Post on 01-Jan-2016
Differentiating Instruction using the
Common Core State Standards
NCDPICurriculum and Instruction Division
2014 Spring RESA
Introductions
cc: Microsoft.com
Norms
A thoughtful and honest conversation amongst those of us who are engaged in our learning community today…
Session Outcomes• What is content differentiation? • What is process differentiation? • What is product differentiation?
• What do these differentiations “look” like and how do we incorporate them into our practice?
• What types of differentiation lead to increased entry points for ALL students? How do we achieve this?
• What types of differentiation challenge students to go beyond lesson targets? How do we achieve this?
Let’s Do
SomeMath!
Always – Sometimes – Never
Always – Sometimes – Never
(x+2)(x-2)=x2+4
“Sorting Equations and Identities”In your groups, take turns to place a card in a column and justify your
answer to your partner.
If you think the equation is ‘sometimes true’, find values of x for which it is true and values of x for which it is not true.
If you think the equation is ‘always true’ or ‘never true’, explain how we can be sure that this is the case.
Another member of the group should then either explain that reasoning again in his or her own words, or challenge the reasons you gave.
When everyone in the group agrees, glue the card onto the poster. Write the reason for your choice next to the card.
• What about Sorting Equations and Identities would you identify as process differentiation?
• What about Sorting Equations and Identities would you identify as product differentiation?
• What strategies, and how, from Sorting Equations could transcend to other lessons? Be specific and share ideas.
“Table Talk”
The Shell Center http://map.mathshell.org/
Just a Minute• In the next four slides you’re going to see
different “types” of addressing instruction.
• You will see each slide for “just a minute.”
• Record your thoughts about this question:What does this imply about the importance of differentiation in CCSS? Which type(s)?
Variety of Prior Knowledge
Student A
Student B
Student C
Student D
Student E
Planned time
Needed time
Lesson START Level
CCSS Target Level
Student A
Student B
Student C
Student D
Student E
I - We - YouLesson START
Level
CCSS Target Level
Student A
Student B
Student C
Student D
Student E
“ANSWER-GETTING”Lesson
START LevelCCSS Target
You – We – I
Student A
Student B
Student C
Student D
Student E
Lesson START Level
Day 1 Attainment
Day 2Target
What does this imply about the importance of
differentiation in CCSS? Which type(s)?
“ It tells me it isn’t enough just to change the way we do things. We must also change the way we see and the way we think. We need to learn how to learn differently.”
David Hutchens “Outlearning the Wolves”
“Orchestrating Classroom Discussion”
1. Read “Orchestrating Classroom Discussions”
2. While reading, use index cards to record reflections and “takeaways” for each of the instructional practices featured. Use More Than One (1) Card per Practice if Needed
• Block Party: Find one or two other people to share two (2) ideas and/or reflections you had or have after reading “Orchestrating Classroom Discussions”?
• Chalk Talk: Following each block party you will write “take away” ideas on the posters around the room
Block Party Protocol Chalk Talk
“Anticipation” ActivityUse the following prompts below to develop the “Anticipation” segment for Sidewalk Patterns.
The teacher must:- do the problem in as many ways as possible.- collaborate with other colleagues to
- anticipate the different strategies and solutions that students may come up with.
- determine how to respond to what students produce.- identify strategies that will be most useful in addressing the
mathematics to be learned
Monitoring • Monitor students’ actual responses during independent work.• Circulate while students work together to solve the problem,
carefully watching and listening. • Record their interpretations, strategies, and points of confusion. • Ask questions to get students thinking “on track” or to advance
their understanding
Selecting • Select student responses to feature during discussion.• Choose particular groups to present because of the
mathematics available in their responses, or students based on individual needs.
Sequencing • Sequence the student responses that will be featured during the
discussion• Purposefully ordering presentations, building a mathematically
coherent story line, so as to make the mathematics accessible to all students
Connecting • Make sure the mathematical concepts that are the focus of the
lesson are clear and accessible. • Connect student responses and lead them to connections
during the discussion by asking purposeful questions. • Encourage students to make and share mathematical
connections between different student responses.
I. Classroom Discourse
• How do lessons that develop “Classroom Discourse” using “The 5 Practices for Orchestrating Math Discussions” by Smith and Stein, differentiate instruction for every learner? Using the CCSSM?
• How might these ideas and practices challenge teachers in your district or school? How might you move their thinking forward?
“Table Talk”
“Down at the Dock”(A Game of Chance in Probability Theory)
II. Games and Stations
• How does “Down at the Dock” differentiate instruction for every learner?
• How does “Down at the Dock” support the CCSSM?
“Table Talk”
Tiered Task From Proportion to Linear Function
• Concrete to Abstract
• Middle School Content
Fractured Numbers
• Inside Mathematics leveled task
• Fractions to Math 3 concepts
Pick the task more appropriate to your level of instruction to explore. We will jigsaw to report out.
“From Proportion to Linear Function”
(Concrete to Abstract)
III. “Tiered” Lessons
• What types of differentiation do tiered task offer? (Content, Process, and/or Product)
• How do tiered lessons support the development of the CCSS mathematics?
• Discuss additional ways lessons can be tiered to meet the needs of every learner and align to the CCSSM?
“Table Talk”
Problem Analysis
“The process of examining an existing
mathematics problem to find ways to
modify and/or extend the problem, creating
a richer learning opportunity that reaches
learners at all levels”(Katie Garcia and Alicia Davis, Dec 2013/Jan 2014 Mathematics Teacher, p. 349)
Problem Analysis
• First – An example as students
• Second – Look at the work from other regions
• Third – Try it out
Dunking Booth
• Student council is holding a fundraising event. They plan to rent a dunking booth as they are quite sure students will pay to dunk teachers or administrators into a tub of cold water.
Create a viable solution to “Dunking Booth”
All four representations should be addressed in your solution.
In text. . . Dunking BoothThe student council at West High School is holding a dunking booth fundraiser as the council is sure that students will pay for an opportunity to dunk a teacher or principal into a tub of cold water. It cost $150 to rent the booth and the council will charge $0.50 for each throw.
a) How many throws need to be sold to cover the cost of the rental agreement?
b) How many throws need to be sold to to raise $200?
c) Predict the number of throws sold if the council raised $350. Show your work.
d) Write a linear function, p(t), showing the profit for t number of throws.
Teachers - Reach all learners simultaneously- Fit old textbooks to new curriculum standards
Students - Experience higher-ordered thinking - Make important mathematical connections
Problem Analysis
High School Content Examples
Exponential Growth Quadratic Functions
Middle School Content Examples
Area and Perimeter of irregular shapes Coordinate Geometry
1. Identify a mathematics problem that has potential to develop deep understanding, but barely skims the surface.
• Use the problem provided below, or choose one of your own!
Example Problem:Find the area of the triangle with vertices at A(-8,-6), B(6,9), C(8, -14)
Problem Analysis Activity
2. Use the guiding questions listed on the activity sheet to modify and/or extend the problem to meet the needs of all learners by;
• Scaffolding to assist students at the beginning
• Including intermediate steps to bridge thinking to higher-levels
• Provide extensions to challenge students to go further.
Example Problem:Find the area of the triangle with vertices at A(-8,-6), B(6,9), C(8, -14)
Problem Analysis Activity
• What thoughts and reflections occurred as you completed this activity.
• When and how will you use this activity to implement the CCSSM?
“Table Talk”
Session Outcomes - “Revisited”• What is content differentiation?
• What is process differentiation? • What is product differentiation?
• What do these differentiations “look” like and how do we incorporate them into our practice?
• What types of differentiation lead to increased entry points for ALL students? How do we achieve this?
• What types of differentiation challenge students to go beyond lesson targets? How do we achieve this?
Illustrative Mathematicshttp://www.illustrativemathematics.org/
Inside Mathematicshttp://insidemathematics.org/
Mathematics Assessment Project (MARS)http://map.mathshell.org/materials/
Mathematics Vision Project (MVP)http://www.mathematicsvisionproject.org/
NCTM Illuminations http://illuminations.nctm.org/
“Open Online Resources”
What Questions Do You Have?
NCDPI Mathematics SectionKitty RutherfordElementary Mathematics Consultant919-807-3841kitty.rutherford@dpi.nc.gov
Denise SchulzElementary Mathematics Consultant919-807-3839denise.schulz@dpi.nc.gov
Johannah MaynorSecondary Mathematics Consultant919-807-3842johannah.maynor@dpi.nc.gov
VacantSecondary Mathematics Consultant919-807-3934
Dr. Jennifer CurtisK – 12 Mathematics Section Chief919-807-3838jennifer.curtis@dpi.nc.go
Susan HartMathematics Program Assistant919-807-3846susan.hart@dpi.nc.gov
Thank You!