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Problems and Concepts and Skills,
Oh My…
Facilitator: Dr. Karen M. Beerer
Discovery Education
What does this have to do with the Common Core Mathematics Standards?
Assess Your Knowledge and Understanding:
Go to www.vot.rsand enter 31 73 32 to vote
CCSS Mathematics StandardsThe Structure: 8 Standards for Mathematical Practice which span K-12 Grades K-8 have grade-level specific standards High School Standards are listed in conceptual categories (e.g., Functions, Number & Quantity)
K 12
Number and Operations
Measurement and Geometry
Algebra and Functions
Statistics and Probability
Traditional U.S. Approach
7
What is a learning trajectory?“Learning progressions,” or, as the concept more often is termed in the mathematics education literature --- “learning trajectories” --- are labels given to attempts to gather and characterize evidence about the paths children seem to follow as they learn mathematics. Hypotheses about the paths described by learning trajectories have roots in developmental and cognitive psychology and, more recently, in developmental neuroscience. These roots… describe the ways children’s actions, thinking, and logic move through characteristic stages in their understanding of the world…
- Daro, 2012
10
Grade Standard Required FluencyK K.OA.5 Add/subtract within 5
1 1.OA.6 Add/subtract within 10
2 2.OA.22.NBT.5
Add/subtract within 20 (know single-digit sums from memory)Add/subtract within 100
3 3.OA.73.NBT.2
Multiply/divide within 100 (know single-digit products from memory)Add/subtract within 1000
4 4.NBT.4 Add/subtract within 1,000,000
5 5.NBT.5 Multi-digit multiplication
6 6.NS.2,3 Multi-digit divisionMulti-digit decimal operations
11
12
The best thing about the Math Common Core Standards is…
30 second pause…• The structure of the Math CCSS• The focus and coherence of the Math CCSS• The placement of topics in the K-8 CCSS Math
curriculum• Learning trajectories and the CCSS Math
curriculum• Computational fluency in the Math CCSS• The CCSS Mathematics instructional shifts
http://padlet.com/wall/mathccss
Kid Snippets Video
Focus Coherence RigorLearning
Trajectories
Standards for
Mathematical Practice
Rigor
Coherence
Learning Trajectories
Focus
Standards for Mathematical Practice
☐ Have you…”unwrapped” the Standards for Mathematical Practice?
What do these SMPs look like?
Third Grade SMP video
On Common Ground with the Common Core Webinar Series
Which Standards of Mathematical Practice were evident in the problem you just viewed?
______Make sense of problems and persevere in solving them.
______Reason abstractly and quantitatively.
______Construct viable arguments and critique the reasoning of others.
______Model with mathematics.
______Use appropriate tools strategically.
______Attend to precision.
______Look for and make use of structure.
______Look for and express regularity in repeated reasoning.
Common Core Math Implementation Considerations
1. An Instructional Model
2. An Instructional Planning Tool
3. Instructional Strategies and Tools
4. Assessments
Common Core Math Implementation Considerations
1. An Instructional technology integration Model
2. An Instructional technology Planning integration Tool
3. Instructional technology integration Strategies and Tools
4. Assesstechnology integrationments
Publish - requiring deep consideration of audience, purpose, structure, text features, and format. Collaborate - forcing students to plan, adopt, adapt, rethink, and revise, all higher-level practices. Evaluate - necessitating that students make critical judgment calls about how information is presented and shared.Integrate - emphasizing design, and producing considerable cognitive load on a learner.
CCSS requires students to:
A CCSS Math Instructional Model
Step One: Task First!
Consideration #1:
Dan Meyer’s Three Act Math Tasks
The Top Five Sites for CCSS Math Tasks
The Top Five Sites for CCSS Math Tasks
The Mathematics Common Core Toolbox: www.ccsstoolbox.com
The Top Five Sites for CCSS Math Tasks
Inside Mathematics: www.insidemathematics.org
The Top Five Sites for CCSS Math Tasks
Illustrative Math: www.illustrativemathematics.org
The Top Five Sites for CCSS Math Tasks
Mathematics Assessment Project:Map.mathshell.org
An Instructional Planning Tool
Consideration #2:
An Instructional Planning ToolPhase 1: Assess Students Describe your exploration assessment activity: Key Reminders: Anticipate the likely student responses to
cognitively demanding mathematical tasks Monitor student responses to the task during
this exploration phase
An Instructional Planning ToolPhase 2: Learning Goals Based on Student Data
Phase 3: Design Instruction
Video: Teacher Debriefing Student Work
Instructional Strategies and Tools
Think-Ink-Pair-Share:T: Without pencils, students think for 1‐2 minute. I: Students may then use pencil to begin working...without talking to partner. P: Students then share their thinking and answer(s) with their partner. S: Pairs then may share with larger group.
Consideration #3:
Instructional Strategies and Tools
I Spy:• One student can go around to other teams
and listen in for one minute. (without paper or pencil)
• Student reports back to the team what was learned.
Instructional Strategies and Tools
Huddle:• One person from each team (teacher’s
choice) is called to the front of the room.• Teacher gives a piece of information, checks
for understanding.• Student goes back to team to share.
Instructional Strategies and Tools
Integrating Digital Videos• Construct mathematical knowledge• Answer challenging mathematical questions• Expand student visualization skills• Mathematically analyze events in video
clips
Mathematics in Movies:Mathematics in Movies
Assessments• Explain your answer using numbers, symbols and words.• Drag tiles to… that make the statement true. There is more
than one correct answer.• Compare these statements from two students…Can both
students be correct? Explain how you know.• Are they both correct? Use the properties of operations to
justify your answer.• Which of the following statements must be true about the
model for …compared to the model you developed for …? Select all that apply.
• Drag tiles to complete the sentences and the equation below based on the results of the experiment.
Consideration #4:
Assessments• Explain your answer using numbers, symbols and words.• Drag tiles to… that make the statement true. There is more
than one correct answer.• Compare these statements from two students…Can both
students be correct? Explain how you know.• Are they both correct? Use the properties of operations to
justify your answer.• Which of the following statements must be true about the
model for …compared to the model you developed for …? Select all that apply.
• Drag tiles to complete the sentences and the equation below based on the results of the experiment.
Assessments
http://www.drawzit.com
Assessmentshttps://bubbl.us
Assessmentswww.infuselearning.com
On Common Ground with the Common Core Webinar Series
You can’t lead the change if you don’t understand the
change.-Dr. Christine Tell