Setting Professional Goals - Not the Same as Setting SGOs

I'm a big believer in setting goals in my teaching and in my personal life. As a teacher in New Jersey, I have to set three goals for my class (student growth objectives). These are usually based on language arts, math, and a goal set by the school, but I don't think that by setting those types of goals, I'm stretching myself as a teacher. I also like to set goals that will push me to change how I teach. For the last few years, I've focused on learning more about how children learn math, and I've changed my teaching considerably because of this learning.

This year I want to dig even deeper and be able to understand exactly where my students are in their cognitive math development. Since I teach kindergarten, a major focus is on identifying their understanding of numbers. Are they able to count to 10 by rote? Can they count a group of objects using one-to-one correspondence? etc. Once I understand where they are, I will devise small group lessons to support their current understanding and stretch them into the next cognitive level. Math work stations will be differentiated based on cognitive levels, so students practice counting and numbers at the level of their understanding.

It will be hard, and I'll probably create a lot of stress for myself, especially since I'm required to follow the textbook; however, the benefits are going to outweigh the stresses. By moving students forward through a cognitive progression, I believe they will learn more and because there won't be gaps in their learning, they will be successful in math in future years.

Teaching Math and Teaching Reading - What's the Connection?

What if we taught primary level math like we teach primary level reading - guided reading, reading workshop, literacy work stations? What would that look like?

Guided Math Groups: The groups would be flexible and would be based on the needs of the students. I like Michael Battista's Cognition-Based Assessment and Teaching series. In these books, Battista explains the developmental levels students progress through as they develop mathematical understanding.

Math Workshop: The mini-lesson would focus on a concept or a skill that mathematicians use. It could be a time to introduce and reinforce the Mathematical Practices. As students move off to practice the skill, they will do it at their developmental level. This cannot be done by "differentiating" with a reteach or an enrichment level worksheet; rather, students work on problems that are interesting and important. The teacher conferences with students and coaches them to stretch their thinking.

Math Work Stations: Students practice math skills with partners during this time. The work stations are differentiated to meet the needs of the students in the class. The stations are engaging and attend to the important work of the grade level.

By using this method, students will be more engaged, gaps in learning can be identified and addressed, and teaching is focused on each student's zone of proximal development.

"What do you recommend we do about it?"

This was the question my vice-principal asked me as I explained how the math textbook we are currently using doesn't align to the Common Core. Great question! Trashing the textbook is not an option, so I pondered where to start that would give teachers a entry point into the changes needed. Starting with the end goals for student learning seems to be a starting point for discussions. These are the questions and ideas that I'd love to discuss with the teachers at my grade level.

•  What do we need our students to understand and be able to do by the end of the year?
• Do the assessments that we are currently using match what students need to understand and be able to do based on the CCSSM? 
• If the assessments do not match what students should learn and be able to do, then this is a good starting point. 
• Once we decide what students need to understand and be able to do, we can create assessments and then lessons to support our final goals. Some of the lessons in the textbook may support the learning. Others might not. Lessons that do  not support what students should know and be able to do should not be used. 
• Lessons should support all learners as they develop mathematical skills and understanding. They should include manipulatives and many opportunities for students to demonstrate and explain their thinking.
• How will we measure what students already know and understand about the CCSSM in the beginning of the year?
• How will we measure if students have mastered the standards at the end of the year?

I'd also love to talk about how children learn math. But I'll save that for another day.

The Cupcake Dilemma (What do you know about fractions?)

Growing up, I learned math by memorizing procedures and facts and completing countless pages of problems. For most of my teaching career, I taught my students the same way. But as fact would have it, I was blessed with seven children of my own. I watched their struggles with math homework. Two of them struggled for years trying to memorize the multiplication facts. Another was lost when she got to algebra, and another suggested that math was easy because all you have to do is memorize the formulas and plug in the numbers. My own kids opened up my eyes to why we need to teach math differently.

Even with the common core in place now for three years, teaching for understanding is not the norm in most classrooms. Just this weekend, my daughter, who was trying to bake cupcakes, called me with this dilemma.

"The recipe says that I need 1/3 cup of oil, but the measuring cup only has a marking for 1/2. What should I do?"

As a seventh grader, she's had years of practice with fractions, but does she really understand fractions? Can she apply what she's learned about fractions in real life situations?

Once I explained how she could estimate 1/3 cup using 1/2 as a reference, she was fine. The cupcakes were delicious. But I'm not convinced that she'll be able to apply that knowledge in the next situation because she doesn't really understand fractions. Memorizing procedures and facts don't always work in real life.

Reflection: How have my math lessons changed to help students develop a deep understanding of mathematics?