SLO 4: Communication, Problem Solving, Reasoning, And Visualization

C. The 4 mathematical process identified for the SLO 4.SP.2 are communication (C), problem solving (PS), reasoning (R), and visualization (V). Communication is defined as students needing the opportunity to read about, represent, view, write about, listen to, and discuss mathematical ideas (Government of Manitoba, 2013). ‘Students must be able to communicate mathematical ideas in a variety of ways and contexts’ (Government of Manitoba, 2012). While making the pictograph, we had each student make their own pictograph based on their chosen rule, and then had each group explain the rule they chose. The students were able to represent and view the rule chosen with the fruits and vegetables placed on the pictograph. The students were able to discuss
and listen to the rules of their classmates, discussing another way that they could have made their pictograph. Communication during the pictograph example was achieved through the use of representation, viewing, listening to, and discussing the mathematical ideas. The next mathematical process identified is problem solving. ‘In order for an activity to be problem-solving based, it must ask students to determine a way to get from what is known to what is sought’ (Government of Manitoba, 2013). Problem solving during the explanation of the pictograph was achieved by having the students gather and represent the information gathered on a pictograph. The students knew the information collected, and they had to learn how to properly represent that data onto a pictograph. The students had to actively think about the way that the data would be represented, by sorting the months of the birthday into categories, and deciding on the legend for the pictograph. The pictograph explanation was problem solving as it asked the students to determine a way to get from what is known, the data gathered, to what is sought, how to represent that data onto a graph. The next mathematical process identified is reasoning. Reasoning is defined as ‘helping students to think logically and make sense of mathematics’ (Government of Manitoba, 2013). Reasoning occurred when the students filled out the worksheet on the bar graph. Students needed to be able to interpret what the bar graph was representing and answer the questions on the worksheet logically.
The worksheet allowed the child to actively think about the bar graph, and make sense of the mathematic behind it. Questions such as ‘what are your values on the Y axis and why did you choose that interval?’ allow the child to think about what the interval is on the Y axis, and why they chose that interval to represent the data. The last mathematical process identified is visualization. Visualization is defined as ‘thinking in pictures and images and the ability to perceive, transform and recreate different aspects of the visual-spatial world’ (Government of Manitoba, 2013). Visualization was achieved by the students using the unifix cubes to build a tower, and then using that information to build the bar graph. The students were able to create the bar graph in their hands with the unifix cubes, allowing the students to actively be able to visualize the information before drawing it on the bar graph. The students were able to perceive and recreate the bar graph the unifix cubes represented, which allowed for the students to be able to achieve visual spatial
awareness.

D.
I would revise our pictograph, and bar graph activity several ways. This activity allowed me to have the chance to get up in front of the class, and try to teach my own lesson. With that, I made several errors, which I would consider valuable experiences for the future. The first error that I would revise is making sure that I had enough worksheet copies for each student. Unfortunately I was 1 worksheet short, which would have been quite problematic if that had happened in an actual grade 4 classroom. Running to the photocopy room would have wasted valuable class time, and so it was a valuable lesson to double check that I have enough work sheets for each student. A similar mistake made was miscounting the students in the room. We had split the class up into too many groups, which was an easy fix by dividing the students from one group into the other groups. This was a valuable lesson as well, always making sure to count and plan the groups of students accordingly. I would revise the activity by making sure that I have counted the groups to coordinate with the supplies I have available. From the feedback I was given, it was suggested that the slides from the PowerPoint match the activity we had planned. We included pumpkins in our pictograph slide, and it was suggested to use the fruits and vegetables we gave each child when they were to make their own pictograph. I think this is an excellent suggestion, as it would allow the child to visualize the PowerPoint pictograph
with the materials they were given. Students need to be able to connect the explanation, and then be able to show they have understood the explanation, so providing an explanation using the same pictures as they would be working with would allow the child an easier time in visualizing. The last suggested revision for feedback from my peers was making sure to explain the instructions and the worksheet more explicitly. My group forgot to explain and have the students work on the worksheet we provided after they had made their own pictograph. This caused the students to become confused, as some students tried to rush through the worksheet while we moved onto bar graphs.