Math Strategies to Meet the Needs of the 5TH QUINTILE Janet Carlson Westerville City Schools Slideshow Adapted from a presentation at The Ohio Association For Gifted Children by: Leanne Ross, Tollgate Elementary, Pickerington Local Schools Special thanks to Dr. Raj Shah MathPlus Academy.com

Identified Weaknesses from Grade 3 OAA 1. Draw an angle that is smaller than a right angle. Explain how you know the angle you drew is smaller than a right angle. (District Average 1.4/2 points) 2. On the measurement question involving time (showed 3:30 and asked the kids what time it would be 45 minutes from now...), our kids scored 85% correct (district). We had schools as low as 69% on this question. 3. On a measurement (time) question involving a calendar (first race Jan 24, second race Feb 21, how many weeks after first race was second race) question, we were at 82% as a district. Most building scores were clustered in this area. 4. On a geometry question with a pyramid and cube, students were asked which statement is true about the two objects... Though we were at 86% as a district, building scores were as low as 69%. 5. On a measurement question involving shading two measuring cups (1/2 cup and 3/4 cup) and telling which is more, we were at 1.56/2 as a district average. There was a.67 point range on this question!

Identified Weaknesses from Grade 3 OAA continued Other measurement and geometry questions (not released this year) that kids have struggled with in the past include: 1.Selecting appropriate units to measure length, volume, weight, and temperature. 2. Establishing referents for units (gallon - container of milk or square inch - postage stamp... got hit hard on this exact question in grade 4 this year) 3. Use a ruler to construct a rectangle specified lengths and widths. 4. Make estimates for perimeter, area, and volume using links, tiles, cubes, etc. 5. Locations on coordinate grid (improvement shown...) 6. Symmetry (multiple lines, like stars!) 7. Identifying how many more cubes are needed to finish a shape.

Essential Questions What can be done to ensure challenge for our 5 th quintile students? What strategies are available to meet the educational needs of these students? Are we willing to become flexible enough to use these strategies? Is it worth our time?

Strategies Known to Help 5 th Quintile Students Grow and Learn Flexible cluster grouping Enriched grade level content standards Focus on higher level interpretations and communication Differentiation Formative assessment for appropriate and clear learning targets Opportunities for authentic work Acceleration

Flexible Cluster Grouping A study examined the use of cluster grouping in two elementary graduation classes (n=197). During the three program years, students involved in the school using cluster grouping were more likely to be identified as high achieving or above average, and all students had significant increases in achievement test scores. Gifted Child Quarterly, v52 n3 p Marcia Gentry

Characteristics of Flexible Cluster Grouping 1.All students are initially placed in an ability based cluster group using testing data. 2.Professional development is provided for teachers based upon the group level with which they are working 3.Students are constantly reassessed based on achievement and moved between groups as needed.

Flexible Cluster Grouping Advantages Students receive instruction related to their own specific needs. Teachers are better able to direct their planning to one or two subsets of students rather than five or six. Student placement is fluid. Obstacles to overcome Scheduling – the same subject must be taught at the same time in multiple classrooms. Teacher control of “her students” – teachers start to share students and are not able to be self contained.

Defining Enrichment “Activities that add or go beyond the existing curriculum. Activities may occur in the classroom or in a separate setting” “Deeper coverage of content often provided for gifted students.” Horizontal curriculum expansion.” “Extension of the regular curriculum to include higher level thinking skills and more advanced knowledge acquisition related to the content”

Enriching Content Standards How to Enrich Teach students grade level standards with extensions and more in depth activities. Replace skill acquisition lessons with higher level thinking activities. Have high level students work collaboratively on group projects. Teaching above grade level standards. Giving students packets of “extra” materials to cover when they are done early. Having students peer tutor. Giving students more of the same. How Not to Enrich

Differentiation “Differentiation is just a teacher acknowledging that kids learn in different ways, and responding by doing something about that through curriculum and instruction.” Carol Ann Tomlinson

Differentiation “Three components of differentiation are: content – what is being taught; process – how it is being taught; and product – tangible results produced based on students’ interests and abilities. Expand the definition by addressing the teacher’s role, evaluation methods, and the goals of differentiation.” Susan Dinnocenti

Best Practices in Differentiation Teachers share and collaborate to create, implement and revise differentiated lessons. Teamwork (jigsaws, literature circles, centers, Socratic seminars) Workshops Connections (graphic organizers, inquiry learning) Independent study Experiences (online projects, simulations) Presentations (storytelling, multimedia, skits) In depth projects (portfolios, research, interviews)

Formative Assessment “Assessments must become an integral part of the instructional process to help teachers improve their instruction or modify their approach to individual students.” Thomas Guskey

Authentic Work Students work with real world problems and questions Students create solutions or projects that are shared with someone outside of the classroom Students conduct research that includes interviews, web and news searches, analyzing authentic materials and exploration beyond the classroom

Traits of Authentic Learning Learning is centered on authentic tasks. Students are engaged in exploration and inquiry. Learning is interdisciplinary. Learning is closely connected to the world beyond the walls of the classroom Students become engaged in complex tasks and higher- order thinking skills. Students produce a product to be shared with an audience outside the classroom. Learning is student driven with teachers and outside experts assisting/coaching in the learning process. Students have opportunities for social discourse. Resources are available.

Mathematics is the Art of Explanation “If you deny students the opportunity to pose their own problems, to make their own conjectures..., to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs, you deny them mathematics itself.” -- Paul Lockhart, Mathematician

Mathematical Thinking ExperimentingConjecturing EstimatingSimplifying OrganizingInventing StrategizingReasoning ProvingConnecting ConnectingWondering Imagining

Mathematical Thinking ExperimentingConjecturing EstimatingSimplifying OrganizingInventing StrategizingReasoning ProvingConnecting ConnectingWondering Imagining

Would You Rather Know How to Think or How to Compute? Do your 5 th quintile students need to spend most of their time computing?

Knowledge is Important Thinking is Essential Knowledge Builders: Flashcards Worksheets Workbooks Math Drill Websites

Cultivate Mathematical Thinking Perseverance - “I refuse to give up.” Confidence - “I can do it.” Intuition - “I have an idea...” Curiosity - “I wonder...”

Mathematical Thinking Perseverance -Reward effort not natural talent Confidence-Built through incremental successes (Be less helpful) Intuition - Do lots of problems (there’s no shortcut) Curiosity - Extend problems and always ask why

Use What High Ability Math Students Already Enjoy: Play Problem Solving Competition Exploration

Classic Games Chess Go (Othello) Backgammon Dice games - Yahtzee, Shut the Box,... Card games - Rummy, Cribbage, Racko... Tip: Verbalize your strategy Ask WHY?

New Games Think Fun Rush Hour, Chocolate Fix, Tilt, Solitaire Chess... Set Gamewright Loot, Zeus on the Loose,... Qwirkle Blokus

Mathematical Brain Teasers Logic puzzles Sudoku KenKen Kakuro Sudoku KenKen Kakuro

Puzzle Sites puzzles.com (try class brainstorms) figurethis.org nrich.maths.org mathpickle.com nikoli.com krazydad.com

Real Life Math Applications Calculate recipe quantities Estimate travel time Calculate sports statistics Estimate grocery bill Learn to write checks Compute taxes, sale prices, etc.

Math Competition Continental Math League Multi-step word problems What is the problem asking to be solved? Underline the question. Answer the question one step at a time. Not one way to solve the problem. Draw pictures, use numbers, equations… Convince us your answer is correct.

CML Sample Problem Grade 3 Adam looks in the backyard and sees 4 dogs, 3 cats and 2 chickens. He knows there are 9 heads and ___________ legs in the backyard.

Differentiated Lesson Examples Packet List menu Tic-Tac-Toe Menu Menu Game Show Menu Research Famous Mathematicians Learning Contract Tiered Lesson

Bibliography Activities for a Differentiated Classroom- Standards and Research Based; Wendy Conklin; Shell Education Balance Benders – Level 1; Robert Femiano; The Critical Thinking Co. Can You Count In Greek? Exploring Ancient Number Systems; Judy Leimbach and Kathy Leimbach; Prufrock Press Differentiating Instruction With Menus – Math; Laurie E. Westphal; Prufrock Press Differentiation That Really Works – Grades 3-5; Cheryll M. Adams & Rebecca L. Pierce; Prufrock Press Inc. Primary Grade Challenge Math; Edward Zaccaro; Hickory Grove Press.