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Thinking back to my own statistics at university… how do you even teach statistics without a lot of other math first? Analysing data is similar. I'm all for it

by Arnt 3y ago

Thinking back to my own statistics at university… how do you even teach statistics without a lot of other math first? Analysing data is similar. I'm all for it, it's clearly useful on the days when my main working tools are slack and powerpoint, but it's not clear to me how teach that without math. One of my math textbooks even had the word "analysis" in its title. ("Calculus and analytic geometry" perhaps?)

seanhunter 3y ago
You can absolutely teach basic statistical literacy without too much other maths and certainly without any higher maths. That’s how it’s done in schools in other countries - for example here is the statistics component of the maths GCSE for one of the exam boards in the UK (the others will be similar) https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300/subject-content/3.6-statistics https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics... GCSE starts after the third year of secondary school in the UK so most people will have completed their GCSE in the year they turn 16. Then 16-18 year olds wanting to study STEM subjects go on to do maths A-level, which includes more topics that in the US would be considered precalc as well as some calculus, more probability and statistics and some mechanics. Here’s the A-level syllabus from the same board. As you can see, for stats it includes distributions and hypothesis testing, so much more depth https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/mathematics-7357/specification-at-a-glance https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/m...
- steve_gh 3y ago
  A level maths is not a necessity for all STEM courses. My daughter is doing AS maths (half way between GCSE and A level, heavily weighted to stats), alongside A levels in Biology and Chemistry (and one non science A level)
  - seanhunter 3y ago
    Aah I forgot about AS levels actually. Best of luck to your daughter.
- Ancapistani 3y ago
  I'd argue that very little - or even no - math is required to teach the concepts. The ideas of standard deviation and confidence intervals can be taught visually, for instance. You needn't be able to calculate them to understand what they mean when they're presented. The extent of my statistics education in high school was "mean, median, mode". That was it, and I exhausted every math course that was offered at my school by the time I entered 11th grade.
  - pokerface_86 3y ago
    [dead]
consp 3y ago
> math textbooks even had the word "analysis" in its title My (mostly) calculus classes were even called "analyse" (analysis).
DonsDiscountGas 3y ago
I think you would stick to discrete statistics, so teach sums/sigma notation but you wouldn't need to get into integrals.
michaelt 3y ago
You can teach basic statistics without a lot of math background. If your class of 12 year old physics students has just timed a block of wood sliding down a sloped plank at different angles, and plotted an X/Y chart of their results, you can just have them put a best fit line through the points by eye. No need for matrices or differentiation or X-transpose-X-inverse-X-transpose-y - just bang a line through the data by eye.

by Arnt 3y ago

seanhunter 3y ago

You can absolutely teach basic statistical literacy without too much other maths and certainly without any higher maths. That’s how it’s done in schools in other countries - for example here is the statistics component of the maths GCSE for one of the exam boards in the UK (the others will be similar) https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics-8300/subject-content/3.6-statistics https://www.aqa.org.uk/subjects/mathematics/gcse/mathematics... GCSE starts after the third year of secondary school in the UK so most people will have completed their GCSE in the year they turn 16. Then 16-18 year olds wanting to study STEM subjects go on to do maths A-level, which includes more topics that in the US would be considered precalc as well as some calculus, more probability and statistics and some mechanics. Here’s the A-level syllabus from the same board. As you can see, for stats it includes distributions and hypothesis testing, so much more depth https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/mathematics-7357/specification-at-a-glance https://www.aqa.org.uk/subjects/mathematics/as-and-a-level/m...

steve_gh 3y ago
A level maths is not a necessity for all STEM courses. My daughter is doing AS maths (half way between GCSE and A level, heavily weighted to stats), alongside A levels in Biology and Chemistry (and one non science A level)
- seanhunter 3y ago
  Aah I forgot about AS levels actually. Best of luck to your daughter.
Ancapistani 3y ago
I'd argue that very little - or even no - math is required to teach the concepts. The ideas of standard deviation and confidence intervals can be taught visually, for instance. You needn't be able to calculate them to understand what they mean when they're presented. The extent of my statistics education in high school was "mean, median, mode". That was it, and I exhausted every math course that was offered at my school by the time I entered 11th grade.
- pokerface_86 3y ago
  [dead]

consp 3y ago

> math textbooks even had the word "analysis" in its title My (mostly) calculus classes were even called "analyse" (analysis).

DonsDiscountGas 3y ago

I think you would stick to discrete statistics, so teach sums/sigma notation but you wouldn't need to get into integrals.

michaelt 3y ago

You can teach basic statistics without a lot of math background. If your class of 12 year old physics students has just timed a block of wood sliding down a sloped plank at different angles, and plotted an X/Y chart of their results, you can just have them put a best fit line through the points by eye. No need for matrices or differentiation or X-transpose-X-inverse-X-transpose-y - just bang a line through the data by eye.