Streets or roads
Y8 (11/2009)  
Explanations for full credit fall into these main types:
Fewer than 10% of students gave explanations such as these: The lines dont in this case represent anything. It is only the dots that do. A line graph shows the answers in between and that is rough [wrong]. Because the sections are joined. If the lines were not there it would be easier to understand. Suggests another appropriate form of graphic such as a bar graph, dot plot, or pie graph or any other graphic suitable for discrete, nominal data. Do not accept a histogram (as this is for continuous data). Accept even if there are other errors or misconceptions in the explanation.
It is better to use a bar graph. 
very difficult
moderate 
NOTE: Three students gave these valid explanations that the category "Other" was needed.
 Some students might live on farms.
 There might be more st names like coldasack (sic).
 There should be "other".
Ask these students "Is a line graph a good way to show this data?"
Students who got partial credit should be asked to justify why these other graphs are more suitable. This may indicate they have an understanding of discrete, nominal data, or may just indicate that they are more used to bar graphs, pies graphs etc.
The key concept that is being assessed is that the type of data influences the appropriate choice of graph. In this example the data is nominal, which is one kind of discrete data. For more on this, click on Types of data: Statistics.
Nominal data is nonnumerical and there is no relationship between the categories. There is nothing half way between a Street and a Road (not a "Stroad" or a "Roeet"; a "Play" or a "Wace"). This means that there should be no lines joining the points.
Common alternative explanations (do not target the type of data being plotted) 
Sees the graph as hard to read (either for themselves or for others)

Thinks line graphs lack accuracy

Says the graph does not have enough detail (about the total number of children or their names)

Graph will not be valid if more data is added or changed

Sees tables or tally charts as better options

Sees the line graph as good
Doesn't know that it is inappropriate to join the points on the graph. Does not appreciate the nominal, categorical nature of the data. It can only take on particular named values, such as Street, Road, etc. There is nothing that is halfway between "Street" and "Road". Joining the points implies there is. 
Students who got partial credit had a similar mean ability than those who gave these misconceptions. An exception was that students who thought that the line graph was acceptable had a lower mean ability. Students who said that the graph should show the total number of children had higher mean ability than ones who gave other explanations.
Sees the graph as hard to read
This may be the result of not being familiar with line graphs. Students may have only had exposure to graphs such as bar graphs, pictographs, pie charts, or dot plots. Students need to have experience drawing their own line graphs. To find some of these, use the keywords or click on the link line graphs AND graph construction.
Thinks line graphs lack accuracy
Ask students why they think the graph is hard to read or inaccurate. Some students may relate the lack of accuracy or the difficulty of reading the graph to the way Excel puts the category names (Streets etc) between the tick marks rather than aligned with the tick marks.
Sees tables or tally charts as better options
The student may need to have more experience constructing and reading various graphs, and looking at the trends, shapes, and patterns they show. Graphs show these better than tables do.
The graph does not have enough detail
Students need to have the idea that graphs and tables are there to get an overall picture of the trends or patterns in the data, rather than retaining information about individual people. The stemandleaf graph combines the individual data with the overall shape (distribution) of the data. Some computer programmes (for example Tinkerplots) allow individual names to be displayed.
Graph will not be valid if more data is added or changed
The student needs to realise that all graphs need to be updated when new data becomes available or data changes. This is easy with pictographs, dot plots, and to a lesser extent with bar graphs or histograms. Graphs like pie graphs or line graphs need to be redrawn. Computer packages can support students to focus on the meaning of the graph rather than spending time on construction.
Sees the line graph as good (potentially the other listed misconceptions have this issue as well)
For ALL these above alternative explanations, especially the last one:
Students need to be aware of different types of data and how to graph them.
Have a class or group discussion about what the lines on Olivia's graph mean
 Ask "Is it OK to join the points like Olivia did?"
 Get those who think it is OK, and those who think it isn't to defend their decision.
 Ask "What kind of address has 7 houses?" — The answer seems to be "half way between Street and Road". You could ask students "What is halfway between a Street and a Road – Is it a Stroad or a Reet?"
 Use examples to make students aware of the different types of data.
 Get students to compare different types of graphs and what data types they should be used for. For more on the different kinds of data, click on Types of data: Statistics.
For more on conducting discussions click on Mathematical classroom discourse.
 Computer comparisons (Statistics, L34, pages 67).
 Surf Stats (Statistics, L4, book 1, pages 89).
 Mad minute (Statistics, L4, book 1, pages 1415).