All Teachers Reaching All Students

All Teachers Reaching All Students
Math Teaching Specialists Co-presenters: Cynthia and Astrid Bernard and Mary Kasten Bridget and Mary Rosann and Jill Dring Pandora and Laura Beth and Lee Ann Start at 8:45 AM Banking Day March 14, 2011

Pattern Time What is Size 7?
On your own, think about how you would approach this problem. With a partner Share your strategies Determine the Size 7 Communicate clearly how you arrived at your solution As a table group, everyone shares their strategy Record all strategies Be prepared to share out whole group * 25 min *Handout At your tables, introduce yourselves Steps 1-2: 3 mins Caution them to THINK about their approach and NOT work it out… how is the shape “growing”? Step 3: 5 min Step 4: 15 min

Logistics Introductions Announcements Norms Agenda Parking Lot
*5 minutes Introductions: be sure everyone includes their “role” (e.g. grade 7 teacher, SpEd support) Announcements: bathroom locations; this will be posted on the mmp website soon-website given on last slide; other? Norms: refer to the norms poster Agenda: morning session, Lunch/break = 1 hour, afternoon session Parking Lot: refer to the parking lot poster; use post-its; include school name; may or may not get to it at end of day.

Learning Intention Success Criteria
We are learning to understand the connections between the Principles of Formative Assessment and math instructional practices. Success Criteria We will know we are successful when we can… articulate the connections between the Principles of Formative Assessment and math instructional practices. develop a plan of action to embed formative assessment principles into our math instructional practices. *1 minute

Comprehensive Mathematics Framework
*10 minutes Handout (back to back with CCSS) Debrief CMF with respect for what we have done in the past to communicate the process standard, how to plan lessons to reach that goal, and how we will continue this work in the district as the new CCSS will support a similar idea. Connect to L pattern problem: Where did you see each of these components in the L problem?

Common Core State Standards
Standards for Mathematical Practice K – 8 Grade level standards High School standards “conceptual categories” 3 minutes for Slides 6-7 6

Emphasize connection with CMF.
This is the focus of study for this year (Your MTL is being introduced monthly to a new Practice Std) Practice standard are student actions Teachers need to think about what they need to do to ensure all students K-12 are engaged in these actions. Participant read

Standards for Mathematical Practice
3. Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. *25 min for Slides 8-9 *Handout Participants Read and highlight

Linking the Mathematical Practice Standard to the Classroom
What would this practice look like in a classroom? Students would be… Teachers would be… Each table records table discussion using a graphic organizer of their choice, e.g. Venn diagram, two column chart on own paper (not chart) whole group discussion: facilitator charts 1 ideas per group until all have shared ideas Students: make conjectures, analyze situations, use counter examples, justify conclusions and communicate them to others, listen to and respond to argument of others, reason inductively about data, compare effectiveness of 2 plausible arguments, distinguish between accurate and flawed reasoning, ask questions Teachers: invite students to share strategies, strategical (purposeful) use of multiple representations/approaches to the problem, provide manipulatives and resources, students get multiple experiences, Transition: Structure of work of MMP has been around standards. We now have new standard so we need to think about how that looks in classroom. The MMP has also done a lot of work around formative assessment. They are closely connected and we need to think about how they both work together. 9

What is Formative Assessment?
Think On your own, think about what formative assessment means to you…. Pair Turn to a partner and share your thoughts. Discuss similarities and differences… Share Share with the whole group some of your thoughts and discussions. * 5 minutes

Instructional Cycle Informed by Assessment
Know your students * 3 min The graphic comes Rick DuVall. He’s a literacy-differentiated instruction guru type. There are different entry points to the cycle. Emphasize the cyclical nature as this is an ongoing process to be used throughout a unit of study. Graphics connects to the work of the MMP for the last 8 years around formative assessments and bridges the work of district focus on differentiation Assessment: all about knowing your students, use of variety of formative assessments strategies which we will cover through out the session Plan: as we develop an understanding of students how are we purposefully planning to meet all student needs? Model: teachers need to determine how to design a plan of how “model” would look like in the classroom to ensure conceptual understanding of big math idea Guided practice: traditional thought of guided practice is few problems where kids do sit and do procedural work. Not what DuVall is referring to. Refers to structured time where students are working on concepts while teachers assess formatively. Practice and Application: again traditional thought is homework with procedural work. Not what DuVall is referring to. Refers to an opportunity to apply their conceptual understanding. The teacher has used a variety of formative assessment strategies to be informed on where their students are in the learning process. This information is used to help plan tomorrow’s lesson Rick DuVall

Assessment for Learning
Assessment for learning is about far more than testing more frequently or providing teachers with evidence so they can revise instruction, although these are part of it. Assessment for learning must actively involve students. Richard Stiggins 1 min Emphasis assessment for learning MUST include students

What Are the Purposes of Assessment for the TEACHER?
Assessment for Learning Formative assessment Supports learning by providing information about what a child knows, understands, and is able to do. where the learners are in their learning and how to achieve learning goals. Assists teacher in making instructional decisions for the individual child and the whole class. * 1 min Have participants read and reflect; share out 13

What Are the Purposes of Assessment for the STUDENT?
Assessment for Learning Formative assessment Supports learning by providing information about what a child knows, understands, and is able to do. where the learners are in their learning and how to achieve learning goals. Encourages child to identify their areas of weakness or strength so they can focus on their efforts more precisely. * 1 min Have participants read and reflect; share out 14

Research by: Richard Stiggins
“Achievement gains are maximized in context where educators increase the accuracy of classroom assessments, provide students with frequent informative feedback (versus infrequent judgmental feedback), and involve students deeply in the classroom assessment, record keeping, and communication process. In short, these gains are maximized where teachers apply the principles of assessment for learning.” * 1 min Have participants read and reflect; share out Transition slide to our MMP form 15 15

MMP Learning Team Continuum Aligned with Formative Assessment Principles
(1) Prior to teaching, teachers study and can articulate the math concepts students will be learning. (2) Teachers use student-friendly language to inform students about the math objective they are expected to learn during the lesson. (3) Students can describe what mathematical ideas they are learning in the lesson. (4) Teachers can articulate how the math lesson is aligned to district learning targets, state standards, and classroom assessments (CABS), and fits within the progression of student learning. (5) Teachers use Classroom assessments that yield accurate information about student learning of math concepts and skills and use of math processes. (6) Teachers use assessment information to focus and guide teaching and motivate student learning. (7) Feedback given to a student is descriptive, frequent, and timely. It provides insight on a current strength and focuses on one facet of learning for revision linked directly to the intended math objective. (8) Students actively and regularly use descriptive feedback to improve the quality of their work. (9) Students study the criteria by which their work will be evaluated by analyzing samples of strong and weak work. (10) Students keep track of their own learning over time (e.g., journals, portfolios) and communicate with others about what they understand and what areas need improvement. Stage 1 Learning Targets Stage 2 Align State Framework and Math Program Stage 3 Common CABS Stage 4 Student Work on CABS Stage 5 Descriptive Feedback on CABS Understand importance of identifying and articulating big ideas in mathematics to bring consistency to a school’s math program. Develop meaning for the math embedded in the targets and alignment to state standards and descriptors and to the school’s math program. Provide a measure of consistency of student learning based on standards/descriptors and targets. Examine student work to monitor achievement and progress toward the targets and descriptors. Use student work to inform instructional decisions, and to provide students with appropriate descriptive feedback. * 5 min Handout -Have participants read to become familiar: -quick share out, what are you familiar with -we will engage in activities that help to solidify understanding of each principle and strategies that make these come alive in the classroom

What does a Math Block Look Like?
Problem-centered teaching opens the mathematics classroom to exploring, conjecturing, reasoning, and communicating. Lappan, Fey, et al., 2006 * 3 min Title: Individually reflect, partner share Quote: flies in Individually reflect then partner share

Building with Toothpicks
Learning Intention We are learning to describe a symbolic rule for a given pattern. Success Criteria We will know we are successful when we can communicate clearly our thought process in developing a symbolic rule. * 1 min Will discuss Formative Assessment Principles and formative assessment strategies as we engage in math task. Participants will shift between student and teacher roles.

“…children are more motivated and task oriented if they know the learning intention of the task, but they are also able to make better decisions about how to go about the task. “ Shirley Clark, 2001 * 1 min Transition into research of why we do , connects strategy with Principle

Formative Assessment Strategies
Learning Intentions Help students make better decisions about how to go about a task. Emphasizes what the students will learn rather than what they will do. “What is the Big Math Idea?” What do I want students to know…? What do I want students to understand…? ...as a result of the learning and teaching activities. Success Criteria Criteria for assessment. Helps teachers and students decide whether the learning intention has been achieved Helps teachers and students determine next steps for learning Principles of Assessment for Learning Learning Intentions and Success Criteria support which Principles? * 5 min How many have done work around Learning Intention and Success Criteria? Discuss learning intention and success criteria Have them look at handout, find which Principles addressed Whole group share out as to what they find Answer: 1-4

On your own, think about how you would approach this problem Use a pattern from the shapes above to determine the perimeter of the fifth shape in the sequence. With a partner Share your strategies. Work together to determine the perimeter of the fifth shape. Discuss how you arrived at your solution. * 15 min Handout Launch: “Yesterday”, we worked on a pattern L problem that dealt with area-the number of tiles needs to build the shape. Today we are working on another pattern that we will have to determine perimeter. What do you know about perimeter? What does the word sequence mean when asked to find the next shape in the sequence? Explore: Bullet 1 flies in: remind participants bullet 1: DO NOT SOLVE, JUST THINK at first Allow about min of work time Ok if not done since will continue working later Facilitator must use questioning strategy that helped us find out what “students” Know, understand, and are able to do: Examples: “ How would you explain what you know right now?” “What is the problem about?” “What do you need to do next?” “What do you predict will happen as you build the next one?” “Is there a real-life situation where this could be used?” “How are you sure your answer is right” “What ideas that we learned before were useful in solving this problem?”

“Sharing of learning intentions is only the first step in the process of formative assessment, leading to pupil self-evaluation and teacher or peer feedback after the work is completed.” Shirley Clark, 2001 * 1 min Transition: moving into questioning: which is type of feedback

Formative Assessment Strategy
Strategic use of questioning Not only a pedagogical tool but a deliberate way for teachers to find out what students know, understand and are able to do. Provides teachers with the opportunity to identify and correct misconceptions and gaps in knowledge. Also identifies the need for extension work for those children whose knowledge and skills base demand it. Informs the teacher’s planning and selection of teaching strategies to move students from where they are in relationship to the learning target and where they need to go. Principles of Assessment for Learning Strategic use of questioning supports which Principles? * 5 min Answer: Principle 6, 7, 8 23

Strategic Use of Questioning
Think about the questions you or your group were asked. At your table, discuss what questions we used to find out what “students” know, understand, and are able to do. What questions would you ask students? With a partner, write questions for Building with Toothpicks that would: access background knowledge push student reasoning summarize math learning * 20 min Examples: “ How would you explain what you know right now?” “What is the problem about?” “What do you need to do next?” “What do you predict will happen as you build the next one?” “Is there a real-life situation where this could be used?” “How are you sure your answer is right” “What ideas that we learned before were useful in solving this problem?” Handout: Questioning handout

More Building with Toothpicks
On your own write a formula that you could use to find the perimeter of any Shape n. Working with your partner Explain how you each found your formula On blank piece of paper, record your formulas and explanations of how you arrived at your solutions Be prepared to share your solutions * 15 min This time as facilitators, we will focus on giving “student descriptive and/or effective feedback” Make sure they write stuff down since will be using later! Examples: Please be sure to pre-think possible feedback statements “I like how you drew the Stage 5. How does your drawing connect to your formula?” We will transition out of math block and talk about formative assessment strategy and formative assessment principle

Research by: John Hattie
“The most powerful single modification that enhances achievement is feedback. The simplest prescription for improving education must be ‘dollops of feedback’.” 1 min Transition into Principles of Formative Assessment 26 26

Type of Feedback Motivational Evaluative Descriptive Effective
Goal is to make the learner feel good. Evaluative Goal is to measure student achievement with a score or a grade. Descriptive Goal is to improve student achievement by telling the learner how to move forward in the learning process. Effective Goal is to get student to internalize the effective feedback to use the suggested strategies independently on future work. A D C * 2 min Handout: Types of Feedback Most likely familiar with these, many schools writing feedback on CABS and CRs Briefly go over each type 27 27 27

Effective teacher feedback Focuses on Success Criteria and tells children what they have achieved, where they need to improve. Provides specific suggestions of how that improvement might be achieved. Principles of Assessment for Learning Effective teacher feedback supports which Principles? * 5 min Principle is not just referring to giving written feedback 1x month on CABS or 3x a year on CRs. We need to push to give students oral feedback to students as they work. Answer: Principles 7,8, possibly 9 if using exemplar, possibly 10 if tracking, and 1-4 since connects to learning intentions and success criteria

Peer feedback Children offer each other advice about their work which references what is done well in relation to the Success Criteria. what still needs to be done in order to achieve the Success Criteria or learning target. specific suggestions on how the improvement might be achieved. Principles of Assessment for Learning Peer feedback supports which Principles? * 5 min Answer: Principles 7,8, possibly 9 if using exemplar, possibly 10 if tracking, and 1-4 since connects to learning intentions and success criteria

Peer Feedback Strategies
Plus, minus and what’s next? Two stars and a wish Thinking Hats Traffic lights * 5 min Handout Teacher needs to model each strategy before students can use This is not an exhaustive list….many more strategies, just selected “easy” ones to model 30

Trying Peer Feedback With your partner, decide which peer feedback strategy you would like to try. Find another partner pair to try out your strategy. As a group of 4 Share your work on Building with Toothpicks Give feedback Make adjustments to your work as needed * 10 min Participants are in student mode. Walk to each group and give each partner pair two of the same numbers. Ex. 2 people at the table get two 6’s and the other partner team gets two 8’s. The other two 6’s and 8’s will be at other tables. When it’s time to find another partner pair, the 6’s find each other to form a new group.

Using models or exemplars Teachers demonstrate for students how they can match the work of a peer to an exemplar which most closely resembles its qualities. Students explain to the peer why they have selected this particular exemplar and, using other exemplars, explain what the peer needs to do in order to improve. Exemplars of various products can be displayed in the classroom for use both by individuals to self-assess and also by peers to provide feedback. Students use the exemplars to help them articulate what changes they need to make to their own work in order to achieve the success criteria. Set learning targets based on what they still need to learn. Principles of Assessment for Learning Using models or exemplars supports which Principles? * 5 min Table discussion If there is concern that providing a model will lead to copying or stifle imagination and creativity, the teacher might consider providing exemplars of parts of the product - for example, an effective introduction or an interesting use of media in an artwork. Answer: Principle 9,

Personal Reflections An idea that squares with my beliefs. . .
A point I would like to make. . . *3 min Handout: half form…Complete to help process the morning Do not collect Parking Lot: if have this they want to address A question or concern going around in my head. . . 34

Lunch Time 1 hour (lunch + break) Please return on time!

What are the Sources of Evidence for Assessment?
“… Whatever conclusions we may make about children’s thinking must be based on observations [and] or products.” Bell, et al., 2007 * 1 min What is formative assessment? Make the point here that observations also include listening to students talk about their understanding, not just watching. 36

Wrapping It Up With your group of four, prepare your final presentation of Building with Toothpicks Be sure to include Your work around “What is the perimeter for the fifth shape?” Your work around “Write a formula that you could use to find the perimeter of any Shape n.” * 10 min Make the poster Reminder: final presentation should include adjustments based on peer feedback

Carousel Each table group passes their poster clockwise to the next table group when the facilitator calls “switch”. Each person takes individual notes about each poster around these ideas What question do you have about the strategy they used to build the formula and the written formula? What “aha” did you have about their strategy or written formula? How was their strategy or written formula similar to or different from yours? What other comments or questions do you have for the group about their poster? * 20 min Make as many switches as time permits. May not make it all the way around. Stress that each person takes their own notes. Hang posters on wall when finished

What Did We Learn? What question do you have about the strategy they used to build the formula and the written formula? What “aha” did you have about their strategy or written formula? How was their strategy or written formula similar to or different from yours? What other comments or questions do you have for the group about their poster? * 15 min Summarize: Whole group debrief Big math idea that need to be pulled out of summary: multiple representations of a pattern; identifying patterns; developing symbolic rules; equivalent expressions; developing understanding of some properties Facilitator: “lets start talking about the posters. Lets start with how the groups built the formula” (Be on the look out for what poster you want to begin with. Start with the easiest building of the formula to the more complex as you debrief questions about strategy, aha, similarities and difference for each of the posters selected.) Less time on this part Move on to written formula. Again be on the look out for the poster you want to begin with. Start with the easiest formula to the more complex as you debrief questions about formula, aha, similarities and difference for each of the posters selected. More time on this part ADD IN FORMULAS

Student self-assessment Understand the Learning Intention and Success Criteria Use the Success Criteria to evaluate their learning and what they still need to learn Act on feedback received from teacher and peers Set learning targets based on what they still need to learn Engage in oral reflections. Whole class or small group reflections are often more useful than written reflections. Principles of Assessment for Learning Student self-assessment supports which Principles? * 10 min for slides 40-42 Table discussion only ANSWER: 8, 1-4 since connects to learning intention and success criteria,

Student Self-Assessment Strategies
Traffic Lighting ‘I can explain this aspect to someone else.’ (green light) ‘I think I understand this aspect but I’d have difficulty explaining it to someone else.’ (yellow light) ‘I don’t understand this aspect.’ (red light) Reflective & Growth activities What have you learned? What did you find easy about learning to …? How would you do things differently next time? What did you find difficult while you were learning to …? What helped you when something got tricky …? How would you change this activity for another group/class who were learning to…? Handout This is not an exhaustive list….many more strategies, just selected “easy” ones to model

Self Assessment What helped you when something got tricky as you worked on the task or critiqued the reasoning of others? Silently reflect for moment Call on few to share out

Learning Intention We are learning to describe a symbolic rule for a given pattern. Success Criteria We will know we are successful when we can communicate clearly our thought process in developing a symbolic rule. * 1 min

Formative Assessment Strategies
Identifying the big math idea Unpacking the standards CCSS Grade Level Standards CCSS 6-8 Domain Progression Expressions and Equations Principles of Assessment for Learning Identifying the big math ideas and unpacking the standards support which Principles? * 5 min As we prepared this lesson, we talked about big math idea, and specific standards we addressing in order to develop the learning intention. We are going to ask you to engage in that process as well in a bit as well. Before we do that, align to Principle of Assessment for Learning Answer: 1, 4 44

Content Standards K-8 Structure
Domain: Expressions and Equations (6.EE) Cluster: Apply and extend previous understandings of arithmetic to algebraic expressions. Standard 1: Write and evaluate numerical expressions involving whole-number exponents. (6.EE.1) 1 min Standards define what students should understand and be able to do. Clusters summarize groups of related standards. Note that standards from different clusters may sometimes be closely related, because mathematics is a connected subject. Domains are larger groups of related standards. Standards from different domains may sometimes be closely related. 45

Middle Grades Domains Ratio-Proportional Relationships 6-7 The Number System 6-8 Expressions & Equations 6-8 Functions 8 Geometry 6-8 Statistics & Probability 6-8 * 1 min

Unpacking the Content Standard
What is the big math idea in the activity? What standards did we address? Individually read Grades 6-8 Domain Progression for Expressions and Equations With your group, discuss questions and highlight key ideas in this standard. Whole group discussion * 15 min Handout Big math idea: multiple representations of a pattern; identifying patterns; developing symbolic rules; equivalent expressions; developing understanding of some properties (commutative property), Group discussion: share out a few questions and highlights be sure they pull out 6.EE.4, 6.EE.9, 7.EE.2 can make arguments for others. 47

“Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.” Introduction to Common Core State Standards, 2010 * 3 min Individually Read Facilitator summarizes: “asking teacher to assess whether student has understood” goes beyond quizzes, CABS, CRs. Think of all the Principles and strategies we talked about and model that get at understanding what our student know As we develop our understanding of what students know, the need for differentiation arises (transitions to next slide)

District Definition Differentiated Instruction is a concept that makes it possible to maximize learning for ALL students. It is a collection of instructionally intelligent strategies based on student-centered, best practices that make it possible for teachers to meaningfully respond to the needs of diverse learners. It is made possible by modifying the content, process and/or product of instruction of a particular student or small group of students (typically to scaffold and extend learning), rather than the more typical pattern of teaching the class as though all individuals in it were basically the same. Differentiated instruction is an approach to ensuring all children achieve to the same high standards; instructional approaches are varied, not the expectations or the standards. * 10 min Handout Read use focus reading strategy: ? They have, * this makes sense, ! New idea react at table

Next steps…

Planning Time Decide which formative assessment principles you want to embed into your math instructional practices this month. Develop your plan of action * 20 min for slides 51-53 They are “on their own” developing their own unique plan of action. Slide 53 is where they begin planning using guiding questions We’re not collecting their plans. We are walking around acting as resources. Talk about next slide (Tools) and then they can start…

Tools of the Trade Comprehensive Mathematics Framework
Standards for Mathematical Practice Common Core State Standards Developing Effective Questions Types of Feedback Peer Feedback Student Self-Assessment Lesson Planning with Formative Assessment All these top ones handed out through out the session New handout lesson planning with formative assessment: can help you guide your conversations as you embedded principles

Planning Time Decide which formative assessment principles you want to embed into your math instructional practices this month. Develop your plan of action When and how will you implement your strategy? What additional information do you need? How can your MTL support you? How can your MTS support you? Plan a lesson embedding your strategy Keep this slide up so they can refer to it during planning.

3-2-1 Take Away School: 3 ideas you are walking away with from this session are… 2 ideas you will take back to your school to share with other grade level teachers are… 1 idea you will take back to your classroom to try with your students is… * 5 minutes Ask them to write on the large note cards Collect Please add your school name to this card as it will go to MTS and MTL to better support your needs.

Thank you. www.mmp.uwm.edu
The Milwaukee Mathematics Partnership (MMP), an initiative of the Milwaukee Partnership Academy (MPA), is supported with funding from the National Science Foundation 56

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