Developing Deeper Learning through Rich Mathematical Tasks 2019 Mathematics Institute 6-8 Session Welcome and Introductions Community Builder Stand up if: 3 Just Like Me
Stand up if you are a pet owner 4 Just Like Me Stand up if you have used tasks in your classroom 5 Just Like Me Stand up if you drove over an hour to get here today.
6 Just Like Me Stand up if you have scored student work with a rubric before. 7 Just Like Me Stand up if you have been teaching less than five years.
8 Just Like Me Stand up if you have an administrative role. 9 Just Like Me Stand up if you have heard of visible learning. 10
Just Like Me Stand up if you you believe you have an impact on student learning. 11 Turn and Talk How might you use this activity in your classroom to build community? What is the importance of building a classroom community? What additional ways do you foster
Reflection and Closure 13 Opening Video Message from VDOE 14 Learning Intentions Content: I am learning about strategies and approaches that make teaching and learning more visible. Language:
I am learning to use the language of a visible learning mathematics classroom. Social: I am learning how to listen and respond to my colleagues ideas in ways that move everyone forward as learners. 15 Module I Overview Visible Learning, Equity, and Identity
Success Criteria I can recognize strategies in teaching and learning that have high impacts (effect size) on student achievement. I can recognize and support equitable learning opportunities for all students that promote positive student mathematical identity and agency. I can describe how to create a classroom environment that supports the development of assessment-capable mathematics learners. 17 Barometer of Influence and Effect Size
Le Vi ar sib ni le Pa ng B ge o 5 ok Adapted from Hattie, J. (2009) Visible Learning: A Synthesis of Over 800 Meta-analyses Relating to Achievement. New York, NY: Routledge. 18
The Barometer of Influence Reverse Effects Have reverse consequences on learning Developmental Effects Students could achieve to this level on their own. Teacher Effects The effect that any teacher can produce Zone of Desired Effects Will have greater than average influence on achievement 19 Hinge Point
20 Desmos Barometer Sort Go to Student.Desmos.com Enter the code: Complete the sort When you are finished please stand 21 Desmos Barometer Sort Pair Up Find an eye contact partner Answer the following prompts:
My name is I am from My familiarity with Hatties research is My reaction to the sort is 22 Effect Sizes of NCTMs Mathematical Teaching Practices 23 Establish mathematics goals to
focus learning. 24 Implement tasks that promote reasoning and problem solving. 25 Facilitate meaningful mathematical discourse. 26
Pose Purposeful Questions 27 Support productive struggle in learning mathematics. 28 Elicit and use evidence of student thinking.
29 We should not hold any influence, instructional strategy, action, or approach to teaching and learning in higher esteem than students learning. Using the right approach at the right time increases our impact on student learning in the mathematics classroom. -Teaching Mathematics in the Visible Learning Classroom: Grades 6-8 Math Identity, Agency, and Equity 31
Mathematics Identity Graph See H an d ou t Draw a timeline of your mathematical experiences indicating 3-5 distinct high and low points. 32
Vi s ib le Teacher Mindframes Le Bo ar The teacher has the capacity to select and ok nin Pa implement geenhance g various teaching and learning strategies that 1 their adolescent learners in mathematics.
The decisions the teacher makes about their teaching have an impact on their students learning. Each and every student can learn mathematics and the teacher takes responsibility to teach all learners in their middle school mathematics class. The teacher must continuously question and monitor the impact of their teaching on student learning. How do the belief statements you wrote in last question from the Math Identity Graph handout connect to these mindframes? 33
Positive Mathematical Identity Empowering students to see themselves as capable of participating in and being doers of mathematics developed in a classroom where students: Are active participants; Engage in reasoning and sense making;
Strive to make their thinking visible and intelligible to others; Use multiple forms of discourse; and Critique their world through using mathematics. Adapted from Catalyzing Change in High School Mathematics Initiating Critical Conversations. Reston, VA: NCTM, 2018. 34 Supporting Equitable Learning Mathematical identity dispositions and
deeply held belies that individuals develop about their ability to participate and perform effectively in mathematical contexts and to use mathematics to change the conditions of their lives. (Martin, 2012, p. 57-58) Mathematical agency students capacity and willingness to engage mathematically (Schoenfeld, 2014, p. 407) 35 Identity and Agency
36 A Visible Learning Classroom is... Teachers Learners Predict: What do you think visible teaching looks like? What do you think visible learning looks like? 37
Creating Assessment-Capable Visible Learners Vi s ib Assessment-Capable Visible lLearner e Le Bo ar Pa ok ni ng ge 10
Adapted from Teaching Mathematics in the Visible Learning Classroom: Grade 6-8 39 Vi Impact of Visible Teaching sible Le Visible Teaching Visible Learning Bo ar Pa ok ni Clearly communicates
So that learners g understand n the g e the learning intention intention of the learning 20 experience. Identifies challenging success criteria arr
ow So that learners know what success looks like. Utilizes a range of learning strategies So that learners develop a range of learning strategies. Continually monitors student learning
So that learners know when they are not progressing and can make adjustments. So that learners can seek feedback about their learning. Provides feedback to learners Source: Teaching Mathematics in the Visible Learning Classroom: 40 https://us.corwin.com/en-us/sam/teaching-mathematics-in-the-visible-learning-classroom-grades-6-8
Assessment-Capable Visible Learners 41 Mistake-Friendly Classroom Mistakes are not only opportunities for learning, as students consider the mistakes, but also times when our brains grow. Understanding the power of mistakes is critical, as children and adults everywhere often feel terrible when they make a mistake in math. They think it means they are not a math person, because they
have been brought up in a performance culture (see Boaler, 2014) in which mistakes are not valuedor worse, they are punished. You cubed 42 Focus of 2018 Mathematics Institutes Adapted from Smith, M. et al. (2017) Taking Action Implementing Effective Mathematics 43 Teaching Practices Series, National Council of Teachers of Mathematics.
Focus of 2019 Mathematics Institutes Establish mathematics goals to focus learning. Implement tasks that promote reasoning and problem solving. Build procedural fluency from conceptual understanding. Facilitate meaningful mathematical discourse. Use and connect
Pose purposeful mathematical questions. representations. Elicit and use evidence of student thinking. Support productive struggle in learning mathematics. Adapted from Smith, M. et al. (2017) Taking Action Implementing Effective Mathematics Teaching 44
Practices Series, National Council of Teachers of Mathematics. Reflection on Success Criteria I can recognize strategies in teaching and learning that have high impacts (effect size) on student achievement. I can recognize and support equitable learning opportunities for all students that promote positive student mathematical identity and agency. I can describe how to create a classroom environment that supports the development of assessment-capable mathematics learners.
45 Square, Circle, Triangle Reflection See Refle ctio Shee n t Based on Module I... What is one idea that squared with
your thinking? What is a question circling in your mind? What point(s) would you like to remember, that might impact your work? 46
Module II Task Implementation (Before) Success Criteria I can identify how teacher clarity about learning intentions and success criteria contributes to student success. I can identify strategies, methods or approaches to meet the learning needs of individual students. I can distinguish between tasks that will engage students in higher levels of cognitive demand versus lower levels of cognitive demand. I can describe the factors associated with the decline or maintenance of the cognitive level of a rich mathematical
task. I can anticipate student solution strategies and misconceptions associated with the implementation of a mathematical task. 48 Ingredients for Progress Toward Mastery 49 Vi sRich ib
Clear Progress Clear Learning le Learning Mathematica Toward Intentions l Tasks Mastery Le Intentions Pa Bo arn
ge oand in k social Dividing learning intentions into content, language, g 4 varieties can provide teachers and students alike a7clearer -4 sense of the days expectations. 8 -Teaching Mathematics in the Visible Learning Classroom: Grades 6-8
Content Language What is the math I am supposed to use and learn today? How should I communicate my
mathematical thinking today? Social How should I interact with my learning community today? 50 Writing Clear
Mastery SOL 6.6b The student will solve practical problems involving operations with integers. Content Language What is the math I am supposed to use and learn
today? How should I communicate my mathematical thinking today? Social How should I interact with my learning
community today? 51 Vi s ib le Le Pa Bo arn ok ge involving in SOL 6.6b The student will solve practical problems
g 8 0operations with integers. 81 Writing Clear Learning Intentions Clear Learning Intentions
Rich Mathematical Tasks Progress Toward Mastery Content I am learning to use my understanding of integer addition and subtraction to solve problems about temperature comparisons or changes.
Languag e I am learning to explain my problem-solving approach verbally and in writing. Social I am learning to explain my problem-solving thinking clearly to my peers. 52
What Does Success Look Like? Clear Learning Intentions Rich Mathematical Tasks Progress
Toward Mastery Success Criteria: I can find and explain temperature relationships among the cities in the task. I can compute missing values accurately. I can explain the process used to figure out missing values. 53 Establish mathematics goals to
focus learning. 54 How do tasks and their implementation impact mathematics learning? Student learning is greatest in classrooms where the tasks consistently encourage high level student thinking and reasoning and least in classrooms where the tasks are routinely procedural in nature. (Boaler and Staples 2009; Hieber and Wearne 1993;
Stein and Lane 1996) 55 Rich Mathematical Tasks - Definition Rich mathematical tasks engage students in sensemaking through deeper learning that require high levels of thinking, reasoning, and problem solving. 56 Characteristics of Rich Tasks Promote high levels of cognitive demand Allow multiple entry points to students with a wide
range of skills and abilities Allow for multiple solution pathways Promote reasoning and sense making Encourage the use of varied representations Require justification or explanation Encourage connections among ideas Are authentic, relevant, or problem-based 57 Implement tasks that promote reasoning and problem solving.
58 Task Launch Source: Adapted from 2015 MARS, Shell Center, University of Nottingham 59 The Task See Cards on
Table 1. Place all cards face up on the table. 2. When it is your turn, connect two City Temperature cards using a Changes in Temperature arrow card. Figure out any missing temperatures. Explain your calculations verbally to your group. 3. If others in your group disagree, they should explain why. Then as a group, figure out the answer together. 4. When you have reached an agreement, record your strategy on the poster paper and write your solution in the box on the card.
Source: Adapted from 2015 MARS, Shell Center, University of Nottingham 60 Stop and Reflect Why is it important to experience the task prior to implementing in class? What is the benefit of experiencing the task in a collaborative learning team? How could this task be scaffolded to support differing student needs? See Refle
ction Shee t 61 Scaffolding 62 Effective Task Implementation Jigsaw 1. Complete the sort for your group.
2. Identify key characteristics of the vocabulary assigned to your group. 3. Be prepared to share your findings! See Hand outs Clear Learning Intentions Rich
Surface, Deep, and Transfer Learning in Mathematics Ongoing assessments inform teachers that students are in various places along this path, and sometimes will move interchangeably between these phases of learning. It is the teachers goal to provide interventions and strategies students need at the right time for the right reason. Hattie, J. , Fisher, D., Frey, N. (2017) Visible Learning for Mathematics: What Works Best to Optimize Student Learning. Thousand Oaks, CA: Corwin. Corwin Website 65 Its not just about the task..
Moderate 66 Factors Associated with the Decline and Maintenance of High Level Tasks Decline
Problematic aspects of the task become routinized Emphasis is shifted to correctness or completeness Not enough time is provided Classroom management problems prevent engagement Inappropriate task Lack of accountability for highlevel products Maintenance
Scaffolding Students provided way to monitor their progress High-level of performance is modeled Sustained justification, meaning, questioning, comments, and feedback Tasks build on prior knowledge Frequent conceptual connections Sufficient time to explore
Resource: Smith, M. et al. (2017) Taking Action Implementing Effective Mathematics Teaching Practices Series, National Council of Teachers of Mathematics. 67 isi Checklist for Creating or VSelecting bl Tasks that Promote Mastery e Le Pa Boo arn in ge k
g 19 7 See Ha n d o ut 68 Goldilocks Challenge the task is challenging enough to provide a productive struggle for every student in the class. Learners who are still
mastering the content may not complete the entire task, but their reasoning and problem-solving skills are challenged by the parts of the task they complete. Learners who are more advanced will progress further into the task and identify some of the more complex missing value calculations. -Teaching in the Visible Learning Classroom: Grades 6-8, pg. 85 69 The Goldilocks effect A Visible Learning classroom uses the right strategy at the right time,
for the right level of thinking, with the right level of challenge. 70 Mathematics Assessment Project 71 VDOE Rich Mathematical Tasks 72
See Ha n d o ut Anticipating Student Responses As math students ourselves, we are often trained to become more efficient and begin pruning what feel like unnecessary steps and computational deadweight. The trouble with this path to efficiency is that these trimmings become expert blind spots when we run a classroom of our own. Many of us have lived through educational experiences in which we were taught to seek the right answers as quickly as possible. With
a core shift to viewing mathematics as a process rather than a collection of products, it is important for us as educators to investigate our own problem-solving process and regrow any trimmed blind spots. It helps to think about mathematics itself as an explanation, in which each individual step comes with purpose and justifiable legitimacy. -Teaching Mathematics in the Visible Learning Classroom: High School 73 Source: Adapted from Teaching Mathematics in the Visible Learning Classroom Planning for Mathematical Discourse Chart
74 Classifying Questions Assessing Questions Advancing Questions Teacher stays to hear the answer to the question. Teacher walks away, leaving students to figure out how to
proceed. Are based closely on the work that the student has produced. Clarify what the student has done and understands about what s/he has done. Gives the teacher information about what the student understands Use what students have
produced as a basis for making progress toward the target goal of the lesson. Move students beyond their current thinking by pressing students to extend what they know to a new situation. Press students to think about something they are not currently thinking about. Source: Taking Action: Implementing Effective Mathematics Teaching Practices
75 Pose Purposeful Questions 76 Reflection on Success Criteria I can identify how teacher clarity about learning intentions and success criteria contributes to student success. I can identify strategies, methods or approaches to meet the learning needs of individual students. I can distinguish between tasks that will engage students in higher levels of cognitive demand versus lower levels of
cognitive demand. I can describe the factors associated with the decline or maintenance of the cognitive level of a rich mathematical task. I can anticipate student solution strategies and misconceptions associated with the implementation of a mathematical task. 77 Stop and Reflect What was the most important point you would like to hold on to? What is something you are most excited to
share with your colleagues? See Refle ction Shee t 78 Module III Task Implementation (During/After)
Welcome Back! Cut out the cards on your table. In groups, work to find two true equations. Each card may only be used once. One integer card will not be used. Source: https://www.openmiddle.com/integer-sums-and-differences/ 80 Synectics Rich Tasks are like ______ because _______.
81 Success Criteria I can implement a rich mathematical task to support deeper learning for all students. 82 Which One Doesnt Belong? 83 Learning Intentions & Success Criteria
Learning Intention(s): Content I am learning about the relationship between area and perimeter of rectangles and the area and circumference of circles. Language- I am learning how to communicate about the relationships and patterns of area, perimeter, and circumference. Social I am learning how to explain my strategy and work to others so I can refine my strategies for problem solving. 84 Learning Intentions & Success Criteria
Success Criteria: I can determine the area and perimeter of rectangles and the area and circumference of circles in a practical problem. I can justify the relationships between area and perimeter using appropriate math language. I can make suggestions and utilize suggestions made by my peers to make revisions to my work and thinking. 85 Planning a Dog Park
See Ha n d o ut Your parents have asked you to design an enclosed area in your backyard for your dog. The enclosed area can be in the shape of a square or a rectangle. The area will be enclosed with a fence that cannot be attached to another structure (i.e., the house, shed, etc.). There is 72 yards of fencing available. The dimensions of your rectangular backyard is 30 yards by 35 yards.
What is the largest area in your backyard that can be enclosed for your dog? What are the dimensions of this enclosed area? Justify how you know that your design provides the largest area. Sequel: What is the largest area in your backyard for your dog if the enclosure can be a circle? How does this change your answer? 86 Debrief What did you notice the facilitators were doing during the task?
What scaffolds may you provide so that all students can meet success with this task? 87 Scaffolding 88 Task Implementation Checklist Adapted from: The 5 Practices in Practice:
Successfully Orchestrating Mathematics Discussion in Your Middle School Classroom. See Ha n d o ut 89 Mathematics Process Goals in Action See Hand out
Communication Connections Problem Solving Representations Mathematical Understanding Reasoning
90 Reflect on Success Criteria I can use effective questioning strategies to assess and advance student thinking. 91 Stop and Reflect What are the benefits of monitoring, selecting, sequencing, and connecting? How does anticipating help you to monitor, select, sequence, and connect
during task implementation? See Refle ction Shee t 92 Module IV Assessing Student Understanding Success Criteria
I can use success criteria to provide effective feedback to students to deepen student learning. I can use a rubric to score student work samples and work collaboratively to calibrate my scores. I can analyze student work to identify what students know and are able to do in order to plan instruction that moves all students forward as learners. 94 Calibration Protocol Purpose Provides a process whereby groups can discuss
student work in order to reach consensus about how to score the work based on a rubric or scoring criteria. Ensures equity in how each scorers contributions are considered Provides a structure that makes it safe to challenge and question one another Makes the most of time set aside for examining student work Increases inter-rater reliability (providing for fair and consistent scoring of student work) 95
Calibration Protocol See Hand out 1. Examination work through task (individual) 2. Discussion of proficient responses (small group) 3. Read and place in groups (individual) 4. Score student work (individual) 5. Score Sharing (small group)
6. Discussion (small group) 7. Debrief Discussion (small group) 96 Group Roles 1. Identify the following roles within your group: Recorder Facilitator Speaker Time Keeper
Preparing to Score Student Work 2. Discuss proficient response (group) - 10 min. Discuss at your table what is expected for a proficient student response in holistic terms. Use the Rich Mathematical Task Rubric as a guide. Se e Hand out
98 See Ha n d o ut Scoring Student Work 3. Read and place in groups (individually) - 10 min Sort student work into 3 piles - low, med, high based on overall impression. 4. Score student work (individually) - 10 min. Score each student work sample.
Record your scores on the Individual Scoring Notes sheet. Use evidence from the work and the rubric to support your scores. Sharing & Discussing Student Work 5. Score sharing without explanation (collaboratively) - 2 min One at a time, team members share their score for each of the rubric criteria while a recorder completes the groups score sheet. 6. Discussion (collaboratively) - 15 min Score each student work sample. Record your
scores on the Individual Scoring Notes sheet. Use evidence from the work and the rubric to support your scores. 7. Debrief (collaboratively) - 5 min 100 Discuss the questions found on the handout. Think Pair Share What are the benefits of the calibration process?
101 Benefits of Calibration Provides opportunity to deepen educators understanding or expectations of student work and the standards of learning Strengthens educators ability to teach and assess in alignment with a rubric Process provides opportunity to identify areas where rubric could be made clearer or better align to expectations and standards Calibration can lead to
Greater insight into instructional practices and curriculum Identification of student strengths and weaknesses at each level of the rubric Reliable identification of students in need of instructional supports or extensions 102 Elicit and use evidence of student thinking. 103 Elements of
Mastery As a table pick one student work sample and discuss the following questions: 1. What misconceptions, if any, does the student have? 2. What feedback would you give the student? 3. What are the next instructional steps for the student? 105 Feedback
106 Anchor Paper Scoring and Rationales Task developers collected comments from scoring sheets to assist in creating final anchor paper rationales Following scoring calibration, developers deliberately selected 4-6 student work samples to serve as anchor papers
See Hand ou t 107 Identified Anchor Papers Serve as examples of student work at varying levels of performance that, along with rubrics, guide formative and summative assessments Include a scoring rationale for each criteria explaining why the work is assessed at a
specific performance level Identify where students are in terms of mathematical understanding Can be examined as a way to understand the learning opportunities we are, and are not, giving our students Can be used to evaluate how accurately and consistently teachers are assessing students 108 Reflect on Success Criteria I can use success criteria to provide effective feedback to students to deepen student learning.
I can use a rubric to score student work samples and work collaboratively to calibrate my scores. I can analyze student work to identify what students know and are able to do in order to plan instruction that moves all students forward as learners. 109 Stop and Reflect What are the benefits of discussing student work with a collaborative learning team?
See Refle ction Shee t 110 Session Closure and Reflection Potential Website Resources 112
Strategy Catcher Community Builders Strong Classroom Cohesion(0.44) Math Timeline Positive Self-Concept (0.41) Jigsaw (1.20) Questioning (0.48) Strategy Monitoring (0.58) Planning and Prediction (0.76) Checklist Setting Standards for Self Judgement (0.62) Scaffolding (0.82) Feedback (0.70) Cooperative Learning (0.40) Reflection Evaluation and Reflection (0.75) Sentence Frames Teaching Communication Skills &
Strategies (0.43) 113 Assessment-Capable Visible Learner Adapted from Teaching Mathematics in the Visible Learning Classroom: Grade 6-8 114 2016 Mathematics Standards of Learning Instructional Resources
Standards of Learning and Curriculum Frameworks Test Blue Prints Practice Items
Mathematics Instructional Plans Co-Teaching Mathematics Instructional Plans Algebra Readiness Initiative Materials o Mathematics Vertical Articulation Tool Static Versions and Dynamic Versions o Remediation Plans o Formative Assessments 2018 Mathematics SOL Institutes Materials Mathematics Vocabulary Word Wall Cards Desmos Resources Rich Mathematical Tasks 115
Desmos Classroom Activities Log (NEW) 116 Teacher Direct Access TeacherDirect from Instruction Link on the left side of the VDOE home page Sign-up Link 117 Math Information Email Teachers, administrators and mathematics
coordinators are encouraged to send an email to [email protected] to receive the VDOE Mathematics Update distributed by the mathematics office. 118 Learning Intentions Content: I am learning about strategies and approaches that make teaching and learning more visible. Language: I am learning to use the language of a visible learning mathematics classroom.
Social: I am learning how to listen and respond to my peers ideas in ways that move everyone forward as learners. 119 Traffic Light Exit Ticket Based on todays presentation One thing I could stop doing is... One thing I could continue doing is... One thing I could start doing is... 120
Give yourself permission to spend more time developing students deep understanding of mathematics as a wellrounded discipline. -Teaching Mathematics In the Visible Learning Classroom: Grades 6-8 Please Contact Us The VDOE Mathematics Team at [email protected]
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