Think sheet – 10/06/12
Right now, I am trying to gain a better understanding of how my Kindergartners think about numbers 0-10, starting with 0. By the end of the year, my students need to be able to read, write, and count objects to 30. I want to make sure that I am teaching numbers in a way that instills a deep understanding of what a number truly means, i.e. develop strong number sense. By the end of the year, I want my students to be able to represent a number in several ways and be able to show their understanding both verbally and through visual representations. For example, showing multiple ways to group numbers to make 10, not just saying the number 10 is 10.
Right now, I am trying to gain a better understanding of how my Kindergartners think about numbers 0-10, starting with 0. By the end of the year, my students need to be able to read, write, and count objects to 30. I want to make sure that I am teaching numbers in a way that instills a deep understanding of what a number truly means, i.e. develop strong number sense. By the end of the year, I want my students to be able to represent a number in several ways and be able to show their understanding both verbally and through visual representations. For example, showing multiple ways to group numbers to make 10, not just saying the number 10 is 10.
This is important because everything they learn from now on math is contingent on them having strong number sense, whether it's adding, place value, or decimals.
1. Who do you think you might want to have has a focal student? What criteria will you use to choose your focal students? (Some teachers like to choose one high achieving student and two or three of their basic or below basic students.)
All of these students are Kindergartners, ages 5 or 6.
Nora: She is very high achieving in all academic areas. She already shows the ability to use mental math to solve word problems or figure out “how many are left” when the class is trying to get 10 points for an extra recess. I would love to hear how she is thinking about numbers and what they mean. I have a feeling she has a strong understanding and it will serve as an interesting example /baseline of how I want all students to be able to talk about and understand numbers.
Ivan: Ivan can order numbers 0 through 10, sometimes mixing up 6 and 9. He is between Below basic and basic. He is a native Spanish speaker/ELL and has a difficult time explaining his thinking in English succinctly. At this point in the year, he scored Early Intermediate scoring lowest in oral language. I am using a lot of sentence frames with him (and the whole class) when we are sharing as a group. Using him as a focal student will help me think about using scaffolds to help students talk about their mathematical thinking.
Kamaya: She is high performing in reading and writing. From my assessments thus far, I would identify her math ability as basic. I am curious about her use of academic English in explaining her understanding of numbers. I am also choosing her because she is very verbal and assertive which will lend to interesting interviews. She loves to share her ideas and I want to have more time to listen to her one on one.
Eva: I was intending on using a different student but she recently transferred. Eva is still working on number recognition 1-10.
I am choosing all of these students because I have assumptions about where they are at since this is early in the year and want to know more about them. They represent a variety of academic levels and cultural backgrounds at my school site. They all like to talk and I feel like it’s important to choose focal students that are willing and excited to talk about their ideas when conducting interviews as a data source. They all have enough fine motor control that they could draw a somewhat clear picture if asked to "draw" what they thought a certain number is.
2. How would you know what is happening for your focal students? What are you doing now that would make student thinking/ student understanding visible?
I am going to ask all 4 students in one-on-one interviews and in the form of a drawing “what is the number 5?” It’s a very simple question but will tell me about how they visualize this number, what it means to them, and how they talk about numbers. It will also verify or disprove my assumptions about my focal students as well as help refine my question about what my learning outcomes are for my student in this inquiry.
3. What I'm Thinking Now/Next Steps
I am thinking of how to make my learning goal clear and succinct as well as my data sources. I am pretty sure I will have 2 sources:
1. Interviews of the focal students once a month asking then to explain there thinking about a number
we are working on.
2. Drawings by the 4 focal students of the same number I interview them about.
I also know I need a systematic way to study one number each week that is consistent each week. This may be through calendar math, canters activities, morning meeting activities or the morning message. Basically, a way to make sure we work with the number in as many ways as possible over the course of the week as possible.
Hi KC,
ReplyDeleteIn reading your blog I am struck by the way in which working with your colleagues who are teaching third grade is such a rich place in which to think about kindergarten students and their development of number sense. When you can see where your students are going, and what they are going to have to do in third grade, it provides context, and urgency, for your inquiry.
You write about the idea of using interviews and drawings as your data sources. “I am going to ask all 4 students in one-on-one interviews and in the form of a drawing “what is the number 5?” It’s a very simple question but will tell me about how they visualize this number, what it means to them, and how they talk about numbers.” It sounds to me as if what you are doing is opening yourself to how this part of the world looks to your students, and entering into their minds as they encounter these numbers for the first time. You are asking them to talk and to draw, and from that, you will develop your understanding of what your students think about the meaning of a given number. “It will also verify or disprove my assumptions about my focal students as well as help refine my question about what my learning outcomes are for my student in this inquiry.” Tying this to learning outcomes and thinking about it in terms of individual students grounds it in your practice.
As you think about your practice, you write, “I also know I need a systematic way to study one number each week that is consistent each week. This may be through calendar math, canters activities, morning meeting activities or the morning message. Basically, a way to make sure we work with the number in as many ways as possible over the course of the week as possible.”
After I read this, I realized that, as a middle school science teacher, I know little about theory and practice around developing number sense on the part of kindergarten students. I talked with Elizabeth Baker at Mills, who has a great deal of experience with Lesson Study, and who teaches the math and science credential students, and she has a lot of background in this – we had a fascinating conversation about it. I’m wondering if you are looking for resources at this point, and if you would like me to pursue this? And if so, are you more interested in reading about theory, or about practice? Possibly your school has a curriculum that you are required to follow … let me know if you would like me to look into this?
I'm excited that you are looking at this intriguing area of your students' learning!
take care, Claire