formative assessment lesson (fal) classroom challenge for secondary june 27, 2014
TRANSCRIPT
Formative Assessment Lesson (FAL)Classroom Challenge for Secondary
June 27, 2014
WELCOME AND INTRODUCTIONS
Objectives
• Participate in a Formative Assessment Lesson (FAL)
• Understand the Structure and the Resources Provided in a FAL
• Discuss Implementation of FAL• Explore strategies to support
Essential Questions• 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?
Agenda
• Welcome and Introductions
• Standards for Mathematical Practice
• Mistake and Misconception
• Formative Assessment Lesson
• Discuss Implementation
• Academic Language Support
• Challenges
Mathematics teaching assumes that students do not arrive at sessions as
“blank slates”, but as actively thinking people with a wide variety of skills and
conceptions. Research shows that teaching is more effective when it
assesses and uses prior learning so that the teaching may be adapted to the
needs of students. Black & William, 1998
Standards for Mathematical Practice
“Proficient students expect mathematics to make
sense. They take an active stance in solving mathematical problems. When faced with a non-routine problem, they have the courage to plunge in and try something, and they have the procedural and conceptual tools to carry through. They are experimenters and investors, and can adapt known strategies to new problems.They think strategically.”
CCSS-Mathematics
CCSS Mathematical PracticesO
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nREASONING AND EXPLAINING2. Reason abstractly and quantitatively3. Construct viable arguments and critique the reasoning of others
MODELING AND USING TOOLS4. Model with mathematics5. Use appropriate tools strategically
SEEING STRUCTURE & GENERALIZING7. Look for and make use of structure8. Look for and express regularity in repeated reasoning
21st Century Skills (4 C’s)
Critical ThinkingCollaborationCommunicationCreativity
We don’t learn passively. People are active participants in their own learning. We construct bridges between what we are learning now and
what we already know. Misconceptions arise naturally as a result of personal experiences. For instance: A third grader constructs the following “rule” for
themselves based on their previous learning: “I will get larger number whenever I multiply two numbers together.”
http://youtu.be/JqDZqblvOn0
There is a BIG difference between a Mistake and a
Misconception. MISTAKES•Computational Errors•Lack of Attention•Careless Errors•Misreading Own Handwriting•Observed Occasionally/ Infrequently
MISCONCEPTIONS•Wrong applications of Mathematical Rules•Incorrect interpretation of mathematical concepts•Observed consistently
Why is the consideration of misconceptions important?
• Children construct meaning internally by accommodating new concepts within their existing mental frameworks.
• Thus, unless there is intervention, there is likelihood that the pupil’s conception may deviate from the intended one.
• Pupils are known to misapply algorithms and rules in domains where they are inapplicable.
• A surprisingly large proportion of pupils share the same misconceptions.
Undiagnosed Misconceptions Become Owned and Embedded
Misconceptions
Undiagnosed Misconceptions Become Owned and Embedded
Misconceptions
Owned
Formative Assessment is Shown to be more successful than direct
instruction alone.
PRE-Test ERRORS ANALYSIS PERCENTAGES
POST-Test ERRORS ANALYSIS PERCENTAGES (approximates)
A Side-by-Side ComparisonPRE•A(10%)•B (25%)•C (80%)•D (95%)•E (50%)•F (5%)•G (90%+)•H (5%)•J (10%)
POST•A (5%)•B (5%)•C (30%)•D (45%)•E (5%)•F (less than 5%)•G (10%+)•H (30%)•J (5%)
Some Difficult Discussions
Get Out of Your Own Brain!
• Recognize…the rest of the world does not think the way a math teacher thinks.
• …and that’s OK.
#mathteacherproblemshttp://youtu.be/6LSOMiLMvAY
HOW WE THINK HOW THE REST OF THE WORLD THINKS
Things I Can Let Go….
• No Work=No Credit• Pencil Only or No Credit• Do it How I Told You To • Show the Steps…no, not your steps…
the ones I taught you• “MATH RULES”
Motivating Teachers
• THE GAME IS CHANGING: Math is no longer an exercise in choreography, but in true understanding and application–CCSS Content Standards–Standards for Mathematical Practice
Our Plates as Math Teachers
Why Does FAL Matter?
26
What does CCSS-M mean for teachers and students?
• Higher performance targets i.e. richer problems:–More complex– Less routine, with – longer chains of reasoning, requiring –More student responsibility, and
autonomy
What does CCSS-M mean for teachers and students?
• Requires learning activities that are:– Less imitative– Involve more thinking, discussing,
reasoning
• This means new roles and new skills for teachers– Less “This is how to”–More “What do you think?” , “How did
you approach to solve the problem?”
Why assess?
• Formative for learning– Diagnose difficulties and misconceptions
and so inform teaching– Engage learners by showing them what
we value, what they need to improve on and what they still need to learn
Why assess?• Summative for reporting– Celebrate achievement, rewarding effort
and success– Select learners for groups, courses, careers– Keep records to inform teachers or parents
of progress
• Evaluative for research– Assess teaching methods to see which
work more effectively
FORMATIVE ASSESSMENT LESSON
Formative assessment
• All… studies show that … strengthening … formative assessment produces significant, and often substantial, learning gains.
• Black and William, 1998
Why do a Formative Assessment Lesson?
"Informative assessment isn't an end in itself, but the beginning of better instruction." —Carol Ann Tomlinson
“…the student's role is to strive to understand what success looks like and to use each assessment to try to understand how to do better the next time." - Rick Stiggins
Formative assessment is …
“… all those activities undertaken by teachers, and by 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.”
(Black & William, 1998 research review, para, 91)
What does FAL look like?Two kinds of formative assessment
lesson materialsConcept development lessons “Proficient students expect mathematics to make sense”
Reveal students’ prior knowledgeDevelops students’ understanding of mathematical ideas,
connecting concepts to other mathematical knowledge
Problem solving lessons “Students take an active stance in solving mathematical problems”
Assess and develop students’ ability to apply their mathematical knowledge and reasoning to non-routine, unstructured problems
Formative Assessment Teaching vs.
Regular Teaching A change in the teacher’s role from a
focus on teaching to a focus on learning.
A change in the student’s role from receptivity to activity
A change in the student-teacher relationship from adversaries to collaborators.
Formative Assessment Teaching
Formative assessment involves a change in “classroom culture”
Students take more responsibility for, their own work.Students engage in “productive struggle” with rich challenging tasks.Students study fewer tasks, but in greater depth.Teacher’s role is to prompt students reflect and reason through their ideas.
Enhancing Instruction for CCSSM
Upgrading UnitsNumber Talks
A Typical FAL1. An assessment task for students to attempt
before the main lesson.2. Teacher notes to describe common issues in
student work on the assessment and suggesting formative feedback in the form of questions.
3. Collaborative learning activities to help students develop their understanding of the mathematics.
4. A follow-up assessment task – re-engage with the original challenge.
Typical activities
• Classifying mathematical objects and challenging definitions
• Interpreting multiple representations• Evaluating conjectures and assertions• Modifying situations and exploring
their structure• Critiquing supplied examples of other
students’ work
Structure of the FAL
• Before the lesson, students work individually on the assessment task. You then review their work and create questions for students to answer in order to improve their solutions.
• During the lesson, students work individually on a task that requires them to interpret and solve two equations in two variables. Students then compare and discuss their solutions in small groups.
Structure of the FAL
• In the same small groups, students evaluate some sample solutions of the same task.
• In a whole-class discussion, students explain and compare the alternative solution strategies they have seen and used.
• Finally, students use what they have learned to revise their work.
Collaboration Protocols
1. Set norms
2. Focus on student learning
3. Use Standards for
Mathematical Practices as guide
when visiting a colleague’s
classroom
Formative Assessment Lesson
Assessment Task
Assessing Students’ Responses
How can I support students through feedback?
• Give feedback in the form of questions
• What are students’ common misconceptions?
• What are some of their challenges?
• Provide a list of questions --- students can provide feedback of their own work or other’s work
Common Issues
Issues• What’s in the data?
– Five number summary– Shape, center, spread, outlier
• What do the numbers tell?• How can I use the numbers
to tell the story?• Why are numbers
important?
Questions and Prompts• How did you find the
maximum or minimum value?
• Why did you choose ___ as the median? What supports your conjecture?
The box plot represents the scores of students in a test for which the maximum
score of 100.Write all the information you can derive
from the box plot.
Whole Class Introduction
The Box Plot may end up looking like this.
Collaborative Group Work
Whole Class Discussion
Follow-up Assessment Task
Where is the formative assessment?
• Teachers are given information on what students can do unaided;
• Teachers offer differentiated support to students, as this is needed;
• Students get constructed feedback from teacher and other students, as student work is discussed;
• Students act on feedback by improving their responses;
• Teachers get feedback on learning by comparing performance before and after.
The Nature of Tasks Used in the Classroom …
Tasks as they appear in curricular
materials Studentlearning
Will Impact Student Learning!
But, WHAT TEACHERS DO with the tasks matters too!
Stein, Grover & Henningsen (1996)Smith & Stein (1998)Stein, Smith, Henningsen & Silver (2000)
The Mathematical Tasks Framework
Tasks as they
appear in
curricularmaterials
Studentlearning
Tasks as they appear in curricular
materials Student learning
Tasks as set up by teachers
Tasks as enacted by
teachers andstudents
Things to Learn from Our Successes and Mistakes
• Make FAL’s an expectation.• Set time aside to train every single teacher• Re-Train Teachers• Follow up with second time to train every single
teacher in ANALYSIS of STUDENT WORK• Video!!! Praise works better than force!• Provide Materials, Share Materials, House
Materials Centrally• Teachers provide (someone in leadership) dates
of FAL enactment• Ask for feedback from teachers!• Ask for feedback from students!
Objectives
• Participate in a Formative Assessment Lesson (FAL)
• Understand the Structure and the Resources Provided in a FAL
• Discuss Implementation of FAL• Explore strategies to support
