developing analytical thinking in k-2...
TRANSCRIPT
Developing Analytical Thinking in K-2 Learners
How do I implement rigor, relevance, and the Common Core
into my overall instruction?
Meet Your Presenters!
• Nancy Betler Talent Development Facilitator, Eastover Elementary, CMS
• Emily Foley Magnet Coordinator, Irwin Academic Center, CMS
• Kelly Kollar Magnet Coordinator, Tuckaseegee Elementary, CMS
• Lisa Pagano Academic Facilitator, Irwin Academic Center, CMS
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 Analytical Thinking Connection
K-CC.4 Understand the relationship between counting to cardinality. K-CC. 6, 7 Compare numbers.
n/a n/a • Represents numbers abstractly
• Compares numbers as numerals
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.
2.OA1- Use addition and subtraction within 100 to solve one and two-step word problems.
• 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 problems.
Common Core Connections- Math
Kindergarten First Grade Second Grade Analytical Thinking Connection
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.
• Understands the relationship between place value and how it contributes to the overall value of the number.
• Generalizes “rules” about numbers based on examples.
K. MD 1, 2- Describe measurable attributes of objects and compare and contrast them. K.MD 3- Classify objects into given categories.
1.MD 1- Compare and order length. 1.MD 4- Organize, represent and interpret data.
2.MD All Standards- Measure and estimate lengths in standard units, relation addition and subtraction to length, work with time and money, represent and interpret data.
• 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.
K.G. 1 Describe objects in the environment based on shape. K.G. 4,5,6 Analyze, compare, create and compose shapes.
1.G 1,2,3- Reason with shapes and their attributes.
2.G 1, 2, 3- Reason with shapes and their attributes.
• 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 Analytical Thinking Connection
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.
• 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
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.
• Analyzes text structure to determine genre.
• Compare and contrast genres
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.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.
• Understands details in order to determine the relationship between them.
• Can reach generalizations based on individual pieces of
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 well-elaborated 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.
• Writing shows problem/solution.
• Actions are linked by cause and effect.
• Alternative resolutions are evaluated.
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.
•Show advanced spatial ability. •Presents information in a new way. •Makes generalizations based on facts, details.
L. 4-Determine or clarify the L. 4-Determine or clarify the L. 4-Determine or clarify the • Takes apart words in
What Does Research Say about Analytical Thinking?
Let’s explore key ideas
in articles!
Critical Thinking at the Primary Level
“Primary teachers ‘are taught very well how to teach arithmetic,’ but children need to be trained to think about mathematics ‘in a way that’s logical’ and takes them beyond computation.“
“If children become used to making predictions, looking for patterns and applying mathematics to real-world situations, then ‘they won’t be surprised’ when they’re asked to perform such tasks in higher level math classes.”
Critical Thinking at the Primary Level by Judith Gugel, Classroom Leadership
Opportunities for Spatial Awareness
“Drawing, while likely beneficial for all children’s learning, is especially needed as an outlet for “spatially-able” children who have tremendous potential as future scientists or engineers. “
“Have students draw ideas for an invention…sketch an insect found on the playground, and record data from an experiment pictorially and numerically.”
• They Have Eyes, But Do They See? By Steve V. Coxon, Teaching for High
Potential
Importance of Problem-Solving
“Recognizing patterns, combining elements in different ways and repeating this process until the outcome makes sense is pleasing and fundamental to the development of mathematical thinking. “
“As you are planning lessons and selecting problems to challenge your students, look for ones that can create surprises and ah-ha moments for them.”
Thinking about Mathematical Thinking by Eric L. Mann, Teaching for High Potential
Evaluate Reasoning
“ To know whether your students are learning to think critically, you need a window into their thought processes. So challenge them to communicate back to you.”
Ten Takeaway Tips for Teaching Critical Thinking by Mariko Nobori
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 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 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.
Strategies and Resources to Promote Analytical Thinking
Check these out …
Strategies and Resources
Math • 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.
L Line up a plan.
oWhich strategy will you use?
S Study the problem.
oWhat are you trying to find out?
O Organize the facts.
oWhat parts of the story problem will help you answer the question?
V Verify your plan.
oShow all of your work!
E Evaluate your work!
oDoes your answer seem reasonable?
Problem Solving Strategies
Draw a picture or
make a diagram.
Make an organized
list. Find a
pattern.
Use logical reasoning
Guess and check.
Solve a simpler
problem.
Use or make a table.
*Explicitly teach students problem solving strategies so they can exhibit flexibility with applying the different
strategies to story problems.
Problem Solving Strategies *Students should be able to use a combination of strategies when solving and/or evaluating problems
Hoogeboom, S., Goodnow, J. (1987). Problem solver. Chicago: Wright Group/McGraw Hill
Algebraic Thinking
Taken from Balance Benders
(Critical Thinking Company)
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
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
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!
Strategies and Resources
Math • Problem Solving Process
• Algebraic Thinking
• Synthesizing Math Concepts
Writing
• 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
Perspective Students can show complex and
abstract thinking by writing from the perspective of an object or character.
Mini-lessons can focus on describing a setting from different animals' point of view, or describing a day in the life of an object.
R.A.F.T = Raft, Audience, Format, Topic
Ask students to think about:
• 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.
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.
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
adapted from The College of William &Mary
Literature and Vocabulary Webs
These tools allow students to deeply analyze common elements of various pieces of literature and elements of vocabulary words.
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?
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
• 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#!
And Many More ...
Math • Problem Solvers
• Venn Perplexors
• M2 Math
• Mindbenders
Writing
• Lucy Calkins Writer's Workshop
• Readwritethink.org
• Active Questioning
Reading • Jacob's Ladder
• William & Mary
• Analogies
All Content Areas • Building Thinking Skills
• Infusing the Teaching of Critical and Creative Thinking into Content Instruction
• Organizing My Learning: Graphic Organizers
Objective Check
• Research and evaluate strategies for promoting analytical thinking in K-2 learners
Connect with Us!
Join our Facebook group so we can
continue to share resources!
Have a great day!