Focusing On The Mathematical Practices
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Focusing on the Mathematical Practices of the Common Core Grades 6–8 Day 1
Professional Development Facilitator Handbook
--SAMPLER-- Materials Checklist Item ISBN Special Participant Facilitator Quantity Consumable Instructions Computer Note 1 X X 1 each No Projector Note 2 X 1 total No Speakers X 1 set No PowerPoint X 1 total No Participant Workbook X X 1 each Yes Chart paper/graph paper Note 3 X X 1 pad Yes X X 1 for the facilitator and No Colored markers 1 per table Manipulatives (Tile Problem) Personal paper copy of the Common Core State Note 4 X 1 total No Standards for Mathematics Electronic copy of the Common Core State Note 5 X 1 total No Standards for Mathematics Video: Juanita “Nita” Copley, “Balance of Procedure and Note 6 X 1 total No Understanding” Video: Phil Daro, “Standards No Note 7 X 1 total for Mathematical Practice” Video: Phil Daro, “Developing Mathematical Expertise and Note 8 X 1 total No Building Character” Video: John Van de Walle, No Note 9 X 1 total “Teacher Workshop” Video: “Video Case Study: The Tile Problem with Note 10 X 1 total No Commentary” Pens or pencil X 1 each Yes Quotes on perseverance Note11 X 2 sets of 12 No Note1 The school district needs to provide a training room with a computer for the facilitator. Prior to the workshop, the facilitator should obtain information about how to log in to the system. The facilitator should also confirm that PowerPoint is installed on the computer and that the computer has Internet access. The facilitator should install QuickTime Player on his or her computer. To download the application, visit http://www.apple.com/quicktime.
For optimal performance, the facilitator should copy the entire presentation folder onto his or her hard drive. All videos need to be in the same location as the PowerPoint file. For example, if the PowerPoint file is on the desktop, all of the video files also need to be on the desktop. The facilitator should test the PowerPoint file on the computer her or she is using for the presentation, including all videos, before beginning the training.
If the facilitator wishes to use his or her personal computer during the workshop, he or she needs to obtain permission from the district’s Technology Department.
Note2 The district should provide a projector if one is available. If a projector is not available, make arrangements for one to be brought to the presentation site.
Note3 Request that the district provide chart paper, because it is very difficult to travel with. Otherwise, the facilitator should purchase the chart paper prior to arrival.
Note4 The Common Core State Standards are in the warehouse and will be shipped to the workshop site prior to the training. Please check with [email protected] to ensure materials have been shipped. Please contact the school to ensure materials have arrived.
Note5 It is a good idea for the facilitator to have an electronic copy of the CCSSM on a flash drive that he or she brings to the training. The facilitator should download the PDF file named CCSSI_Math Standards.pdf from the Additional Resources folder to his or her computer.
Note6 The file name for the video titled “Balance of Procedures and Understanding” is Copley Interview.mov.
Note7 The file name for the video titled “Standards for Mathematical Practice” is CCSS_Mathematical_Practice.mov.
Note8 The file name for the video titled “Developing Mathematical Expertise and Building Character” is CCSS_Expertise_Character.mov.
Note9 The file name for the video titled “Teacher Workshop” is VanDeWalle.mov.
Note10 The file name for the video titled “Video Case Study: The Tile Problem with Commentary” is PhilDaro_TilePrb_Commentary.mov.
Note11 Find twelve quotes on perseverance either from a personal book or from the Internet. One example is a Web site called the Quote Garden located at http://www.quotegarden.com/perseverance.html. Preparation and Background Content Information
Note to Facilitator: Please check if the state or district where you will be leading the workshop has created their own state documents. States such as Arizona and New York have already released state-specific versions of the Common Core State Standards (CCSS). You should become familiar with the state- specific documents and adapt the workshop materials to use the state-specific CCSS.
*Please note that even though this workshop has a prerequisite, districts may not have fulfilled that requirement. If they have, adjust the content accordingly.
“The Common Core State Standards Initiative is a state-led effort coordinated by the National Governors Association Center for Best Practices (NGA Center) and the Council of Chief State School Officers (CCSSO)” (Common Core State Standards Initiative 2010b).
These standards were developed for three reasons. One is to provide consistency across states. A set of common standards allows for consistent and quality education across all 50 states. Secondly, they align with international standards. In order to compete in global markets, students in the United States cannot lag behind their peers in other countries. The Common Core State Standards (CCSS) are benchmarked against international standards so that students can compete in a global economy. Lastly, the standards help prepare students for college and work. Colleges and universities expect students to read complex texts independently, and employers look for workers who have the skill set to solve problems and the ability to integrate new knowledge. Elementary and secondary education needs to prepare students to be ready for these challenges.
The Common Core State Standards Initiative (2010b) states the following:
The standards were developed in collaboration with teachers, school administrators, and experts, to provide a clear and consistent framework to prepare our children for college and the workforce. The NGA Center and CCSSO received initial feedback on the draft standards from national organizations representing, but not limited to, teachers, postsecondary educators (including community colleges), civil rights groups, English language learners, and students with disabilities. Following the initial round of feedback, the draft standards were opened for public comment, receiving nearly 10,000 responses.
The standards are informed by the highest, most effective models from states across the country and countries around the world, and provide teachers and parents with a common understanding of what students are expected to learn. Consistent standards will provide appropriate benchmarks for all students, regardless of where they live. 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. The standards: Are aligned with college and work expectations; Are clear, understandable and consistent; 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.
“The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important ’processes and proficiencies‘ with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s [NCR] report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently and appropriately), and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy)” (Common Core State Standards Initiative 2010a, 6).
The chart on the next page includes additional resources to read and view in order to have the background knowledge to lead the discussions outlined in this workshop. Read the following prior to the workshop: Work through and take notes on the following prior to the workshop: Adding It Up: Helping Children Learn Mathematics All problems and problem sets o http://www.nap.edu/catalog.php?record_id=9822#toc Companion document for the Comparing Quantities problem set A Nation Accountable: Twenty-five Years After A Nation at Risk (U.S. Companion document for the Tile Problem Department of Education) Copley Interview.mov o http://www2.ed.gov/rschstat/research/pubs/accountable/index. CCSS_Mathematical_Practice.mov html CCSS_Expertise_Character.mov VanDeWalle.mov PhilDaro_TilePrb_Commentary.mov Familiarize yourself with the following: Gather the following from state-specific Web sites: Highlights From PISA 2009: Performance of U.S. 15-Year Old Fordham Institute Comparison Students in Reading, Mathematics, and Science Literacy in an http://www.edexcellence.net/index.cfm/news_the-state-of-state- International Context standards-and-the-common-core-in-2010 http://nces.ed.gov/pubs2011/2011004.pdf State-specific versions of the CCSS. (See Arizona and New York for A Nation At Risk: The Imperative for Educational Reform examples.) http://www2.ed.gov/pubs/NatAtRisk/index.html Major changes in practice Curriculum and Evaluation Standards for Mathematics Education Common Core State Standards state-specific implementation timeline http://www.ericdigests.org/pre-9215/evaluation.htm Appropriate assessment information from either the Partnership for Principles and Standards for School Mathematics Assessment of Readiness for College and Careers (PARCC) or the http://standards.nctm.org/ SMARTER Balanced Assessment Consortium (SBAC) No Child Left Behind information http://www2.ed.gov/nclb/overview/intro/edpicks.jhtml?src=ln Adding It Up: State Challenges for Increasing College Access and Success http://www.cpec.ca.gov/CompleteReports/ExternalDocuments/Adding_I t_Up.pdf Race to the Top Program Executive Summary http://www2.ed.gov/programs/racetothetop/executive-summary.pdf Common Core State Standards http://www.corestandards.org/ Trends in International Mathematics and Science Study (TIMSS) 1999 Video Study http://www.llri.org/html/TIMSS/index.htm Workshop Information
Big Ideas Mathematical proficiency is more than “getting the answer.” It includes the process of using mathematical concepts effectively as identified in the Standards for Mathematical Practice. Developing a student’s ability to use the Standards for Mathematical Practice helps to cement the student’s understanding of mathematical processes and proficiencies. The mathematical practices are consistent for all grade levels, even though they manifest themselves differently as students grow in mathematical maturity. Teachers can embed mathematical practices into daily routines through teacher modeling, task selection, relevant mathematical discourse, lesson structure, and so forth. The Standards for Mathematical Practice provide students with the opportunity to demonstrate their expertise as mathematical thinkers and learners in an intentional and public way. Strategically chosen tasks provide teachers with opportunities to model and teach the mathematical practices. Teachers must practice and teach modeling with mathematics; it cannot be an unspoken expectation.
Essential Quest ions . What are the Standards for Mathematical Practice, and why are they important for mathematical proficiency? . What does “understanding” in mathematics mean, and how do the Standards for Mathematical Practice lead to understanding? . How can strategies and classroom routines help students develop the mathematical practices of mature mathematical thinkers and learners? . How can teachers use problem solving to promote the Standards for Mathematical Practice?
Assessments of Participants’ Learning during the Workshop Reflection: Rank the Standards Reflection: 3-2-1 Activity Reflection: Symbolic Prompts Review: Objectives Essential Questions Review
Assessment Back in the School/Classroom Implement a list of changes to participants’ classrooms that expands students’ use of mathematical practices. Outcomes
Participants will be able to
connect the Standards for Mathematical Practice to the National Council of Teachers of Mathematics’ (NCTM) Process Standards and Proficiencies as detailed in Adding It Up: Helping Children Learn Mathematics; identify a structure for collaboration and use of the eight mathematical practices; connect current practice and articulate the changes needed to implement the Standards for Mathematical Practice; articulate ways to routinely promote and assess the mathematical practices; describe how specific mathematical practices are embedded in the Standards for Mathematical Content; identify the attributes of a rich, instructional, problem-based approach and how it can support access to the Standards for Mathematical Practice; identify sub-performance tasks as a means for providing students the opportunity to routinely demonstrate the eight mathematical practices; and connect the analysis of student work to ongoing support of the Standards for Mathematical Practice.
Facilitator Goals Improve participants’ success in implementing the Standards for Mathematical Practice. Provide participants with specific approach suggestions that will increase students’ use of the mathematical practices. Encourage participants to engage in the mathematical practices as a model for their students. Support participants’ skills in formatively assessing the mathematical practices through observation. Guide participants in encouraging all students (including English language learners (ELLs), special education, and other populations) to engage in the mathematical practices. Section 2: Teaching the Standards for Mathematical Practice (Slides 16–31) Time: 110 minutes Essential Question . How can strategies and classroom routines help students develop the mathematical practices of mature mathematical thinkers and learners? Learning Objectives . Explain how to develop the Standards for Mathematical Practice through choice of task, discourse in the classroom, assigned homework, and daily classroom routines. . Identify features of participants’ instruction that facilitate the development of the Standards for Mathematical Practice. . Create a list of changes needed in participants’ classrooms that will expand students’ use of the Standards for Mathematical Practice. Materials per Section . Computer . Projector . PowerPoint presentation . Participant Workbook, pages 16–24 . CCSSM document, pages 6–8 . Video: Phil Daro, “Developing Mathematical Expertise and Building Character” . Chart paper . Colored markers (each group should have a different color) . Pens or pencils
Topic Presentation Points Presentation Preview
Supporting Students as They Develop Display Slide 16. the Mathematical Practices Introduce this section by making the point that “teaching the Standards for Mathematical Practice” means supporting the development of students as practitioners of the discipline of mathematics. Ask participants to reflect on the question on the slide, ‘How do you currently support students in becoming effective mathematics practitioners?” Ask for volunteers to share their thoughts. Topic Presentation Points Presentation Preview Display Slide 17. Have participants turn to page 18 in the Participants Workbook. In the space provided, have participants individually brainstorm the answer to the question on the slide in the space provided. “How can teachers support students as they develop the mathematical practices?” After participants have created their personal lists, facilitate a discussion about the different ways teachers can support students as they develop the mathematical practices. Chart participants’ responses. Note: PW: Page 18 o Examples of participant responses may include the following: – Provide concrete materials. – Provide real-world contexts. – Require the use of multiple representations. – Ask the questions, “Does this make sense?” and “Why?” o Use participants’ background knowledge to make direct connections between instructional strategies and how instruction will and does impact students’ work within the mathematical practices. Guide the discussion in such a way as to create a global list, but at the same time make sure that participants generate ideas that will support each of the eight Standards for Mathematical Practice. BACKGROUND INFORMATION: Every grade level includes Standards for Mathematical Practice and “describes ways in which developing student practitioners of the discipline of mathematics ought to engage with the subject matter as they grow in mathematical maturity and expertise throughout the elementary, middle and high school years” (Common Core State Standards Initiative 2010a, 8). At this point in the workshop, participants should be familiar with the mathematical practices at a general level. Section 2 focuses on how Topic Presentation Points Presentation Preview instructional strategies can engage students in the mathematical practices.
Display Slide 18. Explain to participants that the video of Phil Daro they are about to watch describes students’ required development of mathematic expertise and character building in order to demonstrate the eight mathematical practices. Note: Participants may have viewed this video during the Foundational Overview of the Common Core State Standards for Mathematics Professional Development Workshop. If this is the case, you may want to consider skipping the video and just continue working with the list and instructional strategies as stated below with Slide 20. As participants to watch the video clip titled, “Developing Mathematical Expertise and Building Character,” ask them to think about the question, “How is it that students build these described habits of minds?” Debrief the video by asking participants if there is anything that they want to add to the list that they generated. Add any additional information to the chart paper list that participants already started.
Display Slide 19. Explain to participants that as they work through the next part of this section, they will want to make note of various ideas for their own classroom practices. o Remind participants of the chart on pages 10–11 in the Participant Workbook and the space provided there for these ideas.
PW: Pages 10–11 Topic Presentation Points Presentation Preview Bringing the Practice Standards to the Display Slide 20. Classroom Use the list that participants created in the previous discussion as a starting point for the next part of the section. Here, participants will use the Instructional Carousel strategy in order to brainstorm ways that teachers can develop the mathematical practices through various classroom activities. Note (Preview of Activity): In the Instructional Carousel strategy, you will hang five pieces of chart paper around the room with one instructional strategy (see Slide 20) as a heading on each. PW: Page 19 Then divide participants into five groups and assign one teaching practice and one corresponding brainstorming question from page 18 in the Participant Workbook to each group. Participants generate answers and ideas to their questions using page 18 for note-taking purposes. Then assign each group a different colored marker. Groups use their colored markers to transfer their ideas to their assigned chart papers. Once groups finish transferring their ideas they will then “carousel” around the room to other groups’ chart papers and, using their assigned colored markers, add additional ideas to what the original group already started. Briefly discuss five ways teachers can develop the mathematical practices in the classroom. Use already-generated responses to begin the conversation by connecting those responses to the following five instructional strategies: o Teacher modeling: The teacher models the mathematical behavior that he or she wants students to develop. o Task selection: The teacher chooses tasks that allow students to develop those behaviors. Topic Presentation Points Presentation Preview
o Relevant student discourse: The teacher allows time for students to discuss what they are thinking and doing when they develop solution strategies. The teacher also has students share their strategies with the class, requires a full explanation, and allows other students to assist and ask questions. o Questioning strategies: The teacher poses questions to students that assist them in delving deeper into the concept. Questions are used in place of providing specific strategies for solving a task. o Classroom routines: The teacher develops classroom routines that create a safe environment for students to explore strategies, develop their conceptual understanding, and work on becoming proficient in the mathematical practices. Explain that you want participants to add to the ideas that they already generated by digging deeper into the specifics of each as they relate to the five instructional strategies listed above and on Slide 20. For example, if one of the previously charted responses was “provide real-world context,” ask participants under which instructional strategy this would fall. It should fall under task selection. Then, have participants expand on this by thinking about what it is about the task and context they would be looking for; for example, something relevant to students’ lives, grade-level appropriate situations, and so forth. Divide participants into five groups. Assign each group to one of the five brainstorming questions listed on page 19 of the Participant Workbook. These questions relate to the ways that teachers can support the development of the mathematical practices: o Teacher modeling: What are your current and future approaches to modeling the Standards for Mathematical Practice for students? o Task selection: What are your current and future criteria for selecting tasks that encourage the development of the Standards for Mathematical Practice? o Relevant student discourse: What are your current and future methods for supporting student discourse that encourage the development of the Standards for Mathematical Practice? Topic Presentation Points Presentation Preview
o Questioning strategies: What are your current and future questioning strategies that encourage the development of the Standards for Mathematical Practice? o Classroom routines: What are your current and future classroom routines that encourage the development of the Standards for Mathematical Practice? Have groups spend five minutes brainstorming ideas for their questions while they use page 19 of the Participant Workbook to take notes. If they have trouble, refer them to the Standards for Mathematical Practice on pages 6–8 of the CCSSM document for ideas.
Display Slide 21. Assign one colored marker to each group. Explain to participants that once they finish with their notes, they should transfer their ideas to their assigned piece of chart paper. Let participants know that they will revisit their posters at the end of this section of the workshop, so they should not worry if they feel they need more time to come up with ideas. Once groups finish with their chart papers, have them carousel around to the other posters and add additional ideas. They should spend two to three minutes reading each poster and making additions. Each group should continue to use its assigned colored marker to distinguish the additions that participants make. Continue to have groups move around the room until they have visited all of the posters. As a whole group, debrief the activity and ask participants for highlights and thoughts on each instructional strategy. Allow participants time to go back and write down the ideas they want to take away on the chart on pages 10–11 in the Participant Workbook. Topic Presentation Points Presentation Preview Display Slide 22. Ask participants to reflect on the following questions: o At what point in time do teachers select a task? o When do teachers model the Standards for Mathematical Practice? o When do teachers support student discourse? o When do teachers use questioning strategies? o What does it look like when teachers integrate the Standards for Mathematical Practice into classroom instructional processes? Explain to participants that most of the various ways for developing the mathematical practices happen within the routines and rituals of the daily classroom. So, suppose you and participants are in a seventh grade classroom at the beginning of a classroom lesson. Model the three-phase lesson structure for the problem sets that are provided in the Participant Workbook on pages 20–22. BACKGROUND INFORMATION: The three-phase lesson structure is a problem-based teaching method described in Elementary and Middle School Mathematics: Teaching Developmentally by John Van de Walle, Karen Karp, and Jennifer Bay-Williams (2010, 48). The lesson structure is divided into three phases: Before, During, and After. Before: During the Before phase the teacher sets-up the problem, activates student prior knowledge without giving away a solution strategy to the current problem, makes sure the problem is understood, and establish clear expectations for how the students will work the problem (i.e. in groups, on their own, verbal responses, written responses, etc). During: In the During phase of the lesson students work the assigned problem. While students are working the teacher circulates throughout the room and allows the students to purposefully struggle with the problem in order to create their own strategy and understand the mathematics, listens actively to determine which students need additional support and provides those students with appropriate hints, and provides worthwhile extensions Topic Presentation Points Presentation Preview for those students who are ready to move on. After: In the After phase of the lesson the teacher brings the students back together and holds a public discussion of the student work in which students publically explain their strategies, other students and the teacher asks questions and listen actively without evaluation. This public discussion is used to promote a mathematical community of learners. At the end of the public discussion the teacher summarized the main (big) ideas and identifies future problems.
Display Slide 23. Set up the Before phase of the model lesson by asking the following questions displayed on the slide: o What is a comparison? o Why do we compare? Chart participants’ responses so that you and participants can refer to them throughout the lesson as necessary and use the responses to gauge and clear up any content misconceptions.
Display Slide 24. Together with participants, examine two types of comparisons by completing Problems 1a and 1b on page 20 of the Participant Workbook.
PW: Page 20 Topic Presentation Points Presentation Preview Display Slide 25. Begin the During phase by asking participants to continue to work through the remaining questions. Tell them that you will be walking around to pose questions and gauge pacing. Let them know in advance that not all groups will finish, but that you will ask various pairs of people to present different questions. While participants work on the task, be sure you adequately prepare for the After phase, or public discussion, of their work. BACKGROUND INFORMATION: Before the workshop, carefully review the companion document in the Additional Resources folder. The companion document provides the answers to the tasks, as well as sample solution strategies and content considerations.
Display Slide 26. Begin the After phase. Have participants follow along in the Participant Workbook on pages 20– 22 as various pairs or groups explain each set of problems. After the presentations, ask participants what they noticed about the structure of this problem set. Listen for specific ideas related to the concept of scaffolding as noted in the background information below. Bring the discussion to a close by facilitating a conversation about the big ideas of this set of problems. Be sure you know the background information well enough to pull out the big ideas—either from the participants’ presentations or by charting the ideas yourself. It is very important not to read directly from your Facilitator Handbook during the workshop.
BACKGROUND INFORMATION: Topic Presentation Points Presentation Preview The big ideas include the following: Students must understand the concept of absolute comparison (using subtraction to find a difference) versus the concept of multiplicative comparison (using division to find a ratio). When using subtraction, if two numbers are each multiplied by the same factor, then the difference also changes by that factor. When using division, if two numbers are each multiplied by the same factor, then the ratio stays the same. Problems 1–3 give students an opportunity to explore the different comparisons via several different examples created by them. They also ask students to defend their answers. Problem 4 gives students an opportunity to contrast the comparisons and demonstrate an understanding of when each comparison is mathematically appropriate. Problem 5, at a higher level of cognitive demand, gives students the opportunity to extend their knowledge by developing an applicable rule. Note that if teachers use Problem 5 as an extension task, the final two bullets above may not be big ideas for this lesson. While the usefulness of scaffolding for increasing all students’ capacities for engaging in mathematical practices is not highlighted until Day 2, Section 6, it might be useful to mention to participants that this problem set is also scaffolded. Instead of asking students complicated questions about the comparisons, the problem set begins by giving students specific tasks in regard to the number of stars, the number of triangles, and how the two quantities could be compared. Next, students extend this knowledge to create different sets of stars and triangles via the specific questions in the problem set. This gives them the opportunity to begin making connections about the two different types of comparisons. Then, problem sets give students the opportunity to engage with specific problem situations that use relative and absolute comparisons. Topic Presentation Points Presentation Preview
Finally, the problem sets asks students (if they are able) to develop mathematical rules based on their experiences with the previous problems.
Display Slide 27. Ask participants to consider the following question: Describe how these mathematical practices would emerge if students worked on this same problem set. Discuss the Standards for Mathematical Practice that relate to this set of comparing quantities mathematical tasks. Possible responses to this prompt may include the following (Common Core State Standards Initiative 2010a, 10): o Make sense of problems and persevere in solving them. Students must understand the difference between comparison by division and comparison by subtraction. o Reason abstractly and quantitatively. Students are asked to decontextualize from the situations of stars and triangles, different people’s salaries, and tables and chairs to ratios. o Construct viable arguments and critique the reasoning of others. Students must be able to explain why one comparison gives better information for the problem than another comparison. o Attend to precision. Students need to take note of the differences between subtraction and division. o Look for and make use of structure. After several problems, students need to write a rule that explains two different situations. Topic Presentation Points Presentation Preview Display Slide 28. Use page 22 in the Participant Workbook to review with participants the three-phase lesson structure they just worked through. o Describe what happened during each phase of the lesson and provide background on the intent of each section. The background information can be found above in the text that corresponds to Slide 22. Explain to participants that the three-phase lesson structure is just one way for teachers to deliver lessons that naturally allow them to implement the five instructional strategies; this would allow teachers to integrate more work with Standards for Mathematical Practice. PW: Page 23
Display Slide 29. Have participants reconvene in their original groups from the carousel activity at the beginning of this section to make revisions to their posters based on their experiences with the previous set of mathematical tasks. As time permits, allow groups to select a spokesperson to share any revisions that they made.
Reflection: 3-2-1 Activity Display Slide 30. Have participants complete a 3-2-1 reflection by following the instructions on the slide and writing their responses on page 24 of the Participant Workbook: o List 3 new ideas related to teaching the Standards for Mathematical Practice that you are going to implement in the classroom. o List 2 strategies you have previously used that support the Standards for Mathematical Practice. o List 1 question you still have about the Standards for Mathematical PW: Page 24 Topic Presentation Points Presentation Preview Practice.
Essential Question Review Display Slide 31. Have participants turn to page 25 in the Participant Workbook and read, discuss, and answer the Essential Question for Section 2. o How can strategies and classroom routines help students develop the mathematical practices of mature mathematical thinkers and learners?
PW: Page 25