Questioning Formative Assessment to Support Student Learning PARTNERS

Slides:



Advertisements
Similar presentations
Common Core Standards, K – 12 Kentucky Core Academic Standards Mathematics 1.
Advertisements

Congruency to Math Standards How do we successfully monitor and support our teachers when we can’t be an expert in every content area?
High Cognitive vs. Low Cognitive 1. An effective mathematical task is needed to challenge and engage students intellectually. 2.
1 Mathematics Tasks for Cognitive Instruction Based on research from the Quasar Project found in Implementing Standards-Based Mathematics Instruction:
Engaging Students in High Level Cognitive Tasks Marjorie Graeff April 21, 2010 Division of Teaching & Learning.
Materials Beliefs Cut-up beliefs Answer key Adjusting support tool Tasks activity Martha’s carpeting problem (on ppt) Fencing problem (labels) 3-5 tasks.
Major Work of the Grade Kindergarten Royanna Jackson and Amy Scrinzi NCCTM Conference 2012.
Math & Science Collaborative Analyzing Mathematical Tasks and the Mathematical Task Framework.
CAAT Follow Up Meeting #1 Clay County High School Clay County Middle School.
Developing and Using Meaningful Math Tasks The Key to Math Common Core Take a moment to record on a sticky: What is a meaningful Math Task?
Amy Jones Lewis November 2010 Green River Regional Educational Cooperative MathPLUS Content Day 1: Student-Centered Problem Solving.
Depth of Knowledge. Let’s review... 1.Students perform simple procedures like copying, calculating, and remembering. They either know an answer or they.
Developing and Using Meaningful Math Tasks The Key to Math Common Core Take a moment to record on a sticky: What is a meaningful Math Task?
TASKS 1. What is a Task? -word problem for which there is no obvious answer -students must create the steps for the solution -causes students to think.
Getting to Know Webb’s. Webb’s Depth of Knowledge Level One (recall) requires simple recall of such information as fact, definition, term, or simple procedure.
Thinking about the ways students encounter mathematics.
Improving Mathematical Number Sense & Technology Integration Teacher Quality Grant Peyton Forest Elementary Atlanta Public Schools Atlanta, GA July 23,
Grade 2 Back to School Night
STRONG START Thursday, June 23, 2016 Morning.
Using High-Level Tasks to Become Better Mathematicians
Welcome!! Please sit in teams of 4
Welcome! Please give this math challenge a try.
Connecting Two- and Three-Dimensional Figures
Component 4 Effective and Reflective Practitioner
Writing in Math: Digging Deeper into Short Constructed Responses
The Learner Centered Classroom
Writing Tasks and Prompts
CHAPTER 3 Teaching Through Problem Solving
Presented by: Angela J. Williams
Elementary and Middle School Mathematics Chapter Reflections: 1,2,3,5,6 By: Amy Howland.
Mathshell in Practice Ready Made Quality Group Work 6-8
K-2 Breakout/ Session 3 Parallel Tasks.
Geometry.
The Art and Science of Teaching
MATHEMATICAL TASKS TO SKILLS
for Mathematics Learning
Module 6 PARTNERS for Mathematics Learning Grade 8 Partners 1
Module 1 PARTNERS for Mathematics Learning Grade 7 Partners
Module 3 PARTNERS for Mathematics Learning Grade 7 Partners
Measurement in K-5.
for Mathematics Learning
Grade Three PARTNERS for Mathematics Learning Module 3 Partners 1
Task Selection PARTNERS for Mathematics Learning
Grade Five PARTNERS for Mathematics Learning Module 1 Partners 1
Module 4 PARTNERS for Mathematics Learning Grade 7 Partners
Kindergarten PARTNERS for Mathematics Learning Module 3 Partners
First Grade PARTNERS for Mathematics Learning Module 3 Partners 1
for Mathematics Learning
Grade Eight PARTNERS for Mathematics Learning Module 3 Partners 1
Formative Assessment to Support Student Learning
Formative Assessment to Support Student Learning
North Carolina Mathematics Curriculum Standards
Kindergarten PARTNERS for Mathematics Learning Module 6 Partners 1
for Mathematics Learning
Measurement.
Module 6 PARTNERS for Mathematics Learning Grade 6 Partners
Module 3 PARTNERS for Mathematics Learning Grade 6 Partners
for Mathematics Learning
Grade Two PARTNERS for Mathematics Learning Module 5 Partners
Grades K-2 Formative Assessment to Support Student Learning PARTNERS
Grade Four PARTNERS for Mathematics Learning Module 6 Partners 1
Adding and Subtracting 10
Connecticut Core Standards for Mathematics
HANDOUT Page for facilitators that lists all the hand outs needed for the workshop and the meanings of icons used on the slides in this workshop. SLIDE.
© DMTI (2018) | Resource Materials |
Big Ideas and Problem Solving
Parent-Teacher Partnerships for Student Success
Overview Share practice from mini-problems
Assessment In Mathematics
Assessing Understanding
Presentation transcript:

Questioning Formative Assessment to Support Student Learning PARTNERS 1 PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 2 Grades K-2 Questioning and Task Selection All Aboard for Learning! Partners for Mathematics Learning

Teaching-Learning Cycle 2 Teaching-Learning Cycle Clear Learning Targets Decisions About Next Steps Questioning & Instructional Tasks Collaboration Around Assessment Student Self- Assessment & Responsibility Making Inferences & Giving Feedback Partners for Mathematics Learning

Overview of Modules  Module 1: Module 2: Module 3: Module 5: Learning Targets Questioning and Task Selection Inferences and Feedback Making Students Active Partners Student Self-Assessment and Responsibility  Module 6: Decisions and Collaboration Around Assessment Partners for Mathematics Learning

 Consider different ways to use questions in 4 Goals of Module 2  Consider different ways to use questions in order to engage and deepen mathematical understanding in our students  Learn how to select tasks that allow for the greatest opportunity for student learning  Utilize the information gleaned from these tasks to guide our instruction Partners for Mathematics Learning

Current Practice Respond in your journal:  How do you decide on the 5 Current Practice Respond in your journal:  How do you decide on the questions that you ask during lessons?  How do you select the tasks to use in your class? Partners for Mathematics Learning

Ways Teachers Use Questions 6 Ways Teachers Use Questions Teachers use questions for many different purposes  To engage students in discussions  To refocus class discussions  To probe students’ thinking Dynamic Classroom Assessment , Bright and Joyner, 2005 Partners for Mathematics Learning

Engaging Questions  Invite all students into a discussion 7 Engaging Questions  Invite all students into a discussion  Keep students involved in the class’s conversations  Invite them to share their work or to get answers “on the table” Examples of engaging questions: What strategies might we use to solve this problem? What do you know that will help you answer this question? Partners for Mathematics Learning

K-2 Context: Engaging Question 8 K-2 Context: Engaging Question What would be the 15 th shape in the pattern? Engaging Question Examples: What do you notice about the pattern? Why do you think this could be called a pattern? Partners for Mathematics Learning

Refocusing Questions  Helps students get back on track or move 9 Refocusing Questions  Helps students get back on track or move away from “dead end” strategies  Reopens conversation to the group if only one or two students are answering Examples: How is this problem similar to the one we just did? What quantities are you comparing? Partners for Mathematics Learning

K-2 Context: Refocusing Question 10 K-2 Context: Refocusing Question What would be the 15 th shape in the pattern? If a student says the pattern is star, heart, star, heart, star, heart Refocusing Question Example: What do you notice about the hearts? Is there a difference in the hearts and stars? Partners for Mathematics Learning

Clarifying and Probing Questions 11 Clarifying and Probing Questions  Help students clarify their own thinking  Help teachers understand students’ thinking  Help students understand each other’s ideas Example Questions How did you figure out your answer? Why did you start with that number? Nika, can you explain, in your own words what Maria just shared? Partners for Mathematics Learning

K-2 Context: Clarifying Question 12 K-2 Context: Clarifying Question What would be the 15 th shape in the pattern? Clarifying Question Example: What makes you say a star would come next in the pattern? Why do you say the pattern will use a lot more hearts than stars? Partners for Mathematics Learning

Integrating Purposes of Questions 13 Integrating Purposes of Questions  Engaging questions can help thread a discussion by involving many students in the conversation  Refocusing questions can help keep a discussion from going off on a tangent  Clarifying or probing questions can help others understand student responses and can help students self-check the relevance of their contributions Partners for Mathematics Learning

Purposes for Questions 14 Purposes for Questions Mary has 4 nickels. Will has 3 dimes, and Carley has 6 pennies. Together how much money do they have?  Possible engaging questions:  What do you have to know to solve this problem?  What do you know about the value of the coins?  One student tells about finding a quarter; other students then want to tell their stories about finding money  Teacher refocuses the discussion:  How much money do these children have? Partners for Mathematics Learning

Purposes for Questions 15 Purposes for Questions Mary has 4 nickels. Will has 3 dimes, and Carley has 6 pennies. Together how much money do they have?  Student writes on paper: 5 10 15 20 30 40 / / / / / / 46  Teacher asks child to clarify:  Tell me how you figured out how much money they have  What other questions might the teacher ask to probe this child’s thinking? Partners for Mathematics Learning

Purposes for Questions 16 Purposes for Questions Three children are having a parade. One child rides a tricycle. Two children ride bicycles. How many wheels are in the parade?  Teacher: What is happening in the story?  Child 1: They are having a parade  Teacher: Who is in the parade?  Child 2: Three children-two boys on their bicycles and their little sister on her tricycle Partners for Mathematics Learning

Purposes for Questions 17 Purposes for Questions Three children are having a parade. One child rides a tricycle. Two children ride bicycles. How many wheels are in the parade?  Teacher: What are we trying to find out in this problem?  Child 3: How many wheels - um, 7 wheels  Teacher: How did you figure this out?  Child 3: I counted the wheels  Teacher: Tell me how you counted the wheels Partners for Mathematics Learning

 Let’s practice generating some engaging 18 Let’s Try It!  Let’s practice generating some engaging questions to introduce the task of sorting the shapes into groups Partners for Mathematics Learning

Let’s Try It!  Let’s practice generating some clarifying 19 Let’s Try It!  Let’s practice generating some clarifying questions around this geometry sorting task:  Suppose a child has completed this geometry sort  What might be some clarifying questions you could ask? Partners for Mathematics Learning

The Role of Questioning 20 The Role of Questioning  “During the course of a school day, teachers ask many questions. In fact, something like 60% of the things said by teachers are questions and most of these are not planned.” Good Questions for Math Teaching , Sullivan & Lilburn, 2002 Partners for Mathematics Learning

 Good questions engage students 21 What are Good Questions?  Good questions engage students  Students do more than recall known facts  Students have opportunities to make connections  Good questions promote development of higher levels of thinking and reasoning in students Partners for Mathematics Learning

 Requires more than remembering a fact 22 Features of Good Questions:  Requires more than remembering a fact or reproducing a skill  Students can learn from answering the question and teachers learn about each student from their attempts at solutions  There may be several possible answers How do questions relate to tasks? Partners for Mathematics Learning

 From research on questioning we know 23 Asking Good Questions  From research on questioning we know  Waiting for answers is important  Questions may need to be rephrased for clarity  More probing questions need to be asked, not just factual questions  Ask only one question at a time  Be flexible with expected answers  So much of questioning is contextual Partners for Mathematics Learning

Routine vs Non-routine Questions 24 Routine vs Non-routine Questions  Routine questions ask a student to give an answer from memory or apply simple procedural or conceptual understandings  What number is in the tens place: 136?  Non-routine questions require a student to think more deeply about a topic  How many groups of 10 could you make if you had 136 toothpicks? Partners for Mathematics Learning

Recognizing “Good Questions” 25 Recognizing “Good Questions”  Explain why the first question is routine and the second one is non-routine  What is the average of 6, 7, 5, 8, and 4?  Identify 5 numbers whose average is 6  Which of the set of numbers are even?  Tom has an odd number of cookies. Can he share them fairly with a friend and himself? Explain your thinking  How do the 2nd questions challenge students? Partners for Mathematics Learning

Transforming a Routine Question 26 Transforming a Routine Question  Learning Target: Use numbers to record the value of a group of coins  Routine Question: What is the value of two quarters, two dimes, and a nickel? NOW…  Write a possible non-routine question that is likely to stimulate student interest and encourage a greater depth of understanding Partners for Mathematics Learning

Transform a Kindergarten Question 27 Transform a Kindergarten Question  Learning Target: Classify 2-dimensional shapes  Routine Question: Which shapes are triangles? NOW…  Write a possible non-routine question that is likely to stimulate student interest and encourage a greater depth of understanding Partners for Mathematics Learning

 Consider different ways to use questions in 28 Goals of Module 2  Consider different ways to use questions in order to engage and deepen mathematical understanding in our students  Learn how to select tasks that allow for the greatest opportunity for student learning  Utilize the information gleaned from these tasks to guide our instruction Partners for Mathematics Learning

Why Focus on Questions and Tasks ? 29 Why Focus on Questions and Tasks ?  Classroom instruction is generally organized around mathematical tasks  The tasks in which students engage determine what they learn about mathematics and how they learn it  “Not all tasks are created equal, and different tasks provoke different levels and kinds of student thinking.” Stein, Smith, Henningsen & Silver, 2000 Partners for Mathematics Learning

“One of the most important and yet difficult 30 “One of the most important and yet difficult aspects of designing a lesson is choosing or creating the worthwhile mathematical task a teacher wants students to engage in.” Lappan & Friel 1993 Partners for Mathematics Learning

Characteristics of Mathematical Tasks 31 Characteristics of Mathematical Tasks  Look at the tasks on the next slides:  How would you go about solving them?  What are the essential characteristics of each task?  What would be a possible learning target you would have for selecting these tasks? Which of the two tasks requires more in-depth thinking and causes them to be more intellectually engaged? Partners for Mathematics Learning

Task 1  You are carpeting a room that is 15 feet 32 Task 1  You are carpeting a room that is 15 feet long and 10 feet wide  How many square feet of carpeting do you need to purchase? Partners for Mathematics Learning

 Our class will raise chickens for the science 33 Task 2  Our class will raise chickens for the science fair and can use 24 feet of fencing to build a rectangular pen  How long are the sides that give the chickens as much room as possible?  How long are the sides if only 16 feet of fencing is used?  How would you determine the pen with the most room for any amount of fencing? Partners for Mathematics Learning

 How are the two tasks alike?  How are they different? 34 Comparisons  How are the two tasks alike?  How are they different?  For each task…  Discuss the flow and progression for supporting each task  What is the role of the teacher and students?  What skills were employed during the task?  What kinds of information about a student’s thinking can be gathered through each task? Partners for Mathematics Learning

Task 3  Mrs. Wilson has 3 green  How many candles does she have? 35 Task 3  Mrs. Wilson has 3 green birthday candles and 4 yellow ones  How many candles does she have?  What is the mathematics in this task?  What action is required of students ? Partners for Mathematics Learning

Task 4  Mrs. Wilson has 7 birthday candles 36 Task 4  Mrs. Wilson has 7 birthday candles  Some candles are green and some candles are yellow  How many of each color could she have?  In what ways is this problem like the previous one? How is it different?  Why is this task more engaging intellectually? Partners for Mathematics Learning

Task Sort  Sort the task cards into piles  Remember: 37 Task Sort  Sort the task cards into piles  One pile you consider to contain higher intellectually engaging tasks  The other pile that you consider to contain lower intellectually engaging tasks  Remember:  Think about intellectual engagement, not difficulty Partners for Mathematics Learning

 What is an appropriate time and place for 38 Turn and Talk  What is an appropriate time and place for lower level tasks? Partners for Mathematics Learning

 Sufficient time allowed for exploration – not 39 Intellectually Demanding Tasks  Sufficient time allowed for exploration – not too much or too little  High level performance modeled by teacher or capable students  Task builds on prior knowledge  Teacher draws on frequent connections  Teacher presses for justifications, explanations, and meaning through questioning, comments, and feedback Partners for Mathematics Learning

 What are your learning targets? 40 Selecting and Supporting Tasks  What are your learning targets?  What background knowledge is needed for the task?  What are ways it can be solved? (misconceptions/errors students may have)  Any challenges to EC/ELL students?  What are your expectations for students? – how will you communicate and assess them? Partners for Mathematics Learning

Selecting and Supporting Tasks 41 Selecting and Supporting Tasks  What questions will you ask – engaging, refocusing, and clarifying?  How will you orchestrate a classroom discussion so you can accomplish your learning target? How will you assess student understanding of the learning target?  What will you do tomorrow to build on this lesson? Partners for Mathematics Learning

 Why is it okay for students to struggle 42 Talk at Your Tables  Why is it okay for students to struggle with a task or a good question? Partners for Mathematics Learning

I nstruction and F ormative A ssessment 43 I nstruction and F ormative A ssessment Partners for Mathematics Learning

Homework for Module 3  Bring a set of class papers to analyze in 44 Homework for Module 3  Bring a set of class papers to analyze in Module 3  Try to decide on the same task as a grade level and bring a class set of papers to be discussed and analyzed during module 3 Partners for Mathematics Learning

Reflection Respond in your journal:  How will you decide on the 45 Reflection Respond in your journal:  How will you decide on the questions that you ask during lessons?  What are three things you will consider as you select tasks for your class? Partners for Mathematics Learning

Partners for Mathematics Learning is a Mathematics-Science 46 DPI Mathematics Staff Chief Consultant Renee Cunningham Kitty Rutherford Robin Barbour Mary H. Russell Carmella Fair Johannah Maynor Amy Scrinzi Partners for Mathematics Learning is a Mathematics-Science Partnership Project funded by the NC Department of Public Instruction. Permission is granted for the use of these materials in professional development in North Carolina Partner school districts. Partners for Mathematics Learning

PML Dissemination Consultants 47 PML Dissemination Consultants Julia Cazin Ruafika Cobb Anna Corbett Gail Cotton Jeanette Cox Lisa Davis R yan D ougherty Tricia Essick Tery Gunter Barbara Hardy Kathy Harris Rendy King R ene L emons- M atney Tina McSwain Marilyn Michue Kayonna Pitchford Ron Powell Susan Riddle Alisan Royster Judith Rucker P enny S hockley Pat Sickles Nancy Teague Jan Wessell Dan Wicks Carol Williams Stacy Wozny Partners for Mathematics Learning

2010 Writers Ana Floyd Katie Mawhinney Kayonna Pitchford Wendy Rich 48 Partners Staff Jeane M. Joyner, Co-PI & Project Director Freda Ballard, Webmaster Anita Bowman, Outside Evaluator Meghan Griffith, Administrative Assistant Tim Hendrix, Co-PI and Higher Ed Ben Klein , Higher Education Katie Mawhinney, Co-PI and Higher Ed Catherine Schwartz, Higher Education 2010 Writers Ana Floyd Katie Mawhinney Kayonna Pitchford Wendy Rich Nancy Teague Stacy Wozny Please give appropriate credit to the Partners for Mathematics Learning project when using the materials. Permission is granted for their use in professional development in North Carolina Partner school districts. Partners for Mathematics Learning

Questioning Formative Assessment to Support Student Learning PARTNERS 49 PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 2 Grades K-2 Questioning and Task Selection All Aboard for Learning! Partners for Mathematics Learning