Elementary & Middle School Math Methods Michelle Koenig (STRITCH in subject) es.com

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 Circles Cuisenaire Rods Counters Paper 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 6 th grade (this is typically started in 4 th grade) and use the instructional time on fractions from 4 th – 6 th 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 3 rd grade assessment-  Any surprises?  Likes/ Dislikes?

Assessment Now grade the 3 rd 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.

8 th 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 grade Don’t be afraid to try something new with assessment or grading Change 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 day Most teachers in the field are VERY TRADITIONAL when it comes to assessment

Articles Best Practice Assessment

Work time in Groups!