Kindergarten counting- Jamie Blankenship

a) Last week my students did an assignment to check their understanding of counting with numbers.  Each student was given a worksheet that had two columns.  The first column had a number numeral written in it, for example, 8, 19, 5, 14...The second column across from that had an empty space.  When explaining the directions to the students, my mentor teacher told them that in that empty space, they were to draw circles to represent the number that was next to that box.  For example, if the number in the first column was 8, the students had to draw 8 circles in the second column. I did not think that this task was a high level task, for one, this task only allowed for one way to get the answer correct.  The students weren't able to count out manipulatives or put up fingers to show that they knew how to count up to those numbers. It was predictable which students could accomplish this task and which students could not.  Some students would draw 5 circles to represent the number 18 and would call it quits. Other students would carefully count as they drew each circle. Finally, some students would draw a couple of circles, go back and count them, and then continue drawing more circles.  They would continue this cycle until they reached the number they were told to draw. I was disappointed that this type of activity did not allow any room for students to complete the problems in different ways. 

b) The questions I would ask would be 1) How does this task accommodate students with different understandings of counting? 2) How come the students weren't allowed to use multiple ways to show that they know how to count to these numbers? 3) How could you make this type of counting task a higher level task?

c) 1. For the first question, I think this task definitely does not accommodate students who learn and think differently.  I think this task could be modified to follow the CGI book in a way where the students would have several different ways to exhibit their counting. Perhaps students could choose to use counters, number blocks, their fingers, tally marks, or any other way that they use to count. I don't think students should be limited to using one particular way, and if they aren't able to do it, then they must not know how symbols relate to numbers. 

    2. For the second question, I think the students were forced to do this worksheet because it is easy for the teacher to look at how many circles the students drew and tell if it is the correct number.  Opening up the assignment and giving the students the freedom to choose their own way to show how they count could potentially be more time consuming and not as neat and organized. 

  3.  I think this type of task could be made into a high level task by perhaps having the students use concrete objects to show the counting.  For example, if the problem asked the students to separate the pens and pencils and other objects in their pencil cases and to then write the number and draw a representation, this would be a problem that has real life meaning. It would also allow them to see the concrete relationship between counting and the actual written number.