Monday, 29 September 2008

Film industry numeracy resource - is it RICH or poor?

I've now had a chance to try out the Guardian film industry pullout that I wrote about on July 22nd. If you keep reading you'll also be able to locate a new Level 2 place value worksheet that I created last week to accompany it (can also be used independently). However, due to embarking upon the Level 5 numeracy diploma, I've now decided it might not be as good as I thought it was!

Level 2 place value session
The main topic of my recent Level 2 session was large numbers (i.e. place value) and I began with one of my favourite 'large number' sites, David Levine's world population clock at which can be used as a prompt for all kinds of questioning and board work. I recommend pausing it by selecting today's date (or maybe one of your student's birth dates?) if you are going to ask students to translate the digits into words - otherwise the whirring last few digits can be very off-putting.

I also wanted (in order to tick the 'equality and diversity' box on the lesson plan) to use a more complicated population clock (different countries, statistics for males and females, etc.) but unfortunately the numbers were too small for clear display on the smartboard so I had to move swiftly on to the film industry poster.

It was obviously not my day for using the smartboard. Again, I had visibility problems: the PDF did not display as clearly as I had hoped and only the large graphics and figures were readable. Fortunately I had printed off an A3 version and we made do with a couple of A3 photocopies (and the original newspaper) shared around the class. (I'm lucky enough to have an old A3 printer at home; don't bother trying to print it on A4 - you won't be able to read it.)

Most of my questioning was based on interpreting the data in the large pie chart or on asking volunteers to write numbers on the poster as whole numbers (e.g. writing 54.2 billion as 54,200,000,000). At this stage, if your students require further input you might find the Level 2 place value chart useful. You can find it on the Level 2 number section of skillsworkshop.

I then used my new worksheet to check and consolidate individual skills. The PDF version is available here or you can click the picture left for a quick thumbnail preview (don't look for it on skillsworkshop as I haven't yet had time to list it - it will appear there during October).

Having now marked 14 worksheets I can report that, as suspected, the extension question caused the most difficulties. In most cases the initial subtraction was OK but there was a lot of difficulty translating the answer of 0.11bn to millions, the most common answer being 11 million rather than 110 million. Another unpopular question asked 'How are the actors listed?' (The answer was 'alphabetically').

However, I was pleasantly reassured by the grasp of maths terminology and symbols: descending and ascending order, greater than and less than - no problems!

Level 5 Numeracy Diploma
In an effort to balance up my numeracy and literacy teaching qualifications (currently weighted towards literacy) I've just started working towards the Level 5 Additional Diploma in Teaching Mathematics in the Lifelong Learning Sector (commonly known as an ADTLLS).

I've really enjoyed the first two sessions but the bad news (for me, not necessarily for you!) is that last week's learning has left me a little deflated. We were introduced to the RICH task concept and now I'm not at all happy with my film industry worksheet. You can read about rich mathematical tasks on the NRICH web site. To borrow another phrase from this site I think my worksheet needs HOTting up. HOTS is an acronym for high order thinking skills and again you can read more about it on NRICH.

However, despite my smartboard display problems I've decided that all is not lost. My introductory warm-up, firing questions and attempting to promote discussion based on the poster and the world population statistics, might not have been very RICH but I don't think it was excessively poor. There's no time left today to get into a discussion about what makes a task or resource RICH. However this thought is now always going to be in my head. The film industry resource is aimed at Level 2 but I'm also very interested in applying RICH and HOTS to my Entry 1 numeracy class. I feel that this may prove to be even more of a challenge.

And I haven't given up on the film poster yet: the original has been sent to the Resources Dept for A2 laminating and will be resurfacing later in the year for work on percentages and representing data.

The poster is still available on the Guardian site as a PDF file.

Sunday, 14 September 2008

Worksheet Genius for instant Entry and preEntry resources

I've just added a wonderful new link to the 'Other sites with printable resources' links page. This page lists about 200 sites that provide printable literacy and/or numeracy worksheets.

Worksheet Genius creates instant randomized worksheets. It's the work of a generous Midlands teacher, Simon Currigan, and all worksheets are completely free - no strings attached! Like Wordle, it's a Java based application - so you may need to speak nicely to your college IT staff and get Java installed on the machines you use in your office or classroom.

For Entry level spelling and phonics there are masses of word lists (or add your own) that can be used for flashcards, bingo games, word searches and much more. Other word lists cover common spelling rules such as -ed endings, take off the 'y', prefixes, etc.

The phonics sheets come with pictures - the clip art is aimed at children but most is also suitable for adults. If you don't like the clip-art/words that appear on your screen, simply click the 'Apply genius' button to make a brand new sheet. You can also create mixed up sentences, anagrams and really useful slide shows which are perfect for instant Look-Say-Cover-Write-Check work if you select the 'add a blank slide between each word' option. Note that the clip art can also be downloaded and used independently - very handy if you want to create your own linked materials.

The numeracy options are just as good. The abacus style place value sheet (top right) is one of my favourites and is earmarked for my Entry 2 numeracy group.

Again, each type of numeracy worksheet can be fully customised: clocks can be set from 1 hour to 1 minute intervals; subtraction can be horizontal or vertical, with or without carrying; and so on.

For preEntry milestone 8 you could use 'count and colour' (up to 12 items) or picture versions of adding on 1, 2 or 3.

Several options are also suitable beyond Entry level: percentages, division with or without remainders, long multiplication, etc.

If you have any specific ideas for using Worksheet Genius with you literacy and numeracy classes please leave your ideas as a blog comment or contact me by email via

I can't describe everything here so do please take a look.

Saturday, 6 September 2008

Hilda Taba (part 2), Wordle, and numeracy

In one of my earlier posts (Aug 16, 2008) on Wordle I said:
"I reckon this idea could be adapted for numeracy: sorting out maths vocabulary words; ranking measures in order of size; sorting measures into length, weight or capacity; sorting shapes (well, names of shapes) according to properties; etc."

Well, site-contributor Dave Norgate has speedily proved my
point: he's created a set of numeracy Wordles that does everything I wished for and more! There are four Wordles in his resource – covering 2D shapes, maths vocabulary, odd and even numbers, and metric units. Dave has also very kindly provided fill-in charts for two word clouds: one provides a structure for straightforward sorting (maths vocabulary); the other demands sorting followed by ordering (metric units).

Linking this back to my previous discussion regarding Hilda Taba - you might like to think of a Wordle cloud as the collection of data (the first stage or strategy in her model) and Dave's blank charts as the next stage where data is organised so that students can visualise and attain concepts.

The number of ‘phases’ in each stage seems to have been extended since Taba’s work was published in 1971. It varies with each source that I look at (see references at the end this post). Here’s my attempt at a summary – but I make no claim to expertise in learning theory.

Stage 1 (three phases)
Concept formation – collecting data through class brainstorming (maybe into Wordle - see below!), individual lists, answers to questions, etc. 3 phases: list, group, label.

Stage 2
Attaining concepts - organising data using: whiteboard, smartboard, flip chart, fill-in tables, handout, Wordle (more on this below), etc.

Stage 3 (I’m not sure how many phases!)
Develop generalisations, compare, explain, apply principles (predicting).

Anyway – I must wander back to some practical uses of Wordle…

Of course you don’t have to start at Stage 1 - phase 1 (listing) to make use of Taba’s model. All the existing (as of Sept 6th 08) Wordle resources on provide pre-collected data in a word cloud; the words or numbers in the cloud may also be partially grouped. Examples of these include (all kindly contributed by Dave N):
Sorting nouns and verbs (and then listing alphabetically)
Identifying misspelt words
Identifying 2D shapes
Sorting odd and even numbers

In all these cases you are starting at Taba’s Stage 1 - phase 2 or 3. However, you could (assuming you have a PC, data projector and Internet access to Wordle) collect the data live in-class and start at Stage 1 - phase 1.

This can be done through brainstorming and/or careful questioning. Before you start you’ll need a clear objective. What concept do you want students to grasp? It could be naming the properties of 2D shapes, distinguishing between odd and even numbers, recognising metric measures and selecting appropriate units, etc. The questioning is crucial if you want to avoid too many stray words or groups in your Wordle. You’ve got to get the balance right: to prevent a wild goose chase you'll need to elicit plenty of relevant data (words) that allow learners to make connections and ‘get’ (attain) the concept.

I recommend enlisting a willing student to type-in the words – or, even better, pass a wireless keyboard around. If accurate spelling is a prerequisite for your Wordle – get the students to type into a Word document (with spellchecker turned on) and then paste the list into Wordle at the end of the brainstorming session. This also keeps Wordle a secret until the last minute – assuming your students haven’t seen it before!

Now, a great feature of Wordle is that, when using it live, you can delete words one by one from your cloud by right-clicking on them. You can use this to facilitate Taba’s crucial middle stage 2 and whittle your data down to one group.

For example, if you were creating a cloud similar to Dave’s (right) you could firstly delete (or ask students to delete) all the words that are not names of shapes or objects (e.g. addition, weigh, perimeter). This could be followed (amidst much discussion about properties, etc.) by deleting all the names of 3D shapes (for example) until you’re eventually left with a set of 2D shapes. If your group is working at Level 1 or 2 - keep going! The possibilities are endless - ask the students how they could regroup and classify what's left. Perhaps they'll suggest deleting those with more than four sides, or those with only one pair of parallel lines.

Of course, I’m not saying that Wordle is the answer to everything! For more advanced grouping and ordering you may well have to stick to the traditional whiteboard, fill-in table, matrix or chart method – although maybe you could have more than one Wordle going on at once!

I’ll leave you to think about Stage 3 and its generalisations and predictions...

I'm guessing this was taken in the 1950s – Taba was born in 1902

Taba, H., Durkin, M. C., Fraenkel, J. R., & NcNaughton, A. H. (1971). A teacher's handbook to elementary social studies: An inductive approach (2nd ed.). Reading, MA: Addison-Wesley.
Chapter 5 is available online at (I’m not sure if this is a summary or the entire chapter as unfortunately I have not read the original – out of print – I’d love to see it though!).

There's also good clear coverage of Taba's model in Teaching Young Adults (Gill Turner, Joe Harkin, Trevor Dawn) RoutledgeFalmer 2001
This book uses a useful egg timer depiction. I'd better not reproduce it here because of copyright issues but if you search for the book in you can preview various pages including the egg timer page 46.
The book also includes an extended Taba model (page 47). This extended version is great for planning: it's full of imperatives for learning objectives. For example, Stage 1-phase 1 not only suggests list but also collect, find, choose, bring, underline, highlight and tick. It also relates Taba's model to the Kolb / experiential learning cycle (page 48 - also viewable via Google books).