mathematics teaching homepage

(previously the 'pedagogy' page)

'Official' advice
books worth reading
people, blogs and posts
themes and debates
our policies
Ofsted Good Practice films &
Ofsted Good Practice Reports
Full On Learning ,
Zoe Elder
blog_bookshelf_thumb.jpg
blog_bookshelf_thumb.jpg

Math teaching blogs and forums
questions.png
questions.png
Questioning



marginal learning gains
(Zoe Elder)
VAK differentiation thumb.png
VAK differentiation thumb.png
Differentiation




stuck_(ball_metaphor)_thumb.jpg
stuck_(ball_metaphor)_thumb.jpg
'Stuckness' and giving hints




progress_graph_thumb.jpg
progress_graph_thumb.jpg
Tracking and progress




problem oriented learning
Sample problems:




memorisation




teachers' marking self assessment adapted for science.doc
teachers' marking self assessment adapted for science.doc
teachers' marking self assessment adapted for science.doc
teachers' marking self assessment adapted for science.pdf
teachers' marking self assessment adapted for science.pdf
teachers' marking self assessment adapted for science.pdf





schrock's revised bloom's taxonomy.png
schrock's revised bloom's taxonomy.png
Kathy Schrock's guide to a digital Bloom's taxonomy adds detail to the section below about Andrew Church's Revised Bloom's Taxonomy.

differentiation
A whole-school focus for us in the coming year is to think more deeply about differentiated instruction. Thers's a great resource at the dare to differentiate wiki

coaching_life_change_(fish_metaphor)_thumb.jpg
coaching_life_change_(fish_metaphor)_thumb.jpg
coaching
I'm setting out my own learning goals for the year and pretty near the top is to develop my coaching skills. There's a new coaching unit which I have explored on the good practice for leaders site and is pretty good, and the coaching and mentoring network, which I haven't explored yet.


I've posted below about setting big goals in relation to the Teaching as Leadership rubric. On a related note, in the investing students section, TaL (I-1), Farr recommends using progress graphs to 'Convince students that they can succeed.' Another section, TaL (E-6), is entitled 'Evaluate and keep track of students’ performance.' In both sections the use of graphs and tracking tools is connected with raising attainment. So here's a simple tool to help that's designed to track pupils' progress in mathematics and core subjects in the UK secondary sector:
a blank:
progress and target sheet.doc
progress and target sheet.doc
progress and target sheet.doc
and a partially filled one:
progress and target sheet example.doc
progress and target sheet example.doc
progress and target sheet example.doc
(09 Oct 2011)





  • It's not (as far as I know) intentionally to do with math, but you might enjoy this



























while you read the rest of this article!
As Jose Gonzalez says "we need hints before we get tired" and "we need a hint to know we're on the right track."
Knowing the right hint to give a pupil who is stuck on a mathematical problem and the right time to give it is one of the core pedagological skills of effective math teachers.
I've discovered a few useful places to start to refine our skills in this: the first is a classic, and was recommended to me over 20 years ago when I was a sixth-former: Georg Polya's //How to Solve It//. This book has been so successful it has its own wikipedia entry, which summarises many of the main ideas. I'd also recommend scan-reading the learn-math.info biography of Polya
What precipitated this entry was a blog entry on math4teaching: scaffolding problem solving in geometry which features a rather nice areas puzzle and a link to a geogebra page with a sequence of hints that you might reveal in turn.
My wanderings have also led me to the heuristixx blog which has a rather nice graphical summary of Polya's ideas.
...
Of course, getting pupils to find the hints for themselves is core to helping them become more independent learners. We laughed today at the craziness of this video:


























Are some of our learners like this at times? What can we do to help learners develop the ability to solve their own sticking points? How can we scaffold their ability to ask the Polya questions for themselves?
How do we change the mindsets to the growth mindset that Carol Dweck talks of on some of these videos. The TeachingAsLeadership.org Teaching Lessons on Malleable Intelligence resources are available as a pdf.
31Aug 2011


getting ready for the new term.

So what to do? We've cleared through the stock in school and chucked out quite literally half a ton of textbooks from the 1980's and 1990's; the premises staff have done us proud and done some repainting of classroom walls; we're not going to let a water leak get us down (hundreds of ruined books though!)
But we've still got a to-do list as long as your arm. We've spent a week in school now - another ten days should see us ready to go with a week of holiday left to relax and mentally prepare for the coming term.
My thoughts are turning to getting to know my new classes and getting off to an effective and brisk start. Set up some expectations - for myself and for them. Plan for investing some time explaining rules and procedures. Plan lessons in the first few weeks to allow time to have a one-to-one conversation with every pupil to discuss expected progress and set curricular targets. Get to know a bit about what makes each kid tick. Getting to know names is obviously the first priority, but also talking about hobbies, interests, influences and if possible, encouraging pupils to reflect on how they think they learn best. I'll post some ideas about that soon.
In the meantime I'm thinking about how I approach a new year to be as effective as possible and I'll share some thoughts with you. Feel free to join in:

Background context:

  • This summer (among other books) I've been reading:
  • these have precipitated a reflection on how I approach what I'm doing in the classroom and I'd heartily recommend both.
  • Amazon allow a fairly useful taster of the style and content of both books if you follow the links above.
  • TeachingAsLeadership.org has some excellent resources for teachers of all subjects, age ranges and experience levels (although the materials were originally developed as a summary of best-practice among the first year trainees on the Teach for America graduate training program).

Setting targets

  • In the context of planning for the new term, the following sub-sites are an excellent starting place:
    • Set Big Goals discusses setting ambitious (maybe even hilarious?!) progress targets. The effect of teacher expectations has been know for over forty years: Rosenthal and Jacobson (1968) demonstrated that how the teacher perceived the outlook for progress influenced the outcome, especially for younger children: a summary of their work Pygmalion in Schools is reproduced in this psychology course reader: What You Expect Is What You Get and another in Teacher Expectations for the Disadvantaged

Creating an effective learning space

  • Apart from chucking out old text books we don't use anymore and getting some graffiti painted over, is there more to creating an effective learning space?
  • Has anyone else been watching the Channel 4 television series on architecture: 'The Secret Life of Buildings'? With the funding falling out of Building Schools for the Future in the UK, but after the summer riots some may question whether urban architecture and environment have contributed to a sense of alienation, and whether we can afford to change things.
  • It got me thinking - what's the research base around designing a healthy and successful classroom environment? Muijs and Reynolds (2011) say a few things about the physical environment (pp131-132) and seating arrangements (pp103-105), but not much about wall-display, paint color, use of fragrance, acoustics, etc. Few of their opinions (unusually in this well-referenced book) in this section quote hard research. Does anyone know any?
  • The Open University spin-off to the series is all about architecture in education. Debate: What makes for good design in school buildings?
  • The Invest Students and Their Families section of Teaching as Leadership has some ideas about displays that get to the point about creating a purposeful team approach to learning.

Rules and routines

  • One of the things that brought me to writing this piece was coming across a video beth oconnor had prepared to talk through in detail exactly how to label each divider in pupils' folder/notebook (it was deleted within hours, sadly) ... now this may be taking preparedness to an extreme, but it made me wonder what routines do I want to instill in my classroom this year and how can I support really efficient and effective teaching by getting the little habits right?
  • Establishing Rules and Classroom Procedures are also given consideration in Teaching as Leadership.

15 August 2011

david_wiley_thumb.jpg
david_wiley_thumb.jpg
David Wiley's fascinating lecture 'Openness, Learning Analytics, and Continuous Quality Improvement' discusses why using wikis and creating open courses and resources that permit reuse, redistribution, revision and remixing could be the key to improving learning when combined with a formative analysis of how learners use them. This makes an interesting parallel with the course-evaluative mode of AfL discussed by Dylan Wiliam below. In the light of this lecture, we're exploring the use of Google Analytics to see if we can find out more about how users use this wiki.

This lecture is one of the high quality presentations from the ELI 2011 annual meeting an event organised by Educause "a nonprofit association whose mission is to advance higher education by promoting the intelligent use of information technology."

horizon_report_thumb.jpg
horizon_report_thumb.jpg
A related resource is the Horizon Report 2011 which categorizes the likely trends in learning technologies over the next few years.


sei_thumb.jpg
sei_thumb.jpg
Educause have a project called Seeking Evidence of Impact which aims to answer the question: "What evidence do we have that [these] changes and innovation are having the impact we hope for?" There's a substantial list of resources about learning technology effectiveness.

bloom_thumb.jpg
bloom_thumb.jpg
Andrew Church has devoted his wiki edorigami.wikispaces.com to reappraising Bloom's taxonomy for a digital world. Have a look at the impressively scholarly article bloom's Digital taxonomy v3.01.pdf . Andrew has much to say about what he calls 21st Century Pedagogy and to encourage you to look here's one of his simple, but informative images:
21st-c-pedagogies-start1.jpg
21st-c-pedagogies-start1.jpg



dylan_wiliam_thumb.jpg
dylan_wiliam_thumb.jpg
Dylan Wiliam's evangelical work on AfL (assessment for learning) has changed many classrooms and schools including ours. The underlying idea of formative assessment is "(1) establishing where learners are in their learning, (2) where they are going, and (3) how to get there."[1] The ncetm made a podcast of an interview with Dylan about what subject leaders need to know about AfL in mathematics teaching.

A simple idea about improving questioning: 'pose, pause, pounce, bounce' in this clip:
This is just one of dozens of education videos at Solution Tree's YouTube channel. The Solution Tree site is worth a visit too.


More ideas:






  1. ^ Devising learning progressions, Siobhan Leahy & Dylan Wiliam