1. Comparing Student Ability to Reason with Multiple Variables for Graphed and Non-Graphed Information. Rebecca Rosenblatt Student comments from experiment 1 suggest perhaps students are simply missing the 3 rd variable in play : o “If x does not affect y, than as I change x I don’t know what will happen to y.” – True if other variables are uncontrolled. o “If x doesn’t change and y does, than x doesn’t affect y.” - Many students seemed to be thinking along the lines of if x affects y than if x does not change y should not change but that did not happen so x must not affect y. Hypothesis: By increasing the salience of this 3 rd variable students will realize it is there and be able to correctly answer questions about vertical and horizontal graphs. Instructions were given to directly include all 3 variables. E.g. “A student is experimenting with a simple pendulum to see what the relationship is between the mass on the bob, the length of the string and the period of each oscillation. For each experimental trial the student varied either mass or length and measured the change in the period…” Also, half the students received a set of graphs with a legend to directly show the changing, or not changing, 3 rd variable. Experiment 2: o Most value errors for up and down trend data are mistakes made by answering a) for up data and not performing the requested task or by making random errors. o On the vertical and horizontal items incorrect students mostly interchanged these answer options. o Students were able to answer the vertical value items. So students knew that the relation for the y values is unknown but did not equate this with and unknown variable relationship. o The errors on these items showed incorrect logic that would only be correct for uncontrolled experiments or were common logical errors made reasoning as if x were the only casual variable (i.e. if and only if). Relation Item: Which of the following best describes the relationship between the variables X and Y? a) Proportional (i.e. when x increases, y increases) b) Inverse (i.e. when x increases, y decreases) c) Independent of each other (i.e. x does not affect y) d) There is not enough information to determine a relationship Value Item : Which of the following best describes the expected relationship between the Y values for X = 1 and X=5? a) Y(X=1) > Y(x=5) b) Y(X=1) < Y(x=5) c) Y(X=1) = Y(x=5) d) A, B, and C are all possible Experiment 1: Comparing students ability to reason with graphed data and the general relationship of the variables vs. extrapolating the relationship for un-plotted data. Conclusions from the three experiments  Students are generally better at analyzing general data relationships than comparing un-plotted extrapolated values.  While students are quite good at the standard increasing and decreasing data trends on graphs this is only true for controlled set ups that change just the two main axes variables.  Because of students’ equally poor graphical and pictorial reasoning with horizontal and vertical data, it seems that students are not good at the more sophisticated reasoning required to consider data where one variable does not change but the second does change. Their responses are consistent with reasoning issues seen in logic curriculum, and seem to be of the same ilk. Experiment 3: To separate reasoning issues from graphical issues. Students were randomly assigned to graphs or pictures which had the “same” data and reasoning comparison. Instructional slides explaining the legend or the figures were shown before the session began. Introduction: Results from three experiments with introductory algebra based students. These experiments address student ability and difficulties reasoning with variables for graphed and un-graphed data. *Students were told that this data was collected via a controlled experiment in which one variable was changed at once and the effect on the vertical variable was measured. Data TrendRelation ItemValue Item UP95%79% Down93%75% Horizontal (None)79%60% Vertical (Unknown)31%63% Results: Students answered almost exactly as they did for the horizontal and vertical question in experiment 1. The legend did not improve performance. It was clear that students did not have the graphical skills to use a legend without instruction. Some students mistaking the icon as outlier data. PictureGraph This set of data says length affects the period but does not say how mass affects the period. This set of data says mass does not affect the period but does not say how length affects the period. Students were asked about other axes or picture configurations Students were asked about situations that are not controlled This set of data says color affects density but does not say how shape affects the density. This set of data suggests nothing about color or shape’s affect on density because too many things changed at once. Item TypeAllControlledNot Controlled Graphs42.3 ± 4.7%65.1 ± 4.5%28.0 ± 2.8% Pictures39.1 ± 3.8%50.1 ± 5.1%34.4 ± 3.4%