Data

• Collecting data

Watching these students reminded me of when kids play a video game in which there is a “map” at the bottom of the screen that shows the path the video game player has traveled. How do they use this map? I’m sure to ask questions about this now!

In my desire to believe that the students were trying to find all the mushrooms “systematically,” I was reminded how some students answer those “list all possibilities” types of questions in math. They think and write and think and write and then when nothing more comes to their minds, they’ve decided there are no more possibilities.

Watching the students in this VR activity has shown me that VR could be an effective tool for students to learn to think in some sort of systematic fashion; a way of thinking that is not drawn out when being handed the data or being asked to count what is visible.

• Writing data in a table

This data table was more complex in that it included 3 variables:

· Month

· Type of field

· Number

• Organizing data on a graph

This was more complex than usual because students had to record three data points, one for each different type of field. The only thing distinguishing the fields was the different color, otherwise kids generally get exposure to just one data point per month.

• Classroom instruction

Dave and Janet did a remarkable job getting the idea of interpolation and best fit line across. These ideas didn’t get lost in the “logistics” of recording the data. As a teacher, I know how complicated things get when you want the class to follow students recording data onto a table that may not necessarily be in the order that they have it on their papers. Then to transfer the information from one place to another by graphing three data points, each in different colors, and all on the same vertical line is an achievement for fourth grade! The interjections that were made were also valuable, such as students making and discussing predictions and then recording them.

Why I thought this activity was rich in mathematical thinking

• The data table and graph dealt with more than two variables at a time.

What I have noticed on data analysis items on standardized tests is that in the middle grades, the items have more than two variables at a time. For example, an item may be about City X, Y, and Z and the amount of rainfall each month for a period of months or for a year. Sometimes this information is “too much” for kids to break down if they haven’t been exposed to it. Questions aren’t the usual one-for-one variable type.

• Students exposed to ideas like slope and steepness and that the steepness of fields meant that one field had more or less mushrooms than the other.

• This is a great activity for fourth grade that parallels other fourth grade labs and spirals to the fifth grade lab, Mass vs. Volume, in which students compare the densities of different objects by the slopes of the lines. In the Bouncing Ball lab, the data for three different types of balls is recorded on the same graph.

• At first, I had thought that students would be more engaged if they made their own data table and graph. But the coordination that it takes to copy and record a data table and then use that to complete a graph that has different colors may interfere with the kids getting the bigger ideas such as why different colors are used and watching peers plot data points and correct any data points. Through observation, students were engaged and attentive to watching a team member go up a month-at-a-time. Being the first real exposure to interpolation, this seems to be an appropriate “whole-class” activity. When students do complete a lab in which they draw a best-fit line, they’ll have a reference point as to why careful data collection is important. Future labs could focus in more on labeling and determining the increments on the graph.

• There are a lot of potential activities for higher level students – like having students or teams make up questions using the graph.

Some thoughts for using this activity in the future:

Maybe actually having a team go back into the VR and encouraging them to think “out-loud” how they are trying to find all the mushrooms and if and how they’re more sure they counted all of them this time than last time. On an Immersadesk, the whole class could think aloud and their comments recorded. That would be fun!

On the assessment, do you think it would make a difference if the question included, “Imagine that your team goes back into the VR to count the mushrooms. How would you make sure that you got a perfectly accurate count of the mushrooms in the field? Would you do anything differently than you did last time?”

From each team, students divide into one “rock,” one “sand,” and one “grass.” The “rocks” take their data to the rock group, “sands” take their data to the sand group, etc. Kids try to see a “trend” from their group’s data and write something up to describe what is happening as the months progress.

If there is no time for dividing up into a rock group, sand group, and grass group, then the teacher can “cover up” two of the fields on the data table at a time and students can summarize what happens in the table as the months go on in that particular field.

Another suggestion is a common one in graphing: students record only rock on a transparency, sand on a second transparency, and grass on a third transparency. The teacher shows what happens if each field were on the same graph by superimposing the transparencies.

Keeping this activity’s data either posted or on a handy transparency allows the teacher to use it as a reference point for discussions like: importance of careful data collection, how to show lots of data on one graph (using different colors).