Frost MS Mathematics Curriculum Overview

Frost MS Mathematics Curriculum Overview

Jennifer Allard David Van VleetHigh School Math Specialist Middle School Math Specialist

Fairfax County Public Schools1

Double Sunglasses

• Dan Meyer 3‐Act Math Tasks

Double Sunglasses


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.

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What is it that you are good

at?

How did you get to be good at

this?

What obstacles, if any, did

you encounter?

What did you do

when you faced those obstacles?

What has given you satisfaction about this endeavor?

With a partner, discuss one or more of these questions:

Think about something you are good at doing.

The Perils and Promise of PraiseCarol S. DweckDo not recover

well from setbacks

Believe that intellectual ability is a fixed trait

Seek tasks that prove their intelligence

Reject opportunities to learn if they might make mistakes

Are afraid of effort because effort makes them feel dumb

The Perils and Promise of PraiseCarol S. Dweck

Intellectual ability can be developed through effort and education

Believe in themselves that they just

haven’t gotten it “yet”

When faced with challenges, escalate efforts and look for new learning strategies

Believe anyone can be good at

anything because your abilities are entirely due to

your actions/effort

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‐They feel defeated and overwhelmed because they are struggling and they don’t know how to struggle

They don’t know how to learn math because it “came so easily” when they were younger.

They struggle to explain why things work and say things like “I just know that’s the answer.”

• Growth Mindset‐They are struggling with the concepts and their achievement but are not defeated. They want to get help and they are open to having to work hard at math.

They want help in the form of how to understand the math‐not how to get out of the class.

They continually ask “why” and seek to understand instead of just get the right answers.

Child has only known success in mathematics

Grades continue to suggest success

Current grades are not consistent with prior

achievement

Child easily understands concepts

Process memorization

more than concept understanding

Fog

Understanding progression

Achievement progression

Two things to consider in providing appropriate challenges:

– Zone Proximal Development (ZPD)– Productive struggle

Brain Research ‐‐ PiagetStage

ApproximateAge of

Development

Description

www.Mile.mmu.edu.my

Mathematics understanding is highly correlated to the developmental stage of the student

Misconceptions 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 course

So 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 2

Let’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.

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Prove 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

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Examples

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Example:

• Isn’t an odd number really an even number +1

• So –

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Algebraic Approach

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Exhaustion 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.

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• 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, 10/24/2015










Now 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 privately

Talk about things you have learned or

challenges you have faced from childhood to

adulthood.

Reframe failures to setbacks and criticism to feedback. Help them identify strategies for

improvement

Emphasize effort/process over

achievement/outcome

Model a Growth Mindset

Five goals for students to…

– become mathematical problem solvers that– communicatemathematically; – reasonmathematically;– make mathematical connections; and– use mathematical representations to modeland interpret practical situations

Elementary Mathematics

What does this look like in the classroom?

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Secondary Mathematics

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AFDA


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Mathematics 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.

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Mathematics 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.

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Mathematics 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.

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Mathematics 7 Honors

• Key take‐away:

Both Mathematics 7 andMathematics 7 Honors prepare students for Algebra 1 or Algebra 1 Honors in Grade 8.

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Algebra 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

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7th 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?

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8th Grade Mathematics Courses

• Prealgebra (Mathematics 8 SOL)

• Algebra 1 or Algebra 1 Honors• OPEN ENROLLMENT

• Geometry Honors

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Algebra 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)

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Mathematics 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

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Questions?

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Fairfax County Public Schools

David Van VleetMiddle School Mathematics [email protected]‐423‐4723

Jennifer AllardHigh School Mathematics [email protected]‐423‐4623

Documents

Frost MS Mathematics Curriculum Overview