Elementary & Middle School Math Methods

Michelle Koenigkoenig_michelle@yahoo.com

(STRITCH in subject)

http://csumathmethods.wikispaces.c

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Questions, Comments, Concerns…

What did you learn last week?

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.

Multiply Fractions with a Sheet of Paper

Fraction Manipulatives

Fraction CirclesCuisenaire RodsCountersPaper Folding

MAKE SURE THAT STUDENTS GET A VARIETY

OF FRACTION MANIPULATIVES

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

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

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.

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

Assessment

Take the 3rd grade assessment- Any surprises? Likes/ Dislikes?

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.

8th Grade Assessment

What should go into a student’s grade?

How should a teacher determine a student grade?

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?

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.

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

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

Assumptions in a traditional approach to assessment

5 assumptions inherent in traditional approaches to assessment

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

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

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

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

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

5. Good teachers give bad grades

Bell curve: a good teacher only gave a few good grades and many poor grades

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

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

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

Articles

Best PracticeAssessment

Work time in Groups!