Inside a kindergarten classroom with Augustana students

Hitting the Ground Running

This week marks the beginning of our work with the Number Sense Project! It’s fun to see the kindergartners so excited to continue work with “their math teachers,” as so many of them like to exclaim when we come in to the classroom. This year, there are three of us working with the students so we all be in Mrs. Peterson’s class one day of the week, and Mrs. Carmack’s class another day. So far, this has proven to work well because it gives us the chance to work with every student in groups of three for about 20 minutes each. In both classes, we have split the students up into three different groups based on abilities. Each of us is responsible for the “similar” group in both classes. After a few weeks we will be rotating groups so that we get a chance to work with all of the students, and the students will get to work with all of us.

The group that I have begun working with is the group that is ready to be challenged a little further. I chose to start with this group because I had worked with many of the students during our Math Methods class, and therefore could go into the first day with some understanding of where the students were at. A few of the students in my group, however, are new faces to me! Some of these are students who may need more scaffolding than their peers as they work in our group, but I am excited to see all of the students rise to the challenges! A main focus for me these first couple of weeks has been to decide which groups of three students I want to work together. I have realized that I will need to differentiate even within my groups, and have tried to have students work in groups where they will be challenged, but also will not be overwhelmed and shut down.

In my group, there are many students who can count fluently, write numbers to 50 and higher, and have a solid understanding of cardinality and 1-1 correspondence. In the fall, my partner and I had chosen part-part-whole relationships to be a major focus in our activities. These students were very familiar and confident with their numbers and counting skills, but we wanted to make sure that numbers weren’t just thought of as symbols that we write down. To further develop this concept of a quantity consisting of different parts, I worked on a couple of different activities with some of the students. One of these activities was intended to focus on part-whole relationships, but also help students see that a number can be decomposed into many different parts. For this activity, the students each got a note card with a number on the top. Underneath the activity, there were 3-4 different lines containing 3 different numbers, two of which could be combined to make the number on the top. Together and with the use of manipulatives, we worked on figuring out which two numbers were parts of the whole. Some of the conversation during this task included one student stating that “numbers can be made in lots of ways.” It was good to see these connections, and will help inform my planning for next time because many of the students have a developed understanding of this concept. One student in particular demonstrated that he was fluent in addition using 1-5 when he filled out each note card automatically and without the use of manipulatives. The other activity that enforced this concept also involved subitizing dot cards. Two different dot cards were chosen by students and then two corresponding amounts of counters were placed into a cup, and the students each had to write down how many total counters they thought were in the cup. For most, this involved counting the dots on both dot cards, but even in doing so the students were demonstrating the idea of addition as putting together, which is one of the objectives on their report cards. While some students did not need to count the dots to determine the total, it was exciting to see almost every student write out the corresponding addition statement (many without being prompted to do so).  At one point during this, one of the students asked another if he could solve 8+6, and he answered correctly. When I asked him how he knew that 8+6 was 14, he told me that he knew that 10+6 was 16 and 8 was two less than 10. Needless to say, a challenge next week will be to differentiate our activities to ensure that each student can be challenged.

Not all students had taken part in the first activity discussed, and an activity I chose to do worked on teen numbers and creating a number line up to 20, and then also being able to describe the relationship between different numbers up to 20. After my first day with the students, I realized that although most could count to 20 and higher, and could write teen numbers with assistance, practice with number recognition in the teens and practice writing them was needed. After each student had created a number line, they wrote a “super secret number” from their number line on a post-it note without showing me. One at a time, the students put the sticky note on my forehead so I could not see it. I then asked questions such as “is the number more than 10?” “is it less than 15?” etc. and the students had to answer the questions using their number lines. I realized two things while doing this activity: one being that we should work on more than, less than (or perhaps greater than or less than if those are they terms they more commonly use) in the lessons to come, and also that next time we do an activity such as this, I want to incorporate concrete objects because the number line by itself seemed to be too abstract at times. The direction I would like to go in is developing number recognition and a familiarity of the numbers in the teens, while simultaneously working on concepts such as greater than and less than, in order to keep enthusiasm about working with teen numbers up and to provide challenges.

There is so much more I could write, but until next week…

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