Formative Assessment to Support Student Learning

Formative Assessment to Support Student Learning
1 PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 5 Grades 3-5 Decisions about Next Steps Partners for Mathematics Learning

 Module 1: Learning Targets
2 Overview  Module 1: Learning Targets  Module 2: Questioning and Task Selection  Module 3: Inferences and Feedback  Module 4: Making Students Active Partners  Module 5: Decisions about Next Steps  Module 6: Collaboration Around Assessment Partners for Mathematics Learning

Teaching-Learning Cycle
3 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

Making Decisions about Next Steps
4 Making Decisions about Next Steps Learning targets for this module  Understand and use information about learning needs of individual students to make decisions about next instructional steps  Identify strategies for intervention and differentiation Partners for Mathematics Learning

5 Making Decisions about Next Steps  The quality and depth of student learning is influenced by the decisions teachers make  Thus, formative assessment should  Give information about students’ understanding  Guide teachers in choosing interventions for individual students  Assist in planning next steps for the whole class  Formative assessment data has value according to how well we use it to plan Partners for Mathematics Learning

Information About Students
6 Information About Students  We gather information about students’ understanding in many ways…  Students’ written work  Conversations or interviews with individuals  Class discussions  Pre-assessments for learning targets Partners for Mathematics Learning

7 Making Decisions about Next Steps  Whole Class Instruction  Differentiated Instruction – designing instruction to meet needs of all students across the spectrum of mastery  Within the context of whole class instruction  Interventions – specific strategies to meet identified needs of children  Individualized/small group instruction  In this module, we focus on children at risk Partners for Mathematics Learning

Three Stars and a Wish  In your journal…
8 Three Stars and a Wish  In your journal…  List ways you are using formative assessment to inform your instructional planning  List the ways you are currently differentiating instruction in your classroom  List the interventions you currently use  Star the 3 most effective of these  Write one specific wish for ideas related to these Partners for Mathematics Learning

 To effectively meet all students’ needs…
9 Research Suggests Strategies  To effectively meet all students’ needs…  Keep focus on concepts and sense-making  Use formative assessment strategies to understand students’ thinking  Maintain high expectations for achievement of learning targets for all students  Use ongoing assessments to identify students who need additional support or extensions  Involve students more in self-assessment  Use assessment to make flexible groupings Partners for Mathematics Learning

Flexible Groups  Flexible grouping is a hallmark of a
10 Flexible Groups  Flexible grouping is a hallmark of a classroom that meets students needs  Groups are not static but are ever- changing based on a variety of criteria  Responses to tasks  Readiness  Work habits  Performance  Student Interests and choices Partners for Mathematics Learning

Types of Groups  Whole class  Learning styles  Individual work
11 Types of Groups  Whole class  Individual work  Teacher designated groups  Random groups  Readiness for tasks  Like readiness  Different levels of readiness  Learning styles  Similar  Random  Student interests  Student choice What other ways do you group students? Partners for Mathematics Learning

 Daily practice may be used to make
12 Looking at Student Work  Daily practice may be used to make decisions about the needs of students  Look at the student work and talk at your table about what you know about these students and their knowledge  What would you do in a whole class lesson?  How might you group students based on the work?  Be prepared to share your ideas Partners for Mathematics Learning

Whole Group Lessons  Whole group lessons
13 Whole Group Lessons  Whole group lessons  Provide common experiences  Expose students to a variety of thinking  Can support individual needs and strengths • Use think/pair/share strategy Allow wait time before responses Encourage responses from several children Connect comments to previous speakers  We learn much more together than we can alone Partners for Mathematics Learning

Whole Group Lessons  Have students look at examples and discuss
Two Strategies 14 Whole Group Lessons  Have students look at examples and discuss which are correct, which are not and why  Put samples on an overhead, document camera, or write them on the board  Be sure no student names are attached  Let students - not teacher - discuss errors  Teacher chooses 3 or 4 problems to discuss with the class and then gives students an opportunity to solve 3 or 4 similar problems Partners for Mathematics Learning

Class Discussions  Classroom discussions provide information for
15 Class Discussions  Classroom discussions provide information for teachers and builds understanding among students  Misconceptions surface which help teachers identify what students do and still do not understand  Students realize their own lack of knowledge or understanding when they are asked to talk or write about a concept  Discussions help meet individual needs within whole class lessons Partners for Mathematics Learning

Tools for Classroom Discussions
16 Tools for Classroom Discussions  Teacher re-voices child’s statement  “So you’re saying that…”  Students restate another’s reasoning  “ Can you put her idea into your own words?”  Students share different strategies  “Who solved the problem in a different way?”  Apply own reasoning to another’s reasoning  “Do you agree or disagree? Why?” Partners for Mathematics Learning

Tools for Classroom Discussions
17 Tools for Classroom Discussions  Prompting further explanation  “Say more about that”  Prompting further participation  “Would anyone like to add to his idea?”  Prompting a response from all students  “Thumbs up if you understand the solution”  Wait before and after responses  “Take your time… We’ll wait for you to think”  Wait at least 5-10 seconds for students to think Partners for Mathematics Learning

P re- A ssessment of L earning T argets
18 P re- A ssessment of L earning T argets  Pre-tests, pre-assessments, diagnostic assessments  Need to be narrowly focused on content in next instructional unit  Results highlight needs of students who appear at either extreme (know content or miss almost everything)  Results identify areas that need more or less time for the class as a whole Partners for Mathematics Learning

Pre- Assessment of Learning Targets
19 Pre- Assessment of Learning Targets  Pre-Assessments help you know:  How familiar are my students with this concept?  What knowledge, skills and strategies do they already have to support learning in this area?  What misconceptions do they have?  Are they comfortable with the vocabulary within this topic? Dacey and Lynch, Math For All: Differentiating Instruction , 2007 Partners for Mathematics Learning

Pre- Assessment of Learning Targets
20 Pre- Assessment of Learning Targets GRADE LEARNINGTARGET PRE-ASSESSMENT 3 Comparewhole numberslessthan 10,000withsymbols andwords Joehad7,892baseballcards. Juanhad7,985cards.Who hadmorecards?Tellhowyou know. 4 Comparefractions anddecimalsusing benchmarks Sortthesefractionsascloser to0,½,or1.Tellhowyou madeyourchoices. (5/8,1/5,7/9,3/5,2/10,3/4) 5 Usemeasurement ofelapsedtimeto solveproblems IfLeihastobeatschoolat 7:50andittakesher35 minutestogetthere,when shouldsheleavehome? Partners for Mathematics Learning

Creating a Pre-Assessment
21 Creating a Pre-Assessment  In your grade level groups determine a potential learning target for your students that you will address in the coming weeks  Together write a 3-4 question pre-assessment for the learning target that will allow you to “take the pulse” of your class  Think about the different kinds of knowledge students will use to respond to the questions Partners for Mathematics Learning

? ? ? ? What Next? Making Plans  Questions to ask yourself:
22 What Next? Making Plans  Pre-Assessments may cause us to change  Learning Targets  Instructional Plans  Questions to ask yourself:  Where are we going?  Where are we now?  How can we get there? ? ? ? ? Partners for Mathematics Learning

What Next? Making Plans  Learning targets for this
23 What Next? Making Plans  Learning targets for this pre-assessment include  Identification of angles  Comparing and contrasting polygons  Using pre-assessments  Examine the results of a third grade pre- assessment for a geometry unit  Identify common misconceptions and gaps in understanding Partners for Mathematics Learning

What Next? Making Plans  What do you notice?
24 What Next? Making Plans  What do you notice?  Is there a whole group lesson that will benefit all students?  Are there students who need specific interventions?  Are there students who already demonstrate mastery of the learning targets?  How can a lesson be differentiated to meet the needs of these students? Partners for Mathematics Learning

25 What Next? Making Plans “…our job is to challenge students’ comfort level and then to help them find their next boundaries. …we try to identify evidence for what the child knows or has mastered, areas where initial ideas are formed but additional experience with them is needed, and those concepts and skills that require further scaffolding or additional readiness development.” Dacey and Lynch, Math for All: Differentiating Instruction, 2007 Partners for Mathematics Learning

Keep in Mind… Zone of Proximal Development
26 Keep in Mind… Zone of Proximal Development Vygotsky (1978), Fleer (1992), Jacobs 2001) Student’s Current achievement Partners for Mathematics Learning

Differentiated Instruction
27 Differentiated Instruction  “Differentiated Instruction is an organized , yet flexible way of proactively adjusting teaching and learning to meet students where they are and help all students achieve maximum growth as learners.” Carol Ann Tomlinson (1999). How to Differentiate Instruction in Mixed-ability Classrooms. Alexandria, VA : ASCD Partners for Mathematics Learning

Differentiated Instruction
28 Differentiated Instruction  Flexible groupings Scaffolding Tiered Assignments Choices/Anchors/Menus Learning Contracts Compacting Pre-teaching and Mini-lessons Partners for Mathematics Learning

Scaffolding Learning  Scaffolds are structures put in place to
29 Scaffolding Learning  Scaffolds are structures put in place to allow students to be successful learners of mathematics  Scaffolding gives children opportunities to accomplish tasks that they would be unable to complete alone Partners for Mathematics Learning

Scaffolding Learning  Teacher becomes a coach –
30 Scaffolding Learning  Teacher becomes a coach – helping all children reach their potential  Scaffolding learning is guiding the student toward the kind of thinking that is necessary to do the task, not toward one specific strategy or answer  Scaffolding learning does not mean replacing student thinking with teacher thinking Partners for Mathematics Learning

Scaffolding Learning  Scaffolds may
31 Scaffolding Learning  Scaffolds may  Include questions that lead students to be more systematic or logical  Encourage students to go beyond their level of comfort and understanding  Help develop strategies explicitly for working with new mathematical content and activities  Connect new learning to prior knowledge Partners for Mathematics Learning

Scaffolding: Questions
32 Scaffolding: Questions 2  Task: Shade of this set: 3 Teacher : What is this task asking you to do? What do you already know that will help? Partners for Mathematics Learning

33 Partners for Mathematics Learning

34 Scaffolding: Questions 2  Task: Shade of this set: 3 The student responds by shading as shown Teacher: Show me how what you shaded represents 2/3 of the set Partners for Mathematics Learning

 Task: Shade of this set:
35 Scaffolding: Questions 2  Task: Shade of this set: 3 Student shades second group Teacher: How do you know that you have Partners for Mathematics Learning shaded of the set?

36 Scaffolding: Questions 2 3 Teacher: How many Partners for Mathematics Learning  Task: Shade of this set: circles are in of the set?

Scaffolding: Graphic Organizers
37 Scaffolding: Graphic Organizers  How are a square and a rectangle alike and different? Alike Different Word Bank Partners for Mathematics Learning

Scaffolding: Graphic Organizers
38 Scaffolding: Graphic Organizers  Together Todd and Kerri earned 28 points in the basketball game. Todd earned 3 times as many points as Kerri. How many points did Todd earn? Partners for Mathematics Learning

 Together Todd and Kerri earned 28 points in the
39 Scaffolding: Graphic Organizers  Together Todd and Kerri earned 28 points in the basketball game. Todd earned 3 times as many points as Kerri. How many points did Todd earn? 28 Todd Kerri Partners for Mathematics Learning

 Tim had $1.00 in coins. He had 15 coins which
40 Scaffolding: Graphic Organizers  Tim had $1.00 in coins. He had 15 coins which were only dimes and nickels. How many of each kind of coin did he have? Work Space: dimes nickels Partners for Mathematics Learning

Scaffolding: Vary Problem Structures
41 Scaffolding: Vary Problem Structures  Sean drove 120 miles and stopped for lunch. Then he drove another 180 miles before he reached his destination. How many miles did Sean drive?  What do we know?  What are we trying to find out? = ? Partners for Mathematics Learning

42 Scaffolding: Vary Problem Structures  Sean drove 120 miles and stopped for lunch. Then he drove some more. By the time he got to his destination, he had driven 300 miles. How many miles did he drive after lunch?  What do we know?  What are we trying to find out? 120 + ? = 300 Partners for Mathematics Learning

43 Scaffolding: Vary Problem Structures  Sean drove for awhile before he stopped for lunch. After lunch he drove 180 miles to reach his destination. When he got there he had driven 300 miles. How many miles did Sean drive before lunch?  What do we know?  What are we trying to find out? ? = 300 Partners for Mathematics Learning

44 Scaffolding: Vary Problem Structures  Sean drove 120 miles and stopped for lunch. Then he drove another 180 miles before he reached his destination. How many miles did Sean drive?  Sean drove 120 miles and stopped for lunch. Then he drove some more. By the time he got to his destination, he had driven 300 miles. How many miles did he drive after lunch?  Sean drove for awhile before he stopped for lunch. After lunch he drove 180 miles to reach his destination. When he got there he had driven 300 miles. How many miles did Sean drive before lunch?  How does varying the order in which you give students problems provide support for students? Partners for Mathematics Learning

45 Scaffolding: Vary Problem Structures Set 1 Set 2 Total Partners for Mathematics Learning

Scaffolding: Vary Problem Difficulty
46 Scaffolding: Vary Problem Difficulty  Sean drove ( 60, 120, 3407 ) miles last year on his vacation. He drove ( 93, 180, 2159 ) miles on this year’s vacation. How many miles did Sean drive on both vacations?  Teachers may direct which numbers to use  Students may choose numbers to use What conversations might students have when you use this type of task? Partners for Mathematics Learning

Scaffolding: Using Models
47 Scaffolding: Using Models Models and representations help students  Make sense of mathematics  Organize their thinking  Justify their responses  Communicate their ideas  Create mental images of mathematical ideas that they can use in solving problems Partners for Mathematics Learning

Scaffolding Learning  All children - even our most advanced
48 Scaffolding Learning  All children - even our most advanced students - should be challenged to struggle with tasks that require some support to accomplish  Support through graphic organizers  Support by working with a partner  Support by working in a group  Challenges should involve meaningful mathematics to develop depth of thinking Partners for Mathematics Learning

Tiered Assignments  Tiered activities or lessons
49 Tiered Assignments  Tiered activities or lessons  A series of related tasks of varying complexity  Relate to essential understandings and key skills that students need to acquire  Assigned as alternative ways of reaching the same goals taking into account individual student needs  Can utilize alternative tasks in textbooks Partners for Mathematics Learning

Process of Tiered Assignments
50 Process of Tiered Assignments  Identify the learning target  Form groups based on assessments  Plan a meaningful activity for each group depending on the students’ needs NeedsAttention DevelopingMastery NeedsChallenge Partners for Mathematics Learning

Flexible Groups: Tiered Assignments
51 Flexible Groups: Tiered Assignments  Students work in groups assigned by the teacher so that two groups can work independently while the teacher works with one group  If students have a question, and are not in the group that the teacher is currently working with, they must ask at least two other people in their group before they can ask the teacher Partners for Mathematics Learning

What Now? Student Choice
52 What Now? Student Choice  Anchors, Choice Boards, and Menus  A collection of activities from which students may choose while the teacher is working with another individual or group (or whenever a choice is appropriate)  Activities are worthy of a student’s time, focus on essential skills, and are appropriate to learning needs  Activities are meaningful tasks that provide extensions or reinforcement of mathematics Partners for Mathematics Learning

53 What Now? Student Choice  Think-Tac-Toe  A grid of activity choices or problems  Teacher tells students how to choose their activities, ex. choose one from each row, or complete one activity from each column, or complete all tasks in any row or column Partners for Mathematics Learning

54 What Now? Student Choice  RAFTS  Role – Audience – Format – Topic  Allows imaginative students to share their mathematics knowledge creatively  Allows for demonstrations of knowledge based on learning styles  Incorporates writing with mathematics Partners for Mathematics Learning

Interventions Formative assessment provides a basis for
55 Interventions Formative assessment provides a basis for interventions  Some districts use benchmark or other district-developed tests to identify students  Some districts have teachers identify students based on classroom performance  Interventions are often required for any student in danger of being retained Partners for Mathematics Learning

Intervention Process  Identify students at risk related to learning
56 Intervention Process  Identify students at risk related to learning targets  Choose highly effective strategies designed specifically to address particular students’ needs  Implement the strategies faithfully  Monitor progress through assessments  Adjust instruction Partners for Mathematics Learning

Interventions  Teachers should consider the method of
57 Interventions  Teachers should consider the method of instruction and not just the content when working with students who need interventions  Not more of the same that already has not worked for them  New strategies and representations  Should be interesting, appealing, focused on essential understandings and skills Partners for Mathematics Learning

Instructional Intervention Is…
58 Instructional Intervention Is…  Targeted instruction based on ongoing assessments  Additional instruction administered by the teacher or a resource person  Pre-teaching or mini-lessons on needed skills  Teaching additional strategies  Modifications in curriculum  Changes in types and methods of feedback Partners for Mathematics Learning

Instructional Intervention is…
59 Instructional Intervention is…  Modifications in  Modes of task presentation  Instructional time  Group size  Amount and kind of cues and prompts  Task structure (increase)  Task relevant practice (increase) Partners for Mathematics Learning

Instructional Intervention is NOT…
60 Instructional Intervention is NOT…  Preferential seating* Shortened assignments* Parent contacts* Classroom observations* Suspensions or retention Doing more of the same assignment *Helpful strategies for improved student performance but are not instructional strategies Partners for Mathematics Learning

Interventions: Making the Time
61 Interventions: Making the Time  Share with the group ways that you have found time to provide interventions for students  In your journal list new ways that you would like to try Partners for Mathematics Learning

Meeting Student Needs: Reminders
62 Meeting Student Needs: Reminders  Keep focus on concepts, understanding, and sense-making  Use ongoing assessments to find students who need more support or extensions  Make groupings flexible  Be the guide and facilitator  Assess based on growth and achievement of learning targets Partners for Mathematics Learning

 Go back to the 3 Stars and a Wish in your
63 Meeting Student Needs: Reflections  Go back to the 3 Stars and a Wish in your journal from the beginning of the module  Would you write a different wish now?  What new “stars” do you want to highlight by the end of next year as your strengths?  Respond in your journal Partners for Mathematics Learning

Homework: Putting Ideas Into Practice
64 Homework: Putting Ideas Into Practice  Bring back to the next session an index card on which you describe a way you have used an idea from this module in your classroom  Be specific in your example  Explain why you will continue (or not continue) this practice Partners for Mathematics Learning

Partners for Mathematics Learning is a Mathematics-Science
65 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
66 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
67 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

Decisions about Formative Assessment to Support Student Learning
68 PARTNERS for Mathematics Learning Formative Assessment to Support Student Learning Module 5 Grades 3-5 Decisions about Next Steps Partners for Mathematics Learning

Formative Assessment to Support Student Learning

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