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Student experiences in STEM… where did all the math come from?

Student experiences in STEM… where did all the math come from?. James , Y. Li, M. Wald & E.A . Draffan, ECS Partners, University of Southampton. You and maths…. How maths confident are you?. Up to Level 2 / GCSE. Calculate Calculate 30% of 120 Calculate the ratio of 25p to £2.45

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Student experiences in STEM… where did all the math come from?

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  1. Student experiences in STEM… where did all the math come from? James, Y. Li, M. Wald & E.A. Draffan, ECS Partners, University of Southampton

  2. You and maths….

  3. How maths confident are you? Up to Level 2 / GCSE Calculate Calculate 30% of 120 Calculate the ratio of 25p to £2.45 Circle the expressions that is equivalent to Solve Solve

  4. How maths confident are you? Up to A Level / Higher If , determine Prove by induction that, for all positive integers : The frequency f of the oscillation of the trolley is given by: Calculate the period of oscillation

  5. Why are we concerned about maths and STEM?

  6. University experience of maths

  7. Print disabilities and mathematical notation • Up to 10% of student population may have a print impairment that could affect their ability to read or comprehend maths. Problems may include: • Reading the notation • Recalling names of notation and meanings • Proof reading notation • Recalling the steps of a process to solve a maths problem • Difficulty with comprehending symbols instead of words Access to text to speech with highlighting may improve access to maths notation.

  8. When they get to university…do students expect maths? Biology Business Economics Given the sample, calculate: (i) (ii) (iii) (iv) (v) Consider . Determine and Use the data to obtain Ordinary Least Squares vales of in the following regression equation:

  9. Some students might anticipate maths content… Chemistry Engineering Calculate Which of the following is the Laplace transform of the function ? (a) (b) (c) (d) (e) none of the above

  10. Students that want to do maths…. 1. Using the above results and Skokes’ theorem obtain the value of: Where A is the curved surface of the hemisphere and points outwards from the origin. 2. Mean energy equation can be written as:

  11. Proportion of disabled students in UK HEIs by subject area, 2012/13

  12. Where does “maths” occur? Websites Publications (PDF) and e-books Documents, presentations and spreadsheets Learning materials Videos

  13. Accessibility Requirements Some users may want to • Zoom / re-size • Search / index maths • Braille rendering • Read aloud maths with or without highlighting Reading aloud maths is particularly demanding on working memory. It may not be possible to vocalise diagrams.

  14. The difference between maths & text Maths is a 2-deminsional notation. Location of a symbol affects its meaning Fourier Series equation

  15. The difference between maths & text Symbols may be vocalised differently: [AB]-1 Could mean: “left bracket, boldface capital a, boldface capital b, right bracket, superscript minus one” OR “inverse of the matrix product, boldface capital a, boldface capital b”

  16. Hand writing recognition & maths • Hand-written maths relies on real-time analysis of strokes as symbols are formed • Much more dependent on accuracy & spatial layout than text recognition • Formation of symbols is not consistent • Across countries • Across individuals • Math input panel in Windows (and MathType)

  17. Apps for capturing maths Starting to appear on tablet apps e.g. MathBrush but not necessarily about producing accessible output • Notes & Maths • MathBrush for recongitzing hand-writing • But can also type TeX into a notes app & import to word / editor later

  18. Accessibility barriers to maths notation Most electronic maths is represented as images (PDFs, JPEGs, SVG) Mathematical mark-up MathML designed for accessibility but limited support in browsers and applications <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfrac> <mml:mrow><mml:mi>a</mml:mi><mml:mo>+</mml:mo><mml:mi>b</mml:mi></mml:mrow> <mml:mn>2</mml:mn> </mml:mfrac> </mml:math> MathML support is improving in e-books (epub3) and a few projects continue to develop technologies to read maths aloud

  19. The difference between maths & text: non-linear representation and ambiguity (1) Maths is a 2-deminsional notation. Location of a symbol affects its meaning. GCSE question: Circle the expressions that is equivalent to text read as: “x 4” “4x” “4x” “x times x times x times x” Quadratic Formula: Read as “x = b square root b 2 4 ac slash 2 a”

  20. The difference between maths & text: non-linear representation and ambiguity (2) Maths when read aloud can mean different things Example 1: “a plus b over 2”: Example 2: “3 plus 2 minus 4”:

  21. Accurate reading of maths: Example 1: “a plus b over 2” / “a plus b all over 2” Accurate but verbose alternatives “a plus open fraction b over 2 close fraction” “open fraction open bracket a plus b close bracket over 2 close fraction”

  22. Accurate reading of maths: Example 2: “3 plus 2 minus 4 squared”: “3 plus, open bracket 2 minus 4 close bracket squared”: Accurate reading of maths can be long and verbose – a disadvantage for those with processing or working memory difficulties Earcons, spearcons a have been proposed to replace elements that represent hierarchical structure (e.g. brackets) [2] while use of pitch and intonation has also been used [4]

  23. Mathematical semantics A mathematical expression or equation is like a sentence. It has a grammar and semantic structure. Simple expressions are like simple sentences: “I can run” …… Complex expressions can contain sub-clauses and conjugates "I can run like the wind if the grizzly bear chases after me“… If sighted readers can drill down into the semantics of an equation then audio representation of the notation may be more valuable.

  24. Visualising maths notation Concepts maps & tree diagrams are often used to assist mathematical teaching [3]. Tree diagrams are used to describe semantics Specialist maths tutors have described how concept maps can be used to help dyslexic students visualise problems [6, 8].

  25. STEMReader project Project to develop proof of concept from Feb 2014 – July 2014 funded by BIS, Technology Strategy Board, managed by Techdis. Goals: Improve solutions for reading aloud maths notation for students studying GCSE to degree level maths and science Apply concept of semantic web to allow for navigation and visualisation of maths notation Challenge – to develop usable, sustainable tool for print-impaired students to use alongside their current support strategies. Current proof of concept tool allows MathML equations to be read aloud, navigated by keyboard & display as a semantic tree. Will be able to be used with Office documents by selecting equations.

  26. STEMReader examples - fractions

  27. STEMReader examples – order of operations “Three plus two minus four squared” 2 different trees for the 2 different versions

  28. STEMReader – advanced example Navigate through an equation using the tree Highlight location of variables within the equation Provide users with different options for speaking equations Investigating different ways of displaying tree view Contact a.james@soton.ac.uk for further information

  29. References [1] Bahram, S., Soiffer, N., & Frankel L. (2014) Understanding Mathematical Expressions through Interactive Navigation. In 29thAnnual International Conference on Technology and Persons with Disabilities, Northridge, California, USA. [2] Bates, E., & Fitzpatrick, D. (2010). Spoken mathematics using prosody, earcons and spearcons. Computers Helping People with Special Needs, 407–414. [3] Brown, T. (2013). Meeting the Standards in Primary Mathematics: A Guide to the ITT NC. Routledge. [4] Gellenbeck, E., & Stefik, A. (2009). Evaluating Prosodic Cues as a Means to Disambiguate Algebraic Expressions : An Empirical Study, 139–146. [5] Holden, W., Sunnes, M., & Graffe, S. (2014) The Next Generation Text to Speech Program. In 29thAnnual International Conference on Technology and Persons with [6] Perkin, G. (2004). The dyslexic engineer–issues for mathematics education. International Conference on Engineering Education,(October 2003), 1–11. [7] Sorge, V., Chen, C., Raman, T. V., & Tseng, D. (2014, April). Towards making mathematics a first class citizen in general screen readers. In Proceedings of the 11th Web for All Conference (p. 40). ACM. [8] Trott, C. (2003). Mathematics support for dyslexic students. MSOR Connections, 3(4), 17-20.

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