Math year 11 ext 1 syllabsus - analytical geometry (1 Viewer)

[oasfree]

Guys, I did math ext 1 around 30 years ago and now my kid is doing it as an accelerant at year 10. I feel her teacher could not give her in depth coverage of the topics. Half of the normal students at year 11 seem to be better than her at coping with the subject due to having one extra year. So I had a revision of the year 11 Prelim topics to see what I can help. I realised that I learned them as single topics (long ago) and only integrated them enough to be able to sit exams. There was no attempt by teachers (or seen in textbooks) to integrate all the topics to a philosophical depth or at least to form a completely coherent picture from the ground up.

So I feel there is something missing. I feel there is a need to help students as soon as they have completed introduction to calculus so that they can see a complete journey from basic primary school geometry through analytical geometry all the way to calculus. Then use differentiation to take them back down to straight lines and constant. This allows all things to be examined and mapped out in graphs and areas and equations. Something like a marathon lesson that takes students across the journey so there is a complete and coherent picture of the jigsaw puzzle.

I wonder if this is now part of the HSC math ext 1 syllabus or in the circle of math teachers or students only learn the parts and never really make an attempt to connect all of them tightly? Or teachers just don't care or don't even know or not bother to become competent enough to wrap this up themselves? What do you guys think (or experience)?

 

[BLIT2014]

I think you seem to be quite antagonistic towards teachers.

 

[braintic]

Why do you have to ask the question so negatively?
It seems to be a thinly veiled attempt to attack teachers.

You are the person who suggested six months ago that the teachers at NSB and NSG make no difference to the education of their students because they get tutored anyway. An irrational, misinformed and deliberately provocative comment.

 

[oasfree]

Why do you have to ask the question so negatively?
It seems to be a thinly veiled attempt to attack teachers.

How is my question negative? Do students today get a coherent picture or not? Simple as that or just like the old time where there was none. If this is not in the syllabus, I guess it will not be taught and perhaps teachers won't even pay attention to it. I do not attack teachers. If it is not offered, I will just have to seek another source or do it myself.

 

[Carrotsticks]

It is up to the teacher if they wish to make a 'marathon lesson' as you said. Such a thing is not currently mandatory.

However, something like this is only possible if students are at least somewhat competent with their 'tools' that they've learned over the years. That is already tough enough, as most students forget things once they learn something else. Not an ideal reality, but a reality nonetheless. (I will refer to this at the end of this post)

But such students do exist, and appropriately capable teachers do exist too. This is why we have the Extension 2 course and a topic called 'Conics'. This, as you have said, sufficiently unifies all the tools that students have learned over the years. I daresay that it is the topic that uses the most number of different tools.

- Simultaneous Equations

- Trigonometry

- Linear Functions (and all the tool chest associated with it such as dividing an interval, gradient formula, distance formula, perpendicular distance formula, the list goes on...)

- Calculus

- Locus

I am sure there are other topics that it utilises, but you get my point.

Students seeking such unification of tools are most likely stronger students who are perhaps capable of studying Extension 2, where the 'pieces of the puzzle are glued together' rather than analysed little bit by bit and being blind to the bigger picture.

Also, there is a more mild version of the above course called 'Parametric Equations', which uses all of the above except Trigonometry. This is often taught in the Year 11 Extension 1 course.

Regarding my earlier statement about students struggling and forgetting topics, when I ask students which topics they like/dislike, many of them reply with "Parametrics" and/or "Conics" the most. In actuality, the topic is fairly straightforward with the odd difficult problem here and there, but I feel from experience that students find it difficult NOT because it is actually difficult, but because the unification of topics forces them to draw from the darkest corners of their memory. So if that happens with our most capable students (Extension 2), then for the others ...

 

[braintic]

How is my question negative?

"Or teachers just don't care or don't even know or not bother to become competent enough to wrap this up themselves?"

That was a statement disguised as a question.

And if it wasn't obvious, my issue with you goes deeper. Why did you choose not to address the second part of my comment?

It seems you are prone to making this sort of comment in other threads.
You talk about private schools telling "a fib to cover for its damaging drop in rankings", claiming that they are making up their top ATARS.
This caused one of the BOS moderators to comment: "it seems as if most of what you are saying is conjecture and speculation based on weak inductions".

Then you whine about how your daughter can't compete with all the Asians because they are heavily tutored.
And you suggest that teachers refuse to teach effectively at school, so that they can get more business for their tutoring after hours.
So don't say you don't attack teachers.

The list of negative comments just keeps going on and on.

 

[BLIT2014]

Why do you have to ask the question so negatively?
It seems to be a thinly veiled attempt to attack teachers.

You are the person who suggested six months ago that the teachers at NSB and NSG make no difference to the education of their students because they get tutored anyway. An irrational, misinformed and deliberately provocative comment.

Agree strongly with you braintic.

 

[BLIT2014]

How is my question negative? Do students today get a coherent picture or not? Simple as that or just like the old time where there was none. If this is not in the syllabus, I guess it will not be taught and perhaps teachers won't even pay attention to it. I do not attack teachers. If it is not offered, I will just have to seek another source or do it myself.

Probably largely due to the way mathematics is taught in primary school. Student's for the most part are more capable of learning a lot more 'difficult' concepts then what is currently being taught, coupled with fact the 'building blocks' of secondary Mathematics such as knowing Times table
(by rote) isn't considered as integral as much as it was.

 

[braintic]

Agree strongly with you braintic.

Thanks. I get tired of people who attack a whole group based on their (mis?)conception of one individual (or a few at best)?
I'm guessing that when he sees the number pattern 1, 4, ... this guy thinks he has enough information to generalise to a rule.