Beginning CGI Math In Kindergarten
In this blog, kindergarten teacher, Laura Steele, describes her first two weeks of math lessons with her beginning kindergarteners. Mrs. Steele teaches at a Title 1 school where 82% of the students receive free and reduced lunch. 39% of her students are English Language Learners. Mrs. Steele has been using CGI for 5 years, and CGI is now the foundation of her math instruction. If you are beginning with CGI, and are interested in using some of Mrs. Steele’s lessons, please don’t feel that you have to use all of these lessons within a couple of weeks. As an experienced teacher, you will notice that there are some routines that Mrs. Steele uses with her students that children will learn better if they practice them daily. You could incorporate daily practice with these routines without teaching all of these lessons. Although these lessons were taught in kindergarten, many first and second grade students would benefit from these beginning lessons. You could make the numbers larger, if you teach older children.
Linda Levi, Director, CGI Math Teacher Learning Center
Beginning CGI Math in Kindergarten
by Laura Steele
The beginning of kindergarten is the perfect time to initiate Cognitively Guided Instructional practices into the daily math routine. My first goals are for students to learn that when we are gathered in a whole group, only one person talks at a time and we give the person who is talking enough time to gather their thoughts to say what they need to say. Even though I know that we won’t master these goals in the first week (or month!) of kindergarten, we start working on them right away.
On day one, as we gather in the shape of a circle on the floor in a chaotic semblance of a group meeting, I introduce the “talking sphere.” The talking sphere is a light weight ball that we roll between children in the circle. Only the person with the talking sphere is able to speak. When a student receives the talking sphere they says their name and what they think math is. This establishes that when our friend talks it is important to listen to what he or she is saying. As each student shares, I record responses on a large sheet of paper and write the child’s name under the quote. Some students are hesitant to share, and this is a nice opportunity to talk about wait time. Giving our friend time to collect thoughts without interruption calms nerves and helps our friends think. Below is an example of what our poster looked like one year. Most of my students can’t read most of the words that I wrote on this chart and the charts that follow.
My next goal is that children learn to listen to each other well enough that they can restate what a classmate says. Again, we don’t master this during the first week (or month) of kindergarten, but I start working on it the first week of school. On day two, we gather on the carpet and begin talking about numbers. After reviewing our math routines of only one person talking at a time and respecting wait time, I ask students what they know about zero. This is a difficult concept, and, if they have difficulty getting started, I provide an example that we have zero dogs (living dogs) in our classroom. I then ask a student to repeat what I said to model active listening. Throughout the lesson, students are asked to repeat a friend’s idea in a way that made sense to them. Each student contributes either verbally or non-verbally. Some students prefer not to speak, so I record their contribution by drawing a picture of their zero representation and label it with the student’s name. This procedure also helps me engage my students in the literacy goal of learning that ideas can be represented with words and symbols. Here is an example of what the poster looks like:
On day three, we review our math routines of letting one person speak at a time, providing wait time, listening to each other and repeating others’ ideas. I ask the students what they know about one. Again, I write or draw each student’s response and write their name. Throughout the lesson, we discuss and practice the routines of one person talking at a time, giving wait time, listening to others’ ideas, and repeating or summarizing a friend’s idea. Students are by no means perfect with these routines, but after three days we have the groundwork that we need to progress to solving problems. Our poster looked like this:
Day 4 is a big day for us in that we begin solving problems. One of my goals for day 4 is that students learn that they can generate their own solutions to math problems. As the students gather on the carpet, we quickly review our math routines. I tell the students that our goal today is to solve the problem by showing what happened in the story. This seems like a small and insignificant goal, however, the desire to draw their favorite thing is very strong. If their drawings match the story, it is a major accomplishment! It was Justice’s birthday, so I asked her if she would like to be the subject of the story. She very excitedly agreed. I asked what she liked (a toy or a snack) and she replied, “teddy bears!” I wrote on the chart paper, Justice had 3 teddy bears. She got 2 more teddy bears for her birthday. How many teddy bears does she have now? We reread the problem and checked for understanding. My English Language Learners could not translate teddy bears, so I showed them a picture of a teddy bear.
Students then got a piece of white paper and a marker. (Yes, I know it very scary to consider letting kindergarteners use a marker on the fourth day of school. However, they are housed in a basket by my desk. Each student selects a marker for the lesson and returns it after the lesson. I explain that the markers are their “special pens” so that our friends can clearly see what is written on their papers when we use the document camera.) Students find a work space to solve the problem presented. Although many kindergarten teachers provide manipulatives during the first week of problem solving, I wait until the second week of school to distribute manipulatives.
When students are settled in their work space with their materials, I remind students of our learning goal and read the problem aloud two more times. I continue to read the problem aloud as many times as requested or as I see necessary as I circulate around the room while the students are working. I don’t tell or suggest to students how to solve the problem, because I want them to learn that they can generate strategies to solve problems. As the year progresses and I get to know my students, I may make some suggestions from time to time. Right now it's more important that they learn that they can solve problems on their own than it is for them to get the right answer on this problem.
The work time is limited to five minutes because any longer lends itself to coloring and doodling, and I want their content to be focused on the story problem. Later in the year I often allow a longer work time as the students’ math stamina grows and the problems get more challenging. After five minutes, I ask them to put their marker caps on and walk to the carpet with nothing in their hands. Many students are concerned because they did not finish, but I assure them that they will have time to finish. As they move to the carpet, I strategically select three papers from the class. Here are the papers that I selected one year:
I selected the first paper because the numbers were from the problem and it accomplished our goal for the day. The second paper was selected because it directly modeled the action in the story, and also met the goal of the day. I selected a paper with 3, 2, 5 on it because the student likely figured that three and two more is five, and it also met the goal of showing what happened in the story problem. The other students’ papers did not have a picture that represented the story problem.
Once we got back on the carpet and again reviewed our math routines, I asked the first student to explain his solution. He said that Justice had three bears and then got two more. We underlined the 3 and the 2 in the story as he explained his work for the other students who did not understand why he used those numbers. Another student repeated his explanation of the story. Even though the student did not solve the problem, he was able to extract some information from the problem, which is a great first step in solving the problem.
The second student came to the front to explain that she drew three teddy bears because that is how many Justice started out with. Then she drew two more (she explained) because they were her gifts for her birthday. She said she counted all of the teddy bears and now Justice has 5 teddy bears. After she shared, several students shouted out that they did the same thing! Each student who shouted out was given time to share how he/she had the same idea but didn’t know how to draw or explain it.
The third student explained her solution and demonstrated with her fingers. She put up 2 fingers, then 3 more fingers, and then counted each finger until she reached five and said, “that’s five, five bears.” She didn’t know how to draw her thinking, so she told us that she wrote the numbers 3, 2, 5. Another student listened then raised her hand to suggest she draw her hand. Other students listened to her and were practicing on their fingers. Several other students shared how they thought about the problem, but by this time, many children were having side conversations, and they weren’t all about the math problem. This was a great time for a turn and talk with your partner about how you solved the problem.
Students then returned to their desks to solve the problem a second way or finish the strategy that was started. After each student completed his/her work, they returned the marker, placed their papers in the basket, and went to centers. Here are two strategies that children generated during this work time:
On day five, six, and seven, we talked about the numbers 2, 3 and 4, increasing the duration of the activity with more students speaking during group time. We continue practicing our math routines of one person talking at a time, wait time, listening, and repeating/summarizing ideas preparing for day eight, problem solving again! On day 8 students solved another word problem, following a similar routing to day 4. As the year progresses, more of my lessons are around solving a problem than around talking about a number, but, at the beginning of the year, it is easier to establish math routines through talking about a number.
Incorporating the goals of problem solving (getting information from the text) and the strategies for listening and learning from other students is not confined to our math group time. Throughout every part of the school day, students are asked to turn and talk to their friend if there is a problem, ask another student for help and listen when he/she explains a concept, ask a neighbor for help, or repeat a direction that has been misunderstood. In reading, our goal of getting information from the text helps students to understand where to look when they don’t know the answer to a question. Students are constantly engaging one another with Cognitively Guided Questions and Listening strategies throughout the day.
For more information about Laura Steele and a list of problems she uses with her students, visit her page on our mentor teacher website.