Presentation on theme: "All Teachers Reaching All Students"— Presentation transcript:
1 All Teachers Reaching All Students Math DepartmentBanking DayJanuary 24, 2011Start at 10:00All 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 positionAnnouncements: restrooms, lunch is from 12 – 1, remember to sign in on the sign-in sheetNorms: on the posterHand out Learning Logs – these are to take notesPowerpoint presentation will be available on the Professional Development Directory
4 Learning IntentionWe 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, 20014
5 Success CriteriaWe 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 Practice3 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.10:25Mathematical process is embedded in all the content strandsMath instruction must be taught with rigorStudents 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 PracticeK – 8 Grade level standardsHigh School standards“conceptual categories”10:30Yellow hand-out2 Pieces: The what: conceptual categories (there are 6 and are listed starting on the following slide) portray a coherent view of high school mathematicsThere are 8 mathematical practice standardsThe 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 appropriatelyThe 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 QuantityThe Real Number SystemQuantitiesThe Complex Number SystemVector and Matrix OperationsAlgebraSeeing structure in expressionsArithmetic with Polynomials, Rational ExpressionsCreating EquationsReasoning with Equations and InequalitiesFunctionsInterpreting functionsBuilding functionsLinear, quadratic and exponential modelsTrigonometric FunctionsToday’s focus will be on the conceptual category, Algebra, with a focus on Systems of EquationsAlgebra 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 ModelingGeometryCongruenceSimilarity, Right Triangles and TrigonometryCirclesExpressing Geometric Properties with EquationsGeometric Measurement and DimensionModeling with GeometryStatistics and ProbabilityInterpreting categorical & quantitative dataMaking Inferences & Justifying ConclusionsConditional Probability and Rules of Prob.Using Probability to Make DecisionsThese are like the content standardsRepackaged 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 strandsThis is the focus of study for this year. Our focus today is on standard #310:40Pink hand-outMTL meetings so far have covered standards 1 – 4Justify understanding, reasoning, problem solving, speaking and listening to others, constructing viable arugments, and critiquing the reasoning of others.
11 Whip AroundStep 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.10:45Pink Handout (back side)Reason inductivelyExplaining if something/strategy holds for all numbersA mathematical demonstration of the validity of a lawStudents should be able to…Use stated assumptions, definitions and construct argumentsMake conjectures, build a logical progression of statements to explore the truth of their conjecturesAnalyze situations (decomposing)Recognize and use counterexamplesJustify their conclusionsMake a sequence of connectionsListen and speak to others about their argumentsAsk useful questions to clarify or improve the argumentsMake plausible (reasonable) arguments that take into account the context of the dataCompare the effectiveness of two plausible argumentsDistinguish correct logic/reasoning from flawed infoUse 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-1211:00How 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 studentsEmphasize 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.11:20The cycle brings up a lot of the work that we have already doneStart small and then move to a bigger groupBegin with students that you know wellBegin with formative assessment, know where they are in order to guide them to what they are expected to learn and be able to doDifferentiate in order to reach all studentsLESA is part of the model stage of the cycleRick 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 StigginsRefer 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 feedbackAssessment of learning: summative, final grade, portfolio, reporting out, tests, quizzesAssessment for learning: formative, ongoing, redo a task, change in teaching practiceHomework 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 candescribe whatmathematical ideas they are learning in thelesson.(4) Teachers canarticulate how the math lesson is aligned to district learning targets, state standards, and classroom assessments(CABS), and fits withinthe progression ofstudent learning.(5) Teachers useClassroom 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 1Learning TargetsStage 2Align State Framework and Math ProgramStage 3Common CABSStage 4Student Work on CABSStage 5Descriptive Feedback on CABSUnderstand 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.11:40Yellow hand-outLast three columns: This is showing how assessment is far more than testing more frequentlyYou have to give students a forum to discuss the feedback so that they internalize it and use it to further their mathematical thinkingThe 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 assessmentKnow you studentsContent/process/product are ways to differentiateLESA 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., 2006Problem solving activities create a learning environment that embraces discourseStudents are able to articulate their strengths and weaknesses in mathematicsAs 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 knowledgeTo stimulate, not stymie, thinkingExploreTo become actively involved with the problem, skill, or conceptTo look for patterns and investigate different strategiesTo record and organize the work and thinking that is doneRefer to process that we did with bike problem.White LESA hand-outThe Discovering Series is set up to use the LESA modelThe task was linked to the real-worldThe task had multiple entry approachesDoableEngagingMultiple strategiesThe task must require justifications and explanations for answers or methodsThe task should be accessible to all studentsThe task should pose a challenge
21 What is LESA? Summarize Apply To lock in the learning To articulate mathematical ideas and vocabulary from the lessonTo have students compare and contrast ideas and strategiesApplyTo practice what students learnedTo extend the use of skills and concepts learnedTo make connections to other learningRefer to process that we did with bike problem.We did not do the apply part of LESA with the bike problem
22 Learning IntentionWe 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.11:55End morning and begin afternoon with this slide.1:00So far, we discussed: standards, instructional designAfter lunch, DI and classroom w/ all the elements2222
23 Success CriteriaWe 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.1:00Stop for lunch23
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 = 163f – s = 332f = 196f = 9898 + s = 163s = 65Debrief 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 IntentionWe are developing our understanding of systems of equations.1:20
28 Success CriteriaGiven 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.1:30Hand 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)?1:50Give out chart paper.
31 Thinking about the Math f + s = 163f – s = 332f = 196f = 9898 + s = 163s = 65Refer to chapter 4.4Talk 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 IntentionWe are developing our understanding of systems of equations.2:0532
33 Success CriteriaGiven a situation, you can create and solve a system of equations using the elimination method.33
34 ApplyIn your groups, discuss what situations you could give the students to apply their knowledge?Explain why you chose that situation.2:10As 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 LESAExploreHow 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 IntentionWe 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.2:453939
40 Success CriteriaWe 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 2.2:50Green handout (reading)
42 Differentiated Instruction A strategy that makes it possible to maximize learning for ALL studentsA collection of instructionally intelligent strategies based on student-centered best practicesAssists teachers in creating different pathways that respond to the needs of diverse learnersIncreases 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 challenge42
43 Key Components of Successful Inclusive Education Differentiated InstructionCo-Teaching/Team TeachingCommon Planning TimeEducating 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 placeLaw doesn’t include “inclusion” in it. It talks about LRE (least restrictive environment) onlyWe need to graduate students with skills. SE teachers were trained in intervention procedures, not content43
44 Expected Outcomes of Differentiated Instruction High expectations for All studentsHigher academic achievement for All studentsFewer students in Tier 2 and Tier 3 interventions as well as fewer students referred for special educationTier 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-outInstructionally intelligent strategies: various approachesNot watering-downModification – the making of a limited change in somethingModify – to make minor changesAccommodation – adaptation, adjustmentExample: the automatic adjustment of the eye for seeing at different distances effected by changes in the lense
46 Ways Learners are Different LEARNING PROFILEINTERESTSREADINESSSocial/Emotional Factors:*Language*Culture*Health*Family Circumstances*Special CircumstancesLearning Styles*Auditory*Visual*Tactile*KinestheticMultiple IntelligencesHobbiesLikesDislikesSkills*Language Development*Literacy*Background Knowledge*Pre-AssessmentContent*Formative Assessment*MAPConcepts*Summative AssessmentThis slide should be edited to contain examples for every content area, please provide examples of content, process and product per Dr. RamirezMultiple 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 s46
47 Ways to DifferentiateContent-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?”ExampleContent-Start with the standardScience Standard F.12.1 Evaluate the normal structures and the general and special functions of cells in single-celled and multiple-celled organismsSkill-What are the parts of a plant cell and animal cell?Ongoing assessment is extremely important to maximize student achievementProcess-Think about the different learners in your classObserve a plant/animal cell under a microscopeDraw and label the parts of the plant/animal cellMake a list of words to describe what your observe under the microscopeWhat type of plant/animal cell was observed, research on the internetProduct-What is the end product of learning the skill?Give an oral presentation on the components of a plant/animal cellUse the computer to draw a picture of a plant/animal cellShow pictures of plant/animal cells and have students pick correct picture-use switches/technology if neededCompare/Contrast graphic organizer of plant/animal cellSpecial 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 EducatorsProcess is an easy entry point for teachers because the book already offers this option through the one-step versus multiple step investigations47
48 Learning IntentionWe 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.4848
49 Success CriteriaWe 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.3:10Please put your school name on the index card.If you would like a personal response to your question, please add your nameA 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.3:20White and blue hand-outs
53 Next Steps… Ongoing planning at the district and school level Schools determine their individual school needsDetermine professional development needs at the individual and school levelMove towards more differentiation and inclusive practices at the school and classroom levelTenets 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 Foundation54