Thinking About Math

Tuesday, September 28, 2010

Becoming a Patient Problem-Solver

Dan Meyers, a math teacher, talks about the cookie cutter curriculum we frequently see (and heck, are much more comfortable with) in schools, and how it does a disservice to our kids by leading them through an unrealistic recipe for problem-solving. He emphasizes the need for our kids to be 'patient problem-solvers' in order to be able to use the math we learn today, tomorrow.
When you and your child are struggling through those tough Application, Connection, and Extension exercises, think of this message:

Monday, September 13, 2010

The Trials and Tribulations of Teamwork

Last week we started working in teams. Overall, most teams did an excellent job of communicating, cooperating, and planning. Leaders began to emerge and students began to settle into roles. Some teams learned to deal with a team member refusing to participate. Each team did a fine job of handling the situation, either by convincing the person to participate or by requesting help from the teacher.

While each team member will receive his own performance grade which will count towards 10% of their final grade, to be recognized as a "Best Investigation Team" every member of the team must to Outstanding work. I encourage the students to work with each other's strengths and weaknesses in order to accomplish this task. Problems are designed to be done cooperatively, and will never be an independent learning task. If a student is absent, she should get the 'notes' from a team member by copying their Problem (and any notes that were given via a 'lecture' that day). Teams that finished early were encouraged to let the 'best writer' on the team quickly proofread their sheet, and then each member was encouraged to check his work with the Problem Evaluation Sheet I will use to assess her performance.

Problem Evaluation Sheet

If a team is unable to complete the assigned task during the class period, they are encouraged to meet during study hall or share notes prior to the end of the Investigation. At the end of the Investigation, students will be given a class period to finish any Problems or ACE exercises they were unable to complete on schedule, in addition to time to work on their Math Reflection.

Tuesday, September 7, 2010

Team-Based Learning

The introduction phase of school is winding down, and the academic focus is now beginning in the second week of school. Last week was spent focusing on working together in homeroom, social activities, and academic endeavors. 7th graders at CMS spent time getting to know each other in community building activities during orientation the first day of school. They worked together as a class and in small groups to share commonalities and differences, focusing on respecting each other for the individuals they are. In addition, starting with small groups, all students worked on creating a set of school-wide agreements for behavior and social interaction, culminating in a Social Constitution on Friday. Many homerooms will implement Circles of Power and Respect (CPR) once or twice a week to further work on social development.

In math, the focus was on being a 'Best Investigation Team'. A Best Investigation Team is one that has every team member doing outstanding Problem work. That means by the end of the investigation, every team member has all the Problems complete, and all responses are in complete sentences. Through the Helium Stick activity, students learned that it is not enough just to lookout for oneself, but a successful team has good communication, cooperation, strong leadership, and a plan to reach a goal. Teams exhibited those team-focused characteristics were able to lower the stick to the floor with each team member's index finger in constant contact with the bottom of the stick.

Investigation teams are created based on a secretly coded system of colors, where students chosing someone from another color to group with. This creates groups of students with varying math abilities (as determined by the 'Algebraic Relationships' or the 'Geometry' goals on last spring's MAP test). Prior to grouping, we discussed other strengths each individual could bring to the team, such as: organization, getting everyone involved, keeping track of the time, understanding directions, etc. Students were encouraged to pair up with someone with a strength that was different from their own.

Best Investigation Teams will be posted on the class wiki at the conclusion of each investigation.

Links:
Team-Based Learning
Videos of A Typical Classroom Period
Beloit's CMP Parent Site
CMP's Parent Site
Developmental Designs Family Information sheet

Friday, August 27, 2010

Let's Get Started

Welcome! I am looking forward to working together with you to ensure that your child gains as much as he can from 7th grade math this year. You've been your child's teacher much longer than I ever will be, so your insights, recommendations, and requests are very important to me. I am looking forward to meeting you at the Open House next Thursday, but rest assured I am always available via email and I am open to chatting with you on my teacher Facebook page. I will have cards with all my contact information and resources available at the Open House, at Parent-Teacher Conferences, and any time by request throughout the year.

This week I would like to just give you a taste of what is to come for your child this year in math. The 7th grade Connected Math Program 2 will give your child a first formal look at algebra. We will also cover some 3-dimensional geometry and extend what she learned last year with 2-dimensional geometry. The general schedule for the units are as follows:

Quarter 1: Variables and Patterns (Algebra)

Quarter 1/2: Stretching and Shrinking (2D Geometry)
Quarter 2/3: Accentuating the Negative (Algebra)
Quarter 3/4: Moving Straight Ahead (Algebra)
Quarter 4: Filling and Wrapping (3D Geometry)

Traditionally, students seem overwhelmed in the Variables and Patterns unit as they get used to more frequent homework, organizing and prioritizing activities outside of school, and stretching themselves to learn things they haven't spent much time on in the past. A lot of the 7th grade math program will be covering math skills your child hasn't had as much time to practice in the past. They are starting to get ready for high school math and are in the beginning stages of their secondary education. Be patient with the process. Insist that your child at least try each assigned exercise. If he cannot complete the exercise, have him write down the question he needs answered before he can complete the work. He will have a couple of chances in class to ask that question so he can successfully finish the job.

I am available almost every day after school and I would love to help any student of mine by giving them some individual instruction and encouragement.

This information letter on the Variables and Patterns unit will also give you some insight on the content covered in this unit. Keep this handy for your child, too. The vocabulary on the back may be helpful to your child.

Friday, August 20, 2010

Free Technology for Teachers: 38 Weeks of Algebra Lessons

Free Technology for Teachers: 38 Weeks of Algebra Lessons

This is an excellent algebra resource. This guy can really share the math ideas in everyday language. He includes PowerPoint shows and pdf handouts. We will focus on algebra in Variables and Patterns, Accentuating the Negative, and Moving Straight Ahead. You may way to bookmark this page!

Thursday, August 12, 2010

The Role of Homework

The role of homework has been a controversial one ever since I began teaching. Traditionally it is included as part of a grade in order to give a student credit for trying. It is a measure of effort. What happens, though, when trying still results in an unfinished assignment? The student's grade is reduced in some way or another.

I have taken quite a bit of my methodology from a well-respected high school math educator and author of 'Every Minute Counts' and 'Making Minutes Count Even More', David R. Johnson. Here, Dave suggests the use of a homework quiz given after students have had a chance to correct their mistakes. I have used this technique in the past, and I believe it worked well (though my students may disagree ;). The idea is that more kids will try practicing, or doing the homework, if they know their parents will see the grade they got on it. Yet, there was always the argument, though rarely was it truly the case, that the homework didn't need to be done because the student had already mastered the skills.

When it comes down to it, the primary objectives of homework are threefold:

1) to allow the student to practice the skills they are expected to master,
2) to allow the teacher to see areas of trouble and address them in a timely manner, and
3) to allow parents to monitor the effort their child is putting into learning.

Keeping these objectives in mind, I am considering continuing grading homework in a similar fashion as I have in the past, but not including the actual homework grade in the final grade. This would mean that, almost daily:

1) homework would be checked for completion the day after it is assigned and recorded in the gradebook,
2) students would work as a team to 'check and change' their work,
3) each team would be allowed to ask at least one question, and
4) each student would be expected to fix their mistakes.

Then, at the end of each one or two investigations (5-9 assignments) I would collect and check their homework for the following:

most of the assignments have been completed on time,
all mistakes have been completely corrected, and
a randomly picked problem is correct from every assignment.

If all assignments are complete and corrected, and no more than two assignments were completed late, that student would earn a homework pass eligible to excuse any assignment in the future.

Not including the homework grade in the final grade means that the final grade will be based on tests, quizzes, and reflections. All tests and quizzes will remain open note and open book according to the recommendations of the Connected Math Program, and can be corrected as well.

“Tell me and I'll forget; show me and I may remember; involve me and I'll understand.” - Chinese Proverb