This training is meant for principals and assistant principals. It offers an overview of the Common Core State standards and NC Essential Standards (but does not walk through the standards in detail). It focuses on administrative and management processes and activities that principals need to undertake, in order to ensure successful implementation of the new standards in your schools. Important NOTE: We’ve heard some people ask if the adoption of these new standards means the Standard Course of Study has gone away. The answer is that the Common Core and Essential Standards ARE the new Standards
Talk about the difference between “adoption” and “implementation” here. Look at the picture. How does this illustrate adoption versus implementation ? Think about having electricity in your house (adoption) versus actually plugging in electric appliances-- using (or implementing) electricity in your house.
Today, with the Common Core, every principal has to be an instructional leader. You must be skilled and knowledgeable enough about the standards to be able to recognize if your teachers are actually teaching the standards and are teaching them at a level that is aligned with requirements. We have had standards for years. Yet many of us have visited classrooms and have seen instruction that has not looked much like what was required. And there has been fallout from that: low test scores Students unprepared for college and university Under-skilled workforce If we adopt the new standards but then don’t actually implement them-- teach them and bring them to students at a level that is aligned with the requirements-- then we will not have accomplished anything. We will have failed the students. Principals, in many ways, are everyone’s eyes and ears in this-- the failsafe– to ensure the standards are implemented correctly in classrooms.
SS- Concept—we have always taught events/ TOPICS—now we will teach based on concepts for example “change” Philanthrophy ELA: Text Complexity, scaffolding vs graffling will still scaffold knowledge Remember those television ads from the 70’s-80’s? “Do you know where your children are?” This is a take off on that. Reiterate again: Principals are responsible for ensuring that teachers teach the standards. “Do you know where your teachers are (in the curriculum)?” Are your students learning content and acquiring skills at the level they will need-- and in the manner they require-- to be successful? On standardized tests At the next grade level In college In the workplace
So how are we going to get there? First of all, the Common Core and Essential Standards are for every student-- Mac computer users probably recognize the “Universal Access” symbol. It is used for tools that make the technology accessible to people who are impaired or disabled in some way. On your iPhone a person with limited sight can make the screen size huge, for example. Universal access to the curriculum is a requirement of the Common Core and Essential Standards. Everyone must have access, at all grade levels. Ensuring this is another responsibility that principals must take on. “ Fully operationalized” truly means “universal access.”
Not developed with high school graduation as an end, but rather with college and work requirements in mind. You will notice a new clarity and focus that was missing from previous standards. Not a lot of meaningless verbiage. The rigor is greatly increased, and in many cases is pushed down into earlier grades. Also, questioning and use of “higher order thinking skills” is not just receiving lip service here. It is real. Standards are much more aligned with what other leading education countries are requiring of their students. Makes our students more competitive and better able to function globally. The standards are the result of some of our best thinking in education today, and are research-based and proven. The Common Core is not an educational experiment.
Features of the Common Core that make up the Rationale for Implementation: Equity – Students from poor communities get the same content and instruction that students from wealthy (better resourced) communities get. All are expected to meet (and are supported in meeting) the same high standards. Readiness –The standard for proficiency is raised to actually mean proficient. The new proficient means proficient for college and skilled/professional work. Not simply something that is “enough” to get you out of high school. Comparability – Higher passing rates due to dumbing down/easier tests (from some states) goes away. Common standards mean common assessments across states. Gives us useful data for comparison purposes, and a common baseline for gauging student achievement.
Shared Resources – Imagine partnering with teachers across the state and the country, finding teachers who are working with a similar demographic group of children to your own, and being more successful with them. Not only can you share physical resources, but you can share ideas and partner with other educators on the same curriculum. Economies of Scale – May be possible to cut down on costs due to larger numbers using same materials. Student Mobility – Students coming into school during the year are up to speed, familiar with material. Students leaving are better able to integrate into new school programs-- across the state or even in other states.
Let’s look at some specifics about Common Core Math and ELA. Math first: Number Core – Learning how numbers correspond to quantities, and learning how to put numbers together and take them apart (early addition and subtraction work). K-5 - Solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions, decimals. Readiness for more advanced concepts & procedures, and moving into math applications/modeling later. Continuous Progression - Guidance for teachers on how to navigate successfully through fractions, negative numbers, geometry-- in a continuous progression through the grades. Procedural skills + Conceptual Understanding – Stresses critical information and skills needed to access concepts and succeed at higher levels (rather than just master material for the current level test).
Robust middle school – k-5 foundation prepares students for hands-on learning in geometry and complex, hard, “messy problem solving” in middle school. 7 th grade math prepares students well for 8 th grade algebra . Middle school standards overall prepare students for significantly more advanced (and a different kind of) mathematics in high school (than what we have mostly seen previously).
High school standards call on students to actually use mathematics – do applied mathematics and modeling. Students are prepared to think and reason mathematically, solving real world problems. The high school standards set a rigorous definition of college and career readiness. There is a new depth of mathematical understanding represented in the Common Core Standards. Math is integrated w/other disciplines. Its use is much more relevant and realistic.
“ Staircase” takes students right up to the demands of college and career-level reading-- full preparation by the end of high school. The standards also require the progressive development of reading comprehension so that students advancing through the grades are able to gain more from whatever they read. Reading instruction, strictly speaking, does not cease in elementary school. The standards require ongoing instruction in a variety of text types, right up through high school. There is no strict “Reading List.” Instead sample texts give teachers, students, and parents an idea of the range and complexity of what is required. Teachers, administrators, and school districts decide on the appropriate specific readings and literature content for classes at each grade level.. The standards DO mandate certain critical Types of reading content as part of English Language Arts-- These include: Classic myths Stories from around the world Foundational US documents Seminal works of American Literature (Continue notes on next page) The writings of Shakespeare As well as more general informational texts Sample texts also help teachers know (and prepare students for) what will be required at the next grade level. In sum, the Common Core standards are about reading for a variety of purposes on a large range of subjects. And through reading, students required to: Build and acquire knowledge Gain new insights – stretch intellectually Explore possibilities – dream even! Broaden perspective – get beyond their current world
Writing: The standards teach students to write logical arguments based on Substantive claims Sound reasoning Relevant evidence Opinion writing– a basic form of argument– extends down into the earliest grades (k-1) Research writing – Both short focused projects (resembling workplace writing) and longer in-depth research, are emphasized throughout the standards. Written analysis and presentation of findings are important features of Common Core work– in ELA AND integrated into other subject areas. Annotated samples of student writing accompany the standards and help establish adequate performance levels in writing arguments, informational/explanatory writing, and narriaives in the various grades. These illustrate for teachers, students, and parents, what the expectations are. Speaking & Listening: Standards require students to acquire and gain (listening skills), evaluate & present (speaking skills) increasingly complex information, ideas and evidence-- Listening, public speaking and media skills are emphasized. An important focus of speaking and listening standards is academic discussion in one-on-one, small group, and whole-class settings. Both formal and informal talks and discussions are featured. Collaboration and team problem solving-- through speaking and listening are core pieces of these standards. Language: Grow vocabulary through a mix of conversation, direct vocabulary instruction, and reading. Emphasis on determining word meanings, nuances of words, and expanding repertoire of words and phrases students commonly use in their speaking in writing. Familiarize and make students comfortable and confident using formal English in wiring and speaking. Vocabulary and English language conventions have their own strand-- but not because these skills are meant to be taught in isolation. Rather their use is integrated and extends across all reading, writing, speaking, and listening standards. Media & Technology Critical analysis and production of media are integrated throughout the standards
The idea of “readiness” is that students will be prepared and ready to enter a grade level, and will leave each grade level prepared and ready for the next. Readiness is not just for kindergarten, middle school, and high school and college now. Readiness is a key for advancement to every grade. And readiness definitely extends beyond high school graduation! What this means for teachers is that they MUST be very clear about the standards that come before and after their own grade level. Grade levels cannot operate in isolation with these standards. *** This has extremely important implications for principals – Principals will be responsible for ensuring that teachers engage in the critical conversations and collaboration they need to have in order to address the realities of “readiness.” This will be true both within the school building, and beyond, with teachers from feeder and receiving schools. Articulation and scaffolding has never been more important than now, with the Common Core. 21 st Century Skills are things like: (NOTES continue on next page) Critical analysis (of sources and resources, arguments, tools, media and information, etc.) Effective functioning and performance as a member of a team, as well as the ability to work effectively alone “ Messy” problem solving Creative, efficient, and effective use of the most appropriate technology tools Wide cultural and social (and geographic and language) awareness Extremely strong communications skills
So what is the principal’s role and responsibility in supporting this quite significant change to new Common Core? It starts with the principal understanding the new standards-- and understanding how they are different ( AND SIMILAR) how they look different how they are taught differently How they require different things from students and teachers Than the standards we have used previously.
In the past a principal might have been just somewhat familiar with the standards in a particular grade or subject area that they taught before becoming a principal. Often the principal did not have a core academic teaching background. They might have been a band director or an Athletic Director, PE teacher and coach before becoming a principal. They may not have been comfortable with a particular subject like math or English if they were say, a social studies teacher. These are just examples, as principals come from all corners of the educational landscape. All of these subject area anxieties and discomforts are still out there, but the landscape of requirements for the principal has changed significantly. The new standards require a sea change of thinking in what the role of the principal is, with regards to curriculum. There is no getting around the principal as a true Instructional Leader-- which means sitting down and becoming at familiar with the new standards. You have to read them, refer to them, participate in teacher discussions, do the online modules, be present and involved in the trainings. Really teach yourself about the ways that they are the same and different from current standards, and how they need to be implemented and taught.
(Try to infuse this with some humor, if possible!)
Preparing for Implementation: Part of your role is to help teachers internalize the belief that the Common Core and Essential Standards will bring life-long benefits for students . The tone of your leadership will (or will not) inspire enthusiasm for this (hard) work. So part of your job is ensuring that “buy-in” on the part of staff. Help get them sold on the very real benefits of the new standards and a new way of teaching. The principal needs to manage and structure the workplace in a way that allows for-- requires even– collaboration opportunities for staff. You can’t do this kind of integrated curriculum work without PLC meeting & collaboration time. On way of reducing teacher anxiety, and being more efficient with the new standards roll out is to help teachers find common ground between the new standards and the old standards they’ve been teaching. Our Crosswalk documents are vital for this. But more than that, the principal (and lead teachers and curriculum coaches) need to point out that even where the content is similar, the instructional strategies required may be very different. The principal needs to participate in these important discussions about instruction-- not just content. Help teachers build on what they already know. One of the most significant innovations in the new standards is the explicit inclusion of informational writing in many different subject areas . Not just in English, but in science, and social studies, etc. This is backed by more than a decade of research supporting the strong relationship between nonfiction writing and improved student achievement. Yet in the past, the consistent use of nonfiction writing across the curriculum has been the exception rather than the rule. In order to successfully implement the new standards, schools must make a substantial commitment to increasing informational writing at every grade level, starting in kindergarten . Nonfiction writing can be fun and engaging for students to learn and for teachers to teach. Every teacher in every subject is responsible for helping students think critically, and writing is one of the very best ways to master that skill. We are all teachers of writing in the 21 st century! Principals need to be the leader on this in their buildings, and help even the most reluctant staff members learn their roles and responsibilities with respect to writing instruction. With so much curriculum material coming their way, teachers (and principals) are very likely to feel overwhelmed. Help guide your teachers toward collaboration to identify the most important standards-- sometimes called “power standards” that have the greatest impact on student learning. Figure out how you will need to reallocate the limited resources (both material and human) that you have at your disposal, to keep this complex curriculum work underway throughout the year. Perhaps you need to rethink the role of department head in your building. You may need to institute a schedule of peer observations, so teachers can help teachers with new types of instruction. How will you fit PLC meeting time into the regular school day? You can’t do all of this alone. Who will serve on your school’s Implementation Leadership Team? Common Formative Assessments– a key to this work-- cannot happen and cannot be used effectively unless teachers are given PLC time to create, compare, look at data, and share ideas. Help teachers understand that the standards are a floor not a ceiling . Using standards should not result in the standardization of teaching and learning. One of the most empowering activities you can bring your teachers is to ask them to create a continuum of learning activities that includes the standards requirements and creates opportunities to exceed them. Give teachers back their creativity! Defeat the notion that the use of standards must lead to boring classrooms.
Repeating some key specifics: Think and plan carefully around your Department Heads and Lead Teachers. If their role has been mostly administrative previously (inventory and book ordering and scheduling assistance) now is the time to rethink that and think about the skills of the staff members who are performing in these roles. Also think about reducing other duties (gate duty or homeroom duty, for example) and the teaching load that these staff members carry. Curriculum and implementation need to be their primary focus now. PLCs must happen on a regular basis (at least weekly) in your buildings, preferably during the regular school day. This has to be a priority. And if your teachers have not had some kind of PLC training and do not know how to effectively participate in a PLC meeting, then you need to think about getting them some training in that now. And principals will need to observe and participate in these PLC meetings on a regular basis. Both #1 and #2 lead us to #3-- The principal has to share decision-making and leadership in this new environment. That may be a new way of thinking and operating for some of you, but the reality is, there is too much to be done, and we need the best collaborative thinking of many people in order to be successful in this implementation.
These two questions, I believe, are probably at the root of most principal’s anxiety and concern about their role relative to the new standards. That whole notion of, “ What am I looking for when I walk in the classroom?” “ How do I know if the teachers are doing it correctly?” This get’s right to the heart of helping principals figure out what they need to bring to the table, and what they actually need to do. It would be best if the PD Leads could prepare to address these questions in a concrete way during the presentation. Also, follow up trainings for principals needs to focus on this. It would be great if we could announce that during this training. For now, our (RL) line on this should be to encourage principals to see these two questions as the heart of their work, and to begin to prepare themselves for this, as they dig into the standards.
Then let’s give the principals a chance to share all that has been stirred up by the presentation. Let’s find out what their anxieties are. On the next page, I would recommend actually typing in their comments during the session. Do a Q & A with the curriculum and PD Lead specialists (and us) in the room to begin addressing some of what they bring up. Items that cannot be addressed at the session can be brought back and answers sent out later. NOTE: Depending on your group, you may have to nudge people to speak up about this. Or, you may have some angry person really ripping into us for changing the nature of their jobs (as they see it). Be prepared for all of this and facilitate accordingly.
These are the basics-- things the principal is responsible for making happen -- in order for implementation to truly and effectively occur. Make sure you spell out the difference between knowledge and understanding Knowledge – Familiarity with something, facts, descriptions, etc. Understanding – Comprehending the facts, descriptions, etc. Making judgments and inferences about the knowledge. Being able to put the knowledge to proper and effective use. All stakeholders means talking with students, parents, community members and teachers about the new standards. You have a year to do this, but it should not wait until the beginning of school in 2012-13. Communication efforts also need to be coordinated across the district. Parents and students and members of the community need to be informed early about: - What is coming - How it is an improvement - How it is different - What expectations will look like - Why things are changing - What work is going on now to prepare 3. YOU need to get your teachers connected to the resources they need to understand the standards. It may not be enough to simply say, “Go online and complete the module…” You will need to be more hands-on than that. 4. YOU need to get your teachers the best instructional resources and tools for teaching the new standards. This means more than buying (with your limited resources) some package or curriculum product. YOU need to do research and have conversations with curriculum leaders to help you make decisions about what is best for your students and your teachers. You have to be involved in any adoption process at your school. And you need to partner with other schools in this, if necessary. 5. YOU need to ensure that teachers are receiving adequate ongoing professional development (AND) you need to also take part in ongoing professional development on this. And where you observe weaknesses in your staff and program, you need to ask for appropriate support. 6. YOU need to understand formative and summative assessment-- and know that simply calling an assessment “formative” does not make it so. In order to be “formative” it must inform teachers and students about learning and levels of understanding and it must inform the instructional choices the teacher is making in the classroom. You have to ensure that this is going on in your classrooms. 7. YOU need to collect data to evaluate the effectiveness of the Common Core and Essential Standards instruction in your building. And then use that data to make effective instructional leadership decisions. The Implementation Plan on the next page gives you a roadmap and a tool for doing all of the above. It will help you organize your planning and ensure you don’t leave any of these vital “nuts & bolts” out of the picture.
What kind of help can you count on?
Think, Pair, Share Report Out… Ideas?
Help participants to understand that the Practices are dense statements that describe what students need to know…
Have participants follow the directions on the slide, working first individually, then in pairs on the Button Task. Whole Group Discussion: Depending on available time, consider selecting two or three papers with interesting solution strategies and or representations to share with participants before you begin the discussion of question 3. Don’t linger on the discussion of the task solution strategies, remember the focus of today’s session is the Standards for Mathematical Practice so save time for that part of the discussion. Chart the comments from participants regarding both the mathematical content and practices needed to successfully complete the task. You may also what to push the conversation by asking which elements of the task and/or the way the task was facilitated, triggered students to use specific practices.
First, as we have discussed in the overview session, we need to pay attention to what tasks we select because the nature of the tasks will impact student achievement, but
Having good tasks is only part of the story, how a teacher uses the task can significantly impact students’ learning opportunity Tasks are important, but teachers also matter! Teacher actions and reactions, that is their instructional decisions in the classroom, … influence the nature and extent of student engagement with challenging tasks, and effect students’ opportunities to learn from and through task engagement. In particular, the way teachers choose to use tasks can significantly influence the opportunities students have to develop skills associated with the mathematical practices.
Source of the video is the website Inside Mathematics. Development of the website was funded by the Noyce Foundation with a grant to the Silicon Valley Mathematics Initiative in California. The Noyce Foundation and the Silicon Valley Mathematics Initiative have graciously granted NCSM permission to utilize the website for this resource. 1. First select and show approximately 2 minutes segment from the Lesson Planning Video Clip beginning at 3:00 and ending at 4:49 This segment shows the teacher describing the lesson he has designed and his mathematical goals are for his students. Look for notes about the teacher, his classroom, and school on the website. 2. Next, distribute the samples of student work from Learner A and Learner B provided with this package. Allow teachers to look over the two samples of student work (Learner A and Learner B) and consider the nature of mathematics content and the mathematical practices students might be engaged in as they complete this task. Next, show approximately 2 minutes segment from the Lesson 2 Video Clip beginning at 0:00 minutes and ending at 1:50 minutes. In this segment participants will see the teacher launch the task. Next share a segment or two of students trying to make sense of the sample student work. The video segments from 3:04 to 4:40 showing two girls working on the task and another segment from 5:40 to 6:07 with two boys are nice samples. Again, the question for participants to consider as they watch the video is the nature of mathematics content and the mathematical practices students are engaged in as they complete this task. 4. Finally, show approximately 2 minutes segment from the Closure Video Clip beginning at 0:00 minutes and ending at 2:00 minutes. If you have a bit more time in the session you may want to play this video all the way to the end for a total of approximately 5:10 minutes. Then proceed to the focus questions on the next slide.
Make a hard copy of this slide for each pair of participants for them to use when discussing this work in pairs.
Having good tasks is only part of the story, how a teacher uses the task can significantly impact students’ learning Opportunity. Looking for good tasks that will engage students in use of the 8 mathematical practices is an important start, but we have just seen how the ways in which the teacher uses the tasks also contributes significantly to students’ opportunities to learn.
COMMON CORE AND LEADERSHIP
Implementing theCommon Core State StandardsThe Administrator’s Role Jeff Piontek
“In order to positively impact student achievement, the Common Core State must be not just adopted but implemented.”2
“The goal is to have content standards that actually impact what happens in the classroom. Unfortunately, there are too many examples where states have fine content standards that bear little resemblance to what is actually being taught and learned in classrooms.”3
It’s 2011: Do you knowwhere your teachers are?Do you know what and howyour teachers are teaching? 4
“We need to think carefully about what it will take for the Common Core to become fully operationalized in every classroom, every year, from kindergarten to high school graduation.” L ES al p ation Occu EC AIG5
Common Core Big Picture 1. Aligned with college and work expectations 2. Focused and coherent 3. Includes rigorous content and application of knowledge through higher-order skills 4. Internationally benchmarked – prepares students for global economy & society 5. Based on evidence and research7
Rationale for Implementation EQUITY – Expectations the same regardless of where students live College/Career Readiness – Students need to be more than proficient Comparability – State results will be comparable through common assessments8
Rationale Cont… Shared Resources – Ability to share and team across district and state lines Economies of Scale – Possible savings due to sharing of resources and assessments Student Mobility – Students encounter same standards wherever they go9
Common Core MATHEMATICS Elementary Kindergarten number core K-5 math foundation Continuous progression through grades Procedural skills + conceptual understanding10
Middle Robust middle school standards 8th grade algebra Hands-on, applied learning in algebra, geometry, probability, statistics11
High SchoolHigh School mathematics applicationssolve messy, real world problemsHigh school students apply mathematics to novel situations, ascollege students and professionals do – unexpected problem solvingMathematical modeling in physical, economic, public policy, socialand everyday situations – integrates mathematical and statisticalmethods and reasoning12
Common Core ELA Reading • Staircase of increasing complexity in reading • Diverse array of literature and informational “sample” texts • Critical content “types” mandated13
Writing Logical arguments (opinion writing) Research writing featured prominently Includes student writing samples Speaking & Listening, Language, Media & Tech Each are integrated throughout the ELA standards14
The idea that ALL NEW State standards MUST be developed in alignment with the CC Developed for readiness – elementary, middle, high school, college, workforce, and beyond. Mindful of 21st Century skill requirements Measurable and concise Integrated with other content areas Driven by Revised Blooms Taxonomy (RBT) and/or Marzano’s Taxonomy15
“Principals need to get to know the standards. A criticalprincipal role in implementing the standards changeprocess is to facilitate powerful conversations regardingwhat the new standards indicate students should knowand be able to do by the time they enter and leave eachgrade level. To do this, principals need to becomeintimately familiar with the organization, scope, depthand purpose for the new Common Core.”17
Traps to avoid Relinquishing responsibility “My assistant principal handles curriculum.” “I’m not a math/science/ELA… person.” Overestimating “The teachers are getting plenty of training; they’ve got a whole year to work it out.”18
Underestimating support needs“My people are professionals. I don’t need to be looking over theirshoulders on this.”Expecting it to go away“We change the curriculumevery few years in this state…”Confusing priorities“PLCs (PLN’s) are great, but we don’t really have time for thataround here.”19
Principals Encourage, Facilitate, & Manage: Rationale and “buy in” Collaboration opportunities Common ground (w/old standards) Informational writing “Power Standards” Locate/reallocate resources Common formative assessments Exceed the standards20
Key Management Structures Support Implementation t Department Head/Lead Teacher Role L PLCs (PLN’s) L Shared Decision-Making & Distributed Leadership21
Management Structures Cont… 1. Evaluation Considerations - How do principals know good instruction for the Common Core when they see it? - How do principals incorporate a standards-based lens during classroom walk-throughs and formal evaluations— in so many different subject areas?22
Leader’s Concerns What are some of your questions, fears and concerns about your role in this implementation? ? se Ti ti m er e? p Ex ? Ac c es co un o ur tab i lit R es y?23
III. Utilizing the “Leader’s” Transition Plan24
Standards Implementation: Nuts & Bolts Teachers’ knowledge of the Standards Teachers’ understanding of the Standards Communicating w/ all stakeholders about the Standards Resources & tools (for teacher understanding) Adoption of resources & tools (for instruction) Ongoing professional development support Assessment (formative & summative, online) Data & Evaluation25
Tips on working with a Transition Plan Highlight District Implementation and Transition Process activities that are directly relevant to you in your school. a Think about how the District activities impact what you will do in your building. i Consider the amount and kind of support you will require from your district and your state. c Be mindful of the State’s goals and be sure to address each of these at the school level.26
IV. Meeting Challenges and Accessing Support27
Understanding C urrent A lignment Alignment is one of the first steps for states and districts towards implementing the Common Core.29 29
C hanges in C urriculum and Instruction The Common Core will require significant curricular and instructional shifts that will impact all classrooms.30 30
Professional Development To effectively implement and embrace the Common Core, rich professional development will be required.31 31
C ommon A ssessments Two state consortia are building assessment systems to measure the Common Core State Standards.The assessment systems will: Provide a common measure of college and career readiness Be computer-based and include innovative item types Measure higher order skills and application of knowledge through multiple assessment formats Include formative assessments and performance tasks Provide timely data to educators and parents Ensure comparable expectations regardless of where students live 32
Standards for Mathematical PracticeAND…. Describe mathematical content students need to learn. SP1. Make sense of problems “……. students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends.”33
Connecting Standards for Content andPractice in a ClassroomCreate verbal and tabularrepresentations of the 3 DVD rentalplans below. Mail Flix Online Flix $18 per Movie month $12 per Buster regardless of month plus the number $3 per movie $1 per of movies rented movie rented rented Do the three plans ever cost the same for renting the same number of DVDs? 34
The DVD Rental Task1. Individually do the task.3. Then work with a partner to compare your work.4. Consider each of the following questions and be prepared to share your thinking with the group: a) What mathematics content is needed to complete the task? b) Which mathematical practices are needed to complete the task? 35
Connecting Standards for Content and Practice in a ClassroomCreate verbal and tabularrepresentations of the 3 DVD rentalplans below. Mail Flix Online Flix $18 per Movie month $12 per Buster regardless of month plus the number $3 per movie $1 per of movies rented movie rented rented Do the three plans ever cost the same for renting the same number of DVDs? 36
The Nature of Tasks Used in theClassroom … Will Impact Student Learning! Tasks as they appear in curricular materials Student learning
But, WHAT TEACHERS DO with the tasks matters too!The Mathematical Tasks Framework Tasks as Tasks as Tasks as enacted they set up by by appear teachers in teachers Student and curricular students learning materialsStein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)
www.Inside Mathematics.org A reengagement lesson using the DVD Rental Task Cecilio Dimas Ida Price Middle School Grade 7 http://www.insidemathematics.org/index.php/classroom-video- visits/public-lessons-comparing-linear-functions/264-comparing-linear- functions-introduction?phpMyAdmin=NqJS1x3gaJqDM-1-8LXtX3WJ4e8 39
DVD Rental TaskIn what ways did the teachergive students opportunities tomake sense of the task and buildperseverance in his launch ofthe task?What evidence do you see thatstudents are building thisstandard of practice? 40
Looking at Student WorkExamine the tables generated byStudent H Given this work, what conclusions has the student made? What mistakes (if any) are evident in the tables? Do the tables make mathematical sense, and do they match the plans? 41
Content and Practice in a ClassroomCreate verbal and tabularrepresentations of the 3 DVD rentalplans below. Mail Flix Online Flix $18 per Movie month $12 per Buster regardless of month plus the number $3 per movie $1 per of movies rented movie rented rented Do the three plans ever cost the same for renting the same number of DVDs? 42
Looking at Student Work As you watch the video consider: What evidence do you see that suggests students are developing competency with Standards 3 and/or 4 for Mathematical Practice? In what ways did interactions between students support their ability to develop competency with Standards 3 and/or 4 for Mathematical Practice? In what ways did the teacher facilitate/hinder students developing competency with the practices?44
Teachers and Tasks Matter The Mathematical Tasks Framework Tasks as Tasks as Tasks as enacted they set up by by appear teachers in teachers Student and curricular students learning materials Stein, Grover & Henningsen (1996) Smith & Stein (1998) Stein, Smith, Henningsen & Silver (2000)
Progressions within and acrossDomains K- 5 6-8 High School Expressions Operations and and Algebraic Thinking Equations Algebra Number and Operations―Base Ten The Number Number and System Operations ―Fractions 46
Overarching Concerns - EquityTo what extent do the materials:1. Provide teachers with strategies for meeting the needs of a range of learners?2. Provide instructional support to help teachers sequence or scaffold lessons sothat students move from what they know to what they do not know?3. Provide opportunities for teachers to use a variety of grouping strategies?4. Embed tasks with multiple entry-points that can be solved using a variety ofsolution strategies or representations?5. Suggest accommodations and modifications for English language learners thatwill support their regular and active participation in learning mathematics? 47
Overarching Concerns - EquityTo what extent do the materials:6. Provide opportunities to use reading, writing, and speaking inmathematics lessons.7. Encourage teachers to draw upon home language and culture tofacilitate learning?8. Encourage teachers to draw on multiple resources such asobjects, drawings, and graphs to facilitate learning?9. Draw upon students’ personal experiences to facilitate learning?10. Provide opportunities for teacher and students to connectmathematics to other subject areas? 48
Overarching Concerns - EquityTo what extent do the materials:11. Provide both individual and collective opportunities for studentsto learn using mathematical tasks with a range of challenge?12. Provide opportunities for advanced students to investigatemathematics content at greater depth?13. Provide a balanced portrayal of various demographic andpersonal characteristics? 49
Overarching Concerns -AssessmentTo what extent do the materials:14. Provide strategies for gathering information about students’ prior knowledgeand background?15. Provide strategies for teachers to identify common student errors andmisconceptions?16. Assess students at a variety of knowledge levels (e.g., memorization,understanding, reasoning, problem solving)?17. Encourage students to monitor their own progress?18. Provide opportunities for ongoing review and practice with feedback relatedto learning concepts, and skills.19. Provide support for a varied system of on-going formative and summativeassessment (formal or informal observations, interviews, surveys, performanceassessments, target problems)? 50
Overarching Concerns - TechnologyTo what extent do the materials:20. Integrate technology such as interactive tools, virtual manipulatives/objects,and dynamic mathematics software in ways that engage students in theMathematical Practices?21. Include or reference technology that provides opportunities for teachers and/or students to communicate with each other (e.g. websites, discussion groups,webinars)?22. Include opportunities to assess student mathematical understandings andknowledge of procedural skills using technology?23. Include or reference technology that provides teachers additional tasks forstudents?24. Include teacher guidance for the mindful use of embedded technology tosupport and enhance student learning? 51
Resources The Common Core State Standards Initiative: http://www.corestandards.org/ SMARTER Balanced: http://www.k12.wa.us/smarter/ PARCC: http://www.parcconline.org/ K-12 Center at ETS Guide to the Assessment Consortia: http://www.k12center.org/publications/assessment_consortia.html 52