Inside a kindergarten classroom with Augustana students

Beginning to Wrap Up

Lisa and I used this week to collect additional data for our final paper and presentations. Students were again given teaching tools they had used early in the program. We hoped to compare how students used and explored these tools early in their number sense develop to how they would used them now with a much deeper understanding. We also allowed our other students additional practice with the skills they have been focusing on for the past several weeks.

This week our “level one” students interacted with ipad apps they had used several times early in the program. On Tuesday students explored the Line Em Up app, which addresses number recognition and ordering. Number recognition and ordering are both skills these students have been focusing on all year. When students first explored this app they struggled greatly because they could not recognize numbers 1-10, thus ordering was almost impossible. Many of the students resorted to counting up the boxes from one to help them both identify and order unknown numbers. This week, however, students responded much differently. They were able to recognize and order most numbers 1-20. I did notice that some students are still struggling to recognize numbers such as 12, 18, and 19. On Thursday students switched their focus to number recognition and one-to-one counting as they explored the Count Sort app. One-to-one counting was a skill these students struggled with early in the year, however, this week there were no obvious signs of struggle. All students were able to count the number of dots on the screen with no hesitation or error. Students’ oral sequence has also improved greatly. Because they have a better understanding and take their time students no longer forget or skip over the number “15”. During both lessons the students interacted differently with the apps than they had early in the program. They are now more confident in their abilities and much more comfortable using the ipad apps. After reflecting on our lessons and our students’ past performances, it has become increasingly clear just how much are students have grown and developed over the past several months.

Our “level two” students continued to explore base ten. Though we have worked on this concept for several weeks, we did not feel our students had an adequate understanding. Thus we did not feel comfortable moving on to a new concept or skill. This week, however, our students seem to have developed a deeper understanding. On Tuesday, students represented numbers using base ten blocks, where as on Thursday they explore the Base Ten app. Because both lessons and teaching tools are so closely aligned, students did not seem to demonstrate a deeper understanding using one tool over the other. Almost all students can represent any given number, however, they struggle counting out the number they had just showed. The students can easily show the number “52,” for example, because he or she knows by looking at the number that they need five longs and two units, but when students are asked to count it out many are unable to switch from counting by tens to ones. Thus, even though the students had represented the number “52” they counted to “70.” Each time students showed a number I challenged him or her to count it out for me. There were some students could represent all numbers and correctly count it out. I challenged these students by showing a number with the base ten blocks and asking them what number I had created. This reversal, though more challenging, proved that some of the students have mastered this concept.

Our “level three” students continued to work on problem solving strategies. This week students used their homemade Rekenreks and the Ten Bead Math app to further explore subtraction. On Tuesday students used their Rekenreks to solve random subtraction problems. I gave little instruction hoping the students would learn how to use this tool through their own exploration. Without suggesting it, students move all the beads to one side on the pipe cleaner and starting dragging one bead at a time to solve. Students solved by moving the beads back and forth one at a time. This activity seemed too easy for them so I challenged the students to solve subtraction problems with larger numbers. On Thursday students did a similar activity using the Ten Bead Math app, again this lesson proved to be to easy for these students. They were able to solve all subtraction problems with little to no hesitation. Something different did occur in the lesson, however. When students were given an equation such as “14-10” they dragged ten pieces at once and then counted out four more and then moved the set of ten back to conclude that 14-10 equals four. Students were able to recognize ten beads as a group of ten that could be moved one unit. Thus, students were able to solve these equations more quickly because they were no longer moving pieces one by one.

On both Tuesday and Thursday Lisa and I ended our lessons early to meet with students one on one. We choose two students whom have demonstrated the highest level of understanding to explore Randy and Mike’s newest app, Sum It Up. This app challenges students to find three addends that equal the targeted number. Lisa and I were presently surprised that both of our students were successful using this app. Though they struggled at first, it did not take long for them to discover the purpose of this app and ultimately how to “win.” Their biggest struggled seemed to be moving the pieces around in a way that lined up the numbers in the way they wanted. Both students expressed what numbers they needed to put in a row, but struggled physically doing it. This app gave the students the opportunity to think in a new way and develop a deeper understanding for numbers. Both students seemed to really enjoy this app and it is one Lisa and I hope to expose more of the students too.

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