Elephants, Butterflies and Moths in the Amazon Rainforest: High Epistemic Quality for Equitable Learning in the Mathematics Classroom

Transcription

1 Elehants, Butterflies and Moths in the Amazon Rainforest: High Eistemic Quality for Equitable Learning in the Mathematics Classroom Brian Hudson TEPE 2016 Conference University of Malta 20 th May 2016

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3 Presentation informed by research outlined in two key research aers Hudson, B. (2015) Butterflies and Moths in the Amazon: Develoing Mathematical Thinking through the Rainforest, Education and Didactique, Vol. 9, Issue 2, htt://educationdidactique.revues.org/2322 Hudson, B., Henderson, S. and Hudson, A., (2015) Develoing Mathematical Thinking in the Primary Classroom: Liberating Teachers and Students as Learners of Mathematics, Journal of Curriculum Studies, Vol. 47, Issue 3, htt://dx.doi.org/ /

4 Structure of the resentation Equitable Learning Background context the Develoing Mathematical Thinking in the Primary Classroom (DMTPC) roject The Elehant in the Classroom Butterflies & Moths (and siders!) in the Amazon rainforest Eistemic Quality How high eistemic quality is a necessity for equitable learning in the mathematics classroom. Whose interests are being served by the ush towards high stakes testing and summative assessment?

5 Equitable learning UNICEF/UNESCO reort on the Global Thematic Consultation in the Post-2015 Develoment Agenda stresses education as a fundamental human right. The reort calls for two main education secific goals to be addressed as art of the future develoment framework: equitable access and equitable quality education. We define equitable learning (Hudson et al, 2016) as learning that roduces educational justice ( Bildungsgerechtigkeit ), that enables students to overcome societal limitations of access to and success in education, fosters subject autonomy and allows for the develoment of articiatory cometences for life in society. Hudson, B., Loquet, M., Meyer, M. and Wegner, A. (2016) Equitable Learning in France, the United Kingdom, and Germany An Emirical Research Project on the Process of Schooling and Instruction in Euroe, (Work in rogress). Sayed, Y. (2013) Envisioning Education in the ost-2015 Develoment Agenda: Reort of the Global Thematic Consultation on Education in the Post-2015 Develoment Agenda, UNICEF/ UNESCO.

6 Develoing Mathematical Thinking in the Primary Classroom (DMTPC) Project Funded by the Scottish Government ( ) Collaborative develoment of a Masters level course for teachers involving a technology enhanced blended learning aroach. Piloted with a grou of 24 ractising rimary teachers from the local education authorities of Dundee, Fife, Angus and Perth & Kinross.

7 Rationale for the roject Most mathematics lessons in Scotland still tend to feature some form of teacher-led demonstration followed by children ractising skills and rocedures from a commercially roduced scheme (SEED 2005). These findings were confirmed by TIMSS (IEA 2008) which found that 72% of both P5 and S2 uils were taught using a textbook as the rimary resource comared to the international average of 65% and 60% resectively. Scottish national surveys of achievement in 2009 and 2012 also reorted that uils using textbooks and working quietly on their own was the most common form of activity in mathematics classes in Scotland. IEA (2008) Trends in Mathematics and Science Survey 2007 (Lynch School of Education, Boston College: International Association for the Evaluation of Educational Achievement). Scottish Executive Education Deartment (2005) Assessment of Achievement Programme: Seventh Survey of Mathematics 2004 (Edinburgh: Scottish Executive Education Deartment)

8 Design of the course of study 19 Setember 2011 Online module oens 24 Setember 2011 Worksho 1 10:00 16:00 26 October 2011 Twilight session 1 16:30 19:30 7 December 2011 Twilight session 2 16:30 19:30 4 February 2012 Worksho 2 10:00 16:00 23 Aril 2012 Assignment submission 8

9 Outline structure: three key questions, key texts and an action research roject Key questions n What is mathematics? n What is mathematical thinking? n What is good mathematics teaching? Key texts n Joe Boaler (2009) The Elehant in the Classroom n John Mason et al. (2010) Thinking Mathematically it s OK to get stuck! Action research lan and roject as the module assignment 9

10 The Elehant in the Classroom I have called this book The elehant in the classroom because there is often a very large elehant standing in the corner of maths classrooms. The elehant, or the common idea that is extremely harmful to children, is the belief that success in mathematics is a sign of general intelligence and that some eole can do maths and some can t. Jo Boaler

11 Design research framework 11

12 Research Questions Main Study 1. What are the teachers ercetions concerning their levels of confidence and cometence in relation to teaching mathematics? 2. What are the teachers ercetions concerning their attitudes and beliefs in relation to mathematics as a subject? 3. What are the teachers exectations of the imact on uil learning arising from this course of study? 4. How do these ercetions and exectations change as a result of articiating in this course of study?

13 Methods and data sources Main Study Pre-trial survey of the teachers ercetions (n=26) Pre-trial interviews with a samle of articiants (n=4) Post-trial interviews with a samle of articiants (n=4) Post-trial survey of the teachers ercetions (n=15) Action research reorts from teachers (n=10) One action research reort as the exemlar for this resentation

14 One teacher s Action Research Project To what extent does toic-based mathematics allow children to demonstrate their mathematical thinking? Entry Attack n To what extent do toicbased mathematical questions allow children to verbalise their thinking? n What effect does toicbased mathematics have Review on children s levels of engagement? Ref: Mason, Burton and Stacey (2010)

15 Anna s Action Research Project on The Rainforest Primary 5/6 uils Time: 3 weeks Measurement mainly length and weight First question: How could we measure these lifesized insects accurately? Brazilian Huntsman sider

16 Questions for uils to exlore, analyse and record Four questions corresonding to Lessons 1 to 4: 1. How could we measure these life-sized insects accurately? 2. How could we mark out the different layers of the rainforest in our layground? 3. Can you comare the length of the River Tay and the Amazon River? 4. Is there a relationshi between the weight of an animal and the layer it lives on in the rainforest?

17 Methods of data collection Data was collected in three ways: n Children were recorded informally during conversations with eers, n Quotes were taken during class feedback sessions, and n After the sessions children were informally asked to comment on the lesson and this feedback was recorded. Also live observations were made and various arts of the activities were filmed to watch and analyse later.

18 Lesson 1: Measuring moths and siders

19 Engagement with the activity all uils were actively engaged. This art of the lesson clearly arallels the Entry Phases described by Mason et al. (2010) (Anna) During the measuring rocess, the children were asked to verbalise their thinking and demonstrate their measuring. Most children chose to write their measurements comletely in millimetres only. One Primary 6 girl wrote short sentences to describe her measurements and when asked why, she said, It s easier to see the numbers this way. It s weird, they re all (the sider s legs) different lengths mostly..

20 Data Analysis of Lesson 3: Comaring the length of the River Tay and the Amazon John (Year 5 boy) stated, I drew the Amazon and the River Tay on my iece of aer. I measured the aer and it was about 300 millimetres so we narrowed it down and got that every 5 centimetres was about 1000 kilometres. The River Tay is only 186 kilometres so it s only that size (Pointing to the art of their diagram labelled River Tay.)

21 Tracy s intervention The other children in the class were very interested in this and one Year 6 girl (Tracy) commented: The Tay is tiny comared to that, you could fit like, a hundred of the Tay into the Amazon! Anna notes how this comment was exlored and extended leading to her question: How many times would the Tay fit into the Amazon River?

22 Some reflections The discursive element of this lesson roved to be a very effective tool to assess the uils understanding and mathematical thinking. (Anna) The question develoed tremendously throughout the lesson due to their knowledge of the subject, and their ability to visualise the roblems, the mathematics became accessible leading an evolution in mathematical thinking for all. (Hudson, 2015)

23 Eistemic quality This rocess of mutation (Boaler, 2009) reflects the rocess of didactic transosition, which changes the mathematical knowledge rofoundly and which leads to the eistemic quality of the subject becoming degraded as it is transosed into school mathematics. Hudson et al. (2015) describe this mutated or degraded version of mathematics as mathematical fundamentalism and as being of low eistemic quality. It is characterised by an aroach that resents the subject as infallible, authoritarian, dogmatic, absolutist, irrefutable and certain and which involves rule following of strict rocedures and right or wrong answers. In contrast high eistemic quality is characterised by an aroach which resents mathematics as fallible, refutable and uncertain and which romotes critical thinking, creative reasoning, the generation of multile solutions and of learning from errors and mistakes. (Hudson et al., 2015) 23

24 The sectrum of eistemic quality in mathematics from low to high Low eistemic quality Infallible and authoritarian Dogmatic and absolutist Irrefutable and certain Strict rocedures Rule following Getting right and wrong answers Boring and de-motivating Inducing fear and anxiety Alienation from the subject itself Reinforced by excessive high stakes testing and summative assessment High eistemic quality Fallible and liberating Critical thinking, growth & change Refutable and uncertain Multile solutions Creative reasoning Learning from errors and mistakes Engaging and motivating Enjoyable and fulfilling A creative human activity Suorted by diagnostic feedback through formative assessment for learning 24

25 High Eistemic Quality for Equitable Learning The findings highlight ways in which the framing (Bernstein, 2000) of articular asects of the traditional curriculum had an oressive imact on learners in the ways that suressed creativity and limited the exercise of learner autonomy by both teachers and uils. The weaker framing of Curriculum for Excellence shifted the locus of control over the selection, sequencing and acing of what counts as legitimate knowledge towards these teachers. Teachers own exerience as learners of mathematics highlights the imact of the strong framing over the criteria for the formal assessment system, esecially at secondary school level. On-going challenge for continuing reform is the alignment of criteria for evaluating or assessing of the formal assessment system with the aims and uroses of the formal curriculum.

26 Whose interests are being served by the ush towards high stakes testing and summative assessment?

27 Not those of children who are eager to exlore the world and learn!

28 Thank you for your attention