Leading the Way
to
Accelerating Math
Achievement
Bill Hanlon
Answering the Question:
What are you doing
to help my child
learn?
Rules in Mathematics
Don’t make sense!
Good News!
 Teachers
are already employing
many of the best practices needed
to increase student achievement.
Components 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?
 Refinement
& Reinforcement
of those practices.
Quiet Conversions

Change is difficult for people.

Culture: If I wait long enough, this too will
pass
Best Practices
Relentlessly supporting best
practices will eventually crowd
out poor instructional strategies.
Leadership

Lead by demonstrating success in
classrooms where teachers will modify
their instruction to increase student
achievement.
Overview of Professional
Development
Two standards:
•Common sense
•My kid
Increase student achievement by addressing:
• Content
• Instruction
• Assessment
Two premises:
1.
Testing drives instruction.
2.
Teachers make a difference; teachers working together make a
greater difference.
Build Trust & Confidence

Students will work for teachers for no
other reason than loyalty.

Law of Reciprocity
Structures that support
increased student achievement
Components of an Effective Lesson
Teacher Expectancies
Backward Assessment Model (BAM)
Increasing Student
Achievement
No simple answer-
what works is work
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 beliefs
10 simple 2-letter words
If it is to be, it is up to me
2 Standards

My Kid

Common Sense
My Kid Standard

Treat the kids in your school or classroom
the same way you want your own kids
treated.
Common Sense Standard

Appeal to teachers common sense and
experience, do not get into a citation battle.
Learning
Students learn best when they are
given feedback on their performance
and praised for doing things well
Student-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?”
Success on Success

Success on Success
– Teach students how to learn effectively and
efficiently.
auditory
 visual
 kinesthetic
Concentration times

Study skills

Good students adjust studying according to
several factors:
–
–
–
–
–
the demand of the material
the time available for studying
what they already know about the topic
the purpose & importance of assignment
the standards they must meet
Study skills
Good students space learning sessions over
time and do not cram
 Good students identify the main idea in
new information, connect new material to
what they already know, and draw
inferences about its significance
 Good students make sure their study
methods are working properly by
frequently appraising their own progress

Expectation - Goals
Being the best!
What does it take to be the best?
What are you willing to do?
Math Wars

It’s not traditionalist vs. constructivist,
students need to get the whole picture.
Balance
Balance in mathematics has been defined as:
Vocabulary & Notation
Concept Development & Linkage
Memorization of Important Facts &
Procedure
Applications
Appropriate Use of Technology
Balance should be reflected in assessments and in the
delivery of instruction.
Vocabulary & Notation
There is no more single important
factor that effects student achievement
than vocabulary and notation
Vocabulary

Find the degree of
4x2y3x5
Vocabulary

Best Bet?
– Bet A
 Probability of winning is 3/5
– Bet B
 Odds of winning 3 to 5
Language Acquisition

Double meanings
area
volume
operation
power
mean
feet
product
Content - Instruction

What you teach affects student
achievement

How you teach it affects student
achievement
Subtraction
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?

Pythagorean Theorem

Parabola

Circumference
Knowledge, Interest, & Enthusiasm
Use simple straight forward
examples that clarify what you
are teaching.
Do not get bogged down in
arithmetic.
Multiplication

by 11

by 25
Concept Cards
 Concept
 Variation
Leading the department

Leaders make sure all department
members know what and how material is
assessed and what a good answer looks
like.

Leaders make sure all members teach and
assess the standards on high-stakes tests.
Different Ways to Measure the
Same Standard
Finding 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 Tendency
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
5. Use the graph to
find the mean.
Frequency
4
3
2
1
0
70
80
90
Scores
100
I can’t teach __________
because my kids don’t know
_____________
Show them how - Linkage
 Introduce
new concepts using familiar
language
 Review and reinforce
 Compare and contrast
 Teach in a different context
Add / Subtract
Rational Expressions
1
3
2
6
1
+
2
3
+
6
5
6
1
5
1
=
+
2
6
3
1
9
1
=
+
5
20
4
1
7
1
=
+
4
12
3
1
8
1
=
+
15
5
3
1
13
2
=
+
5
15
3
2
29
3
=
+
3
30
10
1
3
=
+
5
4
1
19
3
=
+
5
20
4
C
A
=
+
D
BD
B
C
AD + BC
A
=
+
D
BD
B
3
2
=
+
Y
XY
X
3
2Y + 3X
2
=
+
Y
XY
X
2
3
=
+
x+3
(x-1)(x+3)
x-1
2
3(x+3) + 2(x-1)
3
=
+
(x-1)(x+3)
x+3
x-1
+
Polynomials
6 7 2 = 6(100) + 7(10) + 2(1)
2
6 10 + 7 10 + 2
6 n
6x
2
2
+7 n
+ 2
+ 7x
+ 2
5 3 2
+
3 4 1=
(5 +3)(100) + (3 + 4)(10) +(2 + 1)(1) =
(8)(100)
+ (7)(10)
+ (3)(1) =
(800)
+ (70)
+ (3) =
8 7 3
Addition - Left to Right
362
412
+
+ 213 =
(4 +3+2)(100) + (1+6+1)(10) + (2+2+3)(1) =
(9)(100) + (8)(10)
+ (7)(1) =
(80)
+
(900)
+ (7) =
98 7
502
123
+
+ 271 =
(1 +5+2)(100) + (2+0+7)(10) + (3+2+1)(1) =
(8)(100) + (9)(10)
+ (6)(1) =
(800)
+
(90)
8 9 6
+
(6) =
5 3 2 +
3 4 1=
2
8 7 3
2
(5x + 3x + 2) + (3x + 4x + 1)
2
2
(5x + 3x ) + (3x + 4x) + (2 + 1)
2
= 8x + 7x + 3
Relations & Functions
Functions
Special relation in which no
2 ordered pairs have the
same 1st element.
Menu
Hamburger ……….4
00
Hotdog ……………3
00
Sandwich …………5
00
00
H, 4
00
H, 4
00
(H, 4 )
00
Hd, 3
00
Hd,( 3
00
00
S,5
00
S), 5
00
(Hd, 3 ) (S, 5 )
Cold Drinks
1,
.50
00
2, 1
50
3, 1
(1,
.50
)
00
(2, 1 )
50
(3, 1 )
(10, ? )
1,
.50
00
2, 1
50
3, 1
C = n x .50
= .50n
or
y=
1
2
x
(1,
.50
)
00
(2, 1 )
50
(3, 1 )
(10, ? )
(1,
50
)
00
(2, 1 )
00
(4, 2 )
50
(3, 1 )
75
(4, 1 )
Basic Facts & Procedures

Stopping to remember basic facts
interrupts the flow of thought, which
negatively impacts learning.
Memorization

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:
 Reading
 Writing
Reading
Assign reading
 Explicitly introduce vocabulary & notation
 Preview reading
 Connect reading
 Check understanding of reading
 Correct their understanding
 Use paper & pencil

Writing









Definitions
Procedures
Linkages
Applications
Compare & contrast
Describe what they understand
Describe difficulty experienced
Summarize
Explain
Problem 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
Note Taking
Researchers - #1 Memory Aid - Writing it Down
Complete homework assignment
Prepare for unit test
Prepare for high-stakes tests
Rules and
examples
Title
Date
Objective
Vocabulary
& Notation
Pattern
Development
Rule
Examples
Variation
Questioning

Student achievement rises when teachers
ask questions that require students to
apply, analyze, synthesize, and evaluate
information in addition to simply recalling
facts.
Kinds of Questions

Directed

Echo

Cue

Conceptual
Oral Recitation
Language Acquisition
Teaches students how to learn
Embeds in short tem memory
Classroom Oral Recitation

Procedure – Adding/Subtracting Fractions
–
–
–
–
–
1..
2.
3.
4.
5.
Find a common denominator
Make equivalent fractions
Add/Subtract numerators
Bring down denominator
Reduce
Classroom Oral Recitation

Quadratic Formula
b  b  4ac
x
2a
2
Practice

Guided

Group

Independent
Homework

Homework should reflect what you say
you value.
– Vocabulary & Notation
– Conceptual understanding & Linkage
– Basic Facts & Procedures
Which will
help the
students learn
more?
Reviews
Recently taught material
Long term review
Student Assessment
Assessing Student Work
What do your students know?
How do you know they know it?
1
7
1
=
+
3
12
4
7
5
=
+
18
24
Reducing Method
18/24 = 3/4
18
3
=
24
4
18 x 4 = 72
24 x 3 = 72
CD = 72
5
15
=
24
72
7
28
+
=
18
72
43
72
18
3
=
24
4
Testing
Test what you say you value
Instruction – Assessment – Balance
Cumulative Questions
Practice Tests
Setting a Date
Memory Aids

Help your students remember
Time on Task
Stake 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.
Why Teacher Expectancies???
Concept Development
• Not a matter of if they are going to forget, it is a matter of when
• Understanding and ability to reconstruct information
• Test preparation; different was of measuring the “mean”
• Triangle Sum Theorem / Pythagorean Theorem
Linkage
• Provides an opportunity to make students more comfortable, review
& reinforce
• Slope, distance formula to Pythagorean Theorem, Equation of a
Circle
Reviews
• 1st - short term knowledge, recently taught material
• 2nd – long term knowledge, address mastery, student deficiencies,
high stakes tests – not necessarily part of that year’s curriculum, but
based on student knowledge
Why Teacher Expectancies???
Homework
• Homework should reflect what is valued, vocabulary and
notation, important facts, procedures, open-ended questions
on concept development
• Guided practice
• Reading – introduce vocabulary words, preview reading,
relate to previous knowledge, retell the reading, summarize
reading assignment
Testing
• Make testing a reflection of your teaching
• Test what you value as in homework
• Ask questions with the same formality they are asked on
high-stakes tests – avoid the disconnect
Why Teacher Expectancies???
Note Taking
• Number one memory aide – writing it down
• Helps students complete their homework
• Foundation for test preparation
• Teachers should be very prescriptive and directive
Oral Recitation
• Imbeds information in short term memory
Improving Student Grades
• Use simple, straight-forward examples that do not bog students
down in arithmetic – focus on concepts being taught
• Teach the big idea
• Use practice tests
Improving Students’ Achievement
Have a positive attitude – build success on success.
Treat students the same way you want your own children treated.
Try these strategies:
• State the day’s objective, teach it, and then tell them what you taught the and what
they should have learned when you close the lesson – closure.
• Develop concepts. Teach to the big ideas.
• Link concepts to previously learned material and and/or real-world experiences.
• Use, simple, straightforward examples that clarify what is being taught.
• Use numbers in examples that allow students to focus on the concept and don’t
bog students down in arithmetic.
Improving Students’ Achievement
Try these strategies (continued):
• Incorporate guided practice to monitor student learning before assigning homework.
• Use practice tests to prepare students for unit tests. In first yea algebra, use
multiple test versions.
• Tell students how you personally remembered (learned) important information.
• Use choral recitation to imbed information in short-term memory.
• Require students to take notes and keep notebooks.
• Require student reading as part of the daily assignment
• Require students to write about what they have learned.
• Use the second review period to reinforce long-term knowledge and address
student deficiencies.
Questions for the department
What does the data look like?
 What are the root causes and contributing
factors of the data results?
 Do all department members know what
and how material is assessed and what a
good answer looks like?
 Do all members teach and assess the
standards on high-stakes tests?

Questions
How does the department monitor
individual student progress on standards?
 How does staff intervene with students not
meeting proficiency?
 What are the department’s most commonly
used interventions for students not
achieving?
 How successful are those interventions?

Plan
– Specific
– Measurable
– Achievable
– Relevant
– Timely