3-5 Differentiation for Gifted Learners

1. 3-5 Differentiation for Gifted Learners “How to fit it in”

2. Math Differentiation Examine resources and methods to fit problem solving into the Math Workshop for gifted math students. Reading Differentiation Learn about alternative literature and questioning strategies to use in Reading Workshop for gifted reading students.

3. Math Objectives You will learn how to fit advanced problem solving into math workshop for gifted math students. You will learn how to provide gifted students opportunities and instruction for explanation of thinking.

4. First… A Few “Musts” • Classroom teachers must meet with groups of gifted learners in math or reading workshops on a regular basis. • Gifted learners need enrichment activities to be modeled, taught, and guided through first, before they will be able to be successful and work to full potential. • Gifted learners must be held accountable for the work assigned to them. • Consider use of notebooks to keep these gifted differentiation strategies organized.

5. Creative Problem Solving • A problem solving handbook for teachers • Four Step Method • Problem solving strategies • Sample problems and solutions for each strategy • Topics in problem solving (Addition, multiplication patterns, divisibility rules, etc.)

6. 4 Steps of Problem Solving

7. Step #1Understand the Problem

8. Step #1: Understand the Problem~Read the problem carefully. What is important?~Does the problem give enough information? Too much information?~What is the question you are being asked? UNDERLINE IT!~What should your solution look like?

9. Step #2Plan How to Solve the Problem

10. Step #2: Plan How to Solve the ProblemChoose a reasonable problem-solving strategy:Draw a picture or diagramMake an organized listMake a tableSolve a simpler related problemFind a patternGuess and checkExperimentAct out the problemWork backwardsWrite an equation (algebra)

11. Step #3Carry Out the Plan

12. Step #3: Carry Out the PlanThis is where the “rubber meets the road,” or in this case, the pencil meets the paper. Actually use your strategy to work out the problem.REMEMBER if a problem involves two or more steps, check your work at the end of EACH step.

13. Step #4Look Back

14. Step #4: Look Back~Reread the question.~Consider the reasonableness of your answer. Does it answer the question?~Look over your work and check your calculations.

15. Solve the following using the 4 steps of problem solving.A wooden cube that measures 3 cm along each edge is painted red. The painted cube is then cut into 1 cm cubes as shown. How many of the1 cm cubes do not have red paint on any face?

16. Math Olympiad Online Team: 35 students for $109 You get : Current year Quiz Bowls, 2 previous years of quiz bowl questions Book: available from Math Olympiad website with problems and answers

20. Problemoids Focuses on developing and using problem-solving strategies, not on memorization or operations. The hints and solution sheets are designed to introduce, teach, and reinforce 19 problem-solving strategies. The program provides students with means of self-checking the most difficult part of their work.

21. United We Solve • Designed to supplement problem solving oriented math curriculum • Students work in groups • Tasks assume high standards for student performance, communication, and understanding of mathematical ideas • Problems organized into 4 categories: Patterns, Spatial, and Open-ended

22. Why Use Group Work in Mathematics? Interest: students engaged Success: can solve harder problems Multiple Approaches Peer Help Communication: natural use of mathematical vocabulary Contributions from all Collaboration Ready to try one? The RULES: 1-You may not look at anyone else’s clue. 2-If you have questions,check with the group first. 3-Be sure everybody participates 4-When you’re done, everyone raises their hand to share with the teacher.

23. The Problem Solver • Assign weekly problems to be recorded in a notebook to be reviewed or shared in group meeting with teacher • Great way to MAKE gifted math students SHOW their work! • Provides teacher with excellent documentation on student performance.

26. Singapore Math Model Drawing • Model drawing trains students to think analytically, providing an important transition between the concrete and the abstract (the algorithm). • 2 Stages • 1) learn the process of model drawing • 2) apply that process independently Eventually they won’t need to follow the steps.

27. Why is this good for AIG students? • It helps them show their work versus just saying “I just know the answer.” • Students may not see the validity of Model Drawing for an easier problem but start with a harder problem and they will see the value. • Helps keep their work neat and organized, especially on multiple step problems.

28. Step-by-Step Model Drawing 1) Read the entire problem. 2) Rewrite the question in sentence form, leaving a space for the answer. 3) Determine who and/or what is involved in the problem. 4) Draw the unit bar(s). 5) Chunk the problem, adjust the unit bars, and fill in the question mark. 6) Correctly compute and solve the problem. 7) Write the answer in the sentence, and make sure the answer makes sense.

29. Example Problem Easier Problem: A group of students were watching basketball practice. When the bell rang, ¾ of them went back to class. The other 12 students stayed to watch. How many students were there in all? Answer:

30. Another Example Problem Harder Problem: In a 9th grade class, ⅔ were girls and 12 were boys. ⅙ of the boys played a sport and ⅔ of the girls played an instrument. What fraction of the students played a sport or instrument? Answer:

31. Challenge Math Primary Grade Challenge Math Understanding the Power of Mathematics

36. Reading Objectives • You will find suggestions for incorporating Jacob’s Ladder into the Workshop Model. • You will experience an overview of Socratic Seminar/Shared Inquiry as ways to incorporate higher level questioning into your Workshop for gifted learners. • You will be able to incorporate Navigator Novel Study Guide as a tool to support book and genre studies. • You will understand the needs of gifted learners in preparing for End of Grade tests.

37. Characteristics of Gifted Readers • Reads fluently and well • Reads at an early age in many instances • Interested in words and word relationships (satire and jokes) • Process key ideas about what is read at a more rapid pace • Enjoys talking about literature and books • Writes descriptively to communicate stories • Reads often-inside and outside of class • Advanced vocabulary for age or cultural population • Enjoys verbal puzzles and games

38. Needs of the Gifted Reader • Research skills • Reading a variety of genre • Independent research projects • Opportunities to pursue areas of interest in depth over a long period of time • Guidance in critical reading and literary analysis • (Halsted, 2002)

39. This Semester This semester’s curriculum maps include units for: • Book Clubs (3-5) • Interpreting and Comparing the Meaning of Texts (5) • Interpreting the Meaning of Texts (4) • Test Prep (3-5) Each of the following resources can be used within these units.

40. Jacob’s Ladder Overview • Includes 10 reading selections of each of the following genres: ~Fables/myths (Level 3), interdisciplinary reading connections (picture books that link core curriculum with reading comprehension-Primary 2), short stories and essays ~Poetry ~Nonfiction (Draft version-through Benchmark Education) • Each reading selection (except poetry-Level 1) includes 2-3 ladders based on best fit with reading selections

41. Overview Cont. Revised Edition from Prufrock Publishing, Inc. • Primary 1 (K-1): Short Stories, Poetry… Ladders A-F • Primary 2 (1st-2nd): Short Stories, Interdisciplinary Reading Connections, Poetry… Ladders A-F • Level 1 (2nd-3rd): Myths/Fables, Poetry, Non Fiction…Ladders A-D • Level 2 (4th/5th): Short Stories, Poetry, Non Fiction… Ladders A-D • Level 3 (5th/6th): Short Stories, Poetry, Non Fiction… Ladders A-D • Level 4 (7th-9th): Short Stories, Poetry, Non Fiction… Ladders A-D Draft version includes Levels I, II, and III… Nonfiction books available through Benchmark Ed. Try using selections once or twice per quarter

42. Purpose of Jacob’s Ladder • To enhance reading comprehension skills • To build reading skills from lower order to higher order thinking • To enhance student discussion of textual • meaning • To promote instructionally sound test preparation • Build scaffolding for students to better employ higher level thinking skills with a variety of text • To cover language arts standards such as sequencing, cause and effect, classification, making generalizations, inference, and recognizing themes and concepts

43. Introduction to Jacob’s Ladder • Students engage in the inquiry process that moves from lower order to higher order thinking skills. • Organized into 4-6 ladders, each focusing on a different skill…depending on the grade level. • Students answer lower level questions on the lower rungs of each ladder and move to higher level questions at the top of each rung.

44. Summarizing the Ladder Goals Ladder A: predicting and forecasting skills by encouraging students to make connections among information provided. Ladder B: develop deductive reasoning skills, moving from concrete elements in a story to abstract ideas. Ladder C: developing literary analysis skills based on an understanding of literary elements. Ladder D: develop skills in creative synthesis in order to foster students’ creation of new material based on information from the reading. Ladder E: (Primary 1 and 2) Helps students develop skills in using their emotional intelligence in order to regulate and modulate behavior with respect to learning. Ladder F: (Primary 1 and 2) Focus on Word Study… to move students from understanding meanings of words or figurative language to appropriately using words within an applicable context or their own creation.Ladder

46. After completing the Ladders, students should be able to….. • Articulate their understanding of a reading passage using textual support Engage in proper dialogue about the meaning of the selection • Discuss varied ideas about intention of a passage both orally and in writing

47. Inquiry Discussion Selecting an appropriate text for Inquiry Discussion • must be open for interpretation to promote discussion • needs to have a theme centered around ideals or values example: friendship, responsibility, bravery, etc.

48. Shared Inquiry Discussion • empowers students to think for themselves and not just strive for the "right" answer • promotes the establishment of a dialogue and "piggybacking" of ideas/questions • students are given an opportunity to examine a common text • after reading the text, an open-ended question is posed and small group time is given for discussion • groups come back together and spend time sharing ideas and posing questions to promote a deeper understanding of the text • works on communication skills, not interrupting, listening to other viewpoints, respectfully sharing opinions, etc. www.youtube.com/watch?v=FTyUL6LMCTs

49. Navigators Navigators were developed by The Center for Gifted Education at the College of William and Mary. Each book is a collection of questions and activities intended to support the study of a novel.

50. Goals of the Navigators • To develop analytical and interpretive skills in literature • To develop understanding of selected literary themes. • To develop linguistic competency through vocabulary and language study • To develop skills in written and oral communication • To develop higher level thinking and reasoning skills in language arts • To develop research skills