Mathematics Teachers Kindergarten Grade 2 Joy Donlin & Ryan
Dunn October 7, 2013
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Welcome and introductions Discussion how do students learn
mathematics? Exploring the paradigm shift Participating in a lesson
that meets the shift Translating the standards Designing a lesson
Reflections Agenda
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Participants will consider their educational platform.
Participants will increase their knowledge and understanding of
Operations and Algebraic Thinking and the Standards for
Mathematical Practice in the CCSSM. Participants will apply their
knowledge and understanding to develop a lesson. Outcomes
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Design Methodology Standards Interpretation Expected Evidence
of Student Learning Text-based Discussion (Research) Model
Construction (Trying on the work) Task & Instructional Plan
Student Work Examination Revision of Task & Instructional
Plan
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5 College and Career Readiness SCUSD Strategic Plan 2010 - 2014
Common Core State Standards (CCSS) Focus Pillar One: Career and
College Ready Students The focus of the CCSS is to guarantee that
all students are college and career ready as they exit from high
school.
Content Focus Areas Content Focus Areas for Teachers
2012-20132013 - 2014 Grades K 2Counting and Cardinality (K);
Operations and Algebraic Thinking & Number and Operations in
Base Ten Grades 3 5Number and Operations Fractions Operations and
Algebraic Thinking & Number and Operations in Base Ten Grades 6
7Ratios and Proportional Reasoning The Number System Grade
8Expressions and Equations Functions Grades 9 12Integrated Math
1
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This is a 2 player game. The idea of the game is to be the
person that lands on zero. You begin at the number 10 Each turn you
can choose to go back by 1 or 2. Race to 0
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What are some questions we could ask to prompt students to
think more deeply about this game? Is this a rigorous activity to
undertake with kindergarten students? Race to 0
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Some questions to prompt deeper thinking: Is there a strategy
that can help you win the game? Are there numbers along the way
that can help you land on zero? (powerful numbers) Race to 0
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How would the game change if we: Started at 12 or 15 Raced from
0 to 10 Could move by 1, 2 or 3 What are some variations
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Why do you think it is so common for students (and adults) to
talk about mathematics as being hard? 2 minutes to discuss this
with the person next you. 3 minutes to share thoughts with your
table. 5 Minute Brainstorm
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Make a list of the top 5 things that support elementary
students in learning mathematics. Rank them from 1 to 5.
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Share your #1s with a neighbor. Are your #1s the same?
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There are two major theories on how children think and learn:
Behaviorism has long been associated with mathematics learning.
Constructivism has been shown to promote meaningful learning. How
do children learn mathematics?
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Has roots in stimulus response and conditioned learning.
Asserts that behavior can be shaped through rewards and punishment.
Focus on low level thinking, not mathematical thinking.
Behaviorism
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Behaviorism has had a significant impact on mathematics
programs: Students are shown algorithms. Mathematical relationships
are illustrated in textbooks. Produces mastery of specific
objectives but lacks critical connections that make knowledge
meaningful and useful Behaviorism
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Constructivism advocates that: Knowledge is not passively
received, but actively constructed by the learner. The learner uses
prior knowledge to construct new meaning (Piaget). Learning is a
social process (Vygotsky) Constructivism
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Think back to your list of top 5 things that support elementary
students to learn mathematics. Is there evidence of Behaviorism
and/or Constructivism on your list? What is your Educational
Platform?
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CCSS for Mathematics Paradigm Shift Mathematics learning that
goes beyond the demonstration of procedural content by: providing
extensive opportunities to reason and make sense of the mathematics
students are learning emphasizing student understanding, problem
solving and sense making developing deep understanding of content
and use of conceptual understanding as a precursor to developing
procedural or symbolic fluency.
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L Standards for Mathematical Practice 1. Make sense of problems
and persevere in solving them 6. Attend to precision 2. Reason
abstractly and quantitatively 3. Construct viable arguments and
critique the reasoning of others 4.Model with mathematics 5.Use
appropriate tools strategically 7. Look for and make use of
structure 8. Look for and express regularity in repeated reasoning
Reasoning & Explaining Modeling & Using Tools Seeing
Structure & Generalizing Overarching Habits of Mind of a
Productive Mathematical Thinker Legend
Choose a playing card from the materials bag. 1 Student 2
Observer for SMP 3 Observer for use of teacher moves/ questioning
strategies 4 - Observer for use of formative assessment
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Grade 1 OA.6 Add and subtract within 20, demonstrating fluency
for addition and subtraction within 10. Use strategies such as
counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);
decomposing a number leading to a ten (e.g., 13 4 = 13 3 1 = 10 1 =
9); using the relationship between addition and subtraction (e.g.,
knowing that 8 + 4 = 12, one knows 12 8 = 4); and creating
equivalent but easier or known sums (e.g., adding 6 + 7 by creating
the known equivalent 6 + 6 + 1 = 12 + 1 = 13). Grade 2 OA.2
Fluently add and subtract within 20 using mental strategies. By end
of Grade 2, know from memory all sums of two one-digit numbers.
Lesson
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The Task Using only the numbers 3, 4, 5, 6, 7. Place any 4
numbers into the frame below to make a true equation. Try to find
other solutions. ___ + ___ - ___ = ___ Number Tiles
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How many solutions do you think there are? How would you know
when you have found them all? What do we notice from the solutions
we have already found? Deepening the Investigation
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How could students apply the mathematical knowledge from this
investigation? Applying the Knowledge
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For the original problem, the tiles are consecutive starting at
3. What happens if you use five consecutive numbers beginning with
a different number? (4, 5, 6, 7 and 8) Will there be the same
number of solutions? Deepening the Learning
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As a school team discuss the following: 1.Describe what the
student(s) know, understand and are able to do based on your role
during the lesson and provide evidence to support your answer.
2.Describe the implications for instructional design of a
mathematics lesson. Debrief
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LUNCH
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Try these as a warm up after the lunch break. Given the numbers
on the edges try to work out the numbers in the vertices. Here is
an example: Arithmagons
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Try these
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3 Big Ideas: 1.Read 2.Translate 3.Design Units and Learning
Activities Wiggins, 2011 Honoring the CCSSM
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Domain: Operations and Algebraic Thinking Kindergarten: 1
Cluster Grade 1: 4 Clusters Grade 2: 3 clusters Unpacking the
Standards
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As the grade level/band teacher leader at your school, you will
have a role: 1.As the content expert 2.As a content pedagogy expert
3.As the leader of collaborative planning units of study and lesson
design 4.As the leader of peer observation experiences 5.As the
lead learner and sharer of information Taking It Back
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you cant lead where you wont go Barth, 2002
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In a lesson that you will be teaching in the next week, will my
students be experiencing a similar kind of learning? Work with a
colleagues to adjust your lesson design as necessary for the
following: 1.How will the problem/task or activity provide students
the opportunity to engage in the Standards for Mathematical
Practice? 2.How/when will students make sense of problems and
persevere in solving them? 3.How/when will students be reasoning
abstractly and quantitatively? 4.How/when will students be
explaining their thinking to each other? 5.How/when will students
be critiquing the reasoning/thinking of others? 6.How/when will
students be modeling with mathematics? 7.How/when will students be
attending to precision? 8.How/when will students be looking for and
making use of the structure of the lesson content? Be prepared to
share the lesson with another grade level team and your school
team. Lesson Design
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Share the lesson(s) with another grade level team. Share the
lesson(s) with your school team. Receiving feedback
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Reflection One idea that interests me is Something I plan to
try One step I will take tomorrow to lead other math teachers in my
grade is I wonder
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Enter the following link and complete the online questionnaire:
https://www.surveymonkey.com/s/TYP8Z MG Reflection
Questionnaire
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Professional development works, if it works at all, by
influencing what teachers do... Instructional Rounds in Education,
pg. 24.