In this WitCH we will again pick on the Cambridge text Specialist Mathematics VCE Units 3 & 4 (2019): see the extract below. (We’d welcome any email or comment with suggestions of other generally WitCHful texts and/or specific WitCHes.) And, a reminder that there is still plenty left to discover in WitCH 2 , WitCH 3 and Tweel’s Mathematical Puzzle still have room for comment.
Well, WitCH 2, WitCH 3 and Tweel’s Mathematical Puzzle are still there to ponder. A reminder, it’s up to you, Dear Readers, to identify the crap. There’s so much crap, however, and so little time. So, it’s onwards and downwards we go.
Our new WitCH, courtesy of New Century Mathematics, Year 10 (2014), is inspired by the Evil Mathologer‘s latest video. The video and the accompanying articles took the Evil Mathologer (and his evil sidekick) hundreds of hours to complete. By comparison, one can ponder how many minutes were spent on the following diagram:
OK, Dear Readers, time to get to work. Grab yourself a coffee and see if you can itemise all that is wrong with the above.
Well done, craphunters. Here’s a summary, with a couple craps not raised in the comments below:
- In the ratio a/b, the nature of a and b is left unspecified.
- The disconnected bubbles within the diagram misleadingly suggest the existence of other, unspecified real numbers.
- The rational bubbles overlap, since any integer can also be represented as a terminating decimal and as a recurring decimal. For example, 1 = 1.0 = 0.999… (See here and here and here for semi-standard definitions.) Similarly, any terminating decimal can also be represented as a recurring decimal.
- A percentage need not be terminating, or even rational. For example, π% is a perfectly fine percentage.
- Whatever “surd” means, the listed examples suggest way too restrictive a definition. Even if surd is intended to refer to “all rooty things”, this will not include all algebraic numbers, which is what is required here.
- The expression “have no pattern and are non-recurring” is largely meaningless. To the extent it is meaningful it should be attached to all irrational numbers, not just transcendentals.
- The decimal examples of transcendentals are meaningless.
First, a quick note about these WitCHes. Any reasonable mathematician looking at such text extracts would immediately see the mathematical flaw(s) and would wonder how such half-baked nonsense could be published. We are aware, however, that for teachers and students, or at least Australian teachers and students, it is not nearly so easy. Since school mathematics is completely immersed in semi-sense, it is difficult to know the rules of the game. It is also perhaps difficult to know how a tentative suggestion might be received on a snarky blog such as this. We’ll just say, though we have little time for don’t-know-as-much-as-they-think textbook writers, we’re very patient with teachers and students who are honestly trying to figure out what’s what.
Now onto WitCH 3, which follows on from WitCH 2, coming from the same chapter of Cambridge’s Specialist Mathematics VCE Units 3 & 4 (2018).* The extract is below, and please post your thoughts in the comments. Also a reminder, WitCH 1 and WitCH 2 are still there, awaiting proper resolution. Enjoy.
* Cambridge is a good target, since they are the most respected of standard Australian school texts. We will, however, be whacking other publishers, and we’re always open to suggestion. Just email if you have a good WitCH candidate, or crap of any kind you wish to be attacked.
Well, WitCH 1 is still not satisfactorily resolved, and Tweel’s puzzle is also still out there. But, we may as well get another ball rolling.
The second in our What is this Crap Here series comes from Cambridge’s textbook Specialist Mathematics VCE Units 3 & 4 (2018). Enjoy, and please get to pondering, and posting.
OK, Dear Reader, you’ve got work to do.
So far on this blog we haven’t attacked textbooks much at all. That’s because Australian maths texts are, in the main, well-written and mathematically sound.
Yep, just kidding. Of course the texts are pretty much universally and uniformly awful. Choosing a random page from almost any text, one is pretty much guaranteed to find something ranging from annoying to excruciating. But, the very extent of the awfulness makes it difficult and time-consuming and tiring to grasp and to critique any one specific piece of the awful puzzle.
The Evil Mathologer, however, has come up with a very good idea: just post a screenshot of a particularly awful piece of text, and leave others to think and to write about it. So, here we go.
Our first WitCH sample, below, comes courtesy of the Evil Mathologer and is from Cambridge Essentials, Year 9 (2018). You, Dear Reader, are free to simply admire the awfulness. You may, however, go further, and what you might do depends upon who you are:
- If you believe you can pinpoint the awfulness in the excerpt then feel free to spell it out in the comments, in small or great detail. You could also offer suggestions on how the ideas could have been presented correctly and coherently. You are also free to ponder how this nonsense came to be, what a teacher or student should do if they have to deal with this nonsense, whether we can stop such nonsense,* and so on.
- If you don’t know or, worse, don’t believe the excerpt below is awful then you should quickly find someone to explain to you why it is.
Here it is. Enjoy. (Updated below.)
* We can’t.
Following on from the comments, here is a summary of the issues with the page above. We also hope to post generally on index laws in the near future.
- The major crime is that the initial proof is ass-backwards. 91/2 = √9 by definition, and that’s it. It is then a consequence of such definitions that the index laws continue to hold for fractional indices.
- Beginning with 91/2 is pedagogically weird, since it simplifies to 3, clouding the issue.
- The phrasing “∛5 is irrational and [sic] cannot be expressed as a fraction” is off-key.
- The expression “with no repeated pattern” is vague and confusing.
- The term “surd” is common but is close to meaningless.
- Exploring irrationality with a calculator is non-sensical and derails meaningful exploration.
- Overall, the page is long, cluttered and clumsy (and wrong). It is a pretty safe bet that few teachers and fewer students ever attempt to read it.
As long as we’re busy bashing Oxford, the above graphic and note are from the Australian textbook My Maths 8, 2015, published by the esteemed Oxford University Press.