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

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.

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.

Math Objectives

➔ 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.

First… A Few “Musts”

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.)

4 Steps of Problem Solving

Step #1Understand the Problem

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?

Step #2Plan How to

Solve the Problem

Step #2: Plan How to Solve the ProblemChoose a reasonable problem-solving strategy:

Draw a picture or diagramMake an organized list

Make a tableSolve a simpler related problem

Find a patternGuess and check

ExperimentAct out the problem

Work backwardsWrite an equation (algebra)

Step #3Carry Out the Plan

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.

Step #4Look Back

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.

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?

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

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.

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

Interest: students engaged

Success: can solve harder problems

Multiple Approaches

Peer Help

Communication: natural use of mathematical vocabulary

Contributions from all

Collaboration

Why Use Group Work in Mathematics?

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.

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.

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.

• 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.

Why is this good for AIG students?

• Helps keep their work neat and organized, especially on multiple step problems.

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).

Step-by-Step Model Drawing

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.

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?

Example Problem

Answer:

Harder Problem:In a 9th grade class, ⅔ were

girls and 12 were boys. of ⅙the boys played a sport and ⅔ of the girls played an instrument. What fraction of the students played a sport or instrument?

Another Example Problem

Answer:

Challenge Math This book teaches thinking and math problem solving skills using the fun characters that appear in the other Zaccaro math books. Problems at four levels of difficulty are included that test a student's application of each concept as it is learned. The book is designed for advanced math students in grades 1-4, however it also works well for older students with grade level math skills.

Each chapter's questions are broken down into four levels: Level 1 (easy) Level 2 (somewhat challenging) Level 3 (challenging) Einstein (very challenging)

Includes chapters on: Sequences, Problem-solving, Money, Percents, Algebraic Thinking, Negative Numbers, Logic, Ratios, Probability, Measurements, Fractions, Division.

Primary Grade Challenge MathUnderstanding the Power of Mathematics

• 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.

Reading Objectives

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

✧ 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)

Needs of the Gifted Reader

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.

This Semester

Jacob’s Ladder✧ 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

Overview

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

Overview Cont.

Draft version includes Levels I, II, and III… Nonfiction books available through Benchmark Ed.

Try using selections once or twice per quarter

✧ 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

Purpose of 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.

Introduction to Jacob’s Ladder

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

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

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.

• 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

Shared Inquiry Discussion

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.

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

All can be used for writing or discussion:

❖ While You Read❖ Exploring the Story❖ Meeting the Characters❖ Understanding the Ideas❖ Connecting to You

http://education.wm.edu/centers/cfge/curriculum/languagearts/materials/navigators/index.php

Navigator Question Types

“Gifted children sometimes do poorly [or don’t show growth] on achievement tests… and therefore can’t demonstrate what they’ve learned in the way the test asks them too. Or sometimes they overanalyze test questions and can’t make decisions.”

-Helping Gifted Children Soar: A Practical Guide for Parents & Teachers

“EOG” Study Groups for Gifted Readers

❖ For the students at 96%+ on achievement- showing growth can be difficult. Missing just one or two questions could be the difference in whether they demonstrate “growth” or not.

❖ Assumptions about logical answers can be detrimental- for students and teachers.

❖ Make a point to work with gifted students in small study groups to work on specific EOG skills - listen for responses and misconceptions (over- analysis, can defend/argue several answers) - guide them through a typical response.

Points to Conisder

Courtney Oliver had wanted to work in a veterinarian’s office for as long as she can remember. The 10-year-old had often joined her mother in taking her family’s pet dogs and hamsters to the vet. “It always bugged me when the vet took our dogs to the back of the office and closed the door,” says Courtney. “I wanted to know what was going on.

What is meant by the sentence below?

“ ‘It always bugged me when the vet took our dogs to the back of the office and closed the door’ ”?

A Courtney was bothered that she could not be with her dog. B There were flies and other insects biting her dogs. C Courtney was afraid her dog would never come out. D There were other animals that might harm the dogs.

EOG Example 1

Dr. Neary uses special exercises and massage to help pets that have joint problems, such as knees that hurt when the animal walks. Dr. Neary often uses special treadmills placed in a shallow pool to help injured animals exercise safely. In water, a dog puts less pressure on its joints when it walks. That way it can exercise and strengthen its muscles without hurting them.

According to the selection, why do some animal exercises take place in shallow water?

A It is comfortable for them. B They enjoy getting wet. C It is easier on their joints. D They need the exercise.

EOG Example 2

❖ What questions were answered for you today?

❖ What questions do you have?

❖ What other information would you like to have?

QUESTIONS?