Inside a kindergarten classroom with Augustana students

Back in Action

After another long break, Julie and I finally returned to Longfellow to continue working with our Kindergarten students! To our surprise, we found that two students had left Longfellow over break, but two brand new students now joined Mrs. Carmack’s class! Other than that, Julie and I picked up right where we left off with our students and with our Number Sense research.


“Level one” or our first group continues to work on number recognition. However, Julie and I have decided that instead of doing repetitive number recognition activities such as flash cards, we want to challenge these students more and more each week. Through moving onto other concepts and skills, our hope is that they will continue practicing number recognition while still developing higher level thinking skills. Thus, on Tuesday, we provided each student in this group with a worksheet that would help them practice their counting on skills. The worksheet presented the students with a number and asked them to write in the remaining numerals in the number sequence. For example, if the students were presented with the symbolic number 5, the students would have to write in 6, 7, 8, 9, 10, etc. until all the boxes in the row were filled. The particular student that I worked with during this activity demonstrated excellent counting on abilities. When reflecting on activities done previously in the year, I can remember students having to begin counting at number one in order to “count on”. During this activity, however, the student was able to identify what number comes after (and even before!) the presented number immediately. On Thursday, we had the students complete a similar activity. This time, however, the students were asked to “count down” or “count backwards” from a given number. We provided the example of counting down like “3, 2, 1, 0, blast off!” Once the students had grasped the concept of how to count down, they did surprisingly well! I worked with our focus student in this group, and he was able to do the first few problems independently. Once presented with numbers in the teens, however, this student became very frustrated and confused. His frustration appeared to stem from the fact that he was unable to recognize the number “15” which he was asked to count down from. One “fault” of this activity, however, was that students had to write all the numerals. To save instructional time and minimize student frustration, I began having the students count as I recorded their answers in the boxes for them.


The students in our second group continue to work on representing numbers and number value. On Tuesday of this week, we had the students explore the “Make Another B” iPad App (Julie and I actually helped Randy and Mike develop this app in previous weeks by suggesting the content and layout of the app!) This app focuses on representing numbers in different ways. The students were given a number and asked to represent the number in two ways using colored chips. For example, if given the number “6”, students could represent it as “3+3”, “4+2”, “5+1” or even “6+0”. This is a concept that our students had demonstrated no understanding for when previously tested, hence our idea for the app! While many of the students tended to represent the number by creating two patterns (for example four orange and two green and then four green and two orange), I felt that this app decreased their tendency to do so. Because the area for them to drag the chips was an open space, rather than a formatted space, the chips were not necessarily placed in a row. This app seemed to greatly benefit the students understanding and I think it will prove to again be useful in upcoming lessons that focus on the same skill. On Thursday of this week, we again had the students represent a number in two ways. This time, however, we had the students complete the activity using connecting cubes. I immediately noticed the difference in time between using the app and using the connecting cubes; it took students a significant longer time to connect the cubes than drag the chips. Because the students took longer to handle and connect the blocks than it did to drag chips on the screen, it greatly limited the number of problems the students were able to do in the given time when using the manipulatives. Other than that, however, I did not observe any differences in student understanding or performance when they used the iPad App versus when they used the manipulatives.


The students in the third group continued to work on and develop their problem solving skills and abilities. On Tuesday, the students practiced their addition skills with the use of “Number Line Math” iPad app. The students were given an “x+y=?” addition problem and asked to solve the equation using the number line by first locating “x” and then making “y” humps on the line. On Thursday, the students practiced the same skill through the same activity. This time, however, the students were given a laminated number line and a dry erase marker. The students were asked to again solve “x+y=?” addition problems using the tangible materials. In both lessons, a handful of students demonstrated some confusion about how to use the number line to solve an equation. Because the students only had limited time to explore using both the app and the manipulative, I felt that the students were not adequately exposed to these materials. Though the students have seen number lines previously, they needed assistance and guidance in understanding how to utilize these materials to solve an addition problem. Up until this point, we have focused on solving addition problems through the use of manipulatives such as counting chips, or the shapes on the screen while using an app. When presented with a different problem solving strategy, however, the students appeared confused. I am interested to see if the students would react differently, or appear to be more comfortable or confident, if we again utilized the number line to solve addition problems at later time.


Julie and I have seen tremendous growth in all of our students over the past term and a half. We too, have made tremendous strides as teachers. We are excited and eager to see where the remaining weeks take our students and us as we conclude our research and work with our Kindergarten students in the Number Sense Program.

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