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Math in the Common Math in the Common Core Era:Core Era:
Helping All Students Helping All Students SucceedSucceedArchdiocese of Dubuque
October 1, 2015
Knowledge of Mathematics Knowledge of Mathematics and General Pedagogyand General Pedagogy
Teachers should have a deep knowledge of –
•Sound and significant mathematics•Theories of student intellectual development across the spectrum of diverse learners•Modes of instruction and assessment•Effective communication and motivational strategies
Knowledge of Knowledge of Student Student
Mathematical Mathematical LearningLearning
Teachers must know and recognize the importance of – •Ways students learn mathematics;•Supporting students as they struggle to make sense of mathematical concepts and procedures•Ways to help students build on informal mathematical understandings•Ways to stimulate engagement and to use the standards for mathematical practice
Worthwhile Mathematical Worthwhile Mathematical TasksTasks
Teachers should design experiences and pose tasks that – •Engage students’ intellect•Develop mathematical understandings and skills•Stimulate students to make connections and develop a coherent framework for mathematical ideas•Call for problem formulation, solving, and mathematical reasoning
That’s a lot of words, That’s a lot of words, what does this mean what does this mean
for me?for me?Fluency: knowing how a number can be composed and decomposed and then using that information to be efficient and flexible when solving the problem through the use of strategies.
Rigor: the development of conceptual understanding, procedural skill and fluency, and application with equal intensity.
Without talking,
without writing,
without counting
one by one,
how many unit
squares are in the
shaded portion
surrounding the
figure?
Whole Number Whole Number ComputationComputation
For each probe, choose the method that closely matches how you would solve the problem.
Then discuss the other methods with your partner.
Number Talks:Number Talks: Key Components Key Components
1. Classroom Environment and Community
2. Classroom Discussions
3. Changing the Role of the Teacher
4. Role of Mental Math
5. Purposeful Computation Problems
ScreenScreenersersWho should administer?When should this occur?Why should it be used?How will the results be used?What can be used?
What can be What can be used?used?
Resource
K-1: Number Knowledge Test Number Sense Screener
2-5: Delaware Screeners Boulder Valley, CO (K-5)
6-8: Math Reasoning Inventory
InterventioIntervention Plann Plan
Who should administer?When should this occur?Why should it be used?How will the results be used?What can be used?
What can be What can be used?used?
K-1: Number Sense Intervention
1-8: Do the Math
5-10: Trans Math
K-12: Engage NY
Progress Progress MonitoringMonitoringExit Tickets in the Engage NY curriculum at the end of each lesson can be used for progress monitoring. The following rubric with each exit ticket question could be used after every 3 lessons for a total of 9 points.
Student has a full understanding of the
question (3)
Student has a good understanding of the question
making minimal mistakes(2)
Student has a partial understanding of the
question (1)
Student has no understanding of the
question(0)
Lesson 1
Lesson 2
Lesson 3