Inside a kindergarten classroom with Augustana students

## Providing opportunities for students to expore understanding on their own

Blog #1
11/23/11
I have started my first week with the kindergarteners for Number Sense at Longfellow, and I am already learning so much! The first day in the classroom, my cooperating teacher suggested that I take the students into the hall one at a time for a pre-assessment of their mathematical understanding. This was not only beneficial to help group students by strengths and needs, but also gave me time to get to know each of the kindergartners as well. Before the assessment, my cooperating teacher explained that the most prominent challenge she has been working on with many students is number recognition. I observed this challenge myself working with the students one-on-one. When asked to count as high as they could many students recited the numbers up to or past 30. However, when shown a visual number symbol and asked to count out that number of marbles, several students had difficulty correctly identifying the number. From a teacher’s perspective, this situation helped me realize the importance of gathering information about the students’ understanding through a variety of assessments. Just because the students seemed confident and comfortable reciting the numbers aloud does not mean that they can recognize the number visually or fully understand how it compares to other numbers quite yet.
Another interesting discovery arose when I was working with a student to practice number recognition using note cards. My initial plan was to have the student practice representing a number with counters. However, for whatever reason, the student was not eager to use the counters to practice. (It may have been simply that the counters are used frequently in class, so the material was not different or exciting for the student.) I also had large pink and yellow index cards with numbers 1-20 on the table. Student V. began to pick up the cards and examine the numbers by pointing to the ones she recognized. From my pre-assessment notes I knew that the student was struggling with teen numbers, so I decided to use the number cards to help the student to see a pattern. I held up the number 10 and asked the student “which other numbers look like a 10?” The student then chose the number 1 saying, “look there’s another 1”, and proceeded to line up the 1 under the 10. I further prompted the student to look for more similarities, and she chose the number 12 because “there is another 1 in 12”, she explained. I then held up the number 10 and the number 2 together and said “hmm I like the way you grouped these numbers together. They both almost look like the number 12”. By holding the number 2 card over the “0” on the 10 card, it was clear that by combining both cards, the student could see the number 12. The excitement of the mutual discovery lead the student to choose another card—number 3—and place it over the “0” in the ten as well, exclaiming there is 13! The simple aid of the notecards to explain the concept of teen numbers as “a ten and some more” really helped spark the pattern in numbers past 10. Although student V. was still not fluent on the names of all the teen numbers by the end of the lesson, the discovery and self-exploration of patterns really helped the student to develop a deeper understanding of number order.
My important lesson of the day: Always keep student interests in mind during lesson planning, and be prepared to provide ways for students to experience knowledge on their own—instead of simply being told to see or think about something a certain way. Listen to how the students view things and learn with them!

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