Assessment in the Mathematics Classroom Jane Silva Instructional Leader K-8.
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Transcript of Assessment in the Mathematics Classroom Jane Silva Instructional Leader K-8.
Objectives for the Day
> To examine the principles of effective assessment
> To explore ways of assessing mathematics
>To explore the link between assessment and instruction
>To examine how to collect and interpret assessment data
“From their earliest school experience, students draw life-shaping conclusions about themselves as learners on the basis of the information provided to them as a result of classroom assessments.”
- Stiggins, Student-Involved Classroom Assessment, Prentice-Hall, 2001, p.48.
Recall your own assessment experiences as students.
What kind of meaningful classroom assessment information do we want to provide to our students?
Purposes of AssessmentAccording to the Ministry of Education’s curriculum policy documents, the purposes of assessment and evaluation are to:
• improve student learning;• help teachers to determine students’ strengths and weaknesses in
their achievement of the curriculum expectations;• guide teachers in adapting curriculum and instructional
approaches to students’ needs, and;• assess the overall effectiveness of programs and classroom
practices.
Assessment is an ongoing awareness of students’ learning and needs, rather than an occasional event in the program.
Key Messages
Of all the assessment strategies, formative assessment is the most valuable strategy for supporting students’ learning and for promoting students’ independence and responsibility as learners.
Key Messages
Observation is the most efficient and effective way for teachers to assess students’ mathematical abilities, and is an integral part of all assessment strategies.
Key Messages
Teachers should use a variety of assessment strategies in order to assess students’ mathematical development as completely as possible.
Key Messages
Teachers should not provide a grade/mark/level on an individual assessment or a collection of assessments unless the grade/mark/level serves a clear purpose: to communicate achievement of curriculum expectations to students, parents, other teachers, and administrators.
Key Messages
SELECT EXPECTATIONS
SUMMATIVE/ DIAGNOSTICCULMINATING ASSESSMENTASSESSMENT ANDEVALUATION
ADAPT PROGRAM SELECT AND IMPLEMENTBASED ON FORMATIVE LEARNING EXPERIENCESASSESSMENTS
ONGOING, FORMATIVE ASSESSMENTS(PROVIDE FEEDBACK TO STUDENTS)
THETEACHING/ LEARNING CYCLE
Instruction and Assessment
Types of Assessment
Diagnostic AssessmentAssessment FOR Learning
Formative AssessmentAssessment FOR Learning
Summative AssessmentAssessment OF Learning
Assessment AS Learning
Evaluation
Summative (after)
Judging
Assign Grades
Report on Achievement
Assessment
Diagnostic (before)
Formative (during, ongoing)
Feedback
OF LearningFOR Learning
Types of Assessment
Diagnostic AssessmentAssessment FOR Learning
• The collection of information that occurs before a unit or new teaching (e.g., lesson);
• enables teachers to determine student strengths and learning needs;
• enables teachers to build on students’ prior knowledge;
• provides direction for the adjustment and improvement to programs for individual students or for the whole class.
CubeProbability Prompts
IMPOSSIBLE
LIKELY
CERTAIN
Describe probability as a measure of the likelihood that an event will occur, using mathematical language
CubeAddition and Subtraction Prompts
Face 1: I understand…
Face 2: I don’t understand…
Face 3: I find it easy to…
Face 4: I find it difficult to…
Face 5: I learned…
Face 6: I still want to know…
Work in pairs to decide what this graph might be about.
0
10
20
30
40
50
60
70
80
90
Open QuestionsData Management
What does this observation tell you about Jane’s understanding?
Mom!Why did Jamie get 4
sandwiches and I only got 2?
Gathering Diagnostic Information• Ask students to explain what they already know about a
concept or skill;
• Have students use manipulative materials to represent and explain a mathematical idea;
• Conduct brief, informal conversations with students about new ideas;
• Observe and talk with students as they solve a problem or complete a task that involves the concept or skill.
Provides ongoing day to day feedback for the teacher regarding the following:
• Identifying where to focus students’ attention and effort and encouraging progress and achievement of goals
• Monitoring of student learning, identifying areas of growth or concern and providing descriptive feedback
• Identifying the effectiveness of instruction and programming in order to modify and adjust it as necessary
Formative Assessment Assessment FOR Learning
What evidence will I look for to know that learning has occurred?
Application
Knowledge and
Understanding
Thinking
Mathematical Process
Expectations
Communication
What learning opportunities should I provide to promote learning?
Teaching strategies?
Opportunities?
Experiences?
Resources?
Personal communication?
Paper-and-pencil tasks?
Performance tasks?
Observation?
What are the most appropriate methods of assessing student
learning?
What evidence will I look for to know that learning has occurred?
Problem Solving
Representing
Mathematical Process
Expectations
Communication
What learning opportunities should I provide to promote learning?
Modeling problem solving process
Cooperative learning
Manipulatives made available
Pig and Chicken Performance Task
Observation
What are the most appropriate methods of assessing student
learning?
How should I record or document significant assessment information?
Teacher Grade Assessment FOR Learning Observation & Interview
Term Year
Unit of Study Date Mathematics Lesson Task/Problem Learning Goal/Curriculum Expectations Possible Solutions/Strategies
Questions about student learning…
Student Errors
Teacher’s Assessment
The student has difficulty understanding the problem (i.e., misread the question, omitted information - 22 legs), or selecting appropriate problem solving strategies.
14 7 chickens have 14 legs
16
Inference From Assessment
The student may have difficulty identifying important information when reading problems or lacks a strategy for selecting an appropriate problem solving strategy.
Next Instructional StepThe teacher models the problem solving process. The teacher reads and rereads the problem aloud, underlining important information and crossing out extraneous information. The teacher prompts the student restate the problem in his/her own words.
The teacher models how to develop a plan to solve the problem, suggesting appropriate tools and strategies. The teacher uses questions and cue to prompt the student.
The teachers asks the student to explain his/her thinking to determine whether he/she understand the problem.
Teacher’s Assessment
A grade 5 student has difficulty remembering the order of the steps when using the standard long division algorithm.
Inference from the Assessment
Based on this observation, what inference can you make about this student?
Inference From Assessment
The student may not understand, at the conceptual level, the procedure for long division.
Feedback• Telling whether response is correct or incorrect
• Informing the learner of the correct answer
• Explaining what is accurate and inaccurate
• Asking the learner to keep working on a task until he/she succeeds
• Timing of feedback
Feedback• Telling whether response is correct or incorrect
– negative effect• Informing the learner of the correct answer
• Explaining what is accurate and inaccurate
• Asking the learner to keep working on a task until he/she succeeds
• Timing of feedback
Feedback• Telling whether response is correct or incorrect
– negative effect• Informing the learner of the correct answer
– positive effect• Explaining what is accurate and inaccurate
• Asking the learner to keep working on a task until he/she succeeds
• Timing of feedback
Feedback• Telling whether response is correct or incorrect
– negative effect• Informing the learner of the correct answer
– positive effect• Explaining what is accurate and inaccurate
– most positive effect• Asking the learner to keep working on a task until he/she succeeds
• Timing of feedback
Feedback• Telling whether response is correct or incorrect
– negative effect• Informing the learner of the correct answer
– positive effect• Explaining what is accurate and inaccurate
– most positive effect• Asking the learner to keep working on a task until he/she succeeds
– positive effect• Timing of feedback
Feedback• Telling whether response is correct or incorrect
– negative effect• Informing the learner of the correct answer
– positive effect• Explaining what is accurate and inaccurate
– most positive effect• Asking the learner to keep working on a task until he/she succeeds
– positive effect• Timing of feedback
– the more delay, the less improvement
Feedback• Telling whether response is correct or incorrect
– negative effect• Informing the learner of the correct answer
– positive effect• Explaining what is accurate and inaccurate
– most positive effect• Asking the learner to keep working on a task until he/she succeeds
– positive effect• Timing of feedback
– the more delay, the less improvement
Students who are given comments only – rather than marks or marks and comments – make more gains in achievement and feel more positive about the experience (Butler, 1998).
Feedback
>Numerical score
>Right/wrong
>No grade necessary for formative tasks
>Anecdotal feedback
57
>General(“need more practice”)
Identify what is done well,
what needs improvement,
and how to get there.
Specific,Focused
Feedback
What does this work tell you about the student’s understanding of addition?Identify what is done well, what needs improvement, and how to get there.
What does this work tell you about the student’s understanding of addition?Identify what is done well, what needs improvement, and how to get there.
What does this work tell you about the student’s understanding of addition?Identify what is done well, what needs improvement, and how to get there.
What Code is This?
Code 20Annotation:
Student demonstrates some understanding of the relationships between important elements of the problem; shows 11 quarters equals $2.75 and draws quarters to continue adding towards the target of $5.25. 13 more quarters does not give a total of $5.25.
Code 10Annotation:
Student demonstrates a minimal evidence of a solution process; draws 14 quarters with no justification and subtracts the 11 given to conclude 3 more.
What Code is This?
What Code is This?
Code 40Annotation:
Student demonstrates a thorough understanding of the relationships between all of the important elements of the problem; shows groups of 4 quarters to make $1.00; uses diagram to show an additional 10 quarters are needed to make $5.25.
• Analyse students’ written work
• Observe students as they work on learning tasks
• Conduct conversations with students about their learning
Gathering Formative Information
• Usually carried out at the end of a unit, term, semester or year;
• informs teachers’ formal judgments about students’ achievement to be used in reporting;
• helps confirm what students know and can do and whether they have achieved the curriculum expectations.
Summative Assessment Assessment OF Learning
Summative Assessment…
Examples:
• Interviews • Problem solving situations• Performance tasks• Paper-Pencil Tests
Evaluation is the summative process of:
• judging the quality of student work on the basis of previously established criteria
• assigning a value (letter or percentage grade) to represent that quality.
Evaluation
What to do if Students Responses Don’t Follow a Logical Pattern
- Realize that no assessment can ever provide perfectly accurate data about a student
- Drop some items because they are deemed to be invalid
- Rethink the classification of specific items
- Meeting individually with students
Evaluation Decide early which assessments will form the basis for
grades and which will be used in a formative way
Compare student performance against criteria and standards
No single measure will give you all the information you need
Communicate your explicit expectations about both quantity and quality to students
Involve students in the selection process
Assessment AS Learning
• Focuses on the active involvement of students in the assessment of their own learning;
• Students personally monitor their own learning and use the feedback to adjust or adapt their understanding;
• Emphasizes students as critical assessors who can use metacognition in the self-assessment process.
Let’s Review:
• Diagnostic (Assessment for learning): is assessment helps to determine entry points.
• Formative (Assessment for learning): is assessment helps to promote learning and progress.
• Summative (Assessment of learning): is assessment reflects student achievement at a given time in a specific context e.g. at the end of year to determine placement or programs.