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All Teachers Reaching All Students

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1 All Teachers Reaching All Students
Math Department Banking Day January 24, 2011 Start at 10:00 All students must have the opportunity to learn rigorous mathematics. We should focus on students’ understanding rather than on what skills or procedures they either have or do not have. Many teachers do not plan and conduct classroom dialogue in ways that might help students to learn. (Inside the Black Box: Assessment for Learning in the Classroom) Black and Wiliam 2004

2 Let’s Do Math! Explore multiple approaches to demonstrate your solution: Uncle Eddie asked the girls to order 54 new wheels for the 21 skateboards and bicycles in his repair shop. How many bicycles and how many skateboards are in the shop? Share your approaches with your group. Choose one approach to post on chart paper. Only title comes up – we say something fun – that’s the launch. Then the rest comes in and we do the explore. We will summarize later when we debrief standard #3. Work independently or in partners

3 Logistics Introductions Announcements Norms Learning Log 10:15
Attendance sheets. Introductions: Name, school and position Announcements: restrooms, lunch is from 12 – 1, remember to sign in on the sign-in sheet Norms: on the poster Hand out Learning Logs – these are to take notes Powerpoint presentation will be available on the Professional Development Directory

4 Learning Intention We are learning to deepen our understanding of the Standards and the district’s vision of Instructional Design and Differentiated Instruction and make connections with classroom practice. 10:20 (2 min) Standards: Common core state standards (this is the “what” we teach) and mathematical practice standards (this is the “how” we teach) We are spending more time on the standards for practice this year because the WKCE has not been changed to reflect the content standards. We will spend more time on those soon. Children are more motivated and task orientated 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 Clack, 2001 4

5 Success Criteria We will be successful when we can articulate the connections between the Standards, Instructional Design, and Differentiated Instruction and utilize these ideas when planning a math lesson. Standards refers to both the Common Core State Standards and the Standards for Mathematical Practice 3 min

6 Comprehensive Mathematics Framework
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. 10:25 Mathematical process is embedded in all the content strands Math instruction must be taught with rigor Students must engage in discourse as they grapple with challenging mathematics…this would help them to communicate mathematically

7 Common Core State Standards
Standards for Mathematical Practice K – 8 Grade level standards High School standards “conceptual categories” 10:30 Yellow hand-out 2 Pieces: The what: conceptual categories (there are 6 and are listed starting on the following slide) portray a coherent view of high school mathematics There are 8 mathematical practice standards The standards for mathematical practice define what mathematics looks like in you classroom everyday. Process standards of problem solving, reasoning and proof, communication, representation and connections. Skill in carrying out procedures flexibly, accurately, efficiently and appropriately The standards define what students should understand and be able to do in mathematics. The standards provide clear signposts along the way to the goal of college and career readiness for all students. 7

8 High School Conceptual Categories with Clusters
Number and Quantity The Real Number System Quantities The Complex Number System Vector and Matrix Operations Algebra Seeing structure in expressions Arithmetic with Polynomials, Rational Expressions Creating Equations Reasoning with Equations and Inequalities Functions Interpreting functions Building functions Linear, quadratic and exponential models Trigonometric Functions Today’s focus will be on the conceptual category, Algebra, with a focus on Systems of Equations Algebra is an example of the conceptual category, the bullets under the category are called clusters. The standards appear under the clusters and are not shown on these slides. We are going to focus on Reasoning with equations and Inequalities.d

9 High School Conceptual Categories with Clusters
Modeling Geometry Congruence Similarity, Right Triangles and Trigonometry Circles Expressing Geometric Properties with Equations Geometric Measurement and Dimension Modeling with Geometry Statistics and Probability Interpreting categorical & quantitative data Making Inferences & Justifying Conclusions Conditional Probability and Rules of Prob. Using Probability to Make Decisions These are like the content standards Repackaged NCTM standards

10 Emphasize connection with CMF.
The content standards were around the learner communicating mathematically in the CMF, they are still around the learner in this new diagram. The learner communicating mathematically is embedded in all strands This is the focus of study for this year. Our focus today is on standard #3 10:40 Pink hand-out MTL meetings so far have covered standards 1 – 4 Justify understanding, reasoning, problem solving, speaking and listening to others, constructing viable arugments, and critiquing the reasoning of others.

11 Whip Around Step 1: Write down or highlight all of the words or short phrases that really stand out to be important as you read the Standard for Math Practice #3. Step 2: Stand up! One person at a time, read one item that is important to you. Step 3: When one of your ideas is said (by you or someone else), check it off. Step 4: When everything on your list is checked off, sit down. 10:45 Pink Handout (back side) Reason inductively Explaining if something/strategy holds for all numbers A mathematical demonstration of the validity of a law Students should be able to… Use stated assumptions, definitions and construct arguments Make conjectures, build a logical progression of statements to explore the truth of their conjectures Analyze situations (decomposing) Recognize and use counterexamples Justify their conclusions Make a sequence of connections Listen and speak to others about their arguments Ask useful questions to clarify or improve the arguments Make plausible (reasonable) arguments that take into account the context of the data Compare the effectiveness of two plausible arguments Distinguish correct logic/reasoning from flawed info Use objects, drawings, diagrams

12 Standards for Mathematical Practice
Use this slide to support the Whip Around Strategy. On back of pink hand-out

13 Making Connections Share and justify your strategies.
Analyze the posters that were created for Uncle Eddie’s Wheels. Where do you see evidence of the standard we just studied? Groups may need to explain their approaches and solution in order to truly bring the standard alive. Stress that planning for the SFP should and must be ongoing in classrooms throughout the school year. Students need to be engaged in the all areas of practices throughout K-12 11:00 How does your solution relate to the task? Scaffold our answers (building from different levels of complexity)

14 Assessment Think – Pair – Share What does assessment mean to you?
What types of assessment do you use in your classroom? Highlight key areas, such as, assessment “of” vs “for” learning, district CABS, feedback, involving students, 11:25

15 Instructional Cycle Informed by Assessment
Know your students Emphasize connections of work done in the district around formative assessment as well as the new work to be done to reach all students using the idea of the Instructional Cycle. 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. Note the different ways to differentiate, but we will not cover all of them. The graphic for the ppt. comes from Rick DuVall.  He’s a literacy-differentiated instruction guru type. 11:20 The cycle brings up a lot of the work that we have already done Start small and then move to a bigger group Begin with students that you know well Begin with formative assessment, know where they are in order to guide them to what they are expected to learn and be able to do Differentiate in order to reach all students LESA is part of the model stage of the cycle Rick DuVall

16 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. Richard Stiggins Refer to knowing and understanding the mathematics of a lesson, involving students in all aspects of teaching and learning, that is communicating to students what they are learning; how they will know they learned the material; how it fits in to previous and future math they will learn;, and by all means to give them dollops of feedback Assessment of learning: summative, final grade, portfolio, reporting out, tests, quizzes Assessment for learning: formative, ongoing, redo a task, change in teaching practice Homework can be both

17 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. 11:40 Yellow hand-out Last three columns: This is showing how assessment is far more than testing more frequently You have to give students a forum to discuss the feedback so that they internalize it and use it to further their mathematical thinking The priority in giving feedback is to challenge students to tease out their assumptions and to help them be critical about the quality of arguments (Black and Wiliam, 2004, Inside the Black Box)

18 Looking Back and Looking Forward
The work we’ve done on formative assessment will help guide us as we work with differentiated instruction. This needs to be a comprehensive understanding on the ten principles of FA. Note that many teachers are familiar with Principle 5 and we need to push their understanding of the other principles as they relate to the big idea of formative assessment Know you students Content/process/product are ways to differentiate LESA is a part of the model stage of the cycle

19 How Does This Look? Problem-centered teaching opens the mathematics classroom to exploring, conjecturing, reasoning, and communicating. Lappan, Fey, et al., 2006 Problem solving activities create a learning environment that embraces discourse Students are able to articulate their strengths and weaknesses in mathematics As students wrestle with problems, their ideas are going to be engaged, tested, revised, refined and connected with other ideas they already possess.

20 What is LESA? Launch Explore To capture the learner’s attention
To activate prior knowledge To stimulate, not stymie, thinking Explore To become actively involved with the problem, skill, or concept To look for patterns and investigate different strategies To record and organize the work and thinking that is done Refer to process that we did with bike problem. White LESA hand-out The Discovering Series is set up to use the LESA model The task was linked to the real-world The task had multiple entry approaches Doable Engaging Multiple strategies The task must require justifications and explanations for answers or methods The task should be accessible to all students The task should pose a challenge

21 What is LESA? Summarize Apply To lock in the learning
To articulate mathematical ideas and vocabulary from the lesson To have students compare and contrast ideas and strategies Apply To practice what students learned To extend the use of skills and concepts learned To make connections to other learning Refer to process that we did with bike problem. We did not do the apply part of LESA with the bike problem

22 Learning Intention We are learning to deepen our understanding of the Standards and the district’s vision of Instructional Design and Differentiated Instruction and make connections with classroom practice. 11:55 End morning and begin afternoon with this slide. 1:00 So far, we discussed: standards, instructional design After lunch, DI and classroom w/ all the elements 22 22

23 Success Criteria We will be successful when we can articulate the connections between the Standards, Instructional Design, and Differentiated Instruction and utilize these ideas when planning a math lesson. End morning and begin afternoon with this slide. 1:00 Stop for lunch 23

24 Let’s Play a Number Game!
Find two numbers that add to 15 and when you subtract them you get 3. The purpose is to activate background knowledge. This is our launch. 1:05

25 Let’s Play another Number Game!
This is a mini-lesson. Each participant should solve individually. Partner share. Facilitators ask some groups to chart on paper. 10 min. (1:10) Pick two groups to chart their answers and hang them up.

26 Thinking about the Math
f + s = 163 f – s = 33 2f = 196 f = 98 98 + s = 163 s = 65 Debrief why the equations model the number game. Refer to previous work on equivalent expressions in multiple representations and the work in 4.4 using algebraic properties to show equivalent expressions. Explore how this systems of equations led to one equation and one unknown…don’t give away too much as this is the part they are to explore in the investigation, that is, elicit responses from participants and show restraint in stepping in to showing how elimination works. 5 min. (1:20) Facilitators should chart

27 Learning Intention We are developing our understanding of systems of equations. 1:20

28 Success Criteria Given a situation, you can create and solve a system of equations using the elimination method.

29 Paper Clips and Pennies
Each pair will be given a set of instructions to complete this investigation as partners. As a group of four, record and organize the work and thinking that your group completed on chart paper. Each group will have a different set of instructions. Make sure the “One Step” groups do BOTH systems! This is the “Explore” part. A time deadline will need to be established. Facilitators are walking around listening around the task facilitating conversations. The books already differentiate. There is a step-by-step investigation and a “One Step”. Chart paper is not always available. You may use brain boards. 1:30 Hand out the THREE different sets of instructions. This is the Explore part of the LESA

30 Summarize Let’s look at those posters.
Given a system of equations, what is necessary to find an answer using the elimination method? How does what we learned today compare to the strategies that we learned in previous lessons? Surface why elimination works. How does this connect with 5.1 (tables and graphs) and 5.2 (substitution)? 1:50 Give out chart paper.

31 Thinking about the Math
f + s = 163 f – s = 33 2f = 196 f = 98 98 + s = 163 s = 65 Refer to chapter 4.4 Talk about properties that drive elimination. You may want this on chart paper so you can put side-to-side with the other papers.

32 Learning Intention We are developing our understanding of systems of equations. 2:05 32

33 Success Criteria Given a situation, you can create and solve a system of equations using the elimination method. 33

34 Apply In your groups, discuss what situations you could give the students to apply their knowledge? Explain why you chose that situation. 2:10 As you plan your lessons you should think in terms of the LESA model

35 LESA Launch How did we capture the learner’s attention?
How did we activate prior knowledge? How did we stimulate, not stymie, thinking? Refer to process that we did with pennies and paper clips problem. Refer to LESA. Make sure you summarize every day. Participants are reflecting on what the facilitators demonstrated during the teaching process

36 LESA Explore How did we become actively involved with the problem, skill, or concept? How did we look for patterns and investigate different strategies? How did we record and organize the work and thinking that is done? Refer to process that we did with pennies and paper clips problem. Refer to LESA. Make sure you summarize every day.

37 LESA Summarize How did we lock in the learning?
How did we articulate mathematical ideas and vocabulary from the lesson? How did we have students compare and contrast ideas and strategies? Refer to process that we did with pennies and paper clips problem. Refer to LESA. Make sure you summarize every day.

38 LESA Apply How did we practice what students learned?
How did we extend the use of skills and concepts learned? How did we make connections to other learning? Refer to process that we did with pennies and paper clips problem. Refer to LESA. Make sure you summarize every day.

39 Learning Intention We are learning to deepen our understanding of the Standards and the district’s vision of Instructional Design and Differentiated Instruction and make connections with classroom practice. 2:45 39 39

40 Success Criteria We will be successful when we can articulate the connections between the Standards, Instructional Design, and Differentiated Instruction and utilize these ideas when planning a math lesson. 40

41 Introduction to Differentiation
Read and highlight the important ideas. Discuss with a partner why differentiation is important in our math classrooms. Why did the author choose the title, ”The Challenge in Math Classrooms”? Bottom of page 1 and top of page 2. 2:50 Green handout (reading)

42 Differentiated Instruction
A strategy that makes it possible to maximize learning for ALL students A collection of instructionally intelligent strategies based on student-centered best practices Assists teachers in creating different pathways that respond to the needs of diverse learners Increases the success of ALL students (including students with disabilities, ELLs and Gifted & Talented) The more ways you teach, the more students you reach! Differentiation for your students that need extra challenge 42

43 Key Components of Successful Inclusive Education
Differentiated Instruction Co-Teaching/Team Teaching Common Planning Time Educating ALL students using their grade level core content standards to the maximum extent possible (Least Restrictive Environment) What do you think when someone says Least Restrictive Environment? Intent of law was to point out that SE (special education) is a service, not a place Law doesn’t include “inclusion” in it. It talks about LRE (least restrictive environment) only We need to graduate students with skills. SE teachers were trained in intervention procedures, not content 43

44 Expected Outcomes of Differentiated Instruction
High expectations for All students Higher academic achievement for All students Fewer students in Tier 2 and Tier 3 interventions as well as fewer students referred for special education Tier 1 is for all students

45 District Definition of Differentiation
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. As you read/they read this slide, the middle of the slide uses CONTENT, PROCESS, and PRODUCT.  A more complete differentiation sentence is, “The ways we differentiate content, process and product are based on the student’s READINESS, LEARNING PROFILE, AND INTERESTS.” The definition was not meant to be an all inclusive definition rather a springboard for discussion on how to differentiate. White hand-out Instructionally intelligent strategies: various approaches Not watering-down Modification – the making of a limited change in something Modify – to make minor changes Accommodation – adaptation, adjustment Example: the automatic adjustment of the eye for seeing at different distances effected by changes in the lense

46 Ways Learners are Different
LEARNING PROFILE INTERESTS READINESS Social/Emotional Factors: *Language *Culture *Health *Family Circumstances *Special Circumstances Learning Styles *Auditory *Visual *Tactile *Kinesthetic Multiple Intelligences Hobbies Likes Dislikes Skills *Language Development *Literacy *Background Knowledge *Pre-Assessment Content *Formative Assessment *MAP Concepts *Summative Assessment This slide should be edited to contain examples for every content area, please provide examples of content, process and product per Dr. Ramirez Multiple Intelligences-Verbal-Linguistic, Logical-Mathematical, Visual-Spatial, Musical, Bodily-Kinesthetic, Interpersonal, *Planning around student interests often result in students increasing their focus and attention to what is going on in the classroom. Link back to the different tasks: one-step versus multi-step s 46

47 Ways to Differentiate Content-What is the standard I am going to teach? What skill am I going to teach? Process-How am I going to teach that skill in a variety of ways that will hit the developmental levels of each of my students? Product-What will my student produce as evidence of understanding of the skill? Math: Our goal was to model the differentiation of “Process”. Ask participants, “What is the evidence that we differentiated by process?” Example Content-Start with the standard Science Standard F.12.1 Evaluate the normal structures and the general and special functions of cells in single-celled and multiple-celled organisms Skill-What are the parts of a plant cell and animal cell? Ongoing assessment is extremely important to maximize student achievement Process-Think about the different learners in your class Observe a plant/animal cell under a microscope Draw and label the parts of the plant/animal cell Make a list of words to describe what your observe under the microscope What type of plant/animal cell was observed, research on the internet Product-What is the end product of learning the skill? Give an oral presentation on the components of a plant/animal cell Use the computer to draw a picture of a plant/animal cell Show pictures of plant/animal cells and have students pick correct picture-use switches/technology if needed Compare/Contrast graphic organizer of plant/animal cell Special Note: Please hit home the point that when you are differentiating that if you are good at art, you always draw pictures in art class. You have to expand to other ways of showing how you are good at art than just drawing pictures…. For more examples …see DI Samples of Tiered Assignments Resource Booklet by Staff Development for Educators Process is an easy entry point for teachers because the book already offers this option through the one-step versus multiple step investigations 47

48 Learning Intention We are learning to deepen our understanding of the Standards and the district’s vision of Instructional Design and Differentiated Instruction and make connections with classroom practice. 48 48

49 Success Criteria We will be successful when we can articulate the connections between the Standards, Instructional Design, and Differentiated Instruction and utilize these ideas when planning a math lesson. 49

50 Personal Reflections Include your school name on your index card
An idea that squares with my beliefs. . . A point I would like to make. . . Collect all index cards. 3:10 Please put your school name on the index card. If you would like a personal response to your question, please add your name A question or concern going around in my head. . .

51 Hand out blank template and Valerie’s completed template
Hand out blank template and Valerie’s completed template. Let’s hope there’s a little time left for them to discuss and plan with colleagues. 3:20 White and blue hand-outs

52       White hand-out (blank LESA)

53 Next Steps… Ongoing planning at the district and school level
Schools determine their individual school needs Determine professional development needs at the individual and school level Move towards more differentiation and inclusive practices at the school and classroom level Tenets of this page need to be incorporated into your final slide. Tell the teachers that they should be discussing this with their MTLs and that the MTLs will be asked to report back at a later MTL meeting on how differentiation has been going in their buildings. 53

54 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 54


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