Middle School Class


Building capacity to teach multiplicative thinking

There are many options for professional learning about multiplicative thinking. They range from short introductory sessions (1 to 2 hours) as part of staff PL days to a year-long program involving multiple days. We understand that a school’s choice of PL model is heavily dependent on its capacity to provide teacher relief for participants given the expense. Hence, we offer a variety of options and we are open to negotiation for any other forms of PL. We offer the following:

  • ‘Scratching the Surface’
    Introductory session up to two hours for a staff PL day or other similar occasion. This is basically an overview of multiplicative thinking and explains some of our findings and what we can offer. Cost is $200.

  • ‘A Little Bit More’

  Half-day session of 3.5 to 4 hours, which includes the above, plus provides an overview of our diagnostic assessment instrument and a look at some of our teaching resources. Cost is $400.

  • ‘Getting Serious’

One or two full days of approximately six hours which includes the above, plus a detailed expose of our diagnostic instrument and teaching tasks for the first part of our multiplicative thinking model. The aim of this section is to equip teachers to administer the diagnostic instrument, analyse the results, and plan remediation using our specially designed teaching tasks. We would follow-up this work with an online or face to face ‘critical friends’ meeting to discuss findings from the diagnostic assessment.
Cost $600 per day. On the basis of what was done, schools might then opt to commit to the full program (see below)

  • ‘The Full Package’

This is based on the ‘teacher-as-researcher’ model, which is a comprehensive program that we developed directly from our research work. It follows on from the previous level of exposure (‘Getting Serious’). Essentially, this provides teachers with the tools to understand the complexity of multiplicative thinking based on the model we developed and then to analyse the knowledge of their own students through the use of the entire diagnostic assessment tool, the Multiplicative Thinking Quiz, that we used during our research. Teachers then work with a wide range of teaching tasks that we have developed and which directly address specific issues exposed by the diagnostic assessment. Ideally, we would like to work with teachers over a full year using the following structure. Given that the school terms are different in Australia/New Zealand and the United Kingdom, the structure would be somewhat different for the UK, but would include the same elements.

Commencement of school year (Australia Term One)

2 full days to introduce multiplicative thinking, consider some research results, learn about the diagnostic tool and how to analyse results, and work through key teaching tasks. This is what is included in the ‘Getting Serious’ package).

Next 8-9 weeks (Australia Term One)

Teachers administer the diagnostic tool and analyse results for first part of the multiplicative thinking model. Select Key Tasks and Supplementary Tasks for follow-up teaching

Critical Friends on-line meeting of approximately one hour at approximately the half way point

End of Australia Term One

Full day session to discuss the work done so far. This process is repeated throughout the school year. Using the Australian school year as an example, that process would occur each term. During that time, each of the four parts of the multiplicative thinking model are covered. The only change is that for the 2nd, 3rd, and 4th terms, only one day is required at the commencement of the term. In summary, the time commitment for ‘The Full Package’ is 9 full days (cost $5400) and 4 one-hour Critical Friends on-line meetings (no charge).

Cost Reduction Options

Clearly, it is ideal for schools to send a group of teachers to ‘The Full Package’ option. However, as noted above, we understand the costs of funding relief teachers. If schools are able to organise internal relief, then sending a group of teachers may be more viable (say one or two teachers from each of Year Three, Four, Five, and Six).We also promote the ‘train the trainer’ option, where one or two teachers from a school attend the PL and return to school as ‘experts’ so that they can provide professional learning for their colleagues. We would provide additional support for schools wanting to use this option.

Availability of our Teaching Resources

Schools committing to ‘The Full Package’ receive free access to the full range of our teaching and diagnostic resources. These are otherwise available for purchase through paying an initial one-of ‘joining fee’, followed by a yearly subscription.