# Thinking about Teaching and Time Series

Time series data shows the same phenomenon taken at different times. It’s possible, therefore, to plot the data—traditionally with time on the horizontal axis—and see how the data values change with time. As in the “banner” graph above.

The graph tells a story; and we read it chronologically from left to right. As experienced graph-readers, we see the surges and dips in COVID cases, as well as the vertical omicron rise (and as of this writing we have no idea what will happen!).

We see graphs like this all the time in the news; right now, of course COVID is a topic of interest, but you’ll see time series about topics from temperature to stock prices to TV viewership.

The question for us teachers up to high school is, what do students need to know about time series? More pointedly for today, what can we think about as we plan lessons? My first take on this includes:

• Basics: how do you read or make a time series graph? How do you know whether it should be treated as time series?
• Time series and modeling: linear models, rates, nonlinear patterns, and the road to calculus.
• Special tools that work with time series such as smoothing and folding.
• Other sneaky and cool representations such as phase-space diagrams.

## Teaching Time Series Basics

I don’t have a lot to say here, except to imagine that this (a) is not hard, it’s just that students have never seen it before and (b) we can teach these basics embedded in other lessons, more as a just-in-time pedagogy thing than as a whole unit introducing the Principles of Time Series (heaven help us). I think that most of this could happen at middle school, but it’s not unreasonable to reinforce (or introduce) these skills at the high-school level.

For example: imagine a lesson where you’re teaching about COVID and you look at a lot of published graphs of how things are changing. Ask students to identify which quantities are on which axis. Write these up on the board. Then, hey, everybody, what do you notice about what goes on which axis? Yeah, interesting: time seems to go on the horizontal axis in all these graphs. How does that connect with anything else you know about what goes on an axis?

You might also display a graph that’s not a time series and ask groups to describe what’s different about this graph compared to the time series. What is the graph maker trying to get across? Looking back at the time series, what story does that tell?

You can also ask questions that explicitly get at the time/rate/story aspects of a graph, like, “What was happening to the number of admissions in January 2021? How can you tell?” Or “When was the number of new admissions at a maximum? Why would we care?”

Finally, a small note: we expend some effort getting students making graphs by hand to stop connecting all the dots. But time series graphs are often an exception: because each data point connects to a previous point and to a successor, lines connecting the dots often make conceptual and numerical sense. In the example COVID case graph, it’s gone so far that they plot only the lines and leave the dots out!

(In CODAP, use the “ruler” palette in the graph to show connecting lines.)

That’s enough for today. More to come on other time-series topics…

…except for a longer aside…

## Kvetch Corner: Stats courses and time series

I’ll make a claim right away: in a class labeled statistics (like AP stats), the traditional curriculum doesn’t do much with time series at all. This is understandable because the topics and techniques are not about time series but rather are aiming towards inference questions (What is the confidence interval for this proportion? Did the treatment show a significant improvement?). I think it’s worth noticing, though, that time series are everywhere in our students’ lives, and that, with more data available, more technology to display it, and an increased presence of data science, our students might need (yea, deserve) to be exposed to time series more deliberately.

A hardened stats teacher might rightly say that a time series graph like the one above is really descriptive statistics, suitable only for the first few weeks of a serious course of study. I agree that it’s descriptive as opposed to inferential, but would say that today’s tools let us do more with descriptive stats (as in, much of data science) so we ought to look.

Why doesn’t traditional stats treat time series? One reason might be is that a lot of (beginning) statistical tools assume that data values are independent. But the whole point of time series is that we’re looking at a sequence that’s probably causally connected: the temperature today is related to the temperature yesterday. Looking at this another way, consider a dataset of daily COVID cases over a month. We can easily imagine asking students to calculate the standard deviation of the number of cases. This task is a bad idea, because the spread that you get doesn’t reflect natural variability in the data, but rather, at least partly (and often mostly) the change in that case rate over the course of the month.

## Author: Tim Erickson

Math-science ed freelancer and sometime math and science teacher. Currently working on various projects.