This one of those lazy WitCHes, where we really should do the work and critique the thing but we just can’t muster the energy to do it. The WitCH is a video, a recent NSW Education conversation-lecture for K-6 teachers: *Student Engagement in Mathematics*. The star of the show is Catherine Attard, Professor of Mathematics Education at Western Sydney University.*

The *Engagement* video page also contains a transcript, and three links to Further Reading:

- C. Attard,
*Engagement and mathematics: What does it look like in your classroom?*(Journal of Professional Learning, 2015) - C. Attard,
*IPad apps for primary mathematics teaching and learning* - C. Attard and K. Homes, “
*It gives you that sense of hope”: An exploration of technology use to mediate student engagement with mathematics*(Hellyon, 2020)

We have no real idea what this is about, if anything, whether the video is a one-off thing or part of an orchestrated plan. But it annoyed us, which is enough.

*) We last wrote of Professor Attard in her capacity as President of MERGA, when some ~~media stooges~~ education reporters quoted Professor Attard as a “maths expert” while shoring up support for ACARA’s beleaguered draft Curriculum.

Well, there’s only so much I can read of this stuff before dinner, and probably even less afterwards. But in Assoc Prof Attard’s first big soliloquy (about 1/3 of the way into the transcript) she rabbits on about the three “dimensions” of engagement, these being “cognitive engagement”, “the operative dimension”, and “the affective domain”, which are illustrated, according to the transcript, by a “Diagram of overlapping circles” – I don’t know whether this is an Euler or a Venn diagram, and I’m not going to watch the video to find out. She then refers to these “three elements”. Make of this what you will.

I bit later on she refers to the great Jo “I’m not to be criticized” Boaler.

I should say that I don’t have a hatred of all education-speak; some of it is undoubtedly necessary to attempt to understand a very difficult and knotty thing. But I can’t help feeling that all of this verbiage could probably be distilled into a couple of sentences. But then, you don’t get promotions by stating the bleeding obvious!

Attard‘s definition of “operative engagement“ is to engage with the actual mathematics itself. While that is what engagement in a mathematics class should be, I have doubts whether that actually happens in such “engagement oriented” research and classroom practices. Especially since the rest of the interview doesn’t give much hope.

I recently completed a teacher research project at university and my team’s focus was engagement in mathematics. One team member’s conclusion was that increasing technology use in mathematics increases student engagement. My conclusion? Universities are the WitCHes’ covens.

Thanks, Anonymouskouri. Was this part of a Masters of teaching? Or real live teaching?

Masters of WitCHery.

It increases engagement… not with mathematics.

As soon as the teacher looks away the kids are going to be playing games on their iPads. I have first hand experience with this as the kid playing games on his iPad in school.

Well said Alasdair.

This is my recent experience with using various ways to calculate the median of a sample.

Suppose I want to find the first quartile (Q1) of the sample data {6, 7, 15, 36, 39, 41, 41, 43, 43, 47, 49}. There are n=11 data in the sample.

We might appeal to Mathematics Glossary provided by VCAA.

“Quartiles are the values that divide an ordered data set into four (approximately) equal parts. It is only possible to divide a data set into exactly four equal parts when the number of data of values is a multiple of four. … The first, the lower quartile (Q1) divides off (approximately) the lower 25% of data values.”

When I apply this definition, I see that 11/4 = 2.75, and so Q1 is the 2.75th number in the list. This puts Q1 between 7 and 15. Arguably it could be 15, or more precisely 13.

We might use Excel. Put the data in a1:a11 and use the function QUARTILE(a1:a11, 1). This yields the answer 25.5.

We might use R as follows.

data <- c(6,7,15,36,39,41,41,43,43,47,49)

quantile (data)

This also yields the value of 25.5 for Q1.

We might identify the position of Q1 in the ordered list by 0.25(n+1) = 3, and the value of Q1 is then the 3rd number in the list which is 15. See [1] and online calculators [2], [3].

Fortunately, most students have only one calculator. However, I admit that I was engaged.

References

[1] ExamSolutions. Median, quartiles and interquartile range. https://www.youtube.com/watch?v=wNamjO-JzUg

[2] https://www.calculatorsoup.com/calculators/statistics/quartile-calculator.php

[3] https://calculator-online.net/quartile-calculator/

Interesting. Very interesting…

I would argue that for such a sample, the five-number-summary is pretty meaningless as the data itself is not much more than five numbers.

Of course, I would then have to choose another arbitrary number of data points beyond which I believed a five-number-summary to be meaningful and that I cannot do with any conviction, so your point stands.

This does highlight the difference though between contrived textbook examples and genuine applications of basic descriptive statistics.

Suppose though, that there were 100 data points. Is Q1 the 25th data point, the 26th data point or the mean of these two? Does it matter?

There was a case a few yeas ago, where seriously ill cancer patients were treated with extremely high doses of radiation. The radiation was aimed at the tumour with computer assistance. After some time, it was discovered that there was an error (probably small) in the program. In some cases, the consequences were likely to have been fatal.

You’ll have to help me join the dots here…

It was an illustrative answer to your question about whether small errors matter.

I see (sort of).

I was suggesting that the choice of how Q1 is defined (not necessarily in error) can differ between sources, especially when we are describing discrete data sets.

Yes, errors matter. Definitions also matter.

When I teach sample standard deviation, I start with 1, 1, 2, 3 and 3 as my data set because it is obvious that if you don’t include the mean all the numbers are exactly 1 away from the mean. This means that you can tell what the SD is before you start and the process makes more sense.

What App do you use?