PowerPoint Presentation
Ashlee Beatty Wood County SchoolsJudi Hamrick- Tyler County
Schools Sonah Smith- Wirt County Schools Next Generation Standards
2nd grade mathematics
Thinking is a requirement for learning mathematics.Visible
Thinking in MathematicsWhat is thinking?Welcome1Welcome &
IntroductionsIntroductions of team and those at your
table.2GoalsDevelop an understanding of the structure of the Next
Generation CSOsDevelop an understanding of the Standards for
Mathematical PracticeDevelop an understanding of the mathematical
content within the 2nd grade Next Generation Mathematics CSOsGoals
for this training.3Nxt Gen vs OtherKnowing StandardsUsing Standards
for InstructionCCSS ShiftsProcessesStrategiesKnowing and
understanding the standards are the base for your
instruction.4Visible ThinkingTeachers explain their thinking out
loud.Students orally articulate their thinking.Students listen to
other students articulate their thinking.Students engage in
discussion while forming their understanding.
Visible Thinking in the K-8 Mathematics ClassroomHull, Balka
MilesVisible thinking leads to deeper understanding.5Whats in the
Bank?Determine all possible combinations of coins for your piggy
bank. Provide justification for your solution. How do you know that
you have found all possible combinations?
Using the charts near your table, complete this activity. Show
your thinking and work on the chart.6Setting the StageTeachers need
to become students of the standards with his or her collaborative
team.
the standards define what students are expected to know and be
able to do, not how teachers should teach. CCSS authorsWhat is your
reaction to this?7Paradigm Shift in Professional DevelopmentHow
much mathematics a first grade in the United States learns, and how
deeply he or she learns it, in many schools is largely determined
by the students school and, even more directly, the first-grade
teacher to whom the student is assigned. Sometimes, the
inconsistencies teachers develop in their isolated practice can
create gaps in curriculum content with consequent inequities in
students instructional experiences and learning (Kanold, 206)Share
your thoughts on this quote and those on the next 3 slides.8One of
the characteristics of high-performing elementary schools that are
successfully closing the achievement gap is their focus on teacher
collaboration as a key to improving instruction and reaching all
students. (Education Trust, 2005; Kersaint, 2007)9The worlds
highest-performing countries in mathematics or sustained
educational improversSingapore, Hong Kong SAR, South Korea, Chinese
Taipei, and Japanallow significant time for elementary school
mathematics teachers to collaborate and learn from one another.
(Mourshed, Chijioke, & Barber, 2010)10In our schools, we
prioritize teacher development over curriculum development. You do
not make teachers better by handing them a packaged curriculum and
sending them to a few days of training. Instead, teachers need time
to analyze the standards, practice different teaching strategies,
learn from mentors, collaborate with colleagues, observe one
another, look at student work together, reflect on why certain
approaches work better than others, learn from mistakes and
continually improve. None of this is fast or easy, But it is how
teachers become great. Deborah Kenny founder of Harlem Village
Academies11The Structure is the StandardsPhil Daro, Bill McCallum,
Jason Zimba1 thing you learned1 question you have1 reaction to what
youve read
After reading the article share your thoughts.12Next Generation
Content Standards and Objectives for Mathematics in West Virginia
Schools
Standards for Mathematical PracticeContent Standards and
ObjectivesLook at a copy of the grade 2 NextGen standards. There
are 2 sections for each grade.13Standards for Mathematical
PracticeMake 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.
Mathematical StandardsThese are the same for every
grade.14Standards for Mathematical PracticeRead and study resources
related to your assigned Standard for Mathematical Practice.What is
the intent of the Mathematical Practice?What teacher actions
facilitate this Mathematical Practice?What evidence is there that
students are demonstrating this Mathematical Practice?Create a
poster illustrating the key elements of the Standard for
Mathematical Practice.Connect SMP to Whats in the Bank? task. (Be
ready to share evidence.)Be ready to share.
Use handouts for this activity. Work with your group. Be ready
to share.
15
Ashlee Beatty- [email protected] Judi Hamrick
[email protected] Sonah Smith- [email protected]
Presenters for this training. 16Ashlee Beatty Wood County
SchoolsJudi Hamrick- Tyler County Schools Sonah Smith- Wirt County
Schools Next Generation Standards 2nd grade mathematics Day 2
From Memory = Memorize Session 217GoalsDevelop an understanding
of the structure of the Next Generation CSOsDevelop an
understanding of the Standards for Mathematical PracticeDevelop an
understanding of the mathematical content within the 2nd grade Next
Generation Mathematics CSOsGoals for this training.18The Structure
is the standards
Next Generation Content Standards and Objectives for Mathematics
in West Virginia SchoolsCounting and CardinalityOperations &
Algebraic ThinkingNumbers & Operations Base TenNumber &
Operations FractionsGeometryMeasurement & Data5 different areas
of content standards for grades K-820Transition from 21st Century
Standards to Next Generation Mathematics
StandardsFOCUSFOCUSFOCUSCoherenceRigorConceptual
UnderstandingProcedural Skill and Fluency.ApplicationDeeper
understanding.21KnowledgeSkillsConceptual UnderstandingThree areas
work together.22Job #1 for K-5 MathematicsComing to a Stronger
Understanding of Number and OperationsFour Standards Focus on
Number and OperationsCounting & CardinalityOperations &
Algebraic ThinkingNumbers and Operations-Base TenNumber and
Operation-Fractions
23Next Generation Standards
ProgressionPre-KK12345678HSNumber-Counting &
CardinalityCounting & CardinalityNumber and Operations in Base
TenRatios and Proportional RelationshipsNumber & QuantityNumber
and Operations FractionsThe Number SystemNumber-Operations and the
Problems they SolveOperations and Algebraic ThinkingExpressions and
EquationsAlgebraFunctionsFunctionsGeometryGeometryGeometryMeasurement
& DataMeasurement and DataStatistics and ProbabilityStatistics
& ProbabilityGrades K-HS progression of math objectives.24
-> four areas for grade 2-> math practices for every
grade25
Standard listed and clusters for each standard.26Digging deeper
in the standards27Create an irregular shape on the top half of the
chart paper.Use chart paper and work with your group.28Whats the
Area?Use available materials to determine the area of your shape.
Justify your solution.Work with your group to find area using non
standard materials.29
Thinking is a requirement for learning mathematics.Visible
Thinking in MathematicsWhat is thinking?Think aloud with your group
to answer the question.30Next Generation Common Core StandardsRead
and study resources related to Operations and Algebraic Thinking
and Measurement and DataWhat are the grade level priorities related
to OA and MD?Which Objectives in the Cluster Are Familiar?What is
New or Challenging in these Objectives?On what topics do I need
more knowledge?Complete the Analysis Tool for OA and MD.Be ready to
share:1 Ah Ha !1 Oh No !Connect the standards to the Whats the
Area? & the Piggy Bank task. Be ready to share evidence that
supports the standards.Use handouts to read about these standards
and clusters.31What is fluency?Discuss with your group.32Fluency:
Simply Fast and Accurate? I Think Not!Individually read this
article.
As a group, develop a definition of FLUENCY.Provide examples and
non-examples for strategies to develop mathematical fluency of
young students.Work with your group.33Rigor-ApplicationStudent use
appropriate concepts and procedures for applicationProvide
opportunities for students to apply math concepts in real world
situationsOutside of math students are using grade
level-appropriate math to make meaning of and access contentAdapted
from Achieve34Required Fluencies in K-6KK.OA.5Add/subtract within
511.OA.6Add subtract within 1022.OA.22.NBT.5Add/subtract within
20Add/subtract within 100 (paper &
pencil)33.OA.73.NBT.2Multiply/divide within 100Add/subtract within
1000 (paper & pencil)44.NBT.4Add/subtract within 1,000,000
(paper & pencil)55.NBT.5
Multi-digit multiplication (paper &
pencil)66.NS.26.NS.3Multi-digit division (paper &
pencil)Multi-digit decimal operations (paper & pencil)35Pathway
to FluencyFluency has a place but is not the end.36Strategies to
Develop Fluency37Teaching Basic FactsWhat to do---Ask students to
self-monitorFocus on self-improvementDrill in short time
segmentsWork on facts over timeInvolve familiesMake drill
enjoyableUse technologyEmphasize the importance of quick recall of
factsWhat NOT to do---Dont use lengthy timed testsDont use public
comparisons of masteryDont proceed through all facts all at
onceDont move to memorization to soonDont use facts as a barrier to
good mathematicsDont use fact mastery as a prerequisite for
calculator useRead and discuss.38Number Talks
Number talks are short conversations centered around
purposefully crafted computation problems.Show short clip to
explain. 39Designer FlashcardsPersonalized according to individual
student needsBased on number relationshipsRepeated practice of
targeted facts
Use handouts to find what flashcards a student needs to
practice.40
End of session 2.41Ashlee Beatty Wood County SchoolsJudi
Hamrick- Tyler County Schools Sonah Smith- Wirt County Schools Next
Generation Standards 2nd grade mathematicsDay 3
From Memory = Memorize Presenters for session 3.42GoalsDevelop
an understanding of the structure of the Next Generation
CSOsDevelop an understanding of the Standards for Mathematical
PracticeDevelop an understanding of the mathematical content within
the 2nd and 3rd grade Next Generation Mathematics CSOsGoals for
this training.43What do you see?
art-artgallery.comIzabella PavlushkoList geometry terms seen in
this painting.44Next Generation Common Core StandardsRead and study
resources related to Number and Operations Base Ten and
GeometryWhat are the grade level priorities related to NBT and
G?Which Objectives in the Cluster Are Familiar?What is New or
Challenging in these Objectives?On what topics do I need more
knowledge?Complete the Analysis Tool for NBT and G.Be ready to
share:1 Ah Ha !1 Oh No !Connect to previous student tasks.
Use handouts to read about these standards and objectives.45Now
what do you see?
art-artgallery.comIzabella PavlushkoAdd to list.46Curate a
Pinterest BoardGeometric ArtCreate a Board for Geometric ArtInclude
a minimum of 5 works of art that represent 2nd and 3rd grade
Geometry StandardsSave to be able to use again.47Suggested Use
ofWorks of ArtDisplay works of art in the morning. Use the same
piece for a period of time.EnjoyDiscuss What do you
see?Re-createCreate original works of artDisplay student original
piecesPlace copies of Works of Art in the art center.Use art for
math.48Additive/multiplicative structures49Write a short typical
addition word problem.Use post it note. Read and decide if the
variable is at the end, middle, or at the beginning.50Structure vs.
Key WordsEncourages students to ignore the meaning and structure of
the problemKey words may be misleadingProblems may not have key
wordsKey words dont work with two-step problems
Elementary and Middle School Mathematics Teaching
Developmentally
51Problem SortAdditive/Multiplicative StructuresRead each
problem.As a group decide which structure it represents.Use
handouts of questions and charts for types of problems.52Looking at
Student WorkHow Many Windows?Look at the building in the picture.
How many windows do you see in the picture? Share your mathematical
thinking.
Identify Cluster, Objectives, and Standards for Mathematical
Practice supported by this task.
Complete the task as:A student at the novice levelA student on
grade levelA student above grade levelUse handouts of student work.
Decide level of the performance using the performance
descriptors.53Looking at Student WorkEvaluate student work
samples:NoviceGrade LevelAbove Grade LevelHow will you as a
classroom teacher support students at the various levels of
understanding? What are your next steps?Use performance descriptors
as grading rubric.54What Makes a Great Math TaskRevolves around an
interesting problemIs directed at essential mathematical content as
specified in the standardsRequires examination and perseveranceBegs
for discussionBuilds student understandingWarrants a summary look
backNCSM Great Tasks for Mathematics55Mathematical Task vs. Typical
Word ProblemNon-routine problemsMay be solved individually and
collaborativelyEncourages communication among studentsMay evolve
into an entire lessonDevelops or reveals mathematical
understanding.Routine problemsPractice procedures with wordsFocuses
on getting the answer
56Typical Word Problem to Mathematical TasksLia has 13 pencils.
Thomas has 6 pencils Nate has 7. How many pencils do they have in
all?
Answer 13 + 6 + 7 = 26 pencilsLia, Thomas and Nate have 26
pencils. How many pencils could each student have?Use handouts of
word problems and rewrite them as math tasks.57
Ashlee Beatty- [email protected] Judi Hamrick
[email protected] Sonah Smith- [email protected]
58
