Understanding the Standards We Teach -- Mathematics
Slide 2
Entering Activity 1. Using a Post-it note and marker, write
your response to the following question: What does the word
standard suggest to you? Think of an example outside of education.
2. Post your notes on flip charts that best fit your
responses.
Slide 3
Understanding the Standards We Teach Developed by KYAE Source
-- Standards in Action: Innovations for Standards- Based Education.
(November 2009). Produced by U.S. Department of Education Office of
Adult and Vocational Education, MPR Associates, Inc, and Susan
Pimentel, Inc. Presented by -- Pat Marshall, Executive Director of
the Kentucky Association for Supervision & Curriculum
Development, & Connie Spencer-Ackerman, Director, Adult
Education Academy at Morehead State University Developed by KYAE
Source -- Standards in Action: Innovations for Standards- Based
Education. (November 2009). Produced by U.S. Department of
Education Office of Adult and Vocational Education, MPR Associates,
Inc, and Susan Pimentel, Inc. Presented by -- Pat Marshall,
Executive Director of the Kentucky Association for Supervision
& Curriculum Development, & Connie Spencer-Ackerman,
Director, Adult Education Academy at Morehead State University
Slide 4
AGENDAAGENDA Goals & Objectives Overview of KYAE Common
Core Standards for Mathematics Process for Unpacking the Components
of Standards Process for Building Sample Activities Unpacking
Practice Closing Activity Goals & Objectives Overview of KYAE
Common Core Standards for Mathematics Process for Unpacking the
Components of Standards Process for Building Sample Activities
Unpacking Practice Closing Activity
Slide 5
How the Four PD Units Fit Together UNIT 2 Translating Standards
into Curriculum UNIT 3 Focus on Assignments UNIT 4 Observing
Effective Teaching and Learning Practices UNIT 1 Understanding the
Standards We Teach Then revisit units to respond to indentified
professional development needs of staff. Start here and work your
way through the units.
Slide 6
Anticipated Outcomes Participants will... Become active members
of a learning community concerned with the implementation of
standards. Gain a common understanding of the challenges involved
in implementing the standards. Learn to align curriculum, texts,
and other resources to the standards. Create standards-based
instructional resources designed to engage instructors and students
with the most important ideas and skills related to the standards.
Participants will... Become active members of a learning community
concerned with the implementation of standards. Gain a common
understanding of the challenges involved in implementing the
standards. Learn to align curriculum, texts, and other resources to
the standards. Create standards-based instructional resources
designed to engage instructors and students with the most important
ideas and skills related to the standards.
Slide 7
Course Goals 1. Review the purpose of understanding the
standards and using them with students. 2. Develop a consensus with
learning community team a. To unpack the components of standards
and b. To construct real-world activities that align to assigned
standards. 3. Apply a process for unpacking the standards by
completing an unpacking chart. 4. Reflect on the unpacking process.
Course Objectives Program Directors and Instructors will be able
to... 1. Identify the purpose for using the standards with adult
education and literacy students. Activity Discuss with learning
community the skills, concepts, and level of thinking for a set of
standards; complete unpacking charts. ANGEL Discussion Board
Understand the purpose for the Kentucky Adult Education Mathematics
Common Core Standards Develop a learning community as a result of
engaging in a process to unpack the KYAE Common Core Standards
Reflect on readings by answering discussion board questions. View
introduction and read articles. Part 1A- Interim Practice with
teams at the workplace w/ coaching 15 hours With learning community
team, develop student activities and record on the unpacking chart.
1.Apply a process for unpacking the standards. 2.Develop a
consensus with learning community team on the skills, concepts,
context, and cognitive level of thinking by unpacking 50 standards.
3.Develop a consensus with learning community team on student
activities for each of the 50 standards. 4.Reflect on the unpacking
process. With learning community team, complete unpacking charts
for 53 standards. Answer discussion questions in ANGEL reflecting
on the process and outcomes of unpacking standards. Part 1A-
Face-to-Face Information, modeling, and group work 6 hours Format
Develop a learning community by implementing a process to align
program resources with the KYAE Common Core Standards Discuss with
learning community, the process and extent of alignment program
resources to standards. Apply a process for aligning 53 standards
with program resources. Develop a consensus with learning community
on the alignment of program resources to standards and complete the
alignment chart. Reflect on the resource alignment process.
Complete materials for instructional use. Complete alignment charts
aligning program resources to standards. With learning community,
complete an alignment resource chart, aligning program resources to
standards. Answer discussion questions in ANGEL reflecting on the
process and outcomes of aligning program resources to standards.
Part 1B- Interim Practice with teams at the workplace w/ coaching
15 hours Handout 1
Slide 8
Common Core State Standards Mission Statement The Common Core
State Standards provide a consistent, clear understanding of what
students are expected to learn, so teachers and parents know what
they need to do to help them. The standards are designed to be
robust and relevant to the real world, reflecting the knowledge and
skills that our young people need for success in college and
careers. With American students fully prepared for the future, our
communities will be best positioned to compete successfully in the
global economy. http://www.corestandards.org
Slide 9
About the Standards These standards define the knowledge and
skills students should have within their K-12 education careers so
that they will graduate high school able to succeed in entry-level,
credit-bearing academic college courses and in workforce training
programs. http://www.corestandards.org/about-the-standards
Slide 10
The Standards... Are aligned with college and work
expectations; Include rigorous content and application of knowledge
through high-order skills; Build upon strengths and lessons of
current state standards; Are informed by other top performing
countries, so that all students are prepared to succeed in our
global economy and society; and are evidence-based.
http://www.corestandards.org/about-the-standards
Slide 11
About the Standards The KYAE Common Core Standards and the
Kentucky Core Academic Standards (K-12) are the Common Core State
Standards. http://kyae.ky.gov/educators/contentstandards.htm
Standards for English Language Arts & Literacy in
History/Social Studies, Science and Technical Subjects Standards
for Mathematics
Slide 12
Understanding Mathematics...standards define what students
should understand and be able to do in their study of mathematics.
What does mathematical understanding look like? One hallmark the
ability to justify, in a way appropriate to the students
mathematical maturity, why a particular mathematical statement is
true or where the rule comes from
Slide 13
For example.... Please excuse my dear Aunt Sally. OR Knowing
the order of operations. terms inside parentheses or brackets
exponents and roots multiplication and division as they appear left
to right addition and subtraction as they appear left to right
Slide 14
Standards for Mathematical Practice Describe varieties of
expertise that mathematics educators at all levels should seek to
develop in their students Rest on processes and proficiencies with
longstanding importance Sources NCTM process standards National
Research Councils report, Adding It Up
Slide 15
Standards for Mathematical Practice 1. Make sense of problems
and persevere in solving them. 2. Reason abstractly and
quantitatively. 3. Construct viable arguments and critique the
reasoning of others. 4. Model with mathematics. 5. Use appropriate
tools strategically. 6. Attend to precision. 7. Look for and make
use of structure. 8. Look for and express regularity in repeated
reasoning. Handout 3
Slide 16
Connecting Standards for Practice AND for Content Practice
describes ways in which developing students increasingly ought to
engage with the subject matter Content a balanced combination of
procedure and understanding
Slide 17
Introducing the Document How to read...p. 5 Standards for
Mathematical Practices, pp. 6-8 Each grade level, for example --
Introduction, p. 21 Overview/Practices, p.22 Standards, pp.23 26
Glossary, pp. 85 - 87 Tables, pp. 88 - 90
Slide 18
How to read the grade level standards.... Domains are larger
groups of related standards. Standards from different domains may
sometimes be closely related. Clusters are groups of related
standards. Cluster titles are in bold font. Standards from
different clusters may sometimes be closely related, because
mathematics is a connected subject. Standards define what students
should understand and be able to do. Supports for the standard are
sometimes listed under the standard. Quick Reference Guide A
Slide 19
Quick Reference Guide - A How to read the standards.... Number
and Operations Fractions4.NF Build fractions from unit fractions by
applying and extending previous understandings of operations on
whole numbers. 3. Understand a fraction a/b with a >1 as a sum
of fractions 1/b. 4. Apply and extend previous understandings of
multiplication to multiply a fraction by a whole number. a.
Understand a fraction a/b as a multiple of 1/b. b. Understand a
multiple of a/b as a multiple of 1/b, and use this understanding to
multiply a fraction by a whole number. c. Solve word problems
involving multiplication of a fraction by a whole number, e.g., by
using visual fraction models and equations to represent the
problem. Grade levelDomain Cluster title Standards Support for the
standard
Slide 20
Cluster titleStandard/SupportSkills What are learners supposed
to be able to do? Concepts/Conten t What are learners supposed to
know? Through a Particular Context Where, how, or in what context
is the skill applied? Cognitive Demand/Level of Thinking What
thinking process must the learner engage in? Sample Activities
Cluster Title Build fractions from unit fractions by applying &
extending previous understandings of operations on whole numbers.
4. Apply and extend previous understandings of multiplication to
multiply a fraction by a whole number. a.Understand a fraction a/b
as a multiple of 1/b. b. Understand a multiple of a/b as a multiple
of 1/b, and use this understanding to multiply a fraction by a
whole number. c. Solve word problems involving multiplication of a
fraction by a whole number, e.g., by using visual fraction models
and equations to represent the problem. Domain & Grade Level --
Numbers & Operations Fractions4.NF
Slide 21
DOMAINS of MATHEMATICS STANDARDS K-8 K12345678 Counting &
cardinality (CC)X Operations and algebraic thinking (OA)XXXXXX
Numbers and operations in base ten (NBT)XXXXX Numbers &
operations fractions (NF)XXX Measurement and Data (MD)XXXXXX Ratio
& proportional relationships (RP)XX The number system (NS)XXX
Expressions & equations (EE)XXX Functions (F)X Geometry
(G)XXXXXXXXX Statistics & probability (SP)XXX Quick Reference
Guide B
Slide 22
Mathematics Standards for High School Specify the mathematics
that all students should study to be college and career ready (+)
Mathematics that students should learn in order to take advanced
courses such as calculus, advanced statistics Without (+), should
be in common mathematics curriculum for all college & career
ready students
Slide 23
Mathematics Standards for High School Organized in conceptual
categories rather than domains across grade levels 1. Number &
quantity p.58 2. Algebra p.62 3. Functions p.67 4. Modeling p.72 5.
Geometry p. 74 6. Statistics & probability p.79 Handout 4
Slide 24
Unpacking Components of the Standards Chart -- resource that
unpacks each standard into its component parts Skills
Concepts/Content Context Cognitive Demands or Level of Thinking
Chart -- resource that unpacks each standard into its component
parts Skills Concepts/Content Context Cognitive Demands or Level of
Thinking Handout 5
Slide 25
1 Standard 2 Skills Included in the Standard 3 Concepts
Included in the Standard 4 Through a Particular Context 5 Cognitive
Demand/ Levels of Thinking 6 Sample Activity List the standards
here - one per row. Indicate what learners are expected to do to
demonstrate mastery of the concepts and content. Skills are
represented by the verbs in the standard. If multiple skills are
included, align the concepts with the skills to which they apply.
This is unnecessary if the skills listed apply equally to all
concepts. Ask what learners are supposed to be able to do. Indicate
the information or ideas that learners need to know. The concepts
are generally represented by the nouns or noun phrases in the
standard. Ask what learners are supposed to know. Indicate in which
context learners are required to use the standards skills and
concepts, e.g., writing an essay, solving a problem. Not every
standard will have a stated context. Context can be represented by
words or phrases that come before and after a particular word or
phrase that help explain the full meaning. It is the framework,
perspective, or environment. Ask where, how, or in what context the
skill is to be applied. Indicate the level of thinking required to
meet the standard, using the selected taxonomy and considering all
the information in columns 2-4. The cognitive demand is the level
of thinking required if learners are to demonstrate the skill and
concept within the context described. Ask what thinking process the
learner must engage in. Add a teaching activity that encompasses
the concepts and skills of this standard and is pitched at the
right level of cognitive demand. Handout 6
The Unpacking Process (Modeling & Guided Practice) 1.Review
each standard/support in column 1 to identify the skill(s)
addressed in the standard, and record the skill(s) in column 2.
2.Identify the content or concepts related to each skill contained
within each standard, and record in column 3. 3.Identify the
context in column 4. 4.Use the selected taxonomy to identify the
level of thinking/cognitive demand, and record in column 5. Handout
8
Slide 28
Confirming Unpacking Cover the standards or supports in column
1. Do the phrases listed in subsequent columns describe the
standard? Do the unpacked content, skills, and context contain only
words actually appearing in the standards? Is each unpacked skill
linked to the appropriate unpacked content or concept? As you read
the content and skills, do they represent what you would really
expect of a student in meeting this level?
Slide 29
Why Unpack the Standards? Helps staff address how to: Maintain
focus on teaching the right content and skills Teach to the
appropriate level of complexity Plan aligned curriculum/assessments
Support shared professional learning Support common expectations
for students FTPSS Helps staff address how to: Maintain focus on
teaching the right content and skills Teach to the appropriate
level of complexity Plan aligned curriculum/assessments Support
shared professional learning Support common expectations for
students FTPSS
Slide 30
Entering Activity Go to the graph posted on the wall and place
a Post-it Note with your name on all lines with a statement that is
true for you, for example: I teach math only.Cindy, Tim, Diane,
Donna, Jennifer I teach math and other subjects.Nancy, Becky,
Marti, Peggy, Patty I have participated in math PD in the past 2
years.Cindy, Nancy, Diane, Marti, Jennifer I have not participated
in math PD in the past 2 years.Tim, Donna, Becky, Peggy, Patty I
teach math only and have participated in math PD in the past 2
years. Cindy, Diane, Jennifer
Slide 31
Building Sample Activities Real-world activity that matches the
cognitive and conceptual demands of the standard
Slide 32
Why Build Sample Activities? To show how a particular standard
can be addressed in the classroom and to Target instruction to the
right level of complexity. Help instructors design lessons for
students. Articulate the demands across levels and clarify
expectations. Support shared professional learning and common
expectations for students. To show how a particular standard can be
addressed in the classroom and to Target instruction to the right
level of complexity. Help instructors design lessons for students.
Articulate the demands across levels and clarify expectations.
Support shared professional learning and common expectations for
students.
Slide 33
Building Sample Activities Criteria Build sample activities
tied to specific standards that -- Describe a relevant real-life
activity. Attract and hold student interest. Reflect the right
level of complexity given the cognitive demand of the standard.
Result in an end-product that is meaningful to students. Make
connections to other standards, as appropriate. Match the unpacked
standard in terms in cognitive demand. All in a few
sentences.......... (SIA Guide Unit 1-12) Build sample activities
tied to specific standards that -- Describe a relevant real-life
activity. Attract and hold student interest. Reflect the right
level of complexity given the cognitive demand of the standard.
Result in an end-product that is meaningful to students. Make
connections to other standards, as appropriate. Match the unpacked
standard in terms in cognitive demand. All in a few
sentences.......... (SIA Guide Unit 1-12) Handouts 8
Slide 34
Sample Activities -- Examples 3.MD.3 Draw a scaled picture
graph & a scaled bar graph to represent a data set with several
categories. 5.NBT.4 Use place value understanding to round decimals
to any place. 5.MD.3.3 Recognize volume as an attribute of solid
figures & understand concepts of volume measurement. Have
students create scaled graphs (picture & bar) by polling their
classmates (favorite color, number of pets, etc.) Then discuss
questions such as, Who has the greatest # of pets? How many more
like red than blue? Given a list of grocery items in dollars &
cents, estimate cost to the nearest dollar. Design a cereal box w/3
different sizes: super, regular, & mini. Calculate volume &
label dimensions. Which box do you think would be the best seller
in your local market? Why?
Slide 35
Sample Activities -- Examples 5.G.1 Use a pair of perpendicular
number lines, axes, to define a coordinate system, with the
intersection of the lines arranged to coincide w/0 on each line
& a given point in the plane located by using an ordered pair
of numbers, called coordinates. 6.G.1 Find the area of right
triangles, other triangles, special quadrilaterals, & polygons
by composing into rectangles or decomposing into triangles &
other shapes; apply these techniques in the content of solving
real-world & mathematical problems. Use a map with a grid to
determine best location for a new school building. Determine
coordinates within the map. Justify your reasoning for the school
location. Locate proximity of other buildings using coordinate
values. Using a floor plan, with shapes included in the concepts,
using composing & decomposing to determine amounts of floors,
ceiling material, etc.
Slide 36
Independent Practice Using Your Assigned Standards Review team
guidelines. Review unpacking process. Complete skills, content,
context, & cognitive demand. Confirm unpacking. Develop sample
activities. Check against criteria. Review team guidelines. Review
unpacking process. Complete skills, content, context, &
cognitive demand. Confirm unpacking. Develop sample activities.
Check against criteria. Handout 8
Slide 37
Reflections What was beneficial about the unpacking exercise?
Challenging? What was beneficial about the building sample
activities exercise? Challenging? What was beneficial about the
unpacking exercise? Challenging? What was beneficial about the
building sample activities exercise? Challenging?
Slide 38
Next Steps Implement plan. Meet as a team to unpack. Complete
charts electronically. Post on ANGEL or send to coach on a weekly
basis. Coach will review and provide feedback. Consult with coach.
Complete final posting 2 days prior to next face-to- face
session.
Slide 39
Reminders Goal Students who are college and career ready
Resources KYAEs commitment Leadership from director Coaches Your
team Tools