James Y Li M Wald amp EA Draffan ECS Partners University of Southampton You and maths How maths confident are you Calculate Calculate 30 of 120 Calculate the ratio of 25p to 245 ID: 439474
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Slide1
Student experiences in STEM… where did all the math come from?
James
,
Y. Li, M.
Wald
& E.A
. Draffan,
ECS Partners, University of SouthamptonSlide2
You and maths….Slide3
How maths confident are you?
Calculate
Calculate 30% of 120
Calculate the ratio of 25p to £2.45
Circle the expressions that is equivalent to
Solve Solve
Up to Level 2 / GCSESlide4
How maths confident are you?
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
Up to A Level / HigherSlide5
Why are we concerned about maths and STEM?Slide6
University experience of mathsSlide7
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 problemDifficulty with comprehending symbols instead of wordsAccess to text to speech with highlighting may improve access to maths notation.Slide8
When they get to university…do students expect maths?
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:
Biology
Business
EconomicsSlide9
Some students might anticipate maths content…
Calculate
Which of the following is the Laplace transform of the function
?
(a)
(b) (c) (d) (e) none of the above
Chemistry
EngineeringSlide10
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: Slide11
Proportion of disabled students in UK HEIs by subject area, 2012/13Slide12
Where does “maths” occur?
Websites
Publications (PDF) and e-books
Documents, presentations and spreadsheets
Learning materials
VideosSlide13
Accessibility Requirements
Some users may want to
Zoom / re-size
Search / index
maths
Braille renderingRead aloud maths with or without highlightingReading aloud maths is particularly demanding on working memory. It may not be possible to vocalise diagrams.Slide14
The difference between maths & text
Maths is a 2-deminsional notation. Location of a symbol affects its meaning
Fourier Series equation
Slide15
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”Slide16
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 individualsMath input panel in Windows (and MathType)Slide17
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-writingBut can also type TeX into a notes app & import to word / editor laterSlide18
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 Slide19
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”
Slide20
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”:
Slide21
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” Slide22
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] Slide23
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. Slide24
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].Slide25
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.Slide26
STEMReader examples - fractionsSlide27
STEMReader examples – order of operations
“Three
plus two minus four
squared”
2 different trees for the 2 different versionsSlide28
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 informationSlide29
References
[1] Bahram, S., Soiffer, N., & Frankel L. (2014)
Understanding Mathematical Expressions through Interactive Navigation.
In 29
th
Annual 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 29th Annual 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.