elementary & middle school math methods michelle koenig [email protected] (stritch in...
TRANSCRIPT
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Elementary & Middle School Math Methods
Michelle [email protected]
(STRITCH in subject)
http://csumathmethods.wikispaces.c
om
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Questions, Comments, Concerns…
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What did you learn last week?
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FRACTIONS!
Take a set of fraction circles to keep and cut one out as a group to use tonight.
Go through the fraction worksheet and use your fraction circles to calculate the problems.
Create 2 more fraction problems for each operation to share with the class- make sure you can solve the problems with your fraction circles.
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Multiply Fractions with a Sheet of Paper
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Fraction Manipulatives
Fraction CirclesCuisenaire RodsCountersPaper Folding
MAKE SURE THAT STUDENTS GET A VARIETY
OF FRACTION MANIPULATIVES
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Fractions
Fractions is one of the most difficult tasks for middle school children
Fractions are very complex and the rules that children learn for fractions conflict with rules that they are familiar with: 1/3 is less than ½ If a pie is cut into 3 equal parts the pieces are smaller
than a pie cut in half The more the pieces the smaller the pieces
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More Fractions…
There needs to be a shift in the way we are teaching fractions from a focus on algorithms to a development of quantitative understanding, meaning: Order fractions Know about relative size of fractions Estimate with fractions Equivalent fractions Should be based on experiences with manipulatives
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EVEN More Fractions…
Recommendations for Change:
Postponing most operations with fractions until 6th grade (this is typically started in 4th grade) and use the instructional time on fractions from 4th – 6th grade to develop a strong understanding of fractions.
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Manipulatives
Introduce manipulatives by showing how they can represent ideas
Allow students to freely select Encourage the use
Do not structure lessons in which students are being directed in exactly how to use the manipulatvies The focus is no longer understanding the mathematics
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Assessment
Take the 3rd grade assessment- Any surprises? Likes/ Dislikes?
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Assessment
Now grade the 3rd grade assessment like you would had you been the teacher that gave the test.
Keep in mind your individual policies and procedures while you are grading.
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8th Grade Assessment
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What should go into a student’s grade?
How should a teacher determine a student grade?
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Grading ???
Should effort be apart of a student grade?Is responsibility part of a student grade?How should late work or incomplete work
affect a student grade?Should a student ever earn an F?How should extra credit affect a student
grade?
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Teaching behaviors consistent with a teaching and learning focus
A paper/project/ homework can be redone- redo until an acceptable grade is earned
A test can be retaken- goal is to keep students wanting to do better
A passing grade can be given if student has shown content mastery- low marks can be given for late work, incomplete work on a different section of the report card.
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Teaching behaviors consistent with a teaching and learning focus
Students should be allowed to use their text and notes for a max amount of time- goal is to study and organize not just memorize random pieces of information
Teacher should feel responsible for student learning
Work is graded only after nonacademic standards are met
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Teaching behaviors consistent with a teaching and learning focus
Teacher takes pride in the number of students who attained an acceptable grade
Teacher outlines objectives, highlights material to be tested, and makes tests similar to what was covered in class
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Assumptions in a traditional approach to assessment
5 assumptions inherent in traditional approaches to assessment
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1. All students learn the same way and at the same speed
We all know this is not true, YET most teachers continue to test all the students at the same time
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2. Grades are essential to learning
What do grades really mean? Do grades tell us anything about what a student learned or what a student needs to work on?
Grades are considered to be destructive for creativity and higher order thinking
Students are found to be avoid more challenging tasks if they know they are being graded
Students are less apt to find a task interesting if they know they are being graded
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3. Grades motivate learners
Stiggins: this assumption that motivation exists because a student has it or not and grades are a way to manipulate that motivation
This assumption implies that grades will get you a punishment or a reward
Students need to be coerced into learning and grades are the method of coercion
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4. Grades are necessary for control
Since discipline is an issue for many middle school teachers, often teachers will use grades to control student behavior
Once a student is failing, threatening with a failing grade doesn’t matter- giving a student a zero will only work for so long
This behavior will damage the student-teacher relationship
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4. Grades are necessary for control
Ways that grades are used to punish
Taking off points for tardiness, talking, not having a pencil, no name on paper, using pen instead of pencil
THESE PUNISHMENTS
HAVE NOTHING TO DO WITH
LEARNING- YET MAY DRASTICALLY
AFFECT A STUDENT GRADE
Ways that grades are used for reward
Hard work Effort Neatness Following the
rules Conformity Compliance
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5. Good teachers give bad grades
Bell curve: a good teacher only gave a few good grades and many poor grades
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The Theory of Mastery Learning
Uses formative feedback- assumes that continuous improve is desired
Correcting work will allow a student to learn
Offer students the opportunity to correct and redo work to raise their grade
There should be a limit to the number of redos
Effort should not be taken into account when grading redos
EXAMPLES
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Additional Thoughts on Assessment
Don’t assume that students know how to take a test
Keep in regular contact with parents about progress and grades
Students should always know their gradeDon’t be afraid to try something new with
assessment or gradingChange assessment policies at quarter or
semester if they are not working
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Additional Thoughts
Don’t forget what it is like to take tests and quizzes
Feedback should follow the next dayMost teachers in the field are VERY
TRADITIONAL when it comes to assessment
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Articles
Best PracticeAssessment
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Work time in Groups!