Student experiences in
STEM… where did all the
math come from?
A. James,
Y. Li, M. Wald & E.A. Draffan,
ECS Partners, University of Southampton
You and maths….
How maths confident are you?
1
2
• Calculate +
1
2
• Calculate 30% of 120
• Calculate the ratio of 25p to £2.45
• 𝐶 = 2𝜋𝑟
• Circle the expressions that is equivalent to 4 × 𝑥:
𝑥4
4𝑥
4𝑥
𝑥×𝑥×𝑥×𝑥
• Solve 5𝑥 − 2 = 𝑥 + 16
• Solve
3
𝑥−1
−
4
𝑥+2
=2
Up to Level 2 / GCSE
How maths confident are you?
• If 𝑦 = 3𝑥
−2
3
2
+ 2𝑥 , 𝑥 > 0, determine
𝑑𝑦
.
𝑑𝑥
• Prove by induction that, for all positive integers 𝑛:
𝑛
4𝑟 3 + 3𝑟 2 + 𝑟 = 𝑛(𝑛 + 1)3
𝑟=1
• The frequency f of the oscillation of the trolley is given by:
𝑓=
1
2𝜋
2𝑘
𝑚
Calculate the period of oscillation
Up to A Level / Higher
Why are we concerned about
maths and STEM?
University experience of maths
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.
When they get to university…do students
expect maths?
• Given the sample, calculate:
(i) 𝑛 (ii)
2
𝑥 (iii) ( 𝑥)
(iv)
1
𝑛
𝑥 (v)
𝑥
𝑛
Biology
• Consider 𝑦𝑡 = 𝜇 + 𝜃𝑦𝑡−1 + 𝜀𝑡 .
Determine 𝑦1 , 𝑦2 and 𝑦3
Business
• Use the data to obtain Ordinary Least Squares vales of
𝛼 𝑎𝑛𝑑 𝛽in the following regression equation:
𝑌𝑖 = 𝛼 + 𝛽𝑋𝑖 + 𝜀𝑖 ,
𝑖 = 1,2, … , 6
Economics
Some students might anticipate maths
content…
• Calculate

2x  4
2
0
x  4x  3
2
dx
Chemistry
• Which of the following is the Laplace transform of the
function 𝑡 2 𝑒 2𝑡 ?
(a)
2
𝑠 3 𝑠+2 ′
(b)
2
(𝑠−2)3′
(c)
2
(𝑠−2)𝑠 3′
(e) none of the above
(d)
2
𝑠+2 2′
Engineering
Students that want to do maths….
1. Using the above results and Skokes’ theorem obtain the
value of:
𝑧𝐣 + 𝑦 − 1 𝐤 . ⅆ𝐒
𝐴
Where A is the curved surface of the hemisphere 𝑥 2 + 𝑦 2 +
𝑧 2 = 4, 𝑧 ≥ 0 and ⅆ𝐒 points outwards from the origin.
2. Mean energy equation can be written as:
 u u 
 u u
u   u F  u k  q u 

   (Bu)   
t  2 
 2

20
18
16
14
12
10
8
6
4
2
0
30000
25000
20000
15000
10000
5000
0
Disabled 2012/13
No of disabled students
Number of disabled students of all students in
subject area
Percedntage of students in subject areas
declaring disability
Proportion of disabled students in UK
HEIs by subject area, 2012/13
Where does “maths” occur?
• Websites
• Publications (PDF) and e-books
• Documents, presentations and spreadsheets
• Learning materials
• Videos
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.
The difference between maths &
text
Maths is a 2-deminsional notation. Location of a symbol
affects its meaning
𝑓 𝑥 = 𝑎0 +
∞
𝑛=1
Fourier Series equation
𝑛𝜋𝑥
𝑎𝑛 cos
𝐿
+
𝑛𝜋𝑥
𝑏𝑛 sin
𝐿
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”
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)
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
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
𝑎+𝑏
2
<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
The difference between maths & text: nonlinear 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 4 × 𝑥:
𝑥4
4𝑥
4𝑥
𝑥×𝑥×𝑥×𝑥
text read as: “x 4” “4x” “4x” “x times x times x times x”
Quadratic Formula:
−𝑏 ± 𝑏 2 − 4𝑎𝑐
𝑥=
2𝑎
Read as “x = b square root b 2 4 ac slash 2 a”
The difference between maths & text: nonlinear representation and ambiguity (2)
Maths when read aloud can mean different things
Example 1: “a plus b over 2”:
𝑎+
𝑏
2
𝑎+𝑏
2
Example 2: “3 plus 2 minus 4”:
3+2−4
3 + (2 − 4)
Accurate reading of maths:
Example 1:
“a plus b over 2” / “a plus b all over 2”
𝑎+
𝑏
2
𝑎+𝑏
2
Accurate but verbose alternatives
“a plus open fraction b over 2 close fraction”
𝑏
𝑎+
2
“open fraction open bracket a plus b close bracket over 2 close fraction”
(𝑎 + 𝑏)
2
Accurate reading of maths:
Example 2:
“3 plus 2 minus 4 squared”:
3 + 2 − 42
“3 plus, open bracket 2 minus 4 close bracket squared”: 3 +
(2 − 4)2
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]
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” …… 𝑥 + 2
Complex expressions can contain sub-clauses and conjugates
"I can run like the wind if the grizzly bear chases after me“…
𝑥+2 2
𝑥+2
If sighted readers can drill down into the semantics of an
equation then audio representation of the notation may be more
valuable.
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].
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.
STEMReader examples - fractions
STEMReader examples – order of
operations
• “Three plus two minus four squared”
• 2 different trees for the 2 different versions
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
References
[1] Bahram, S., Soiffer, N., & Frankel L. (2014) Understanding Mathematical Expressions
through Interactive Navigation. In 29th 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), 1720.