Inside a kindergarten classroom with Augustana students

Nearing the End

This week Julie and I allowed the students to further practice their numeracy skills through apps and manipulatives that they have already been exposed to in previous lessons. During the lessons this week, we made observations of how our students performed using the tools now compared to how they did when they were first exposed to the tools.

On both Tuesday and Thursday, our “level one” students explored familiar apps such as Line ‘em Up and Count Sort. Though the students demonstrated a deeper understanding of how the apps work (i.e. moving the pieces, instructions, etc) the students still showed similar struggles in recognizing and sequencing numbers. Both students continue to struggle recognizing numbers such as 11, 12, 16, 18 and 19. However, the students’ familiarity with the apps has allowed for them to be more confident in using the apps. As a result, the students were not only able to complete problems more quickly, but more accurately as well. For example, in previous lessons Julie and I noted that the students struggled with one-to-one counting when counting all the chips on the screen. In this week’s lesson, however, we noticed that the students were able to accurately count all this chips on the screen. While the students still have some work to do in terms of recognizing numbers, it is apparent to Julie and I that the students in this group have grown immensely since the beginning of the year.

Our “level two” students continued to explore the concept of base ten through both the base ten blocks and through an iPad app. All the students within these groups demonstrated a different level of understanding for this concept. Many of the students are still struggling to recognize that one long is equivalent to ten ones. Thus, a common misunderstanding many students seem to hold is the value of the blocks. One particular student within this group consistently counts out the number of blocks that is equal to the sum of the numbers in a two-digit number. For example, if asked the represent the number “28” this student will drag out all combination of 10 base ten pieces (2+8=10). Some students, on the other hand, have demonstrated their understanding for base ten. For example, a different student in this group was asked to identify what number the presented blocks were representing. When I put “16” (one long and six units) in front of this student, she wrote “1” for the long, counted six units, and then wrote “6” and told me “16”. While most students in this group are demonstrating a different understanding for the concept of base ten, it is clear that over the past weeks these students have developed a deeper understanding for base ten.

The students within “level three” continued to practice problem-solving strategies. In previous lessons, we had the students use our homemade Rekenrek and Ten Bead Math app to explore addition. This week, we had the students use these tools to practice subtraction. Our focus student within this group demonstrated a deep understanding not only for subtraction, but also for using these tools. The app required the students to drag beads into a shaded area based on the minuend, and then take out a given number based on the subtrahend. The focus student in this group picked up on “groups” of beads, demonstrating his ability to subsitize objects. For example, this student was able to recognize that after dragging all of the red beads into the shaded area, he had ten beads. He was then able to recognize that he needed “x” number more to represent the minuend. In another example, this student dragged two rows of 6 beads (5 of one color and one more) as was able to immediately say that it was 12 beads. Many other students in this group showed their understanding for subtraction, as I had to challenge the students with larger numbers.

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