Inside a kindergarten classroom with Augustana students

Things are Beginning to Click!

While our students enjoyed their two weeks of spring break, Lisa and I turned our complete focus to our research paper. The break from planning and delivering lessons allowed us the opportunity to revise, edit, and continue writing. We have made great progress and feel confident about the work we have completed thus far. However, there is still data we must collect from our students in the remaining lessons to better support claims in our paper. This week we continued to structure our lessons in a way that would allow each group of students to practice a particular mathematical concept or skill using both hands-on manipulatives and technology.

This week our “level one” group continued to focus on number recognition and counting. On Tuesday, students were given a worksheet with a number followed by blank boxes. Students were asked to identify the number in the box and count forward as they filled the boxes in with its corresponding symbolic numbers. On Thursday, students were given a similar worksheet and were again asked to identify the starting number and fill in the remaining empty boxes. In this lesson, however, students were asked to count backward, rather than forward. We found that the students were able to easily count forward orally, but struggled to write the symbolic number in the boxes. They were unsure of how they were to be written and often asked us before first attempting on their own. I also noticed that several of the students would orally stated the number “6” for example, and instead of proceeding “6,7,8,9,10,11” the students would start from one and whisper to him or herself “1,2,3,4,5,6!” (speaking louder) “7,8,9,10,11.” Thursday proved to be a bit more difficult for the students. Though they were able to successfully recognize almost all of numbers presented they struggled to state even the one number that comes before it. Even when we counted along as we point to the hundreds chart, the students did not seem to understand they were counting backwards. One student in particular was able to complete the worksheet on her own after she was given many examples. However, I noticed that this student was counting forward from one each time to figure out the number that came before the number she identified last. For example when given the number 8 the student counted to 7 starting from one, then counting to 6, again starting from one and so on. Though this student developed this strategy on her own and developed somewhat of an understanding, we hope to challenge her in future lessons to count backwards without first counting forward. We plan on continuing to focus on both number recognition and counting in the following lessons.

“Level two” continued to work on representing numbers in multiple ways. On Tuesday, students explored a new app called “Make Another B.” This is actually an app Lisa and I help Randy and Mike created based off an idea we developed after an assessment we administered to our students. Students were told to represent a number using both sets of colors. For example, when students were given the number “6” students dragged 3 green shapes and 3 pink shapes and stated “3 green and 3 pink is 6”. They were then asked to represent the same number in a different way. (e.g. 4 green and 2 pink) The biggest struggle some of the students faced was coming up with a new way to represent the same number. Many students would show 6 as 4 green and 2 pink, but when asked to show another way to represent the number many created a chain of 4 pink and 2 green. Students were reversing the colors, rather than using new numbers. Though, they were also reminded not to make a pattern, many students resorted to this strategy as well. I also noticed that a few of the students struggled with this activity because they struggled with one to one counting. They could not accurately represent the number called with the movable pieces on the app because they kept miscounting them. With much guidance, students were able to eventually come up with two ways to represent the same number. On Thursday, students were involved in a similar activity but used connecting cubes to represent the numbers. They had already explored this teaching tool before, thus Lisa and I felt comfortable explaining how they were to be used and the purpose of the lesson before they began constructing their own understanding. During this lesson, none of the students attempted to represent the numbers by creating a pattern, instead they applied what they had learned from the lesson prior. Students were able to represent numbers in multiple ways more independently then they had on Tuesday. Though we did see similar trends on Thursday (the reversal of colors and miscounting) we do feel they demonstrated a greater understanding for the content.

This week “level three” continued to work on solving problem strategies. For the past several weeks these students have been solving equations using a variety of tools. They have used dominos, the Domino Add app, a home made Rekenrek, Ten Bead Math app, and several others. This week, however, we challenged these students to solve equations using a number line. On Tuesday, students explored the Number Line Math app. The students were presented with an equation and drew “humps” on the screen to solve. They students did great with this activity and demonstrated an adequate understanding for the content. I knew they had developed an understanding because they were able to solve these problems independently. On Thursday, the students again solved equations on a number line, however, in this lesson students were provided with a laminated number line and were asked to draw in the “humps” to show what they were adding and how they got their answer. The students turned to the number line for assistance in solving the problems. There was one student in particular who used his fingers to add, rather than the tools we had provided him with. This student had done this is previous lessons, however, this time something different happened. When the sum was greater than ten and the student had run out of figures to count he would usually tap them on his chin trying to keep track of them or ask to use our fingers; however, in this lesson rather than asking for help he picked up his marker and used the his number line to solve! I was very impressed that this student knew what to do when his personal strategy for solving was not the best. The students responded well to both teaching tools, however, Lisa and I are interested to see how students would responded if given these tools a second time.

Overall I thought this week was a great success. I was happy to again work with the students and see such growth in them over the past few weeks. Lisa and I really do feel we are helping these students develop a greater understanding and are excited to see where the remaining weeks will take us!

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