Deeper Investigations of the Standards: Iowa Core Mathematics Grades 6 8, Day 2 Iowa Department of Education In Partnership with AEA School Improvement Welcome from your feedback last time Things you never hear about Reading and
Writing.. OMJ Iowa Core Mathematics Journal Think About Our Last Session What have we done so far? First Turn, Last Turn
Read your journal entries from the last meeting One person in the group reads one big idea from his/her journal In round-robin fashion, everyone can comment on that idea, with the originator having the last turn Repeat around the table OMJ
Learning Goals for Deeper Investigations Professional Development Understand that the structures of the Iowa Core Mathematics are meant to support focus and coherence Understand that fluency, deep understanding, application and dual intensity support rigor Understand how to investigate the Iowa Core Mathematics
Success Criteria OMJ 1. I can describe 6 of the standards for mathematical practice. 2. I can connect the critical areas for my grade level to the specific standards at my grade level. 3. I can explain the big ideas of content within the domains/conceptual categories at my grade level. 4. I can describe mathematical understanding by explaining how teacher questioning supports it.
5. I can describe how Iowa Core Mathematics provides a structure to change teaching and learning. Recall your personal learning goals written in your journal Supporting Rich Mathematical Tasks Intent of the standards A curriculum is more
than a collection of activities: It must be coherent, focused on important mathematics and well articulated across the grades. Dilemma A Task
Is it a Rich Mathematical Task? Rich mathematical tasks: Emphasize connections across mathematical content areas, to other disciplines, and especially to the real world Are accessible yet challenging to all Can be solved in several ways Encourage student engagement and communication Encourage the use of connected multiple representations Encourage the appropriate use of intellectual, physical, and technological tools
Not all tasks are created equal, and different tasks will provoke different levels and kinds of student thinking. Stein, Smith, Henningsen, & Silver, 2000 Where does this fit within a unit? By teaching through rich mathematical tasks, students develop deep conceptual understanding and skill proficiency. Why is it important to let students work on a math task without first showing them how to solve it?
http://ifl.lrdc.pitt.edu/ifl/index.php/resource s/ask_the_educator/ido_jamar/ How does the task connect with the Standards for Mathematical Practice? Standards for Mathematical Practice 1. Make sense of problems and persevere in 2. 3. 4. 5.
6. 7. 8. solving them Reason abstractly and quantitatively Construct viable arguments & 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 2011 Cooperative Educational Service Agency (CESA) 7 School Improvement Services Permission is granted to the Iowa State Department of Education for dissemination and use in any whole or part in any form within the state of Iowa region. 17 Think-Pair-Share At your table, half of people will read Mathematical Practice 6, the other
people will read Mathematical Practice 7 1. Those reading the same Practice will discuss the big ideas from the reading 2. Those reading the same Practice will
discuss connections to the problem 3. The whole table will share their 18 findings How can you scaffold understanding with questions? After having engaged in the task, write questions to use Before, During and After students engage in the task. In practice, students actual opportunities for learning
depend, to a considerable degree, on the kind of discourse that the teacher orchestrates. The nature of the activity and talk in the classroom shapes each students opportunities to learn about particular topics as well as to develop her or his abilities to reason and communicate about those topics. -Henningsen & Stein, 1997 An Example http://www.pd360.c om/index.cfm?Conte ntId=6114
20 Whats the elephant in the room? What are you wonderin
g about implemen tation of what weve been Poll Everywhere Check To what degree do you feel able to describe 6 of the Standards for Mathematical Practice?
http://www.polleverywhere.com/mul tiple_choice_polls/MjAyMTk5ODQxNQ Poll Everywhere Check To what degree are you able to describe the role of teacher questioning in building mathematical understanding? http://www.polleverywhere.com/mul tiple_choice_polls/MTk3ODM2Mjc2N w
Your turn Choose standards which are connected in your curriculum Determine the intent of the standards Find task(s) Judge whether it is a rich task Link to Standards for Mathematical Practices Create questions that help to foster deep understanding Resources to use
Finding Tasks: www.nctm.org http://illustrativemathematics.org/ http://insidemathematics.org/ http://nctm.illuminations.org/ http://www.smarterbalanced.org/ Google the standard notation you are interested in (ex. 8.NS.2) K-12 Domains
Counting & Cardinalit y Standards for Mathematical Practice Number & Operations in Base 10 The Number System
Operations & Algebraic Thinking Expressions & Equations Ratios & Proportiona l Relationshi ps Measurement & Data
Algebra Functions Modeling Number Operations Fractions Number & Quantity
Statistics & Probability Geometry 2011 Cooperative Educational Service Agency (CESA) 7 School Improvement Services 26 26 Permission is granted to the Iowa State Department of Education for dissemination and use in any whole or part in any form within the state of Iowa Functions Input 9
14 53 n Outpu t 11 Add 2 16 55 n+2
Finding Priorities through Critical Areas 1. Highlight the words or phrases in the standards which represent the important mathematics 2. Turn to the standards and highlight the standards which support this Critical Area (You will do this activity multiple times to learn about each Critical Area, using a different color of highlighting
for each one) A Task Example Comparing Linear Functions http://www.insidemathematics.org/index.php /classroom-video-visits/public-lessons-compa ring-linear-functions/269-comparing-linear-fu nctions-problem-2-part-a? Vertical Connections between Grades Grade 6 , 7 & 8
Connection s to E&E Grade 8 HS connections to the functions domain Connections between the Domains If we think of the domains as
being like rails, then we also have to be able to see the ties or Big Ideas "that bind the 31 Poll Everywhere Check To what degree do you feel confident with the content of the Functions domain? http://www.polleverywhere.com/m ultiple_choice_polls/NDQ4MDE5NT
kx 32 Algebra I 8th grade looks a lot like Algebra I, so what is Algebra I now? Iowa Core Mathematics Transition for Algebra I Traditional Curriculum in Iowa 7th Grade
Grade 8th Grade Algebra 1 Geometry Algebra 2 Iowa Core Mathematics Transition for Algebra I
New Stand ards Algebra 1 7th Grade Geometry
8th Grade Algebra 2 Algebra 1 Statistics Probability PreCalculus
Geometry Algebra 2 Iowa Core Algebra 1 New Standards Statistics/Probability Traditional Algebra 1 Algebra 2
Algebra 1 Iowa Core Standards The Number System Finding Priorities through Critical Areas 1. Highlight the words or phrases in the standards which represent the important mathematics
2. Turn to the standards and highlight the standards which support this Critical Area (You will do this activity multiple times to learn about each Critical Area, using a different color of highlighting for each one) 38 Lets See a Task
https://www.teachingchannel.org/ videos/teaching-subtracting-integ ers Zero Pairs Vertical Connections between Grades Grade 6 Grade 7 Grade 8
40 Journaling Were there instances of many standards funneling into one? Explain. Where there instances of one standard being the launching point for many? Explain. Were there culminating standards? What does this mean?
41 Poll Everywhere Check To what degree do you feel confident with the content of the Number System domain? http://www.polleverywhere. com/multiple_choice_polls/ LTE0ODQzMDYyOQ Poll Everywhere Check
To what degree do you feel able to describe how Iowa Core Mathematics Standards provide a structure to change teaching and learning? http://www.polleverywhere.com/m ultiple_choice_polls/MjA1NzQ0Nz Learning Goals for Deeper Investigations Professional Development Understand that the structure of the Iowa
Core Mathematics are meant to support focus and coherence Understand that fluency, deep understanding, application and dual intensity support rigor Understand how to investigate the Iowa Core Mathematics Success Criteria 1. I can describe 6 of the standards for mathematical practice. 2. I can connect the critical areas for my grade level to the specific standards at my grade level.
3. I can explain the big ideas of content within the domains/conceptual categories at my grade level. 4. I can describe mathematical understanding by explaining how teacher questioning supports it. 5. I can describe how Iowa Core Mathematics provides a structure to change teaching and learning. Give us feedback about your learning 3 Things you learned today 2 Things you will use
1 Question you still have What are the actions I need to take to improve my implementation of the Iowa Core? Are there things you need to learn? Are there things you need to ask for others to be a part
of? Are there resources you need to find? 47 Feedback Survey http://survey.a ea.k12.ia.us/f/ 94656/ac2a/ See you soon
Thanks so much for your participation! Bring your journal and your copy of the Iowa Core Mathematics next time!
Resource sharing (digital/network technologies) Cooperative collection management (resource allocation) Shift in focus to resources of the "system" (or subsets of the system), rather than individual collections Need data to support/illuminate system-wide perspective Characterize/analyze aggregate collections WorldCat: largest aggregate ...
APTC's Key Limitations 'Enclave' Operations. APTC has operated as an enclave in some countries, not integrated into Pacific TVET - complex underlying political, strategic and operational reasons why this is the case
Saving Norfolk's Wildlife for the Future. After your visit, you'll know more about different habitats and what lives in them. Photo: Elizabeth Dack. We'll find plenty of plants and animals too, but it's important to remember that they're all wild...
Simon Fraser University 2010-1 This course will focus on the stories that the people of the classical world told to entertain each other, to explain the nature of their world and its institutions, to reflect on current challenges, and to...
Leonardo of Pisa (1170-1240) Financial engineer; analyzed business problems. Brought Arabic Number system to the West. Liber Abaci (1202) Tools to calculate present value, compound interest, geometric series… Rabbit problem. First western appearance of Fibonacci sequence
Part of the P-Network and interfaces to CE routers P router Provider (core) router, without knowledge of VPN Terminology (cont'd) Route Distinguisher Attributes of each route used to uniquely identify prefixes among VPNs (64 bits) VPN-IPv4 addresses Address including the...
Online referrals. Due to a proliferation in online gambling opportunities (Gainsbury, 2015) including media and sometimes, aggressive and personally targeted advertising, the online contexts of many at-risk and problem gamblers are currently in strong support of continued gambling.. Effective treatments...
is a collection of shared values and beliefs that are reflected as "acceptable" behaviour by a specific group of people. Culture comprises of: core beliefs and values . which are passed on from parents to children and are reinforced by...
Ready to download the document? Go ahead and hit continue!