Inside a kindergarten classroom with Augustana students

Halfway There!

This week marked the halfway point of our journey through the Number Sense Program! As we reflect back on the work we have done thus far, Julie and I have gathered a great deal of useful evidence of student learning. Over the past few weeks of winter term, we have structured our lessons in a way that allows each group of students to practice a particular mathematical skill using both hands-on manipulatives and technology.

This week we continued to focus on number recognition, one-to-one counting, and oral counting with our first group. On Tuesday, the students in this group used counting chips and flashcards to demonstrate their current understanding of number sense. The students were given a pile of chips and asked to count them. The students were then presented with three flashcards, and asked to select the flashcard that showed the corresponding number. While working with these students, it became clear that they continued to struggle with identifying numbers such as 6, 9, 11, 12, and 13. Both of the students did, however, continue to demonstrate a basic understanding of the teen patterns, as they have in previous lessons. We noticed that during this lesson a student consistently counted “13, 14, 16, 17”, forgetting 15 each time he orally counted. To try and help this student recognize that he was forgetting 15, I pointed to a number on the 100’s chart on the wall and had him orally state the number. However, when I pointed to the number 15, he again went from 14 to 16. Julie and I have made note of his struggle to remember the 15 when counting, and it is something we plan to pay attention to in future lessons. On Thursday, the students practiced the same skill in a similar manner, but this time the students used the Count Sort App with the counting setting. The students were shown multiple dots on the screen and asked to count how many in all were on the screen. The students then were asked to select the corresponding number as listed on the screen. Again in this lesson, the students demonstrated similar struggles in identifying numbers 6, 9, 11, 12, and 13, as well as higher teen numbers. Thus, we did not notice a significant difference in the students’ performance when using the manipulative versus using the iPad Apps.

The next group of students we worked with focused on place value, specifically activities dealing with ten-frames. On Tuesday, the students completed a Ten Frame Booklet – an activity that we had done previously in the year with a group who has now moved onto higher-level skills. The students were given a book of ten frames, each page containing blank ten frames and a number in the teens. After identifying the number, the students were asked to make marks/dots in the ten frame boxes to represent the number shown on the page. Some of the students struggled to independently complete this activity, while others were able to correctly complete the booklet with little to no guidance. Some of the students who struggled were unable to identify the number, and others were unable to make the correct number of marks in the ten frames that corresponded with the symbolic number on that page. One student demonstrated a particular example of misunderstanding of place value. The sentence on the pages read “16 is ten ones and ___ more”. The students were to identify 16, make 16 marks, and write 6 in the blank. When asked “how many more”, however, this student responded with 4, meaning that four more boxes needed to be filled in on the second frame. On Thursday, the students practiced the same skill again by using the iPad App Count Sort with the ten-frame setting. The students were shown ten-frames that were partially filled in. The students were asked to determine how many dots were in the ten-frames and select the corresponding number on the sides. I felt that this App proved to be easier for some students to use; the students seemed to have an easier time in “reading” the ten-frame, rather than constructing the ten-frame on their own. Furthermore, by providing the students with the pre-filled ten-frame, it allowed them to work through more problems. However, many of the options listed for numbers beyond ten were number reversals. This proved to be very easy for the students, as they were able to easily distinguish between 51 and 15 before even counting the dots. Julie and I learned shortly after, however, that there is the option to present the students with more than two number choices, which would eliminate the reversal concern. Thus, in the future, Julie and I will be sure to explore all settings and options before using the iPad Apps with the students.

The final group that we worked with this week focused on addition skills. On Tuesday, the students worked with the Ten Bead Math iPad App. The students used this app as an aide to solve the given addition problems. On the screen, the students were shown a “row” containing five white beads and five red beads. The students could drag white beads to the center to represent one of the addends, and the red beads could represent the other. On Thursday, the students were again given a sheet of addition problems. This time, however, the students were given beads on a pipe cleaner to use as an aide. On both Tuesday and Thursday, the students did not seem to enjoy using the beads to help with the addition problems. Rather, many of the students preferred to use their fingers to do simple addition problems. Furthermore, many of the students had difficulties moving the beads both on the iPad screen and on the pipe cleaner, and thus became very frustrated. Overall, we did not note a big difference in the students’ abilities to solve the addition problems when using the pipe cleaners versus using the iPad apps. Rather, the students preferred to use a familiar method of counting, such as using their fingers.

Julie and I are extremely grateful for the experience of working with the Kindergarten students so far! We have seen tremendous progress in our students thus far, and we are excited to see how much more they will grow over these next ten weeks! We plan to continue doing research over our spring break, and brainstorm useful and creative lessons that we will be able to use when we return!

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