Improving Mathematics Improving Mathematics Achievement by Improving Achievement by Improving

Mathematics InstructionMathematics Instruction

“6 Elements of Effective “6 Elements of Effective Mathematics Lessons”Mathematics Lessons”

LaTonya MitchellLaTonya Mitchelllmitchell@fdresa.orglmitchell@fdresa.orgFirst District RESAFirst District RESA

Complete the following Complete the following statement:statement:

Teaching an effective mathematics lesson is a roller coaster because ……………….

Essential QuestionEssential Question

How does my lesson planning How does my lesson planning and delivery compare to a and delivery compare to a

framework designed to framework designed to increase the probability of increase the probability of

student learning?student learning?

Key QuestionsKey Questions• How can I help all students meet or

exceed grade level expectations in mathematics?

• How can I increase the probability that learning will occur for ALL students in mathematics?

State Performance Targets

MathematicsGrades 3-8 CRCT

Percent of Students atProficient or Advanced

2002-2003 Target 50

2003-2004 Target 50

2004-2005 Target 58.3

2005-2006 Target 58.3

2006-2007 Target 58.3

2007-2008 Target 66.7

2008-2009 Target 66.7

2009-2010 Target 66.7

2010-2011 Target 75

2011-2012 Target 83.3

2012-2013 Target 91.7

2013-2014 Target 100

Enhanced GHSGT - Math

Annual Measurable Objectives

AMOs

Annual Step

2003 81.00%

2004 62.30%

2005 62.30%

2006 68.60%

2007 68.60%

2008 74.90%

2009 74.90%

2010 74.90%

2011 81.20%

2012 87.40%

2013 93.70%

2014 100.00%

ObjectivesObjectives

• Identify the three teacher-level factors affecting student achievement.

• Identify the three most important features of high performing schools.

• Describe the six elements of exemplary mathematics lessons.

• Identify similarities and differences among the three organizational structures.

• Recognize the elements and structures in a variety of instructional contexts and grade levels.

• Describe the impact that a balance or rhythm in Teacher-Focused/Student-Focused activities has on promoting and maintaining engagement.

3 Teacher Level Factors3 Teacher Level Factors

• Instructional Strategies

• Classroom Management

• Classroom Curriculum Design

Marzano

90/90/90 Schools90/90/90 Schools

• 90+% of students on free/reduced meals

• 90+% of students are of a minority in the national population

• 90+% of students on or above grade level (In Ga., level 2 or level 3 on CRCT or 60th percentile on NRT)

Characteristics of High Characteristics of High Performing SchoolsPerforming Schools

• High Expectations of Students/Staff

• Focused Teaching and Learning

• Engaged Learning Time

Promoting EngagementPromoting Engagement• Gains attention before beginning

instruction• Observes students for initial

engagement • Stimulates interest by providing

vivid or novel examples or by varying presentation and activities

• Varies the types of responses generated

• Divides opportunities for participation without excessive or prolonged interactions with individuals

• Stimulates covert involvement:– Think of an example– Recall an experience– Prepare to respond– Providing a stimulus for

attentiveness

• Creates expectation of being called on– Call on volunteers and non-

volunteers– Ask questions to total group before

asking for response– Promote thinking by pausing after

question to allow for more students to form a response then ask for response from individual, group, etc.

– Promote thinking by pausing after the response to allow for extensions of ideas or self-corrections

• Generates overt responses:– Respond on paper (jot)– Take notes– Tell a partner– Respond as a group– Signal– Participate in discussions, skits,

simulations, hands-on experiences, and cooperative group learning experiences

Monitoring ProgressMonitoring Progress• Observing facial expressions and non-verbal

behaviors• Asking clear questions at all six levels of Bloom’s

taxonomy• Checking for understanding through signals and

oral questions to individuals• Asking students to explain or clarify answers• Moving among students and interpreting student

behavior– observe all before stopping with one– use Praise, Prompt, Leave

• Use benchmarks to determine progress

Level of challenge

Level of competence

Potential developmental level

Actual developmental level

Teacher-Focused Student-Focused

TEACHER-FOCUSEDTEACHER-FOCUSEDACTIVITIESACTIVITIES

• Explanation– Definitions– Examples– Demonstration– Modeling

• Discussion/Review– Focused questions– Student responses

• Guided Practice– New skills or information

STUDENT-FOCUSEDSTUDENT-FOCUSEDACTIVITIESACTIVITIES

Purposes of Student-focused Activities• Effective Processing of New Content

• Vary widely in design• Match the learning• Meaningful and require thought

• Distributed Practice on Previously Learned Content• Spread over time• Short in number of items• Short in number of skills

Learning Activities

We Tend to Learn Our Involvement Level

PA

SS

IVE

10% of what we readVerbal Receiving

20% of what we hear

30% of what we see Visual Receiving

50% of what we hear and see

Verbal and Visual Receiving

70% of what we sayReceiving and Participating

AC

TIV

E90% of what we both say and do

Doing

ELEMENT #1: DRILLELEMENT #1: DRILL

(“Mastery of Facts”) Always on the “basics” Immediate recall Increase speed Daily (max 5 minutes) Choral or written Individual or group Examples

o Drill Squareo Drill Partners

ELEMENT #2: ELEMENT #2: REVIEW/PREVIEWREVIEW/PREVIEW

(“Math Review” & “Mental Math”) Algorithms/Processes/Steps Old Learning Maintenance of Specific Skills (ITBS or CRCT) Emphasis on essentials Student-focused Increase Accuracy Daily (max 10 minutes) Examples

o Big Fouro Grand Slam

ELEMENT #3: ELEMENT #3: APPLICATION APPLICATION

(“Problem Solving” & “Performance Tasks”) Makes content relevant, purposeful, meaningful Daily May be included in Review/Preview Types of Activities

o Problem Solvingo Estimationo Charts, Graphso Geometryo Measuremento Timeo Moneyo Manipulatives

Usually included in lesson. If not, must be a separate piece.

ELEMENT #6:ELEMENT #6:HOMEWORKHOMEWORK

Distributed Practice Short!! Over Firm ClassworkoChallenging and Relevant

Keeps Learning Warm Given at the Last Moment Possible Consider Positive Grading Move to tiered assignments

The longer the The longer the assignment, the more assignment, the more

students will fail.students will fail.

The shorter the The shorter the assignment, the more assignment, the more students will succeed.students will succeed.

The First Days of School – Dr. Harry WongThe First Days of School – Dr. Harry Wong

Essential QuestionEssential Question

How does my lesson planning How does my lesson planning and delivery compare to a and delivery compare to a

framework designed to framework designed to increase the probability of increase the probability of

student learning?student learning?

HomeworkHomework• Go back to your classroom and implement

a planned drill and review activity. Share the next session with what you expected to happen and what did happen.

• Critique your lesson plans for application pieces. Bring an artifact with an example of application and your purpose for using that particular application problem and be able to tell how it fits into your instruction.