RESEARCH PROPOSAL Bill Kerr update 9th October 2016

There are a few different strings here that come together possibly.

CM, indigenous classroom helper, mentioned she was keen to complete teacher training and keen about maths but a little fearful of grasping algebra.

Since that initial conversation other indigenous classroom helpers have come on board (SH, AL) and the coverage has expanded to the maths content of year 9 NAPLAN.

I would like to assist the indigenous helpers who want to become teachers to grasp maths, along with the more general day to day teaching of taking the students down that path as well. The idea of helping to train the indigenous helpers is particularly appealing, in terms of me feeling that I would be helping “make a difference”.

Further reflection leads me to think there are 4 possible maths pathways:
1) DI / EMM / JUMP. Direct Instruction (Zig Engelmann) / Elementary Maths Mastery (Rhonda Farkota) / Junior Undiscovered Math Prodigies (John Mighton). I am already using parts (modified) of the EMM approach
2) Indigenous culture. Maths that links to elements of indigenous culture. There is a significant literature about this, eg. the work of Dr Chris Matthews, Dr Alan Bishop, Dr Bronwyn Ewing for starters, but I have yet to trial it.
3) Computer microworld. Teaching maths through multimedia / computer coding using the Scratch software, the most recent incarnation of Logo. I have a very strong background in this method.
4) Home grown. Quite often because I feel the textbooks are inadequate I develop my own maths activities to better fit where the class is at. eg. Pythagoras activity requiring the construction of different triangles and modified milk carton volume activity were promising.

Two way street post mortem conversation. A lesson plan is formulated by the teacher / researcher to achieve a learning goal for a class using one or a combination of the above methods. The lesson is taught, with an indigenous helper usually present. Afterwards, a post mortem conversation is held to evaluate effectiveness and possible improvements. This iteration is repeated many times. A mutual exchange of skills and cultural knowledge will take place during this conversation. As the learning process develops the indigenous helper can be invited to trial their own experimental lessons. Both sides of the equation should keep learning journals reflecting on what they have learned and their ideas for the future.



Dan Willingham, Why Don't Students Like School, understands the core issues about learning. Ch 4 Abstract Ideas; Ch 5 Drill; Ch 6 Real Scientists Ch 8 Slow Learners

Liping Ma. Knowing and Teaching Elementary Mathematics. She introduces the concept of Profound Understanding of Maths Fundamentals PUMF). She has worked out very clever ways of measuring this in individual teachers and has come to a most surprising conclusion, that Chinese teachers have a PUMF which their American counterparts lack, despite the latter being trained for 4 more years or more.

Why Warriors Lie Down and Die by Richard Trudgen. This book focuses on health issues of the Yolnu in Arnhem Land. However, it is really a book about communication or rather poor communication between the indigenous and Balanda (whites). Communication breakdown occurs in (1) Language (2) World view (3) Culture. The strength of the book is that the author has crossed over and can see things from the Yolnu perspective. His many case studies of communication breakdown from his personal involvement in helping Yolnu are incredibly impressive. Very relevant to indigenous maths since it is all about communication.


Bill Kerr. The Place of Behaviourism in Schools (for example in the teaching of Quadratics)
This documents my conversion to pragmatic behaviourism (because it works) after I wrote a drill program in Logo to teach quadratics to year 10s in 1998.

Dan Dennett. Skinner Skinned. Skinner is a much maligned behaviourist. It is important to get the criticism of him right. Dennett, it appears to me, is one of the few thinkers to do the hard yards on this question.
Skinner's enemy is mentalism, that talking about people's behaviour using terms such as beliefs, desires, ideas, hopes, fears, feelings, emotions is not allowed because it is not scientific.

Dennett, however, sees a positive role for these mentalist idioms in explaining behaviour / psychology / mind. So this essay, while acknowledging there is some point to Skinner's objections to mentalism, is about clarifying where mentalism is useful and where it stops being useful and becomes unscientific.

Engelmann, Siegfried and Carnine, Douglas. Could John Stuart Mill Have Saved our Schools? (2011)

Bron Ewing. Direct Instruction In Mathematics: Issues For Schools With High Indigenous Enrolments: A Literature Review (2011), 29pp


1) DI / EMM / JUMP.

Engelmann, Siegfried and Carnine, Douglas. Could John Stuart Mill Have Saved our Schools? (2011)

Engelmann, Siegfried; Kelly, Bernadette; Engelmann, Owen. Essentials for Algebra: A Direct Instruction Approach (Textbook) 2008

Engelmann, “Zig”. Teaching Needy Kids in Our Backward System: 42 Years of Trying (2007)

Ewing, Bronwyn.
      • Direct Instruction In Mathematics: Issues For Schools With High Indigenous Enrolments: A Literature Review (2011), 29pp

Explicit And Direct Instruction For Indigenous Students: A Case Study In Meme Warfare, Version 2 Bill Kerr 24th December, 2013

Farkota, Rhonda. The Effects of a 15-minute Direct Instruction Intervention in the Regular Mathematics Class on Students’ Mathematical Self-efficacy and Achievement. PhD thesis, 2003
(I downloaded a copy from the ACER site in 2012 but it is no longer available there)

Farkota, Rhonda. Junior Elementary Maths Mastery (JEMM) 2010

Farkota, Rhonda. Junior Elementary Maths Mastery + (JEMM+) 2016

Farkota, Rhonda. Elementary Maths Mastery (EMM) 2000

GGGA Academy Standing Committee presentation v08 06032016.pdf

Mighton, John. The Myth of Ability: Nurturing Mathematical Talent in Every Child (2003)

Pearson, Noel. Radical Hope.

Pearson, Noel. Up From the Mission: Selected Writings (2009)

Review of school education in Aurukun: School Improvement Unit June 2016

2) Indigenous culture.


      • print and / or review to study, blog, wiki etc.

Multiple authors
      • Contextualising the teaching and learning of measurement within Torres strait islander schools
Bronwyn Ewing, Tom Cooper, Annette Baturo, Chris Matthews and Vicky Sun
(NB section where indigenous and non indigenous teachers answer the question: What do you believe mathematics to be in Torres Strait Islander culture and the wider community beyond the Torres Strait Islands? p. 18)

Warren, Elizabeth, Cooper, Tom, & Baturo, Annette R. (2009) Bridging the educational gap : Indigenous and non-Indigenous beliefs, attitudes and practices in a remote Australian school.
The project used mathematics as the vehicle to improve Indigenous students' learning outcomes by enhancing their beliefs, attitudes and practices. The chapter reviews the literature relevant to the relationship between beliefs, attitudes, practices and performance, outlines the project generally and, for the particular school, describes findings with regard to beliefs and attitudes, and discusses the implications for future intervention projects.

Allan Luke
Luke, Allan (2009) On Indigenous education. Teaching Education, 20(1). pp. 1-5
We – and most in the field – begin from that crucial sociological and cultural caveat: that educational policies, plans and practices in and of themselves by definition cannot ‘compensate’ for destructive material and cultural conditions, genocidal histories and deteriorating economies (Luke, 2006). However, as these papers show, there is evidence that some centralized approaches to policy can have significant collateral effects on conventionally measured achievement, on community culture, and on the lives of learners and teachers.

Dr Chris Matthews,
background information, also contains further links

      • podcast
Dr Chris Matthews joins Amy McQuire on the programme to talk about why its important to open up a new conversation about how we teach maths and science to our kids, and how Aboriginal people had our own sophisticated system of mathematics

      • Prof Tom Cooper
Professor Tom Cooper sets out the essential elements of the pedagogy underlying YuMi Deadly Maths. Tom presents the four elements of the RAMR cycle which encourages teachers to begin with reality, abstract from this to the mathematics, and then reflect back to the real world.

Dr Alan Bishop,
Teachers' Mathematical Values for Developing Mathematical Thinking Through Lesson Study.

Dr Bronwyn Ewing
See various papers by Bronwyn Ewing at the QUT repository:

      • Direct Instruction In Mathematics: Issues For Schools With High Indigenous Enrolments: A Literature Review (2011), 29pp

Prof Grace Sarra
Grace is an Associate Professor at QUT, Caboolture Campus. She is of Aboriginal and Torres Strait Islander heritage. Grace's areas of interest are Indigenous education, values education, social justice, pedagogy and practice, and school change and leadership.

DL Publicaciones
      • Thinking about Numbers (not dated)
Thinking About Numbers follows the conversation of a group of classmates living in a small rural village who, with the help of their teacher, explore mathematical concepts such as accuracy, one-to-one correspondence, sets, and negative and irrational numbers. Over the course of their discussions the group considers the applications of these concepts to day-to-day life, investigating as they do the meaning of justice, service, and progress. In this way the book seeks to help young people not only further their capability of making numerical statements about reality around them but also think about the social dimension of statements regarding the world. The book is intended for youth aged 11 and upward. (55 pages, 8½" x 11")

About the organisation:
DL Publicaciones (DLP) is a nongovernmental organization, currently based in Colombia, dedicated to the dissemination of educational materials designed to enhance the moral and scientific capabilities of individuals, communities, and their institutions. At this stage in its evolution, DLP is primarily occupied with the publication and distribution of a series of textbooks for junior youth—young people from 12 to 15 years old, whose potential to grow into active promoters of the well-being of their communities is so great. In developing the series, DLP connects with organizations around the world that work with junior youth, to give rise to materials that are at once engaging and transformative.

3) Computer microworld.

Papert, Seymour. Mindstorms.
Papert, Seymour. The Children's Machine.

Resnick, Mitch.
A Different Approach to Coding: How Kids are Making and Remaking themselves from Scratch (2015)

Harvey, Brian.

Kerr, Bill
Papert's Ideas: Mainly From Mindstorms - Bill Kerr, October 1991

Educational Software: Designed By Kids For Kids Bill Kerr, Jan., 1994, Paralowie R12 School

Invitation to Immersion. Curriculum Perspectives. Vol 17, No. 3 September1997

Quadratics Software Evaluation November 1996

The Place Of Behaviourism In Schools (for instance, in the teaching of Quadratics) rewritten January 1998

4) Home grown.

5) General
Dennett, Daniel. Brainstorms: Philosophical Essays on Mind and Psychology (1981)

Fleming, John & Kleinhenz, Elizabeth. Towards a Moving School: Developing a Professional Learning and Performance Culture (2007)

Freire, Paulo. The Politics of Education (1985)

Friere Institute: Education, Empowerment, Transformation.

Geary David C (1995) Reflections of Evolution and Culture in Children's Cognition: Implications for Mathematical Development and Instruction. American Psychologist.

Hofstadter, Douglas R. Variations on a Theme as the Crux of Creativity. In: Metamagical Themas: Questing for the Essence of Mind and Pattern (1985)

Jarrett, Stephanie. Liberating Aboriginal People from Violence. (2013)

Kay, Alan re. Non Universals:

Kahneman, Daniel. Thinking, Fast and Slow (2011)

Ma, Liping. Knowing and Teaching Elementary Mathematics: Teachers' Understanding of Fundamental Mathematics in China and the United States (1999)

Nunes, Terezinha and Bryant, Peter. Children Doing Mathematics (1996)

Nussbaum, Martha. Creating Capabilities: The Human Development Approach (2011)

Sutton, Peter. The Politics of Suffering: Indigenous Australia and the end of the liberal consensus (2009)

      • Trudgen, Richard. Why Warriors Lie Down and Die: Towards an Understanding of why the Aboriginal People of Arnhem Land face the greatest crisis in health and education since European contact (2000)

      • Willingham, Daniel T. Why Don't Students Like School? (A cognitive scientist answers questions about how the mind works and what it means for the classroom) 2009