Frost MS Mathematics Curriculum Overview - Jennifer Allard High School Math Specialist - Frost Middle ...
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Frost MS Mathematics
Curriculum Overview
Jennifer Allard David Van Vleet
High School Math Specialist Middle School Math Specialist
Fairfax County Public Schools
1
Double Sunglasses • Dan Meyer 3‐Act Math Tasks
Double Sunglasses
• Dan Meyer 3‐Act Math Tasks
1. What will be the percent tint with
both sunglasses?
2. Write a guess.
3. Write a guess you know is too high.
4. Write a guess you know is too low.
Double Sunglasses • Dan Meyer 3‐Act Math Tasks
Think about something
you are good at doing.
With a partner, discuss one or more of
these questions:
What What did What has
What is it How did
obstacles, you do given you
that you you get to
if any, did when you satisfaction
are good be good at
you faced those about this
at? this?
encounter? obstacles? endeavor?
The Perils and Promise of Praise
Carol S. Dweck
Do not recover
well from
setbacks
Are afraid of Believe that
effort because intellectual ability
effort makes is a fixed trait
them feel
dumb
Reject Seek tasks that
opportunities to
learn if they might prove their
make mistakes intelligence
Intellectual ability can be
developed through
effort and education
Believe anyone Believe in
can be good at themselves
anything because
your abilities are that they just
entirely due to haven’t
your actions/effort gotten it “yet”
When faced with challenges,
escalate efforts and look for
new learning strategies
The Perils and Promise of Praise
Carol S. Dweck
The Power of Why is this so powerful?
What feelings are you hearing your child express about mathematics?
If your Child has a:
• Fixed Mindset‐ • Growth Mindset‐
They feel defeated and They are struggling with the
overwhelmed because they are concepts and their achievement
struggling and they don’t know
but are not defeated. They want
how to struggle
to get help and they are open to
having to work hard at math.
They don’t know how to learn
math because it “came so
easily” when they were They want help in the form of how
younger. to understand the math‐not how
to get out of the class.
They struggle to explain why
things work and say things like They continually ask “why” and
“I just know that’s the answer.”
seek to understand instead of just
get the right answers.Understanding
progression
Process
Child easily
memorization
understands Fog
more than concept
concepts
understanding
Achievement
progression
Current grades are
Child has only
Grades continue not consistent
known success in
to suggest success with prior
mathematics
achievementTwo things to consider in providing
appropriate challenges:
– Zone Proximal Development (ZPD)
– Productive struggleBrain Research ‐‐ Piaget
Stage
Approximate
Age of
Development
Description
Mathematics understanding is highly correlated to the developmental stage of the student
www.Mile.mmu.edu.myMisconceptions about Algebra
• “All the smart kids take algebra in 7th grade”
– Please do not confuse readiness with being smart
– Honors Mathematics 7 provides a challenging
curriculum for “smart” kids too
• Academic/mathematical maturity = social
maturity
– Consider this example: Your 13 year old is tall
enough to reach the steering wheel and the gas
pedal. Should she be driving?
– Students need to be cognitively ready AND have
good study skills to succeed in a high school
courseSo what happens if a student is
enrolled in Algebra too early?
• Lots of memorization – “when you
see this, do this”
• Default is to learn a process, not a
concept
• May leave without enduring
understandings, but those may not show
up until a student struggles in Algebra 2Let’s Do Some Mathematics
• What is the definition of an even number?
• You probably remember some of these facts:
– A number divisible by 2
– A number ending in 0, 2, 4, 6, or 8
• The important concept about even numbers is the
partnering off of items.
• So for an odd number:
– A number not divisible by 2
– A number ending in 1, 3, 5, 7, or 9
• The important concept about odd numbers is partnering of
items and having one left over.
16Prove the following:
• What is the result when you add two odd
numbers together?
• Is this always the case?
• What models can you use to prove your answer?
– Pictures
– Colored chips
– Algebraic method
– Exhaustion
17Examples
18Example:
• Isn’t an odd number really an even number +1
• So –
19Algebraic Approach
20Exhaustion Method
• 3+5
• 9+7
• 1+3
• 17+33
• 121+63
• Students will continue to provide as many
examples as possible until they think they have
provided enough to say it is proved.
21• Opportunities to fail – Inspirational videos • Michael Jordan
Students need to fail and they need to
struggle (in a productive way)
• Consider these examples:
From Robert Kaplinsky, Ignite talk , Northwest Math Conference, Whistler, BC, 10/24/2015Students need to fail and they need to
struggle (in a productive way)
• Consider these examples:
From Robert Kaplinsky, Ignite talk , Northwest Math Conference, Whistler, BC, 10/24/2015Students need to fail and they need to
struggle (in a productive way)
• Consider these examples:
From Robert Kaplinsky, Ignite talk , Northwest Math Conference, Whistler, BC, 10/24/2015Students need to fail and they need to
struggle (in a productive way)
• Consider these examples:
From Robert Kaplinsky, Ignite talk , Northwest Math Conference, Whistler, BC, 10/24/2015Now what??
Communicate with your child:
– They have to believe in
themselves‐do they?
– You have to believe in them that
they can work hard‐and at some
point it will be hard
• Support them with the correct types
of praise
• Help them set priorities to maintain
work/life balance (schoolwork,
extracurriculars, family responsibility)
– Leverage resources that exist at
school or privatelyModel a Growth Mindset
Talk about things you
have learned or
challenges you have faced
from childhood to
adulthood.
Reframe failures to Emphasize
setbacks and criticism to effort/process over
feedback. Help them achievement/outcome
identify strategies for
improvementFive goals for students to…
– become mathematical problem solvers that
– communicate mathematically;
– reason mathematically;
– make mathematical connections; and
– use mathematical representations to model
and interpret practical situationsElementary Mathematics
What does this look like in the
classroom?
34Secondary Mathematics
AFDA
35Secondary Mathematics
36Mathematics 7
– This course provides opportunity for students
to examine:
• algebra‐ and geometry‐preparatory
concepts and skills;
• strategies for collecting, analyzing, and
interpreting data;
• and number concepts and skills especially
proportional reasoning.
37Mathematics 7 Honors
*open enrollment*
• The depth and level of understanding in Mathematics 7
Honors is beyond the scope of Mathematics 7.
Mathematics 7 Honors is an acceleration of the
mathematics curriculum.
• This course is based on Mathematics 8 curriculum and
includes extensions and enrichment. Students will take
the Mathematics 8 SOL test.
38Mathematics 7 Honors
• Students who have not completed Advanced
Mathematics 6 may need support and/or require
additional effort and study to be successful.
• Remember, these students were in a Mathematics
6 class last year and are now learning grade 8
mathematics content. They have missed all of
grade 7 mathematics.
39Mathematics 7 Honors
• Key take‐away:
Both Mathematics 7 and Mathematics 7 Honors
prepare students for Algebra 1 or Algebra 1 Honors in
Grade 8.
40Algebra 1 Honors
• Each of the following criteria needs to be met
for placement in Algebra I Honors at 7th grade:
• Advanced Mathematics 6 or a year‐long accelerated mathematics
course
• Iowa Algebra Aptitude Test (IAAT) score at or above the 91st percentile
• A score of pass advanced (500 or above) on the Mathematics 7 SOL
test
417th Grade Mathematics Courses
• Which course is best for your child?
• Open enrollment/Informed decision
• Recommendation
• A discussion with child and teacher(s).
• Both Mathematics 7 Honors and Mathematics 7
lead to Algebra in 8th grade.
• Based on your child’s schedule, what is best for
him/her?
428th Grade Mathematics Courses
• Prealgebra (Mathematics 8 SOL)
• Algebra 1 or Algebra 1 Honors
• OPEN ENROLLMENT
• Geometry Honors
44Algebra 1 in Grade 8
• Students are on a pathway to Advanced Placement
(AP) Calculus in grade 12
• Opens up different Science options in high school
– Honors Chemistry in grade 10 (co‐requisite
Algebra 2)
– AP Physics in grade 12 (co‐requisite AP Calculus)
45Mathematics in the High School
• Important to take 4 years of mathematics
• Honors classes are open enrollment
• Many mathematics elective courses beyond
Algebra 2.
– Precalculus (Honors) ‐‐ Discrete mathematics
– Probability and Statistics ‐‐ Computer Science
– AP Statistics ‐‐ Calculus
46Secondary Mathematics
47Questions?
48David Van Vleet
Middle School
Mathematics Specialist
dvanvleet@fcps.edu
571‐423‐4723
Fairfax County Public Schools
Jennifer Allard
High School
Mathematics Specialist
jallard@fcps.edu
571‐423‐4623
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