data.
1.G 1,2,3- Reason with shapes
and their attributes.
Analytical Thinking
Connection
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•
•
•
•
•
•
Understands the
relationship between
place value and how it
contributes to the
overall value of the
number.
Generalizes “rules”
about numbers based
on examples.
Compare and contrast
based on parts.
Organizes ideas in
unique ways.
Thinks about concepts
in abstract and
complex ways.
Makes generalizations
based on data sets.
Analyzes alternative
groupings.
Attentive to details
Organizes collections
in unique ways.
Generalizes shapes in
real world.
Common Core Connections- Reading
Kindergarten
First Grade
Second Grade
R.L. 2- Retell familiar stories
including key details.
R.L. 2- Retell familiar stories
including key details and
demonstrate understanding
of the central message or
lesson.
R.L. 2- Recount stories
including key details and
determine their central
message or lesson.
R.L.5- Explain major
differences between books
that tell stories and books
that give information.
R.L.5- Describe the overall
structure of a story.
R.L. 9- Compare and contrast
the adventures and
experiences of characters.
R.L. 9- Compare and contrast
the adventures and
experiences of characters.
R.L. 9- Compare and contrast
two or more versions of the
same story.
•
Examines the parts in
order to determine
similarities and
differences
R.I. 2- Identify the main
topic and retell key details
of a text.
R.I. 2- Identify the main
topic and retell key details
of a text.
R.I. 2- Identify the main
topic of a multiparagraph
text as well as the focus of
specific paragraphs.
•
•
Uses relevant details.
Recognizes how details
contribute to main
idea/theme of story.
Uses cause and effect
relationship.
R.L. 5- Recognize common
types of texts
Analytical Thinking
Connection
•
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•
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R.I. 3- Describe the
connection between two
individuals, events, ideas or
pieces of information in a
text.
R.I. 3- Describe the
connection between two
individuals, events, ideas or
pieces of information in a
text.
R.I. 3- Describe the
connection between a series
of historical events,
scientific ideas or concepts
or steps in a technical
procedures in a text.
•
•
Uses relevant details.
Recognizes how details
contribute to main
idea/theme of story.
Uses cause and effect
relationship.
Analyzes text
structure to
determine genre.
Compare and contrast
genres
Understands details in
order to determine
the relationship
between them.
Can reach
generalizations based
Common Core Connections- Writing
Kindergarten
First Grade
Second Grade
Analytical Thinking
Connection
W.1- Use a combination of
drawing, dictating, and
writing to compose opinion
pieces in which they are
writing about and state an
opinion or preference about
the topic or book.
W.1-Write opinion pieces in
which they introduce the
topic or name the book they
are writing about, state an
opinion , and provide some
sense of closure.
W.1-Write opinion pieces in
which they introduce the
topic or name the book they
are writing about, state an
opinion , supply reasons that
support the opinion and
reasons, and provide a
concluding statement or
section.
.Demonstrates complex
thinking
.Uses details to organize
information or ideas in
relevant ways.
W. 3- Use a combination of
drawing, dictating and
writing to narrate a single
event or several loosely liked
events in the order in which
they occurred and provide
reaction to what happened.
W. 3- Write narratives in
which they recount two or
more appropriately
sequenced events , include
some details regarding what
happened, use temporal
words to signal event order,
and provide some sense of
closure.
W. 3- Write narratives in
which they recount a wellelaborated event or short
sequence of events, include
details to describe actions,
thoughts , and feelings use
temporal words to signal
event order, and provide
some sense of closure.
S.L. 5- Add drawings or
other visual displays to
descriptions as desired to
provide additional details.
S.L. 5- Add drawings or
other visual displays to
descriptions when
appropriate to clarify ideas,
thoughts, and feelings.
S.L. 5-Create audio
recordings of stories or
poems; add drawings or other
visual displays to stories or
recounts of experiences
when appropriate to clarify
ideas, thoughts or feelings.
•
•
•
Writing shows
problem/solution.
Actions are linked by
cause and effect.
Alternative resolutions
are evaluated.
•Show advanced spatial
ability.
•Presents information in a
new way.
•Makes generalizations based
on facts, details.
What Does Research Say
about Analytical Thinking?
Let’s explore key ideas
in articles!
Research Articles: Homework
• Ten Takeaway Tips for Teaching Critical Thinking by
Mariko Nobori
• Critical Thinking at the Primary Level by Judith Gugel
• How Media Literacy Fosters Critical Thinking by
Marlene Thier
• Nurturing Mathematical Minds:
Differentiation Strategies and Curriculum that
Promote Growth
by Michelle Sands, Teaching for High Potential
• Thinking about Mathematical Thinking
by Eric L. Mann, Teaching for High Potential
• They Have Eyes, But Do They See?
By Steve V. Coxon, Teaching for High Potential
• Choose one
article to read.
• Write a
reflection or
response and
post it to
Edmodo or
bring to the
next PD session.
Objective Check
• Define analytical thinking.
Characteristics of
Analytical Thinkers
How do you know if a student is
displaying analytical thinking?
Observable Behaviors
• Solves abstract math problems.
• Able to predict outcomes based on previous
•
•
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•
•
experiences.
Forms associations across time and disciplines
within a topic of study.
Retains details from observation and can write or tell
what they have experienced.
Compares and contrasts ideas, characters, objects,
etc.
Take things/ideas apart to examine how they work.
Writes stories with a problem/solution relationship.
Alternative solutions, outcomes are discussed &
evaluated.
Kingore, B. (2001) The Kingore Observation Inventory. 2nd ed.
Austin: Professional Associates Publishing
Observable Behaviors
• Asks, “what might happen if…”
• Make rules and discuss reasoning about
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•
•
•
•
categorizations and classifications.
Chooses a problem solving strategy & explains
reasoning.
Reaches “big ideas” based on details or examples.
Generalizes theme based on reading selected stories.
Creates original songs, stories or riddles to show
understanding of the whole idea/topic/theme after
having examined & studied details/parts of whole.
Shows advanced spatial ability.
Kingore, B. (2001) The Kingore Observation Inventory. 2nd ed.
Austin: Professional Associates Publishing
Objective Check
• Describe observable behaviors that
analytical thinkers display.
Turn and Talk
Share with a neighbor three
characteristics of an analytical thinker.
What Does Analytical Thinking
Look Like in Student Work
Products?
Let’s analyze a work sample to
find evidence of analytical
thinking ...
Student Work Sample
Leadership Writing Prompt: What Makes A Good Leader?
by Jerome
A good leader must be intelligent kind and listen to other people. I
think I am a good leader. I get a lot of hundreds on my work and I
am responsible. Jason, Sherril and other kids in my class say I’m
smart. Friday is kickball day. They pick me for captain because I
pick girls and boys for my team. I’m f air. Sometimes they argue
and grumble about the kick. I stop the argument by telling them lets
vote. My class picked me for student council. I had to write a speech
and make signs. I organized some of my friends to help me. I like
going to student council. Its like being in congress. We tell are ideas
and vote for the one we want. Some day I want to be a congress man.
I would be fair and make good laws. The End.
Evidence of Analytical Thinking
• Analyzes cause
and effect
• Demonstrates
complex and/or
abstract thinking
• Thinks logically
and uses problem
solving strategies
effectively
What Makes A Good Leader by Jerome
A good leader must be intelligent kind and
listen to other people. I think I am a good
leader. I get a lot of hundreds on my
work because I am responsible. Jason,
Sherril and other kids in my class say I’m
smart. Friday is kickball day. They pick
me for captain because I pick both girls
and boys for my team. I’m fair.
Sometimes they argue and grumble about
the kick. I stop the argument by telling
them lets vote. My class picked me for
student council. I had to write a speech
and make campaign signs. I organized
some of my friends to help me. I like going
to student council meetings. Its like being
in congress. We tell are ideas and vote for
the one we want. Some day I want to be a
senator. I would be fair and make good
laws that help everybody. The End.
Your Turn!
Let’s Jigsaw …
Let’s look at the completed puzzle!
Analytical Thinking Task:
Styrofoam Cup Adventure
Student Work Sample:
Styrofoam Cup Adventure
Analytical Thinking Task:
Pebble Math©
Student Work Sample:
Pebble Math©
Analytical Thinking Task:
A Mission for the Captain
Student Work Sample:
A Mission for the Captain
Analytical Thinking Task:
Scratch Your Brain ©
Brumbaugh, D., Brumbaugh, L., Rock, D. (2001) Scratch your
brain. Pacific Grove:CA.Critical Thinking Books and Software
Student Work Sample:
Shape Logic ©
Analytical Thinking Task:
Inventor with Spare Parts
Name _____________
Teacher _________
Date________
You are an inventor!
•
Create a new invention with the spare parts.
•
Add details to your invention by completing the background space.
•
Write a story about your invention.
Pieces of Learning: Primary Education Thinking Skills (1997) Merritt
Student Work Sample:
Inventor with Spare Parts
Analytical Thinking Task:
Animal Life Cycle Diary Entry
Student Work Sample:
Animal Life Cycle Diary Entry
Student Work Sample:
Animal Life Cycle Diary Entry
Analytical Thinking Task:
Venn Perplexors
Christianson, E. (2003). Venn perplexors. Mindware.
Student Work Sample:
Venn Perplexors
Your Turn!
Let’s Jigsaw …
Let’s analyze two work samples
as a group to find evidence of
analytical thinking ...
Objective Check
• Examine student work products to
identify analytical thinking.
http://padlet.com/wall/5favz7s99z
Strategies and Resources
to Promote Analytical Thinking
Check these out …
Strategies and Resources
Math
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Problem Solving Process
Algebraic Thinking
Synthesizing Math Concepts
Problem Solving Process
*Break story problems down into parts by using a
process, such as S.O.L.V.E.
S
O
Study the problem.
oWhat are you trying to
find out?
Organize the facts.
oWhat parts of the story
problem will help you
answer the question?
L
Line up a plan.
oWhich strategy will you
use?
V
E
Verify your plan.
oShow all of your work!
Evaluate your work!
oDoes your answer seem
reasonable?
Problem Solvers
•
Students may complete several problems above grade
level, explain how solutions were obtained using stepby-step explanation, and create their own problem
using the focus strategy
Hoogeboom, S., Goodnow, J. (1987). Problem solver. Chicago: Wright Group/McGraw Hill
Problem Solving Strategies
*Students should be able to use a combination of
strategies when solving and/or evaluating problems
Problem Solving Strategies
Draw a
picture or
make a
diagram.
Make an
Use logical
organized
reasoning
list.
Use or
make a
table.
Find a
pattern.
Solve a Guess and
simpler
check.
problem.
*Explicitly teach students problem solving strategies so
they can exhibit flexibility with applying the different
strategies to story problems.
Hoogeboom, S., Goodnow, J. (1987). Problem solver. Chicago: Wright Group/McGraw Hill
Algebraic Thinking
Algebra as the language of mathematics
Meaning of variables and variable expressions
Meaning of solutions
Understanding and using properties of the
number system
Reading, writing, manipulating numbers and
symbols using algebraic conventions
Using equivalent symbolic representations to
manipulate formulas, expressions, equations,
inequalities
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Algebra as a tool to study functions and mathematical
modeling
Seeking, expressing, generalizing patterns and rules in
real-world contexts
Representing mathematical ideas using equations,
tables, graphs, or words
Working with input/output patterns
Developing coordinate graphing skills
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•
•
Taken from
Balance Benders
(Critical Thinking Company)
Femiano, R. (2010) Balance benders. Seaside, CA: The Critical Thinking Co.
Synthesizing Math Concepts
• Model how to solve math problems or puzzles, then have students
create their own similar math problems /puzzles based on the ones
that were modeled.
• Provide opportunities for students to write about how they solved a
problem, including showing all work and including labels for pictures or
diagrams.
• Allow students to reflect upon their problem solving process and the
effectiveness of their strategies.
Balance Benders
Challenge students to
create their own!
Math Resources
Venn Perplexors (Problem Solving)
• Fun stories help to catch and keep attention spans
• Great for examining and defining relationships, characteristics and
sorting
• Venn diagrams for sorting solving and getting smarter
• Helps strengthen logic and problem-solving skills
.
Christianson, E. (2003). Venn perplexors. Mindware
Math Resources
•
M2 units
•
Six curriculum units designed to foster inquiry and engage students
in critical thinking, problem solving and communication, student work
samples, journals, products etc.
Math Resources
•
Mind Benders
•
Student use deductive thinking to complete logic
puzzles by using reading comprehension and mental
organization skills.
Harnadek, A. (1999). Mind benders. Pacific Grove: CA. Critical Thinking Books and Software
Strategies and Resources
Math
•
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Problem Solving Process
Algebraic Thinking
Synthesizing Math Concepts
Writing
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Internal/External Elements
Alternate endings
Perspective
Internal/External Elements
*Stories include both an external story and an
internal story.
--external story = what happened; the events/action of
a story
--internal story= responses to the action; character’s
thoughts, feelings, ideas, opinions, etc..
Alternative Endings
*Encourage students
to write various
alternate endings
to
stories/situations
* Students'
responses should be
based on clues,
events or
conclusions drawn
from the story
Writing Resources
Lucy Calkins Writers' Workshop Units of Study
o
o
o
Offer graphic organizers and lessons designed to teach how to
recognize and write a problem/solution.
Strategies for adding details such as the internal/external
timeline.
Focuses on discerning between relevant and irrelevant details.
Adapted from Caulkins, L. (2007). Units of study for primary writing: Grades k-2. Firsthand.
Perspective
Students can show complex and
abstract thinking by writing from the
perspective of an object or
character.
Ask students to
think about:
•
Mini-lessons can focus on describing a
setting from different animals' point
of view, or describing a day in the life
of an object.
•
•
•
What a bird would see when
it flies.
How a pencil feels.
What a tree thinks about.
How a minor character feels
in a story.
R.A.F.T = Raft, Audience, Format, Topic
Role
Audience
Format
Topic
The digit, 2
The digit, 3
postcard
You have been
visiting different
place values. Tell
what it is like in
the ones place,
tens place and
hundreds place.
Adapted from: Tomlinson, C. A. (2003) Fulfilling the promise of the differentiated classroom. Association for Supervision and Curriculum.
Writing Resources
Fulfilling the Promise of
the Differentiated
Classroom by Carol Ann
Tomlinson has
examples and
templates of RAFTS.
Tomlinson, C. A. (2003) Fulfilling the promise of the differentiated classroom. Association for Supervision and Curriculum.
Writing Resources
Active Questioning
• This book contains many
questioning activities that can
be made into writing
prompts/activities.
• Students explore perspective,
multiple outcomes and
alternative solutions.
• Provides the opportunity for
complex thinking through
question stems.
Johnson, N.L. (1996) Active questioning: Questioning still makes the difference. Pieces of Learning.
Strategies and Resources
Math
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Problem Solving Process
Algebraic Thinking
Synthesizing Math Concepts
Writing
•
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Internal/External Elements
Alternate endings
Perspective
Reading
•
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Literature & Vocabulary Webs
Analyzing Cause & Effect
Making Connections
Literature and Vocabulary Webs
These tools allow students to deeply analyze common
elements of various pieces of literature and elements of
vocabulary words.
adapted from The College of William &Mary
Reading Resources
•
William & Mary- These language arts units focus on analytic and interpretive skills in
literature, persuasive writing skills, linguistic competency, listening/oral communications
skills, reasoning skills, and understanding an overarching concept.
recommended for advanced
readers in grades 1-2;
strategies and teaching models
can be modified for other
ability levels
recommended for advanced
readers in grades 2-3;strategies
and teaching models an be
modified for other ability levels
Analyzing Cause and Effect
•
•
Utilize Multi-Flow Maps to show the causes and effects of an
event and analyze consequences of character actions or events
in the text.
Five Why's refers to the practice of asking, five times, why the
problem exists in order to get to the root cause of the problem
Guiding Questions:
What are the causes and effects
of this event?
Where did you get your
information?
Did a specific time period
influence the causes and/or
effects?
Analyzing Cause and Effect
-Teach students to analyze consequences or alternatives
-Infuse question stems from Consequences & Implications
rung into daily instruction!
Jacob’s Ladder Book 1
for Grades 2-3
Making Connections
* Encourage students to form associations across time and
disciplines within a topic of study.
* Challenge students to connect fiction and nonfiction concepts
* Good readers makes connections from the text to their life
(T-S), another book (T-T), or real-world (T-W)
Strategies and Resources
Math
•
•
•
Problem Solving Process
Algebraic Thinking
Synthesizing Math Concepts
Writing
•
•
•
Internal/External Elements
Alternate endings
Perspective
Reading
•
•
•
Literature & Vocabulary Webs
Analyzing Cause & Effect
Making Connections
All Content Areas
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Multiple Formats
Thinking Maps©
Depth and Complexity
Using Multiple Formats
*Provide students with opportunities to express their ideas
in multiple formats that appeal to learning styles and/or
multiple intelligences (poem, story,song, etc..)
*Choice Grids/Contracts
Teaching Gifted Kids in the Regular
Classroom (1992) Winebrenner
Thinking Maps ©
• Integrate Thinking Maps into all disciplines (reading,
science, math, social studies, art, music, etc…)
• Allow students to create their own Thinking Maps to show
what they have learned. This helps them construct
meaning.☺
• Challenge students to use a combination of Thinking Maps
for one topic, novel, etc.. to show depth & complexity.
Depth & Complexity
Introduction to the
Prompts of Depth and
Complexity - Project
Linking Learning
~ Dr. Sandra Kaplan
http://www.youtube.com/watch?v=McEldMETSnw&feat
ure=player_embedded#!
Depth & Complexity
Incorporating these thinking tools becomes a relatively simple way to
differentiate lessons for gifted students. Even something as simple as
popcorn can be extended into an interesting topic.
While popcorn may be plain…
discussing the ethical issues of popcorn creates a fascinating debate…
looking at the trends of popcorn price at movie theaters reveals
economic insights…
examining the rules of popcorn popping becomes a science lesson…
studying the details of what separates popcorn from other corn
broadens thinking…
sharing multiple perspectives about popcorn flavoring opens minds to
other cultures…
analyzing how popcorn has changed over time reveals new information
about our changing society…
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All Content Areas Resources
Building Thinking Skills
This resource provides highly effective verbal and nonverbal reasoning
activities to improve students’ vocabulary, reading, writing, math, logic,
and figural-spatial skills, as well as their visual and auditory processing.
This exceptional series provides a solid foundation for academic
excellence and success.
All Content Areas Resources
Analogies
•
Guides students through the process for solving analogies and builds
critical thinking and vocabulary skills. Students will learn how to read
analogies, the types of words used in analogies, and how to identify the
relationships in analogies.
•
Students will benefit from using the bridge map thinking map in
combination with the following resource books
All Content Areas Resources
This volume provides guidelines and activities for restructuring content
lessons to infuse direct instruction into the important core skills and
processes of critical and creative thinking. It combines text, graphic
representations of important points, sample lessons in core content
areas, and activity sheets. Teachers can use this lesson-design
handbook in constructing their own infused lessons. Suggestions for a
multitude of curriculum contexts in which to construct infused lessons
are also included. Over 30 fully developed model lessons are featured
including lesson plans, supplemental instructional materials, graphic
organizers for student and teacher use, suggested answers, and
assessment procedures.
The featured skills and processes of critical and creative thinking are
analyzed for use in lesson design. Verbal thinking strategy "maps" and
graphic organizers for all of the skills are provided. The lesson-design
process shows how these maps and the other lesson-design tools are
employed in developing infused lessons. Techniques to teach for
metacognition and transfer are illustrated, and their use in infusion
lessons explained. Numerous instructional strategies, questioning
procedures, and collaborative learning activities are analyzed as they
appear in sample lessons, and users are shown how these, too, can be
integrated into newly designed infusion lessons. The book also contains
lesson-observation and lesson-planning forms along with detailed
instructions for their use.
Web Resources
Check out these great web resources if you would like to learn more
about some of the strategies mentioned!
Introducing Depth and Complexity
http://www.byrdseed.com/introducing-depth-and-complexity/
Thinking with Thinking Maps
http://pinterest.com/lucy_n_libby/thinking-with-thinking-maps/
William & Mary Teaching Models
http://education.wm.edu/centers/cfge/curriculum/teachingmodels/index.ph
p
Objective Check
• Research and evaluate strategies for
promoting analytical thinking in K-2
learners
Task: Make it your own
• Choose a strategy and a resource
• Create a lesson plan to implement in
your classroom
• Goal: student sample
Metacognition
• Reflect on the lesson and student
sample
•
•
•
•
What went well?
What would you change?
What do you notice in the student sample?
Where would you go from here?
How did we do?
Have a great day …