ESH322 Inclusive Mathematics Sussan EvansAT1: Weekly Blog Reflections 059030

What is equity in education and why should we promote it?

Equity in education is a social imperative toward fairness, providing meaningful opportunities for all students by adjusting learning experiences to facilitate achievement of learning goals. The interwoven elements of fairness, opportunities and achievement facilitate equity when society’s values influences education in terms of expectations, teaching standards and curriculum (PPI, 2011). Although individual achievements may vary, equity in education aims for students to reach their full potential and participate in society, strengthening the values of equity and inclusion for the future (MEECTYA, 2008).

Filtering from attitude into action, the systems and standards of education are structured to reinforce values of equity. Overarching documents such as the Declaration of Human Rights influence Australia’s anti-discrimination legislation (United Nations, 2015; DoE, 2005). The national curriculum and professional teaching standards echo these values specifying learning content and capabilities, and what teachers must know and do to

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ensure equitable learning experiences and outcomes (AAMT, 2006; ACARA; 2015).

Making reasonable adjustments towards equity considers each students unique circumstance providing students with an equal opportunity to access and engage with learning experiences (DoE, 2005). Constructivism states that without access and engagement with information there is no learning (Van deWalle, 2007). Students with high ability, disability or disadvantage will have challenges accessing and attending to learning experiences if teachers do not consider their unique perspectives – depicted in Image1 (Wells, 2015).

Equity is having expectations that every student will achieve their unique learning goals (MEECTYA, 2008). Due to the nature of diversity, student achievements will vary, but with equitable opportunities achievements will be personally relevant and aimed at excellence.

Equity in education should be promoted because it benefits society. If equitable learning opportunities and expectations of achievement are provided, students will develop values of equity and an educated population will continue to fuel an equitable society (PPI, 2011).

REFERENCE LIST

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Although equity and excellence are the goals, in his article What_have_we_achieved_in_50_years_of_equity_in_school_mathematics? Jorgensen (2015) indicates more needs to be done to address equity in Australian mathematics education.

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Australian Association of Mathematics Teachers [AAMT]. (2006). Standards for Excellence in Teaching Mathematics in Australian Schools. Retrieved from: http://www.aamt.edu.au/About-AAMT/Position-statements

Australian Curriculum Assessment and Reporting Authority [ACARA]. (2015). Student Diversity: Introduction. Retrieved from: http://www.australiancurriculum.edu.au/studentdiversity/student-diversity-advice

Australian Government. Department of Education and Training [DoE]. (2005). Disability Standards for Education 2005. Retrieved from https://education.gov.au/disability-standards-education

Jorgensen, R. (2015). What Have We Achieved in 50 Years of Equity in School Mathematics? International Journal for Mathematics Teaching and Learning, January 20th p.139 Retrieved from: http://www.cimt.plymouth.ac.uk/journal/default.htm

Ministerial Council on Education, Employment, Training and Youth Affairs [MCEETYA]. (2008). The Melbourne Declaration on Educational Goals for Young Australians. Retrieved from: http://www.curriculum.edu.au/verve/_resources/National_Declaration_on_the_Educational_Goals_for_Young_Australians.pdf

Public Policy Institute of Australian Catholic University [PPI]. (2011). Issues Paper 1: Equity in Education [pdf]. Prepared by the Public Policy Institute of Australian Catholic University for the Independent Schools Council of Australia, April 2011. Retrieved from: www.acu.edu.au/__data/assets/pdf.../Paper_1_Equity_Final_080411.pdf

United Nations. (2015). Universal Declaration of Human Rights. Retrieved from: http://www.un.org/en/documents/udhr/

Van deWalle, J.A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson Education Inc.

Wells, J. (2015). ESH320 Lecture: Diversity and Inclusion - Week 6: Differentiated Instruction and Inclusion [Video]. Retrieved from: ttps://mymediaservice.utas.edu.au:8443/ess/echo/presentation/35e10ce1-c72b-4624-be62-e197e8b10db7

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Teaching inclusively means never seeing students learning needs as ‘senseless to deal with’ no matter how mysterious. Whilst little research has been done to explain dyscalculia, explorations on its prevalence, causes and presentation do exist and convey that it can be accommodated with explicit strategies.

Teachers have a moral and professional responsibility to have awareness of and strategies to address difficulties that impact student’s learning, whilst also considering each student’s unique needs (Milton, 2001; Ward, 2015).

Dyscalculia is a Specific Learning Disorder in mathematics occurring in 3-6% of primary-school-aged children (dyscalculia.org, 2015; Price &Ansari, 2013). It is neurodevelopmental with a prevalence of co-morbidity with dyslexia and ADHD (Goss-Tsiri, Mannor,& Shalev, 1996; Wilson & Dehaene, 2007). Dyscalculia can be inherent or acquired, but its exact cause remains unresolved (Michaelson, 2007). Effectively, diagnosis requires that all other possibilities be ruled out. It presents as students of average intelligence with no diagnosis of developmental, neurological or motor disorders, performing two years below their grade-level in mathematics (dyscalculia.org, 2015; Goss-Tsiri, Manor & Shalev, 1996).

Dyscalculia affects number sense, perception of magnitude and relationships between numbers and

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their various representations (Ansari, &Karmiloff-Smith, 2002; tvoparents, 2010). All other numeracy concepts build from number sense, therefore teachers cannot move forward until students have developed this (Messenger, Emerson, &Bird, 2007).

Learning experiences that link language with a variety of number representations – symbolic and numerical – such as card games and coloured MAB’s, develop stronger connections between number names and values (Messenger, Emerson, &Bird, 2007; tvoparents, 2010). Activities that build approximate number sense, including dot arrays, also appear effective in the development of magnitude and number relationships (Van Herwegen, 2014).

Being ‘bad at math’ is perceived as an acceptable incapacity, see images below. Given its frequency and the challenges in diagnosing dyscalculia, students who achieve everywhere except math could potentially have their needs disregarded. However, everyone deserves the opportunity to become numerate (DoE, 2005). Explicit strategies can address dyscalculia and develop number sense, subsequently building a strong foundation for achievement in mathematics.

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Reference ListAnsari, D., and Karmiloff-Smith, A. (2002). Atypical trajectories of number

development: a neuroconstructivist perspective. Trends in Cognitive Sciences, 6 (12), p.511-516

Australian Government. Department of Education and Training [DoE]. (2005). Disability Standards for Education 2005. Retrieved from: https://education.gov.au/disability-standards-education

Dyscalculia.org. (2015). Diagnosis>Law: DSM-V Codes. Retrieved from: http://www.dyscalculia.org/diagnosis-legal-matters/dsm-v-

Gross-Tsiri, V., Manor, O., and Shalev, R.S. (1996). Developmental dyscalculia: prevalence and demographic features. Developmental Medicine and Child Neurology, 38, p.22-38

Messenger, C., Emerson, J., and Bird, R. (2007). Dyscalculia in Harrow. Mathematics Teaching, 204 (Sep), p.37

Michaelson, M.T. (2007). An overview of dyscalculia: methods for ascertaining and accommodating dyscalculic children in the classroom [online]. The Australian Mathematics Teacher, 63 (3), p.17-22

Milton, M. (2001). Who helps children who have learning difficulties in numeracy? Australian Primary Mathematics Classroom, 6 (3), p.6-10

Price, G.R. and Ansari, D. (2013). Dyscalculia: Characteristics, Causes, and Treatments. Numeracy, 6 (1). Retrieved from: http://scholarcommons.usf.edu/numeracy/vol6/iss1/art2

tvoparents. (2010). Discovering Dyscalculia video [28:04]. Retrieved from: https://www.youtube.com/watch?v=LjGwcSgc-GU

Van Herwegen, J. (2014). Mathematics is not an exact science. Mathematics Teaching, 242, p.9-10

Ward, T. (July 21, 2015). Week 2 Reflection [discussion post]. Retrieved From: https://mylo.utas.edu.au/d2l/le/82261/discussions/threads/464306/View

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Wilson, A. J., and Dehaene, S. (2007). Number sense and developmental dyscalculia [pdf]. In Coch, D., Fischer, K, & Dawson, G. (Eds). Human Behavior and the Developing Brain (2nd ed). Retrieved from: http://www.aboutdyscalculia.org/author.html

Visual Processing DifficultiesAccording to the information processing model for

memory, students cannot learn if they are unable to attend to or decipher presented information (Sliva, 2004). Visual Processing Difficulties [VPD] is one of the five main areas that effect information processing. VPD impacts a student’s ability to perceive and process information presented visually (Sliva, 2004). Key strategies to address VPD will target structuring and decluttering visually presented information, supplemented with verbal instructions and tactile resources.

VPD interferes with many mathematical skills such as measurement, estimation, problem solving and geometry (Sliva, 2004). The constructivist approach in mathematics encourages hands-on, concept-based and meaningful experiences to teach all students, which includes those with VPD if the following specific strategies are incorporated into everyday pedagogy (Van deWalle, 2007).

Impacts of VPD(adapted from Sliva, 2004)

Strategies to assist

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Spatial Perception: Difficulty aligning numbers within algorithms

Provide structure with grid paper, ruled columns or turning lined-paper 90 degrees (van deWalle, 2007).

Reversals: Mirroring; and Transposing Digits

Model correct formation of digits with stencils and supply finger trace guides.

Colour numbers differently according to place value. (Sliva, 2004)

Figure-Ground Discrimination: Difficulty discriminating between problems on a page, subsequently using information from unrelated problems.

Isolate problems, paragraphs or sentences using an overlay (van deWalle, 2007).

Separate problems on worksheets, tests or texts using a consistent template.

Cut and paste problems onto individual sheets of paper.

Simplify tests and worksheets to avoid confusion. (Sliva, 2004)

Visual Discrimination: Difficulty reading texts, worksheets and tests with too much information.

Emphasize important material using highlighters

Minimise text and detail on a page and use increased font size

Ensure copies are of excellent quality.

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Present all instructions verbally and in writing. (Sliva, 2004)

Difficulty discerning differences and similarities when comparing numbers and objects including colour, size, form, shape, pattern and position

Always use manipulatives: e.g. real coins for tactile exploration geometric models instead of

pictures Use a multi-sensory approach

to learning: auditory, visual tactile and kinaesthetic. (van deWalle, 2007)

Reference List

Sliva, J.A. (2004). Teaching inclusive mathematics to special learners, K-6. Thousand Oaks, CA: Corwin Press.

Van deWalle, J.A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson Education Inc.

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Teaching with cultural awareness means never making assumptions (Santoro, 2013). Teachers must consider everything they believe, know, say and do in the classroom to ensure every student is acknowledged and included.

Cultural considerations begin with self-awareness. According to Vygotsky, everything people believe, know, say and do is socially constructed and is therefore embedded within

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a socio-cultural context (Van deWalle, 2007). Therefore, teachers must consider how their own perceptions influence the behaviour and knowledge they value in a classroom and how their language, resources, representations, activities and learning environment create or deny meaningful experiences for students (Santoro, 2013). Believing all students can achieve mathematically is essential for success (Ukpokodu, 2011). Jorgensen and Niesche (2008) assert that assumptions of student inability impact teacher’s pedagogical responses, creating self-fulfilling prophesies. Open-ended tasks encouraging engagement at various levels mitigate assumptions. Complex, inquiry-based tasks provide multiple entry-points and pathways for diverse thinking and working mathematically (Jorgensen & Niesche, 2008).

All culturally diverse students command a wealth of skills, knowledge and understandings developed from unique socio-cultural experiences (Santoro, 2013). Inclusive teachers acknowledge this by drawing on student’s specific contexts to create relevant and meaningful learning experiences, use multiple representations, varied resources, examples and activities to connect and extend mathematical understanding (Ukpokodu, 2011; Perry & Howard, 2008).

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Language is the key to developing mathematical thinking (Bresser, 2003). “Language shapes human experience—our very cognition—as it goes about classifying the world to make sense of the circumstances at hand” (Rymer, 2012). Using language to explore and justify mathematical thinking facilitates fluency and flexible use of strategies (Bresser, 2003). However, without connections between native and dominant languages in the classroom, links to prior experiences are denied (Warren Young & DeVries, 2007). To enable equal access to learning, teachers need to include relevant languages and value second-language student’s skills by encouraging translating, summarising and rephrasing discussions (Bresser, 2003).

Teachers who value, acknowledge and include student’s diverse languages and cultures into the classroom through considered pedagogy will addressed the needs of all students.

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Reference ListBresser, R. (2003). Helping English-language learners develop

computational fluency. Teaching Children Mathematics, 9 (6), p.294-299.

Jorgensen, R., & Niesche, R. (2008). Equity, Mathematics and classroom practice: Developing rich mathematical experiences for disadvantaged students. Australian Primary Mathematics Classroom, 13 (4), p.21-27.

Perry, B., & Howard, P. (2008). Mathematics in Indigenous Contexts. Australian Primary Mathematics Classroom, 13 (4), p.4-6.

Rymer, R. (2012). Vanishing Languages. National Geographic, 222 (1), p. 60-87

Santoro, N. (2013). The making of teachers for the 21st Century: Australian professional standards and the preparation of culturally responsive teachers. In Zhu, X., & Zeichner, K. (Ed’s). Preparing Teachers for the 21st Century [electronic resource].

Ukpokodu, O.N. (2011). How do I teach mathematics in a culturally responsive way? Multicultural Education, 18 (3), p.47-56

Van deWalle, J.A. (2007). Elementary and middle school mathematics: Teaching developmentally (6th ed.). Boston, MA: Pearson Education Inc.

Warren, E., Young, J., & deVries, E. (2007). Australian Indigenous Students: the role of oral language and representations in negotiation of mathematical understandings. Mathematics: Essential Research, Essential Practice Volume 2. Proceedings from Mathematics Education Research Group of Australasia Conference.

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Mathematics anxiety [MA] impacts the brains ability to think mathematically. Negative math experiences cause MA and contribute to under-performance and dis-engagement from mathematics which can persist lifelong. However, a number of strategies can reduce MA.

MA is defined as “feelings of tension, apprehension and fear of situations involving maths” (Park, Ramirez & Beilock, 2014). Scans of MA sufferer’s brains show activity in the fear centre during maths tasks, with reduced activity in areas associated with thinking mathematically (Young, Wu & Menon, 2012, in Maths Anxiety, 2013). When MA sufferers attempt math tasks fear monopolises working

memory, much like a computer processor, reducing capacity to process mathematics, effecting math performance (Ashcraft & Kraus, 2007).

MA effects multi-stepped tasks including operations, fractions and formulas, as opposed to fact and processes recall which does not require working memory (Ashcraft, & Krause, 2007; Ganley &

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Vasilyeva, 2014; Jackson& Leffingwell, 1999). Pressure increases MA during timed tests and competition with peers (Park, Ramirez, & Beliock, 2014). Interestingly, MA is more prevalent in women, whose self-perception may be influence by society’s notion that ‘girls can’t do maths’ (Ganley & Vasilyeva, 2014). Socio-cultural beliefs can effect pedagogical choices, potentially aligning teaching with achievement expectations (Bresser, 2003).

Teacher actions do impact MA, negatively and positively. Criticism, hostile experiences or poor mathematics pedagogy create MA by contributing to student difficulty and failure, sparking feelings of frustration, poor self-efficacy and low motivation (Jackson & Leffingwell, 1999; Stuart, 2000). MA stops the brain from processing mathematics, therefore, confidence must be developed within mathematics teaching (Quarder, 2013). Negative thoughts that monopolise working memory are reduced through expressive writing and mathematics journals (Park, Remirez & Beilock, 2014; Stuart, 2000). The supportive strategies listed in Figure 2 and Figure 6 also reduce MA and improve student performances (Jackson & Leffingwell, 1999; Stuart, 2000).

Figure 2:

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Negative experiences, poor pedagogy and perceived lack of ability cause MA. Subsequent withdrawal from mathematics contributes to poor performance, intensifying MA. However, thoughtful and confidence-building classroom practice can overcome MA.

Reference ListAshcraft, M.H., & Krause, J.A. (2007). Working memory, math

performance and math anxiety. Psychonomic Bulletin & Review, 14 (2), p.243-248

Bresser, R. (2003). Helping English-language learners develop computational fluency. Teaching Children Mathematics, 9 (6), p.294-299.

Ganley, C.M., & Vasilyeva, M. (2014). The role of anxiety and working memory in gender differences in mathematics. Journal of Educational Psychology, 106 (6), p.105-120

Jackson, C.D., & Leffingwell, R.J. (1999). The role of instruction in creating maths anxiety in students from Kindergarten through college. The Mathematics Teacher, 92 (7), p.583-586

Maths anxiety (2013). Maths anxiety in Elementary School. Teaching Children Mathematics, 19 (7), p.405-407

Park, D., Ramirez, G., & Beilock, S.L. (2014). The role of expressive writing in maths anxiety. Journal of Experimental Psychology, 20 (2), p.103-111

Quander, J. (2013). Setting Anxious Students at ease. Teaching Children Mathematics, 19 (7), p.405

Stuart, V. (2000). Math curse or math anxiety? Teaching Children Mathematics, 6 (5), p.330-335

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Gifted children have exceptional abilities which enable them to learn at an increased rate. Specific adjustments are mandated to support their learning needs.

Giftedness occurs in 10-15 percent of people, in six categories: intellectual, creative, social, perceptive, muscular and motor control, which develop into talents with “differential opportunities, practice, and motivation” (Gallasch, 2013; Galleger, 2015; Gagne, 2008). Typically, mathematically gifted children [MGC] are remarkably curious about numbers and mathematical information; they have well-developed number sense, intuitively perceiving patterns and relationships (Stepanek, 1999; Tuckerman, 2003). MGC have exceptional verbal reasoning skills, they enjoy puzzles and complex

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problems, applying flexible and creative strategies when problem solving (Siemon.et.al, 2011). MGC understand and apply ideas quickly, and transfer mathematical concepts to new situations; they use metacognition effectively, think abstractly and have exceptional analytical, deductive and inductive reasoning (Tuckerman, 2003; Stepanek, 1999).

MGC have unique combinations of skills and abilities, therefore, assumptions cannot be made when identifying giftedness (ACARA, 2015). Not all MGC develop automaticity, memorize formulas or process calculations quickly and accurately (Tuckerman, 2003). Social and learning difficulties, including disability, can mask giftedness (Ashman &Elkins, 2012). If unrecognised, frustration and disengagement can cause under-achievement or disruptive behaviour (Gagne, 2008; Siemon.et.al, 2011). Varied subjective and objective measures combine for effective diagnosis, including nomination checklists, work portfolios, IQ and achievement tests (Ashman &Elkins, 2012).

In each State, Catholic and Public education systems have mandatory policies outlining adjustments and pedagogical strategies for schools, teachers and support staff to ensure gifted students reach their full-potential (DoE, 2013; MEECYTA, 2008; TCEO, 2014). However, these policies are not always supported by legislation, unlike the rights of disabled students in the Disability Standards Act (CoA, 2006). Subsequently, State and school programs differ in depth and consistency (Long, Barnett &Rogers, 2015).

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Adjustments include IEP’s, pre-assessments and prior-work exemptions, differentiating the curriculum and access to online advanced-learning programs (ACARA, 2015; Gallasch, 2013; Sliva, 2004).

Whether obvious or obscured, schools and teachers are responsible for recognising and supporting gifted students to reach their full-potential.

ESH322 Week 6 Reference ListAustralian Curriculum Assessment and Reporting Authority [ACARA].

(2015). The Australian Curriculum v7.5: Student Diversity - Gifted and talented students [pdf]. Retrieved from: http://www.australiancurriculum.edu.au/studentdiversity/who-are-gifted-and-talented-students

Ashman, A., & Elkins, J. (2012). Education for Inclusion and Diversity (4th ed.). Frenchs Forrest: Pearson Australia

Commonwealth of Australia [CoA]. (2006). Disability Standards for Education 2005 plus Guidance Notes [pdf]. Retrieved From: http://docs.education.gov.au/system/files/doc/other/disability_standards_for_education_2005_plus_guidance_notes.pdf

Department of Education [DoE]. (2013). Learners first, connected and inspired: Acceleration of Gifted Students Procedures [pdf]. Retrieved

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from: https://www.education.tas.gov.au/About_us/Pages/Policies.aspx

Gallagher, J.J. (2015). Education of Gifted Students: A Civil Rights Issue? Journal for the Education of the Gifted, suppl. Special Issue: Tribute to James J. Gallagher, 38 (1), p.64-69.

Gallasch, R. (2013, Sept. 2). Attention needed for gifted students. The Examiner Newspaper Retrieved from: http://www.examiner.com.au/story/1745959/attention-needed-for-gifted-students/

Gagne, (2008). Building gifts into talents: Brief overview of the DMGT 2.0 [pdf]. Retrieved from: nswagtc.org.au/images/stories/infocentre/dmgt_2.0_en_overview

Long, L. C., Barnett, K., & Rogers, K.B. (2015). Exploring the relationship between principal, policy, and gifted program scope and quality. Journal for the Education of the Gifted, 38 (2), p.118-140

Ministerial Council on Education, Employment, Training and Youth Affairs [MCEETYA]. (2008). The Melbourne Declaration on Educational Goals for Young Australians. Retrieved from: http://www.curriculum.edu.au/verve/_resources/National_Declaration_on_the_Educational_Goals_for_Young_Australians.pdf

Stepanek, J. (1999). Meeting the needs of gifted students: differentiating mathematics and science instructions. In Stepanek, The inclusive classroom: It’s just good teaching. Portland, Oregon: Northwest Regional Educational Laboratory

Siemon, D., Beswick, K., Brady, K., Faragher, R., & Warren, E. (2011). Teaching mathematics: Foundations to middle years. South Melbourne, Vic: Oxford University Press.

Sliva, J.A. (2004). Teaching inclusive mathematics to special learners, K-6. Thousand Oaks, CA: Corwin Press.

Tuckerman, S. (2003). Addressing the needs of a mathematically gifted student. TalentEd, 21 (3), p.15-21

Tasmanian Catholic Education Office [TCEO]. (2014). Gifted Education May 2014 [pdf]. Retrieved from: http://catholic.tas.edu.au/our-schools/gifted-education-may-2014/view?searchterm=policy+gifted

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