Sunday, October 31, 2010

Books That Have Impacted my Life

I've been thinking about this blog post all week. There are so many books that I recall as important, it was hard to pick just one. Finally, I decided to pick two books - one from my childhood and one that currently impacts my work.

The first book that made an impact was The Golden Book of Fairy Tales. I got my copy on my 10th birthday from my aunt and uncle. I wasn't able to read all of the stories but I poured over the illustrations, drinking deeply into my imagination as I heard the stories read aloud. I remember counting the fingers in one of the illustrations, checking to see if this was before or after the sister cut off her finger to save her brothers. These were not the politically correct versions kids get now. They were scary and sad and universal in the richness of their stories. I just loved them!

Fast forward to recent times. My next selection is A Whole New Mind by Daniel Pink. I named this blog based on the Design chapter. But story, another chapter in the book, also speaks deeply to me. We connect to each other by story. It is telling that my favorite book from my childhood was a storybook. 

I hope the stories I tell in this blog connect with you, my gentle reader, and lead you back to read more!

Friday, October 22, 2010

My Life as a Math Non-Believer

 I have decent number sense. I can figure out tips at restaurants and how much something is on sale, even if it is 25% off the 40% sale price. Estimation is my best friend. My head hurts when I have to do traditional algorithms

Patterns in Knitting
I get algebra. A lot of it makes sense to me. I look for patterns in all sorts of things and try to balance equations in things like knitting. Can’t for the life of me remember what to do with the creature called a quadratic equation, can you?

I am good with spatial orientation. Friends like to go on trips with me because I can figure out where I am and how to get places with (and without) maps. I can’t remember theorems and made it through geometry in high school by doing extra credit projects (like making math posters for the classroom).

In college I was an art major. I avoided math. Took a class called “Math for Non-Believers”. We looked at math in a very non-traditional way. It challenged me. It appealed to me. I could visualize, and thus understand, three-dimensional objects and how they worked in space. Thanks to M.C. Escher I could make sense of one-dimensional objects, too.

Math had meaning when it had a practical application. Even the course in glazes I took with the ceramic engineering students was a fun challenge. Never knew the abstract concepts in math could have practical applications. I could use math and chemistry to create a glaze with depth and aesthetic beauty.

My problem is that I was taught math by memorizing rules and procedures - hateful stuff - to get the one right answer. To balance out the skills (and drills) and the “only way” to do math I embraced the conceptual understanding of how math works as my lifeline.

We accept the developmental growth a child makes in reading and spelling so why can’t we understand the same child needs to figure out how math works, too? It is my hope more students are given the opportunity that I never had in school to grow in their conceptual understanding of how math works. It’s nice to know we have so many doors in our school that we can walk through to see this in action daily!

Thursday, October 14, 2010

Class Poll: How Do You Want To Learn Today?

My class consists of 70+ certificated staff members. Several of them opened the school almost 30 years ago. One was hired last week. In terms of experience they are a heterogeneous group. When asked, “What do you want to learn today?” their answers are as diverse as their experiences.

My job, as the instructional coach, is to research, design and facilitate professional learning at Neptune Beach Elementary. We are part of the Learning Forward Learning School Alliance (LSA). We believe collaborative professional learning, teamwork, and problem solving are keys to school improvement.
LSA members: 
  • Strengthen school and district culture to focus on educator and student learning;
  • Initiate, refine, or expand the use of collaborative professional learning within your school;
  • Explore ways to evaluate the effectiveness of collaboration within your school; and
  • Develop leaders within your schools to facilitate the transition to a learning school.
Teachers and principals will receive training, coaching, and facilitation to advance their skills in applying the Learning Forward Learning School principles and practices. LSA members will learn together in their own schools, with other schools through webinars and facilitated conversations, and at meetings held at Learning Forward conferences. They will openly share their goals, their progress, and -- over time -- their results.
When people use the term “professional learning” or “ professional development,” they can refer to traditional structures such as a workshop or a conference. It also includes collaborative learning cycles (CLC) among members of a grade level or content team in the school setting. Professional development, however, can also occur in informal constructs such as conversation among colleagues, independent reading and research, observation in another classroom, joining a personal learning network (PLN) on Twitter, or other learning from a peer.

Every year we assess our professional learning using the Standards for Staff Development Assessment Inventory (SAI). Historically we have scored the lowest on question 29: We observe each others classroom instruction as one way to improve our teaching. The poll tells us the teachers want to learn from each other in their own classrooms. This year we designed a number of professional learning activities that include at least one out of every five hours observing in a classroom.

Sometimes a poll tells you more about the conditions a learner desires, how they want to learn, instead of what they want to learn. What you do with the information makes all the difference!

Thursday, October 7, 2010

Differentiation in 1st Grade Math

Differentiated Instruction is a way to insure all students has access to the curriculum. The content, process or product can be differentiated based on the student’s readiness, interests, or learner profile. Sounds simple, right? Talking about differentiation is one thing but acting on it is often a more difficult task. Differentiation is math is especially difficult for some teachers. We work hard making all sorts of “stuff”, different worksheets, tools, and other materials. Despite our best intentions, what typically happens is the standard (or benchmark) get watered down instead of differentiated. In a recent blog post Differentiated Instruction: What Difference Does it Make?   David Ginsburg makes the following point:
But does it really matter whether DI is a bad idea, as Mike Schmoker insists, or a badly implemented one? Either way, effective teaching includes assessing and addressing students' individual differences.
There are three key things every teacher needs to know to be successful at teaching. You need to know:
1.     Your students,
2.     Your curriculum (standards, resources, materials), and
3.     How to make it visible to others (including your students!).

The first two are familiar to all teachers but the last one is generally not given the importance it deserves. Visibility can take many forms. It can be the planning the teacher does before the lesson, recorded in a lesson plan. It can be charted, to keep a concrete record of previous learning. It can be the portfolio of individual student work, documenting growth and acquisition of a skill or strategy. It’s the formative assessment, the assessment FOR learning, that makes differentiation so powerful.

In this video Alane Wright, 1st grade teacher at Neptune Beach Elementary, talks about how she differentiated a math lesson for her students.

Charting in 1st Grade Math from Jill Kolb on Vimeo.

Key in this lesson was the simple changes Alane made to meet the readiness level of her students. By giving some students dice with dots, and some with numbers, and some with a combination of both dots and numbers, all students were able to meet the benchmark. Also key was the charting Alane did with her students. The students with the least efficient strategy – counting each dot on both dice – now have a visual reminder of other options for combining situations when they are developmentally ready for it!

So what is the next step? For me, I am only as good as the resources I have around me. Reading blogs and books are like learning to fish. If I want to keep eating, oops…teaching math to young students, I’ll need to fish for new ideas. One book I love is Math For All: Differentiating Instruction (K-2). There is also another version for Grades 3-5 and 6-8. While it is not the kind of book that you can open up and say, “Oh, I can do that tomorrow!” it is an outstanding resource that will show you how other classroom teachers have differentiated math lessons for their students.

Designing good differentiated lessons includes the important step of making visible all the learning going on in your classroom. Charting with your students is one key way of documenting their growth. I would love to hear about ways you differentiated math with your students or different charting ideas. Thanks in advance for sharing.

Saturday, October 2, 2010

Designing a Math Closing: Charting Matters!

In Duval County Public Schools (DCPS) the math workshop model consists of three parts - Launch, Explore, and Summarize

Launch (Opening Meeting 15-20 Minutes)
Lessons may address:
  • Presentation of conceptual problem
  • Analysis of problem strategies
  • Comparison of related problems
Teacher Role:
  • Teaches mini-lesson that includes the presentation of a conceptual problem to be solved
  • States the focus of the work (concept and/ or skill) clearly connecting it with standards
  • Makes expectations explicit
  • Teachers should not present particular strategies that will lead students to solve problems in that way during Explore.
Student talk should be to clarify questions

Explore (Work Period 20-25 Minutes)
Student Role:
  • Independent work
  • Partner work
  • Small group work
  • Involved in working problems that engage them in different stages of the problem solving process
  • Knows exactly what is expected
  • Contributes to class activities
  • Works with manipulatives and other mathematics tools or resources as needed
  • Generates evidence of process used in problem solving
  • Uses accountable talk
Teacher Role:
  • Monitors student work
  • Engages individuals or groups in accountable talk
  • Observes students’ discussions and explorations of their strategies
  • Makes anecdotal notes on observations, such as misconceptions and strategy development
  • Examines student work as it evolves
  • Small group instruction
  • Conferencing
  • Teacher begins to develop the summarize session by noting different strategies that will be addressed during the closing and selecting students or groups to present during the closing.
Summarize (Closing 20 – 25 Minutes)
Student Role:
  • Shares strategies and approaches to given problems
  • Makes connections to the main concepts from the lesson
  • Justifies strategies and solutions
  • Compares and analyzes solution strategies presented
  • Uses accountable talk
Teacher Role:
  • Scaffolds problem solving strategies from least efficient to most efficient
  • Scaffolds students as they make connections to the main concepts from the lesson
  • Fosters a spirit of inquiry by asking higher order questions
  • Addresses misconceptions
  • Highlights and records student strategies and generalizations for future reference
Teachers often feel teaching only occurs when they are the one in front of the class. This workshop model turns things around, placing the student in the role of the expert with the teaching coming at the end, during the Summarize. The student is the one teaching how they solved the problem to the other students, demonstrating a strategy. The planning begins during the Explore where the “Teacher begins to develop the summarize session by noting different strategies that will be addressed during the closing and selecting students or groups to present during the closing.”

This careful planning for the Summarize section is done while the teacher circulates through the room, observing the student application of strategies. The scaffolding of the closing, from the least to the most efficient use of strategies, gives the class a view into the different ways students solved the same problem. Images shared in front of the room, or projected from a document camera, create a temporary view into the thinking. Charting, on the other hand, creates a permanent record of student strategies.

Learning to chart is not difficult. It just takes practice. It also helps to have models and a few guidelines. Amber McFatter, 2nd grade teacher at Neptune Beach Elementary, is one such model. In this video she explains about charting in her classroom.

Charting in 2nd Grade Math from Jill Kolb on Vimeo.

Sometimes teachers will tell me "I can't chart in front of the students. My charts look so messy!" It really is okay if the charts are messy because learning is messy. There are strategies for teachers to help with charting. 

First make sure your chart paper and at least two markers of different colors are available. Most teachers hang the chart, with magnets or tape, right next to the screen so they have a clear view of the student work being projected. It is nice if you have one color marker for each student. Please don't use yellow or pastel markers or any type of highlighter! They are difficult to read and fade very quickly. At Neptune Beach Elementary teachers are encouraged to not only include the benchmark and/or the essential question on the chart but also to include the date.

More Preparation
During the Explore you are planning your closing and selecting students to present their strategies, scaffolding the strategies. You will get an idea on how much room to allow by looking at the student work. Different strategies may not take the same amount of space. It is important, however, to represent their strategy in the same manner as the student. This includes drawing, labeling, and recording student thinking. After a while it gets easier to identify both the efficiency and maturity in the strategies.

Hopefully this will help you and, more importantly, your students create deeper learning with math closings!