Understanding the Standards We Teach -- Mathematics.

Understanding the Standards We Teach -- Mathematics

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.

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

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

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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Blooms Taxonomy Creating Evaluating Analyzing Applying Understanding Remembering Handout 7

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

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?

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

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

Building Sample Activities Real-world activity that matches the cognitive and conceptual demands of the standard

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.

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

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?

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.

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

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?

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.

Reminders Goal Students who are college and career ready Resources KYAEs commitment Leadership from director Coaches Your team Tools

Understanding the Standards We Teach -- Mathematics.

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Transcript of Understanding the Standards We Teach -- Mathematics.