Transcript Document 7123648

Henrico County Public Schools
New Mathematics Teachers
General Math Session
How to make your horse thirsty and other stuff you might want to know
August 24, 2009
1:30 p.m. – 4:30 p.m.
Hermitage High School
Welcome!
Introductions
• Name, School, Teaching Experience
• What brought you to HCPS?
• What made you decide to teach math?
Objectives
• To familiarize you with curriculum expectations
• To introduce you to the materials, places, people and
processes that can help you do your best
• To teach you how to get what you want
Today’s Schedule
It’s pretty simple…
1. General Information
2. Break
3. Collaborative
Teaching/Differentiation
4. Breakout Sessions
• Middle School
• High School
Planning
VDOE Website:
http://www.doe.virginia.gov/testing/sol/standards_docs/mathematics/review.shtml
• Curriculum Framework – have a copy on your desk!
• Blueprints
• Keep in mind, SOLs are the MINIMUM standard.
If you teach to the SOL test…
Standards of Learning
The Standards of Learning provide a good framework.
However, teaching is more than just learning an SOL!
9
2009 Mathematics
Standards of Learning
 Rigor has been increased
 Repetition has been decreased
 Retention and application of content from previous years
required
 Vertical alignment has been improved
10
Click here for documents
Vertical Articulation Documents
11
Vertical Articulation of Content
Why is it important knowledge to have?
• Consistency
• Connections
• Relevance
All these lead to deeper understanding
and long-term retention of content
• The Mathematics Crosswalk Between the 2009 and
2001 Standards (PDF) provides detail on additions,
deletions and changes included in the 2009 Mathematics
Standards of Learning.
Pay attention to details!
http://teachers.henrico.k12.va.us/math/Teacher/Downloads/NTA/DANCING_BEAR_MOONWALKING_BEAR_CYCLIST_AWARE.wmv
Course Resources and Pacing Guide
All digital curriculum and pacing guides are available on the
HCPS math website: http://henricostaffdev.org/math/
HCPS Teacher Resource Page
A lot of links to important documents!
http://teachers.henrico.k12.va.us/math/teacher.html
1.
2.
3.
4.
5.
6.
ExamView test banks
Online textbooks
Carnegie Learning files
Promethean & ActivEngage information
NTA powerpoint
Graphing calculator instructions
Speaking of calculators…
• Make sure that the calculator is a TOOL used for
instruction!
• It has become a crutch for many students and
teachers.
• Be accountable for them and have a system for
storing and collecting them.
Observations/Evaluations
• “Snapshot” observations
• Teacher requested observations
• Formal Evaluation Process
People who can help you!
Principal
Specialist
Assistant
Principal
Colleagues
Dept
Chair
Mentor or
Buddy
ITRT
YOU
Coaches
In the past, an
acceptable
philosophy for
educators was:
You can lead a horse to
water, but you can’t
make him drink
The present
philosophy for
educators goes
something like this:
If you lead a horse
to water and he
doesn’t want to
drink, it’s your job to
make him thirsty.
Instruction
Make lessons active
• Limit lecture – the least effective teaching
•
•
•
•
method
Model the skills that you want your students
to exhibit
Develop concepts rather than answers
Vary your teaching strategies
Challenge the students - rigor
Have fun learning!
• Encourage students to participate
• Set the stage for student success
A critical point
…a teacher of mathematics has a great opportunity. If he
fills his allotted time with drilling his students in routine
operations he kills their interest, hampers their intellectual
development, and misuses his opportunity. But if he
challenges the curiosity of his students by setting
them problems proportionate to their knowledge, and helps
them to solve their problems with stimulating questions,
he may give them a task for, and some means of,
independent thinking.”
Polya, 1973/1945
Problem Based Learning
The Die Hard with a Vengeance version of teaching
Polya's four-step problem solving process
http://teachers.henrico.k12.va.us/math/Teacher/downloads/nta/die_hard_jugs.mov.wmv
Getting Started & Surviving the first month!
• NCTM – tips for teachers http://www.nctm.org/resources/content.aspx?id=9584
• Develop a support system
• In your department
• In your school
• In your county
• *In your family*
Manage Your Time Wisely
• Planning
• Develop a schedule
• The first year in any job is
the hardest
• Plan effective lessons
• Make objectives clear to
the students
• Routine and structure are
good, but don’t fall into a
rut. Try to vary activities
from time to time.
•
Be prepared for the
unexpected. It will
happen. Daily.
Classroom Management
• Positive first impressions
• Greet and welcome your students as
they enter the room
• Have a plan for the class
• Share your enthusiasm
• Help students to be successful
• Use positive reinforcement to
motivate students - give out awards
for both good academics and for
good effort
• Have structure and procedures
• With these in place discipline follows
• You don’t want students creating
classroom rules on the fly
• Fewer rules are better
• Be fair (fair does not mean equal)
Don’t send mixed messages.
Be consistent!
Assessing Instruction
• Assessment
• More than tests and quizzes
• Assessment for Learning –
ActivEngage!
• Spell out what topics will be on
the test. This will especially help
those with poor study skills.
• ExamView banks
• Grades
• Interims, Quarters, Semesters
• eClass grading program
• Technology
• Graphing and Scientific
Calculators
Changing Instruction
• Dan Meyer – Math class needs a makeover
• Today's math curriculum is teaching students to expect -- and
excel at -- paint-by-numbers classwork, robbing kids of a skill
more important than solving problems: formulating them. At
TEDxNYED, Dan Meyer shows classroom-tested math
exercises that prompt students to stop and think.
• http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html
Questions?
• Please contact me about anything!
• Skip Tyler
• [email protected]
• 652-3753
Break
Differentiate in
the classroom.
Realize that
students have
different skills
sets.
Collaborative Teaching/Differentiated
Learning
• Ms. Ashley Reyher and Mr. Kevin Hoy
• http://teachers.henrico.k12.va.us/math/Teacher/nta.html
• Collaborative Math Classrooms: Co-teaching Tips and Strategies
• Collaborative Math flipchart
Breakout sessions
• High school stays here – Skip Tyler
• Middle school goes to room 160 – Jamie Perkins
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Examine the EOC Vertical Articulation
• Identify the similarities and differences between the
grade levels
• What are the key verbs?
• Was there anything that surprised you?
• http://tidewaterteam.wm.edu/vadoe_math_resources.php
Breaking Down the Standards
• List the 5 most important concepts you see in your
standards
• Can you draw a representation of the topics?
• http://www.doe.virginia.gov/testing/sol/standards_docs/
mathematics/index.shtml
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Course 1 Standards
Grade 6
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Course 2 Standards
Grade 7
36
Course 3 Standards
Grade 8
37
Algebra 1 Standards
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Geometry Standards
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Algebra 2 Standards
Instruction: Why focus on tasks?
• Classroom instruction is generally organized and
orchestrated around mathematical tasks
• The tasks with which students engage determines what
they learn about mathematics and how they learn it
• “There is no decision that teachers make that has a
greater impact on students’ opportunities to learn and on
their perceptions about what mathematics is than the
selection or creation of the tasks with which the teacher
engages students in studying mathematics”.
Lappan & Briars, 1995
Instruction: Two tasks.
Martha’s Carpeting Task
Martha was re-carpeting her
bedroom which was 15 feet long
and 10 feet wide. How many
square feet of carpeting will she
need to purchase?
Fencing Task
Ms. Brown’s class will raise rabbits for
their spring science fair. They have 24
feet of fencing with which to build a
rectangular rabbit pen in which to keep
the rabbits.
1.
2.
3.
If Ms. Brown's students want their rabbits
to have as much room as possible, how
long would each of the sides of the pen
be?
How long would each of the sides of the
pen be if they had only 16 feet of
fencing?
How would you go about determining the
pen with the most room for any amount
of fencing? Organize your work so that
someone else who reads it will
understand it.
Instruction: Tasks - Comparison
Similarities
• Both require prior knowledge of
area
• Area problems
Differences
•
Way in which the area
formula is used
•
The need to generalize
•
The amount of thinking and
reasoning required
•
The number of ways the
problem can be solved
•
The range of ways to enter
the problem
Instruction: Tasks
Not all tasks are created equal, and different tasks will
provoke different levels and kinds of student
thinking.
Stein, Smith, Henningsen, & Silver, 2000
The level and kind of thinking in which students engage
determines what they will learn.
Hiebert, Carpenter, Fennema, Fuson, Wearne, Murray, Oliver, & Human, 1997
If we want students to develop the capacity to think,
reason, and problem solve then we need to start with
high-level, cognitively complex tasks.
Stein & Lane, 1996
Task Characteristics
• High cognitive demand
• Significant content (i.e., they have the potential to leave
behind important residue)
• Require justification or explanation
• Make connections between two or more representations
• Open-ended
• Allow entry to students with a range of skills and abilities
• Multiple ways to show competence
Tying it All Together
• Improved vertical alignment of content
with increased cognitive demand.
• Key conceptual models can be
extended across grade levels.
• Refer to the Curriculum Framework.
• Pay attention to the changes in the
verbs.
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Biggest changes!
• Algebra 1, AFDA, and Algebra 2 have new information
related to statistics.
• Standard Deviation
• Z-scores
• Normal Distribution
• Many students did not have this taught last year. Extra
time and training will be necessary.
Four Scenarios!!!
Read the scenario presented
Think through and jot down answers
Share ideas/Ask Questions
Scenario #1
You want to experiment with a new teaching method and
would like to incorporate manipulatives into your lessons,
but you are unsure if it will go over well with your students.
• What can you do?
• What are some possible solutions?
• Who can assist you with this situation?
Scenario #2
As a new mathematics teacher, you are assigned a
mentor/buddy and are somewhat nervous about your
teaching assignment. You are surprised to learn that your
mentor, though very nice, does not teach your content. You
also learn that the only other teacher who teaches your
content is an old grouch who does nothing but complain.
• What can you do?
• What are some possible solutions?
• Who can assist you with this situation?
Scenario #3
You and your collaborative partner are not seeing eye-toeye on classroom management and instruction. The kids
are beginning to notice that the two of you are not working
as a team.
• What can you do?
• What are some possible solutions?
• Who can assist you with this situation?
Scenario #4
Several students are bored with your lesson on solving
two-step equations. They start to ask the age old question,
“Why do we have to learn this?”
• What can you do?
• What are some possible solutions?
• Who can assist you with this situation?
NCTM Process Standards
• Communication
• Connections
• Problem Solving
• Reasoning and Proof
• Representation
NCTM Process Standards
Communication
• Use the language of mathematics to express mathematical ideas
precisely.
• Writing about mathematics.
• Discussing mathematical ideas.
• You have eleven fruits in your basket, some are one kind of fruit,
and the rest are another kind. How many of each could you
have?
NCTM Process Standards
Connections
• Between different mathematical areas
• Between mathematics and science
• Between mathematics and other subject areas (such as history,
literature, and art)
• Between mathematics and the real world
• Example
• Mr. Goodlock drives to and from Hermitage almost every day.
Along the way the posted speed limits range from 30 mph to 65
mph. Mr. Goodlock has logged his daily commute.
NCTM Process Standards
Connections
• These are the posted
speed limits and the
odometer reading at the
beginning of each drive
segment Mr. Goodlock
encounters:
Odometer
Reading
Posted
MPH
0
60
2.7
55
7.8
45
11.8
35
18.2
65
24.3
30
27.3
Parking Lot
• Calculate the amount of time Mr. Goodlock spends in each speed
zone. Make a graph showing your results. Mr. Goodlock usually
drives at the posted speed limit. If we assume a trip with no traffic
and we ignore time spent at stop signs and traffic lights -- what is
the total driving time for Mr. Goodlock's trip?
WCYDWT Video
• (What Can You Do With This)
• The best motivator of all is connecting math to the real
world.
NCTM Process Standards
Problem Solving
• Build new mathematical knowledge through problem solving
• Solve problems that arise in mathematics and in other contexts
• Apply and adapt a variety of appropriate strategies to solve problems
• Monitor and reflect on the process of mathematical problem solving
• Translation: include one and two-step story problems typically
found in textbooks.
A school auditorium can seat 648 people in 18 equal rows. How
many seats are there in each row?
• Process: requires solution processes other than computational
procedures.
• Application: computation is generally the solution process used
to solve application problems.
How many soda cans would it take to fill the school gym?
NCTM Process Standards
Reasoning & Proof
•
•
•
•
Recognize reasoning and proof as fundamental aspects of mathematics
Make and investigate mathematical conjectures
Develop and evaluate mathematical arguments and proofs
Select and use various types of reasoning and methods of proof
Reasoning
• Look at the set shown
below.
{15, 23, 39, 42}
Which number is prime?
Reasoning
• Look at the set shown below.
{2a, 3a, 4a, 5a}
If a is a prime number, how
many members of the set
are also prime?
NCTM Process Standards
Mathematical Representations
Create and use representations to organize, record, and
communicate mathematical ideas
Select, apply, and translate among mathematical representations
to solve problems
Use representations to model and interpret physical, social, and
mathematical phenomena
Sam went to a store and spent half of his money. Then he gave
one-fifth of what he had left to his sister. Of the amount he had left,
he lost half of it. When Sam got home, he had $0.50. How much
money did he have before entering the store?
Bloom’s Taxonomy
Bloom’s Taxonomy
•
•
What is the
mathematics assessed
in the item on the right?
Which cognitive level
does the question
address?
1. 76, 79, 75, 77, 74
For the data listed,
the value 76.2
represents the
A. Median
B. Mode
C. Range
D. Mean
Bloom’s Taxonomy
•
What is the
mathematics
assessed in the
item on the right?
•
Which cognitive
level does the
question address?
1. The difference in cost
between a large bag of chips
and a small bag of
chips was $.90. Alicia
bought 5 large bags and 3
small bags of chips for her
party and spent $17.22.
What was the cost of a small
bag of chips?
F $5.74
G $2.49
H $2.15
J $1.59
Effective Questioning
Is 15 a prime number?
• Students can answer with
a simple Yes or No.
• What does the student’s
response inform the
teacher about the pupil’s
knowledge about prime
numbers?
Why is 7 an example of a
prime number?
• Not a one-word answer.
• This requires a student to
recall prior knowledge to
explain and justify their
reasoning.
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Examine the 5-8 Vertical Articulation
• Identify the similarities and differences between the
grade levels
• What are the key verbs?
• Was there anything that surprised you?
Breaking Down the 6-8 Standards
• List the 5 most important concepts you see in
Grades 6 and 7
• Can you draw a representation of the topics?
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Number and Number Sense &
Computation and Estimation
Grade 6
66
Number and Number Sense &
Computation and Estimation
Grade 7
67
Number and Number Sense &
Computation and Estimation
Grade 8
68
Measurement and Geometry
Grade 6
69
Measurement and Geometry
Grade 7
70
Measurement and Geometry
Grade 8
71
Probability, Statistics, Patterns, Functions,
and Algebra
Grade 6
72
Probability, Statistics, Patterns, Functions,
and Algebra
Grade 7
73
Probability, Statistics, Patterns, Functions,
and Algebra
Grade 8
Parting words of wisdom…
Try to anticipate how a student
might misuse equipment
Encourage your
students to pay
attention and
make detailed
observations.
Make sure there is substance
to your lesson.
Set realistic expectations for
your students