Ask Uncle Colin: A Cosec Proof | Colin

Dear Uncle Colin

I’m stuck on a trigonometry proof: I need to show that $\cosec(x) – \sin(x) \ge 0$ for $0 < x < \pi$. How would you go about it?

– Coming Out Short of Expected Conclusion

Hi, COSEC, and thank you for your message! As is so often the case, there are several ways to approach this.
The most obvious one

The first approach I would try would be to turn the left hand side into a single fraction: $\frac{1}{\sin(x)} – \sin(x) \equiv \frac{1 – \sin^2(x)}{\sin(x)}$.

The top of that is $\cos^2(x)$, so you have $\frac{\cos^2(x)}{\sin(x)}$.

In the specified region,…

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A key flaw in the idea of comparing effect sizes | Greg Ashman

I was alerted* to a new paper by Hans Luyten, Christine Merrell and Peter Tymms about effect sizes. Effect sizes get bandied around a lot in education and many will have heard of John Hattie’s figure of d=.40 (0.4 of a standard deviation) as an effect size worth having. However, this is pretty blunt. We know, … Continue reading A key flaw in the idea of comparing effect sizes

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Lucy Rycroft-Smith: Cambridge Mathematics, Setting, Times Tables and Anxiety | MrBarton

On this episode of the Mr Barton Maths Podcast, I spoke to Lucy Rycroft-Smith.

Lucy is a former maths teacher and head of maths, who is now the Research and Communications Officer at Cambridge Mathematics.

The reason I wanted to have Lucy on the show is that I am a little bit addicted to her espressos. Now, anyone who knows me will know my chosen brand of coffee is a very milky and pathetically weak cup of Mellow Birds, but these are mathematical espressos – bite-sized chunks of mathematical research into key areas. I originally planned to ask Lucy about five of these areas, and have…

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Engelmann Connecting Maths Concept Textbook series: Number Families Part 1 | admin

During my second year at Michaela Community School, the department used Siegfried Engelmann’s Connecting Maths Concept Textbook series as the main teaching tool for Intervention. The textbook series comes with:

A pupil textbook
A pupil workbook
Prepared Tests (after every 10 lessons)
Teacher Presentation book

Each lesson would have:
4/5 Teacher-led exercises (using  the presentation book)
Independent pupil work

I know that some teachers would feel uncomfortable using a presentation book with prepared scripts but when I read through it I realised that Engelmann had written it…

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