Tag: maths

Early Steps in Blended Learning

I think a penny has finally dropped. I’ve been mulling over blended learning for a while but have never quite summoned up the energy. I’ve also been thinking about ways I can apply the DRY (Don’t Repeat Yourself) principle to my teaching, so I can spend more time doing the fun parts of teaching.

Slower than most, I suspect, but I have had my mini-Damascus moment. One of the more repetitive parts of my work is explaining worked problems from the necessary evil that is practice papers. By recording myself working through these I could, in theory, only have to explain a working out once and point students to the video.

One of my classes is a scholarship maths set so I’m trialling the process with them. My first bash is this: answers to the Mathematics Paper B from the Eton King’s Scholarship 2014.

In terms of the mechanics, I’ve bought an IPEVO Point 2 View Camera so I could scribble down my workings out. It’s a little fiddly but seemed to be the cheapest option short of buying a tablet.
In terms of sound, that’s recorded directly to my Macbook and the video files are unedited from the IPEVO bundled software. Levels are a little low, but that may just be me mumbling self-consciously.

Do let me know if you see mistakes, better solutions or have questions about the explanations. Equally, any tips as to how to improve the actual video gratefully received!

Research on Ability Grouping and Setting in Maths Classes

I’ve been trying to tie together some of the various bits of research I’ve come across for and against ability grouping in maths. Below is what I’ve got so far, but would love any other pointers, for or against.

The last 30 years’ research suggests setting marginally improves high-achievers, but to the detriment of everyone else.
Sources are: DfES (2004) Making Mathematics Count (London: TSO), Askew, M. and Wiliam, D. (1995) Recent Research in Mathematics Education 5-16 (London: HMSO), Sukhnandan, L. (1998) Streaming, setting and grouping by ability: a review of the literature (Slough: NFER), Education Endowment Foundation, http://educationendowmentfoundation.org.uk/toolkit/ability-grouping/

This may be for various reasons but some relevant findings are:

  1. Summer births are penalised (Much like ice-hockey players with December birthdays) (Ed Endowment link above)
  2. Approximately one-third of the students taught in the highest ability groups were disadvantaged by their placement in these groups because of high expectations, fast-paced lessons and pressure to succeed. This particularly affected the most able girls.
    Boaler, J., William, D., & Brown, M. “Students’ experiences of ability grouping —disaffection, polarisation and the construction of failure.” – http://www.nottingham.ac.uk/csme/meas/papers/boaler.html
  3. Surprisingly, too, we all as teachers actually differentiate more poorly in set classes than when teaching mixed ability classes, teachers typically use methods and materials that allow students to progress at their own pace through suitably differentiated material. By contrast “setted lessons are often conducted as though students are not only similar, but identical – in terms of ability, preferred learning style and pace of working.” (Boaler and Wiliam)
  4. Setting is for life, though, not just for Christmas. Most children never change sets.
    Ollerton, M. (2001) “Inclusion, learning and teaching mathematics” in Gates ed. (2001b: 261-76)
  5. And nobody is very good at setting well. We are all more fallible and subjective than we like to admit.
    Watson, A. (2001) “Making judgements about pupils’ mathematics” in Gates ed. (2001b: 217-31)
  6. Ability grouping within a class has had tentatively positive results.
    Sukhnandan 1998: 17-8, 37-9. see above
  7. The conclusion from the research is that if it helps, it helps teachers more than children
    Director of IoE, Chris Husbands, https://ioelondonblog.wordpress.com/2014/09/04/setting-by-ability-what-is-the-evidence/
  8. The most successful maths countries set the least – PISA rankings

Doodling and Maths

Vi Hart’s site is fabulous. I keep banging on to my students that it’s not just OK but important to doodle in maths. It helps you ‘see’ problems if nothing else. Some get it, some think it’s just a bit weird. Then I show them videos like this.

Vi, despite the manic voiceovers, shows that maths can be explored with doodling. In fact, doodling helps you make mathematical discoveries. It gets the students hooked. Do have a look at her page: Vi Hart: Math Doodling


The Indiana Jones of Solar Power

Aidan Dwyer – at 13 years old – has made a solar power breakthrough by looking at the way trees are shaped. That’s pretty darn impressive – a little bit like the Blackawton primary school science class and their academic paper on bees.

What I love, though, is his explanation of the process of his discovery. It has pattern-spotting, curiosity, research, maths, geography, history, design, science and more all thrown in. Aidan is clearly a model problem solver and I’m looking forward to seeing how my class react.

He starts:

People see winter as a cold and gloomy time in nature. The days are short. Snow blankets the ground. Lakes and ponds freeze, and animals scurry to burrows to wait for spring. The rainbow of red, yellow and orange autumn leaves has been blown away by the wind turning trees into black skeletons that stretch bony fingers of branches into the sky. It seems like nature has disappeared.

But when I went on a winter hiking trip in the Catskill Mountains in New York, I noticed something strange about the shape of the tree branches. I thought trees were a mess of tangled branches, but I saw a pattern in the way the tree branches grew. I took photos of the branches on different types of trees, and the pattern became clearer.

Then there’s this.

The branches seemed to have a spiral pattern that reached up into the sky. I had a hunch that the trees had a secret to tell about this shape. Investigating this secret led me on an expedition from the Catskill Mountains to the ancient Sanskrit poetry of India; from the 13th-century streets of Pisa, Italy, and a mysterious mathematical formula called the “divine number” to an 18th-century naturalist who saw this mathematical formula in nature; and, finally, to experimenting with the trees in my own backyard.

I love the breadth of the approach. And I love the way it is problem-solving, but problem-solving that is not constrained by subject, period or style. It is, I think, very Indiana Jones.


Passwords and Powers

xkcd’s Password Strength cartoon might be a fun prompt for a maths lesson.


Children at primary school seem to like cracking codes, and hackers have a certain murky glamour to them. Better yet, password, security and spying is a rich topic. My Year 5’s have loved some basic frequency analysis. It ties in with the Tudors and the Babington Plot which ties in with Religious Studies which ties in with PSHE etc etc.

Now need to do a quick bit of research to see what else indices & password cracking to tie in to and make it a richer topic than just a cartoon. Any suggestions welcome.