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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. • • • • • • 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 • • • • • • • 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 • • • • • • 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 • • • • • • 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. http://padlet.com/wall/5favz7s99z 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. 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 • • • • • 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 • • • • 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 • • • 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 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 • • • Problem Solving Process Algebraic Thinking Synthesizing Math Concepts Writing • • • Internal/External Elements Alternate endings Perspective Reading • • • 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 • • • 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… • • • • • • 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 …