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 [email protected]@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.