Helping Students Learn – Helping Students Learn – What an awesome experienceWhat an awesome experienceColumbus Public - Crestview Middle SchoolColumbus Public - Crestview Middle School

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Cooperating Teacher: Mrs. CavineeCooperating Teacher: Mrs. Cavinee

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Winter 2006

Winter 2006

Student, Teacher, and Community Student, Teacher, and Community PopulationPopulation

Very diverse racial and ethnic Very diverse racial and ethnic student populationstudent population

Approximately 75% of Approximately 75% of teachers are whiteteachers are white

Many single family Many single family householdshouseholds

Many students do not live Many students do not live with a parent (relative or with a parent (relative or foster care)foster care)

Lower income communityLower income community

““Ah Ha” Moments Related to Student Ah Ha” Moments Related to Student LearningLearning

Peer relationships and acceptancePeer relationships and acceptance is much more important to is much more important to middle school students than grades or obeying the teachermiddle school students than grades or obeying the teacher

School is not a prioritySchool is not a priority for some students/families – bigger for some students/families – bigger concerns such as taking care of family, eating, sleeping concerns such as taking care of family, eating, sleeping

Homework is seldom completedHomework is seldom completed – there appears to be little – there appears to be little support at home or motivation to encourage the students to support at home or motivation to encourage the students to complete homeworkcomplete homework

Students lack pre-requisitesStudents lack pre-requisites - 75% of students in one class - 75% of students in one class could not complete a basic multiplication and division could not complete a basic multiplication and division worksheet – they have no chance of computing volume and worksheet – they have no chance of computing volume and areaarea

All students have dreamsAll students have dreams - 5 out of 6 in my Advisor/Advisee - 5 out of 6 in my Advisor/Advisee group want to be doctors but don’t understand what it will group want to be doctors but don’t understand what it will taketake

Content Covered in UnitContent Covered in Unit

Patterns, Functions, and AlgebraPatterns, Functions, and AlgebraPalindromes (racecar, 1234321)Palindromes (racecar, 1234321)

Pascal’s TrianglePascal’s Triangle

Arithmetic and Geometric SequencesArithmetic and Geometric Sequences

““nth” term in a sequencenth” term in a sequence

Rules for a patternRules for a pattern

Linear and non-linear graphsLinear and non-linear graphs

Functions and function tablesFunctions and function tables

Function graphsFunction graphs

Data AnalysisData AnalysisMeanMean

MedianMedian

ModeMode

RangeRange

OutliersOutliers

HistogramsHistograms

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Ohio Academic Content StandardsOhio Academic Content Standards Patterns, Functions, and Algebra StandardPatterns, Functions, and Algebra Standard

GLI 1 - Represent and analyze patterns, rules and functions, GLI 1 - Represent and analyze patterns, rules and functions, using physical materials, tables and graphs.using physical materials, tables and graphs.

GLI 2 - Use words and symbols to describe numerical and GLI 2 - Use words and symbols to describe numerical and geometric patterns, rules and functions.geometric patterns, rules and functions.

Data Analysis and Probability StandardData Analysis and Probability Standard GLI 4 - Understand the different information provided by GLI 4 - Understand the different information provided by

measures of center (mean, mode and median) and measures of measures of center (mean, mode and median) and measures of spread (range).spread (range).

GLI 5 - Describe the frequency distribution of a set of data, as GLI 5 - Describe the frequency distribution of a set of data, as shown in a histogram or frequency table, by general appearance shown in a histogram or frequency table, by general appearance or shape; e.g., number of modes, middle of data, level of or shape; e.g., number of modes, middle of data, level of symmetry, outliers.symmetry, outliers.

Goals – Students Will Be Able To:Goals – Students Will Be Able To:

Identify character and numeric Identify character and numeric palindromes.palindromes.

Recognize and extend a pattern.Recognize and extend a pattern.

Determine the patterns within Determine the patterns within Pascal’s Triangle and add Pascal’s Triangle and add additional rows.additional rows.

Write & match a rule or function to Write & match a rule or function to a pattern.a pattern.

Compute and graph the input and Compute and graph the input and outputs for a function.outputs for a function.

Goals – Students Will Be Able To: Goals – Students Will Be Able To: (continued)(continued)

Complete additional rows and Complete additional rows and columns in a table based on columns in a table based on recognizing a pattern and recognizing a pattern and understanding a function. understanding a function.

Identify & match a pictorial Identify & match a pictorial representation to a function. representation to a function.

Compute the mean, median, and Compute the mean, median, and mode within a set of numbers or mode within a set of numbers or from various graphs. from various graphs.

Rationale for Choosing SWBA GoalsRationale for Choosing SWBA Goals

Columbus Columbus Public Public School School Curriculum Curriculum GuideGuide

Alignment Alignment with with standardsstandards

Preparation for Preparation for achievement testachievement test

Student centeredStudent centered

Methodologies Used to TeachMethodologies Used to Teach

Discovery with manipulatives to help students Discovery with manipulatives to help students “see” the math“see” the math

Peer tutoring (with tutor passes)Peer tutoring (with tutor passes) Small group activitiesSmall group activities Student board/overhead work for motivationStudent board/overhead work for motivation Math Jeopardy (most effective and engaging)Math Jeopardy (most effective and engaging) Real-life references (sports and more sports)Real-life references (sports and more sports) Direct instruction for definitions and examplesDirect instruction for definitions and examples Worksheets for repetition and re-enforcementWorksheets for repetition and re-enforcement

Methods of DifferentiationMethods of Differentiation

Individual instructionIndividual instruction Pre-written Pre-written

notes/definitionsnotes/definitions

Peer tutoring Peer tutoring (tutor passes)(tutor passes)

Co-operative Co-operative groupinggrouping

Pre-Assessment DataPre-Assessment Data

6 questions, 5 multiple choice and 1 graph, given 6 questions, 5 multiple choice and 1 graph, given to the students on 1to the students on 1stst day of the unit. day of the unit.

Sample question: Sample question: Which rule is used to make this number pattern?Which rule is used to make this number pattern?

3, 5, 9, 17, 33, 653, 5, 9, 17, 33, 65A. Add 2 to the previous termA. Add 2 to the previous termB. Multiply the previous term by 1 and then add 2B. Multiply the previous term by 1 and then add 2C.C. Multiply the previous term by 2 and then subtract 1 Multiply the previous term by 2 and then subtract 1 D. Subtract 1 from the previous term and then multiply by 2D. Subtract 1 from the previous term and then multiply by 2

Post-Assessment DataPost-Assessment Data

6 questions similar to pre-assessment were 6 questions similar to pre-assessment were included in the written post-assessment, but included in the written post-assessment, but students had to figure out their answers students had to figure out their answers instead of having multiple choice.instead of having multiple choice.

Sample question:Sample question:Complete the table for the rule 2x + 4 = y. Complete the table for the rule 2x + 4 = y.

XX 22 33 44 55 66 77

YY 88 1010 1212 1414 1616 1818

Pre-Test / Post-Test ComparisonPre-Test / Post-Test Comparison

Pre-Test / Post-Test Change

0

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6

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< 0 0 + 1 + 2 + 3 + 4 + 5 + 6

Correct Response Change (out of 6)

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Pre-Test Avg: 2.0 Pre-Test Avg: 2.0 out of 6out of 6

Post-Test Avg: 3.3 Post-Test Avg: 3.3 out of 6out of 6

61% increase in 61% increase in correct answerscorrect answers

79 % of students (44 79 % of students (44 out of 56) increased out of 56) increased scorescore

Collecting Evidence of Student LearningCollecting Evidence of Student Learning

Formal AssessmentsFormal Assessments Written unit testWritten unit test Worksheets and homeworkWorksheets and homework

Informal AssessmentsInformal Assessments Board/Overhead work following Board/Overhead work following

group activitiesgroup activities Individual discussionIndividual discussion

The “REAL” Evidence –The “REAL” Evidence –A Thank You note from a studentA Thank You note from a student

Observations on How Students Observations on How Students Learn BestLearn Best

Many students need very clear Many students need very clear instructions and expectations.instructions and expectations.

Students need to enjoy the lesson and Students need to enjoy the lesson and the material in order to be engaged.the material in order to be engaged.

Students possess multiple learning styles Students possess multiple learning styles – some need to “see” it, others – some need to “see” it, others “hear” it, and many need to “do” it.“hear” it, and many need to “do” it.

Professional Standards AddressedProfessional Standards Addressed

NMSA INMSA I - provide opportunities that support student - provide opportunities that support student development and learningdevelopment and learning

Evidence Evidence post-assessment post-assessment

NMSA VNMSA V - employ a variety of strategies for a - employ a variety of strategies for a developmentally appropriate climate to meet the varying developmentally appropriate climate to meet the varying abilities and learning styles of all studentsabilities and learning styles of all students

Evidence Evidence lesson plans lesson plans

NMSA VIINMSA VII - understand the complexity of teaching young - understand the complexity of teaching young adolescents, and they engage in practices and behaviors adolescents, and they engage in practices and behaviors that develop their competence as professionalsthat develop their competence as professionals

Evidence Evidence journal entries journal entries

Supervisor and Cooperating Supervisor and Cooperating Teacher CommentsTeacher Comments