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MansfieldMansfield
Leading the Way Leading the Way to to
Accelerating Math Accelerating Math Achievement Achievement
Bill Hanlon
What are you doingWhat are you doingto improve instruction?to improve instruction?
Organizing Student LearningOrganizing Student Learning5 + 1 5 + 1
Instruction, concept development-linkage Note taking Homework Test Preparation Assessment
Bill Hanlon [email protected]
+1+1
Student-teacher relationships
Answering the Question:Answering the Question:
What are you doing to help my
child learn?
Rules in MathematicsRules in Mathematics
Don’t make sense!
Good News!Good News!
Teachers are already employing many of the best practices needed to increase student achievement.
Best practicesBest practices
Note takingHomeworkTests
Components of an Effective LessonComponents of an Effective Lesson Before presenting a lesson, refer to the assessment blueprint for
the unit.
Introduction
Daily Reviews
Daily Objective
Concept and Skill Development and Application
Guided / Independent / Group Practice
Homework Assignments
Closure
Long-Term Memory Review
Build on Strengths
What’s needed?What’s needed?
Refinement & Reinforcement of those practices.
Quiet ConversionsQuiet Conversions
Change is difficult for people.
Culture: If I wait long enough, this too will pass
Best PracticesBest Practices
Relentlessly supporting best practices will eventually crowd out poor instructional strategies.
Build Trust & ConfidenceBuild Trust & Confidence
Students will work for teachers for no other reason than loyalty.
Law of Reciprocity
Increasing Student Increasing Student AchievementAchievement
No simple answer-
what works is work
It’s about you!!!It’s about you!!!
You cannot and should not depend on products, programs or services to address the needs of your student population, close the
achievement gap or increase student achievement.
Actions follow beliefsActions follow beliefs
10 simple 2-letter words
If it is to be, it is up to me
2 Standards2 Standards
My Kid
Common Sense
Student-Teacher RelationshipsStudent-Teacher Relationships
1. Treat your students the way you want your own children treated.
2. Build success on success.
3. Talk to your students. Be friendly.
4. Talk positively to your students about their opportunity to be successful.
5. Call home early with information and good news.
6. Make testing as much a reflection of your instruction as their studying.
7. Teach your students how to study effectively and efficiently (visual, audio, kinesthetic, concentration time).
8. Tell them you like them.
9. Go over expectations explicitly and give examples.
10. Build trust, make sure they know you are there for them by telling them you are.
11. Tell them you want them to succeed.
12. Continually answer the question; “What am I doing to help my students learn?”
Unsuccessful StudentsUnsuccessful Students
Contributing FactorsContributing Factors
Contributing FactorsContributing Factors
How do you see your students?
Contributing FactorsContributing Factors
How do your students see you?
Contributing FactorsContributing Factors
What are you currently doing to motivate, to address, unsuccessful students?
Anything special for ELL, special education, or students living in poverty?
Contributing FactorsContributing Factors
Belief Systems
– Teachers believing in students– Students believing in themselves– Teachers believing in themselves
Contributing factorsContributing factors
What factors do you control?
Success on SuccessSuccess on Success
Success on Success– Teach students how to learn effectively and
efficiently.auditoryvisualkinesthetic
Concentration times
StudyingStudying
Reading Thinking Reflecting Organizing Writing
Analyzing Visualizing Reviewing Remembering Recalling
ExpectationsExpectations
Grade Distributions
BalanceBalance
Vocabulary & Notation
Concept Development & Linkage
Memorization of Important Facts & Procedure
Applications
Appropriate Use of Technology
Balance in mathematics has been defined as:
Balance should be reflected in assessments and in the delivery of instruction.
Vocabulary & NotationVocabulary & Notation
There is no more single important factor that effects student achievement than vocabulary and notation
VocabularyVocabulary
Find the degree of
4x2y3x5
VocabularyVocabulary
Best Bet?
– Bet AProbability of winning is 3/5
– Bet BOdds of winning 3 to 5
Language AcquisitionLanguage Acquisition
Double meanings
areavolumeoperationpowermeanfeetproduct
MLLMLL
Math Language Acquisition
SpeakingSpeaking
Oral recitation
Speaking
Working in pairs (groups)
Oral RecitationOral Recitation
Language Acquisition
Teaches students how to learn
Embeds in short tem memory
Classroom Oral RecitationClassroom Oral Recitation
Procedure – Adding/Subtracting Fractions
1. Find a common denominator
2. Make equivalent fractions
3. Add/Subtract numerators
4. Bring down denominator
5. Reduce
Classroom Oral RecitationClassroom Oral Recitation
Quadratic Formula
2 4
2
b b acx
a
Time on TaskTime on TaskStake and local school districts usually determine the classroom time available to teachers and students. However, regardless of the quantity of time allocated to classroom instruction, it is the classroom teacher and school administrator who determine the effectiveness of the time allotted.
According to a survey conducted by the American Association of School Administrators, teachers identify student discipline as the single greatest factor that decreases time on task in the classroom. Generally, teachers with well-managed classrooms, have fewer disciplinary problems. These classrooms typically have teachers who have established rules and procedures are in the classroom when the students arrive, and begin class promptly. They reduce the “wear and tear” on themselves and students by establishing procedures for make-up work, they arrange their room to accommodate their teaching philosophy and style, and they develop routines that increase overall efficiency. The benefits of establishing these classroom procedures and routines become apparent as the total time on task approaches the allocated time.
When teachers begin class immediately, students view them as better prepared, more organized and systematic in instruction, and better able to explain the material. Students also see these teachers as better classroom managers, friendlier, less punitive, more consistent and predictable, and as one who values student learning.
Routines like beginning class immediately, reviewing recently taught material, orally reciting new material, having students take notes, and ending the class by reviewing important definitions, formulas, algorithms, and the daily objective keep students engaged and on task. Quality time on task is not a “silver bullet” that can cure all the problems facing education. However, it can play an important role in increasing student
achievement.
1st Essential - Instruction1st Essential - Instruction
Content - InstructionContent - Instruction
What you teach affects student achievement
How you teach it affects student achievement
SubtractionSubtraction
5 – 1 15 – 6 8 – 8 14 – 6
13 – 5 9 – 2 15 – 9 7 – 1
14 – 5 16 – 9 4 – 4 10 – 4
6 –2 12 – 4 10 – 3 6 – 3
When will I ever use this?When will I ever use this?
Pythagorean Theorem
Parabola
Circumference
Knowledge, Interest, & EnthusiasmKnowledge, Interest, & Enthusiasm
Use simple straight forward Use simple straight forward examples that clarify what you examples that clarify what you
are teaching. are teaching.
Do not get bogged down in Do not get bogged down in arithmetic.arithmetic.
MultiplicationMultiplication
by 11
by 25
Different Ways to Measure theDifferent Ways to Measure the
Same Standard
Finding Measures of Central TendencyFinding Measures of Central Tendency 1. Find the mean of the following data: 78, 74, 81, 83,
and 82.
2. In Ted’s class of thirty students, the average on the math exam was 80. Andrew’s class of twenty students had an average 90. What was the mean of the two classes combined?
3. Ted’s bowling scores last week were 85, 89, and 101. What score would he have to make on his next game to have a mean of 105?
Finding Measures of Central TendencyFinding Measures of Central Tendency
0
1
2
3
4
5
70 80 90 100
Scores
Fre
qu
en
cy
4. One of your students was absent on the day of the test. The class average for the 24 students present was 75%. After the other student took the test, the mean increased to 76%. What was the last student’s score on the test?
5. Use the graph to find the mean.
I can’t teach __________ I can’t teach __________ because my kids don’t know because my kids don’t know __________________________
Show them how - LinkageShow them how - Linkage
Introduce new concepts using familiar language
Review and reinforceCompare and contrastTeach in a different context
+ Polynomials
6 7 2 = 6(100) + 7(10) + 2(1)
6 10 + 7 10 + 22
6 n + 7 n + 22
6x + 7x + 22
5 3 2 + 3 4 1 =
8 7 3
(5 +3)(100)
+(2 + 1)(1) =+ (3 + 4)(10)
(8)(100) + (3)(1) =+ (7)(10)
(800) + (3) =+ (70)
213 =
9 8 7
(4 +3+2)(100) + (2+2+3)(1) =+ (1+6+1)(10)
(9)(100)
(900)
+362412 +
(7)(1) =+(8)(10)+
(80)+ (7) =+
123 + 271 =
8 9 6
(1 +5+2)(100) + (3+2+1)(1) =+ (2+0+7)(10)
(8)(100)
(800)
502+
(6)(1) =+(9)(10)+
(90)+ (6) =+
Addition - Left to RightAddition - Left to Right
(5x + 3x + 2) + (3x + 4x + 1)2 2
= 8x + 7x + 32
5 3 2 + 3 4 1 = 8 7 3
(5x + 3x ) + (3x + 4x) + (2 + 1)2 2
Add / Subtract
Rational Expressions
1
+
3
12
26
56
36
+
1+
312
=56
1+
415
=920
1+
314
=712
1+
315
=815
2+
315
=1315
3+
1023
=2930
3+
415
=
20+
4135
=19
2+
X3Y
=
XY
2+
X3Y
=2Y + 3X
XY
A+
BCD
=AD + BC
BD
A C +
B D=
BD
3+
x-12
x+3=
(x-1)(x+3)
3+
x-12
x+3=
(x-1)(x+3)
3(x+3) + 2(x-1)
Relations & Functions
Functions
Special relation in which no
2 ordered pairs have the
same 1st element.
Menu
Hamburger ……….4
Hotdog ……………3
Sandwich …………5
00
00
00
400(H, ) (Hd, ) (S, )300 500
H, Hd, S,400 300 500
400H, Hd,( S), 300 500
.501,
2,
3,
100
150
.50(1, )
(2, )
(3, )
(10, ? )
100
150
Cold Drinks
.501,
2,
3,
100
150
.50(1, )
(2, )
(3, )
(10, ? )
100
150
C = n x .50 = .50n or
y = x12
50(1, )
(4, )200
100(2, ) 150(3, )
175(4, )
Basic Facts & ProceduresBasic Facts & Procedures
Stopping to remember basic facts interrupts the flow of thought, which negatively impacts learning.
MemorizationMemorization
Memorizing can help students absorb and retain information on which understanding and critical thought are based.
The more sophisticated mental operations of analysis, synthesis, and evaluation are impossible without rapid and accurate recall of bodies of specific knowledge.
It is my job to teach:It is my job to teach:
Reading
Writing
ReadingReading
Assign readingExplicitly introduce vocabulary & notationPreview readingConnect readingCheck understanding of readingCorrect their understandingUse paper & pencil
Organizing Student ThinkingOrganizing Student Thinking
What’s the easiest way to help students to organize their thinking?
Writing
WritingWriting
Definitions Procedures Linkages Applications Compare & contrast Describe what they understand Describe difficulty experienced Summarize Explain
Problem SolvingProblem Solving
Go back to definition Look for a pattern Make a table or list Draw a picture Guess & Check
Examine a simpler case
Examine a related problem
Identify a sub-goal Write an equation Work backward
2nd Essential - Note taking2nd Essential - Note taking
Researchers - #1 Memory Aid - Writing it Down
Complete homework assignment
Prepare for unit test
Prepare for high-stakes tests
Note TakingNote Taking
Rules and examples
TitleDate ObjectiveVocabulary & NotationPattern DevelopmentRuleExamplesVariation
Algebra Algebra
Address the challenges brought on by an increasing student population enrolling in algebra.
Hpot,Ball, Qback
Helping Students SucceedHelping Students Succeed
Students not rememberingStudents not remembering
Do it right on the first go around
Take the time you need to more fully and appropriately develop concepts and skills
Link concepts/skills to previously learned material & outside experiences
Student deficienciesStudent deficiencies
To address student deficiencies:
– Use the long term memory review
– Use linkage when introducing new concept or skill
Make sure students understand the concept or skill beforepracticing
Use simple straight forward examples to clarify what you are teaching!
Increase difficulty later.
3rd Essential - Homework3rd Essential - Homework
PracticePractice
Guided
Group
Independent
HomeworkHomework
Homework should reflect what you say you value.
– Vocabulary & Notation– Conceptual understanding & Linkage– Basic Facts & Procedures
HomeworkHomework
Page 270, 1–32 odd
HomeworkHomework
Read Sec. 9.4 - Expressions involving logarithms
Define logarithmWrite a procedure for converting logarithms to
exponentialsExplain why when multiplying log with the
same base, you add the logs log (AB) = logA + logB
Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21,23, 31
HomeworkHomework
Read Sec 9.4 - Adding FractionsDefine FractionDraw a model for adding fractionsWrite a procedure for adding fractionsExplain the link between adding fractions
and decimalsPage 270, 1, 3, 6, 7, 9, 12, 13, 14, 21, 23, 31
ReviewsReviews
Recently taught material
Long term review
Student Assessment
What do your students know?
How do you know they know it?
Assessing Student Work
1+
413
=712
5+
247
18= 18
24=
34
CD = 72
18 x 4
24 x 3
= 72
= 72
Reducing Method
18/24 = 3/4
1824
=34
5=
241572
7=
182872
+
4372
4th Essential- Test Preparation4th Essential- Test Preparation
Test what you say you value:
Instruction – Assessment – Balance
Cumulative Questions
Practice Tests - Parallel construction
Setting a Date
TestingTesting
Testing drives instruction
TestsTests
Test Design
– Design tests that encourage study.
– Test what you say you value
Test PreparationTest Preparation
Do you know what you are going to test your students on BEFORE you begin to teach a unit?
Use the * System in notes for test prep
Practice TestsPractice Tests
TestsTests
Monitor student learning
Memory AidsMemory Aids
Help your students remember
5th Essential - Tests5th Essential - Tests
Form A ~ Form B
Organizing Student LearningOrganizing Student Learning
Making the connection -Instruction to
Note taking toHomework to
Test Preparation toTests
Organizing Student LearningOrganizing Student Learning
Helps students focus and study more effectively and efficiently resulting in increased student achievement
This organization strategy leads toThis organization strategy leads to
Transparency
Credibility
Trust
Next stepsNext steps
What are you willing to do to increase student achievement?
– Address linkage/concept development– Address student notes– Address homework assignments– Address test preparation– Look at yourself
KISSKISS
What are you willing to do?What are you willing to do?
SummarySummaryMy Kid StandardSuccess on Success ModelSimple straight forward examplesOrganize students for learning; “5 + 1”Demonstrate – think aloudIt’s about you!