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transcript
SVMI Network Meeting
April 10, 2013
Assessing and Using Prior Learning to
Adapt Teaching to the Needs of
Students Network Meeting, April 10, 2013
Silicon Valley Mathematics Initiativewww.svmimac.org
Formative Assessment
Welcome
Please sign in, help yourselves to refreshments,
find a seat, and introduce yourself to your tablemates.
Agenda Welcome
Announcements, Norms and Introductions
Re-visiting Formative Assessment with a MAP Module
Doing Collaborative Mathematics: A Problem Solving Task
Announcements
SVMI is … still accepting applications for the
SCVMP Leadership Institute: 5 Tuesdays in May and a week in June. The application is on our website: www.svmimac.org. Each member of SVMI is entitled to one scholarship.
holding two Summer Institutes: Peninsula location is Sequoia HS July 29-August 2 and East Bay is Sunset HS August 5-August 9. The application is on our website: www.svmimac.org.
SVMI is … offering Lesson Study mini-grants
again this year. The mini-grants are for teams of 5 to 7 teachers; the stipend is for $3,000. The application will be out May 1, 2013.
presenting the preliminary results of the 2013 MAC assessment at our General Meeting on May 15, 2013. We encourage everyone to attend.
SVMI Calendar for 2013/2014
Please be sure to pick one up.
Field Testing K-3 Tasks
SVMI needs at least two classes for each task.
A teacher may only do one task; there is no need to do all five.
If possible, the field testing should be done as soon as possible.
Field testing to be done in the stated Grade Level
Kinder Tasks
Alphabet Count: Counting and Cardinality/Op. and Alg. Thinking
Classroom Helpers: Op. and Alg. Thinking
Kinder Measurement: Measurement/Geometry
Dog Park: Counting and Cardinality
Crayons: Op. and Algebraic Thinking
First Grade Tasks Field Day: Op. and Alg. Thinking/ Number
Ops. In Base 10
Number Puzzles: Op. and Alg. Thinking/Number Ops. in Base 10
Recess Equipment: Op. and Alg. Thinking
Weather: Data/Op. and Alg. Thinking
Shapes, Shapes, Shapes: Geometry
School Garden: Measurement/Geometry
Second Grade Tasks Seasons: Data
Quilt Designs: Geometry
Town Zoo: Linear Measurement
Can You Tell?: Op. and Alg. Thinking/Number Ops. In Base 10
Our Gardens: Op. and Alg. Thinking – Mult. and Div.
Favorite Planets: Data
Third Grade Tasks Dinosaur Museum: Measurement - Time
Tamiko’s Puzzles: Fractions
That’s Entertainment: Op. and Alg. Thinking/Number Ops. In Base 10 using 4 operations
The Queen and her Pears: Fractions
Mowing for Money: Geometric Measurement
Odd and Even School: Op. and Alg. Thinking
Norms
The Social Culture of our Network
Seek to Understand
Respectfully Speak your Truth
Monitor your Airtime
Getting Acquainted or Re-Acquainted
Goals and Outcomes
Goals and Outcomes
Explore Social Norms and Socio/Mathematical Norms in the context of experiencing a formative assessment problem solving lesson
Strengthen and enhance participants’ leadership abilities by experiencing a high-quality professional development module to support teachers in their classrooms
Deepen participants’ understanding of the effectiveness of Formative Assessment in the classroom for teachers and students
Lenses to Consider During Professional Development
Sessions
Learner Lens Coach/Admin Lens
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the
reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated
reasoning.
Mathematical Practice
Socio-Mathematical Norms
Harold Asturias
Errors are gifts…they promote discussion and learning
The math is important…not just the answer
Ask questions…until it makes sense
Think with language…use language to think
Use multiple strategies…multiple representations
Setting the Stage
A Look at Module 4 and an Alpha FAL
Network Meeting, September 5, 2012Silicon Valley Mathematics Initiative
www.svmimac.org
Questioning
A Look at Module 5 and Collaborative
Tasks
Network Meeting, October 31, 2012Silicon Valley Mathematics Initiative
www.svmimac.org
Collaboration
Exploring Cognitive Demand
Network Meeting, January 9, 2013Silicon Valley Mathematics Initiative
www.svmimac.org
A Look at Addressing Curriculum Needs
Assessing and Using Prior Learning to
Adapt Teaching to the Needs of
Students Network Meeting, April 10, 2013
Silicon Valley Mathematics Initiativewww.svmimac.org
Formative AssessmentHow can I respond to students in ways that improve their learning?
Introduction
Students do not arrive in classrooms as “blank slates.”
Students come with a wide variety of skills and conceptions.
Research shows that teaching is more effective when it assess and uses prior learning so that teaching may be adapted to the needs of students.
Assessing and Using Prior Learning to Adapt Teaching to the Needs of
Students Prior learning may be uncovered
through any activity that offers students opportunities to express their understanding and reasoning.
It does not require testing.
It can take the form of a single written question given at the beginning of a session to elicit a range of explanations that may then be discussed.
Assessing and Using Prior Learning to Adapt Teaching to the Needs of
Students Defining Formative Assessment: Black and
Wiliam, 1998
…all those activities undertaken by teachers, and their students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged. Such assessment becomes ‘formative assessment’ when the evidence is actually used to adapt the teaching work to meet the needs.”
Assessing and Using Prior Learning to Adapt Teaching to the Needs of
Students –Our Focus How can problems be used to assess
performance?
How can this assessment be used to promote learning?
What kinds of feedback are most helpful for students and which are unhelpful?
How can students become engaged in the assessment process?
Research on Formative Assessment
Inside the Black Box: Raising Standards through Classroom Assessment Black and Wiliam, 1998
Working Inside the Black Box: Assessment for Learning in the Classroom Black and Harrison, 2002
Assessment for Learning: Putting it into Practice Black, Harrison Lee, Marshall & Wiliam 2003
Mathematics Inside the Black Box Hodgen & Wiliam, 2006
Activity A
Introducing Formative Assessment
Activity A
Introducing Formative Assessment
To summarize, there are two main purposes of assessments: Summative Assessment: to summarize and
record overall achievement at the end of a course, for promotion or certification. Most ‘high stakes’ tests and external examinations are designed for this purpose. It is also used to evaluate the relative effectiveness of a particular course, teaching method, or even an institution.
Formative Assessment: to recognize achievements and difficulties at the beginning or during a course so that teachers and students can take appropriate action. This type of assessment forms an integral part of teaching.
Activity A
Introducing Formative Assessment
The potential of formative assessment to improve learning:
Setting the Case: “We checked many books and nine years’ worth of more than 160 journals, and earlier reviews of research. This process yielded 580 articles or chapters to study. We prepared a review using material from 250 of these sources. All…studies show that…strengthening…formative assessment produces significant, and often substantial, learning gains. These studies range over ages, across several school subjects, and over several countries… Black and Wiliam, 1998
Activity B
Teachers’ Own Experiences of Formative Assessment
We begin with the following situation:
Think of two students, one who is particularly strong and one who is finding the work very difficult. Using a dyad format, describe the students’ strengths and difficulties in as much detail as possible to your partner.
Protocol: Individual Solo Think Time-30
seconds Dyad-1 minute per partner
Activity B
Teachers’ Own Experiences of Formative Assessment
We begin with the following situation:
How did you become aware of these strengths and difficulties?
On what evidence do you base your judgments? Test results? Memories of oral responses during lessons? Observations of the student working? Written work?
Protocol: Individual Solo Think Time-1/2
minute Dyad -1 minute per partner
Activity B
Teachers’ Own Experiences of Formative Assessment
The third part of the situation:
In what ways do assessments of these students affect lesson planning? Give examples.
Protocol: Individual Solo Think Time-1 minute
Dyad-1 minute per partner
Activity B
Teachers’ Own Experiences of Formative Assessment
Activity C
Principles for Formative Assessment
Handout #2 Keeping in mind the difficulties discussed in
Activity B, please read Principles for Formative Assessment. 1 minute
Please discuss these principles with your partner. Which of these principles do you see implemented in
classrooms? Which of these do you or teachers you know find
most difficult to implement? Why? What other principles do you think are important? 2 minutes
Activity C
Principles for Formative Assessment “It’s all very well telling us to assess our
students, but how can a busy teacher know what is going on inside 30 individual heads?” How would you answer this teacher?
What strategies do you have for finding out what students are thinking in your lessons or the ones you observe?
1 minute for individual think time Please discuss these strategies with your
partner. 2 minutes
Popcorn Sharing with Whole group 1 minute
Activity C
Principles for Formative Assessment
Handout #3 Please read Making Reasoning Visible.
1/2 minute Please discuss these strategies with your
partner. Why are these tools an indispensable resource for
teachers? 1 minute Watch two Video Clips with students in action.
6 min Suggest some further strategies for making
reasoning more evident. 2 minutes
Activity C
Principles for Formative Assessment
Handout #3
Whole group sharing on the video clips. 2 minutes Comments from the module. Teachers can see at a glance with every student
thinks. Allows teachers to ask new kinds of questions, e.g.,
“Show me an example of….” Posters allow students to externalize their thinking-
articulate their reasoning and justification. Posters can be used to show what they already know
not necessarily what they have just worked on. Whole group sharing on additional strategies for
making reasoning evident. 2 minutes
Doing Mathematics
A purposeful shift
Engaging in one of three selected problem solving lessons addressed and used in this module
Lenses to Consider During Professional Development
Sessions
Learner Lens Coach/Admin Lens
PROBLEM SOLVING LESSONS
LET’S DO SOME MATHEMATICS
Optimizing: Security Cameras
Assessment Task: Solo
Assessment Task What are the big mathematical
ideas in this task?
What strategies might students use in completing this task?
Please anticipate what students will understand about this task.
Please anticipate where students may have difficulty with this task.
Protocol
Discuss these questions and anticipations with a neighbor. 2 min
Share with members in your table group. 2 min
Popcorn share with whole group. 2 min
Assessment Task What are the big mathematical
ideas in this task?
What strategies might students use in completing this task?
Please anticipate what students will understand about this task.
Please anticipate where students may have difficulty with this task.
Feedback Questions/Prompts
Feedback Questions/Prompts
Collaborative Activity: Improving the Solution
Sharing Work and Learning From Each Other
Collaborative Work: Planning a Joint Solution
1. Take turns to explain your work and how you think it could be improved.
1. Listen carefully to each other and ask questions if you don’t understand or agree.
1. Once everyone in the group has explained their method, plan a joint method that is better than each of your separate ideas.
1. Make sure that everyone in the group can explain the reasons for your chosen method.
1. Write a brief outline of your planned method on your large sheet of paper.
Break
Collaborative Analysis of Sample Responses
Analyzing Sample Responses to Discuss
P-62
1. Simon
2. Ellie
3. Rhianna
Sample Responses to Discuss: Simon
P-63
Sample Responses to Discuss: Ellie
P-64
Sample Responses to Discuss: Rhianna
P-65
Whole Class Discussion
Whole Class Discussion Compare the different solution methods
and comment on their strengths and weaknesses.
How is this work similar/different to what you did?
Did analyzing the responses enable anyone to see errors in their own work?
Of the three sample pieces of work, which do you think has the most complete and accurate solution? Why? In what ways could it be improved further?
Individual Reflection
Sample Responses to Discuss: Rhianna
P-69
Returning to the Module
Activity D Analyze Students’ Responses to Pb Solving
Tasks The three tasks in this Activity, Counting Trees, Cats
and Kittens, and Security Cameras have a variety of mathematical content, but all focus on problem solving and the modeling skills described in the SMP.
Students are required to choose and combine techniques in non-routine ways.
Traditional summative assessment often focus on isolated content standards and fail to test these ‘process skills’.
Formative Assessment is an effective way to ensure that students are developing these practices.
Activity D
Four Phases of Problem Solving: A Useful Tool to Analyze Students’ Work on These
Tasks Formulate questions, choose appropriate
representations and techniques.
Reason logically, construct hypotheses and arguments, compute accurately.
Interpret and evaluate results obtained.
Communicate and reflect.
Teacher Discussion of Sample Student Responses
What does each sample student’s response [Simon, Ellie, and Rhiana] tell you about his or her capacity to use each of the phases of problem solving:
Formulate
Reason
Interpret and Evaluate
Communicate and Reflect
Discuss with your shoulder partner. 5 minutes
Questions for FeedbackH-17 and H-19 [Handout #6]
If you were the teacher of these students, what feedback would you give them to help them improve their responses?
Frame this help in the form of oral questions you could ask in the classroom.
You may find it helpful to refer to the generic questions on Handout #6.
Discuss with your shoulder partner. 5 minutes
Whole group share out-Round Robin Protocol.
Watching 3 Teachers Discuss Feedback Questions to
Students
Were these questions similar or different to the ones you and your partner discussed?
Watching 3 Teachers Discuss Feedback Questions to
Students
Were these questions similar or different to the ones you and your partner discussed?
What have you learned from this video clip?
Popcorn Whole Group Sharing
Activity E
Observe Formative Assessment in Action
In an earlier lesson, these teachers had asked students to sit in different places and attempt one of the tasks individually, with no help.
They then collected their students’ responses, assessed the work qualitatively and prepared written feedback in the form of questions.
The film clips you are about to see are taken from the follow-up lesson. Students have returned to their normal seats and most have solutions that are different than their partners.
Activity E
Observe Formative Assessment in Action
As you watch the video clips, consider these questions:
What different kinds of assessment can you see?
What is the purpose of each kind of assessment?
What do both the teachers and the students learn?
Activity E
Observe Formative Assessment in Action
Debrief in your table groups:
What different kinds of assessment can you see?
What is the purpose of each kind of assessment?
What do both the teachers and the students learn?
Activity G Consider the Effects of Feedback on Student
LearningSo far we have focused on the teachers’ role in providing
assessment feedback to students. In Activity G, we will consider the use students make of different types of feedback and the impact this has on their learning.
As you watch the video clip consider these questions:
Which of their comments strike you as particularly perceptive and important?
What are the implications of their comments?
Activity G Consider the Effects of Feedback on Student
LearningSo far we have focused on the teachers’ role in providing
assessment feedback to students. In Activity G, we will consider the use students make of different types of feedback and the impact this has on their learning.
As you watch the video clip consider these questions:
Which of their comments strike you as particularly perceptive and important?
What are the implications of their comments?
Give yourselves ½ minute to gather your thoughts and then have a 2 minute dyad with a partner.
Activity G Consider the Effects of Feedback on Student
LearningHandout #8
Please read The Effects of Feedback on Students’ Learning. 1 minute
Have a discussion with your table group and compare the students’ comments with the research quotes in this handout. 3 minutes
Activity G Consider the Effects of Feedback on Student
LearningHandout #8
Consider the following questions individually:
The dangers of giving marks, levels, rewards, and rankings
What are the implications of this for your practice? What would happen if you stopped giving marks
or levels on your pupils’ work? Why are so many teachers resistant to making
this change?
Discuss in your table groups.
Activity G Consider the Effects of Feedback on Student
LearningHandout #8
Consider the following questions individually:
The advantages of giving clear, specific, content-focused feedback
What are the implications of this for your practice?
Does this kind of feedback necessarily take much longer to give?
Discuss in your table groups.
Activity G Consider the Effects of Feedback on Student
Learning Research shows that students benefit
most from feedback that: Focuses on the task, not on grades or scores Is detailed rather than general Explains why something is right or wrong Is related to objectives Makes clear what has been achieved and
what has not Suggests what the student may do next Offers specific strategies for improvement How could you involve students in improving
your assessment practices?
MAP Mathematics Assessment
Project
Lunch