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Maths for Biology
January 9th 2016 ASE
Carys Hughes
Christian Bokhove
Hilary Otter
Rebecca D’Silva
Nicky Miller
Introductions
• Carys Hughes
• Christian Bokhove
• Hilary Otter
• Rebecca D’Silva
• Nicky Miller
This study
• Design a CPD course on Maths for A level
Biology
• Involve teachers in its design
• Implement the day
• Evalu...
Why this day
• Changes in the A level Biology curriculum
• More maths
• Maths used interdisciplinary
• Principles
– Instru...
Part I: designing the day (process)
• Communities of Interest and Boundary Objects
• Involve three Biology teachers, and t...
Part 2: delivery of the CPD day (product)
• 20-30 teachers
• Whole day, free
• Focus on exponentials/logarithms and statis...
• Update and strengthen knowledge on some
topics for the new Biology A level curriculum;
– Exponential growth and decay, l...
Example of data collection
Focus group questions
• What, in your view, did you manage to contribute to the design of the C...
Example of data collection
modified Fennema-Sherman Attitude Scales
Tentative findings: process
• Usefulness of the Community of Interest
• Knowledge acquisition
• Improved confidence in tea...
Tentative findings: product/day
• Valued content exponentials/logarithms
• More confident statistics but worthwhile to
com...
Challenges
• Getting teachers away from school for CPD
– Design phase twilight
– Day was free
– After A-level exams
• Data...
Taster from
the CPD day
Powers and
exponential
Slide exam curriculum
From (i) A.0 - arithmetic and numerical
computation
A.0.5 Use calculators to find and use power, exp...
Powers of 10
Movie on youtube
ThereisanewerversioncalledCosmicVoyage,narratedby
MorganFreeman.It,however,doesnothavethesta...
17
ACTIVITY
Exponentials
Take an A4 sheet of paper.
How many times can you fold it in half?
MYTHBUSTERS
Movie on youtube
19
How many layers do you produce? HANDOUT
Number
of folds
(x)
Number
of layers
(y)
Mult Power Heig
ht
(cm)
0 1 0.01
1 2 2...
20
Plot your values on graph paper:
- 3 - 2 - 1 1 2 3 4 5 6 7 8
- 100
100
200
300
x
y
- 3 - 2 - 1 1 2 3 4 5 6 7 8
- 100
10...
21
Exponential growth
Imagine you contracted a virus (such as SARS)
where you infected the first five people that
you met,...
22
How many infections?
Number of interactions
(x)
Number of infected
people (y)
0 1
1 5
2 25
3
4
5
Table of results
23
General form:
y=bt
where b is the base and x is the power (or exponent)
24
The exponential graph
- 2 2 4 6 8
- 200
200
400
x
y
ACTIVITY: Use Desmos or Geogebra online to graph
25
How many layers do you produce?
Number
of folds
(x)
Number
of layers
(y)
Heig
ht
(cm)
0 1 0.01
1 2 2
2 2*2
3 2*2*2
4 2*...
26
Common features of y=bx
all curves pass through (0,1)
exponential growth (and decay) takes
place very rapidly
b > 0
...
Number of
interactions (x)
Number of people with the
disease (y)
0 1
1 5
2 25
3 125
4 625
5 3,125
6 15,625
7 78,125
8 390,...
Statistics
Slide exam curriculum
From (i) A.1 - handling data
A.1.9 Select and use a statistical test Candidates may
be tested on the...
Statistical tests
• Type of data collected
– Measurements
– Frequencies
• What are you looking for?
– Associations
– Diffe...
(Source: TES site)
Conclusion
• CPD day designed by Community of Interest for
Biology teachers
• Improvement maths confidence
• Now writing u...
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Maths for Biology

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Presentation for the ASE 2016 conference on January 9th 2016

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Maths for Biology

  1. 1. Maths for Biology January 9th 2016 ASE Carys Hughes Christian Bokhove Hilary Otter Rebecca D’Silva Nicky Miller
  2. 2. Introductions • Carys Hughes • Christian Bokhove • Hilary Otter • Rebecca D’Silva • Nicky Miller
  3. 3. This study • Design a CPD course on Maths for A level Biology • Involve teachers in its design • Implement the day • Evaluate impact of the two groups of teachers.
  4. 4. Why this day • Changes in the A level Biology curriculum • More maths • Maths used interdisciplinary • Principles – Instruction but also hands-on tasks – Collaborative, doing it together, ask questions – Want to customise the course to where you need support
  5. 5. Part I: designing the day (process) • Communities of Interest and Boundary Objects • Involve three Biology teachers, and two researchers, one Maths, one Biology • Two development sessions of 2 hours • All the teachers’ contributions will be recorded through notes and audio. • After delivery of the day teachers interviewed in a group interview/focus group. Research questions: • In what way can these teachers contribute to the design of the delivered session? • What impact does the involvement in the design process have on their own professional development.
  6. 6. Part 2: delivery of the CPD day (product) • 20-30 teachers • Whole day, free • Focus on exponentials/logarithms and statistics (came from the design part with teachers) • Data collection: maths confidence, evaluation, impact Research question: • What impact does a CPD day on maths for the new Biology A-level curriculum have on participant’s maths confidence and teaching practice?
  7. 7. • Update and strengthen knowledge on some topics for the new Biology A level curriculum; – Exponential growth and decay, logarithms – Statistical tests • Hear and discuss ideas for teaching them; • Want to hear your opinions for improvements; • You leave with: – Ideas, knowledge and some resources
  8. 8. Example of data collection Focus group questions • What, in your view, did you manage to contribute to the design of the CPD session? • What impact, in your opinion, did the involvement in the design process have on their own professional development. – Did have an impact on your confidence in teaching Biology? – And the maths component in particular? (engagement, confidence, liking, valuing) • What impact, in your opinion, did the participation in the whole project (including the actual CPD day) have on their own professional development. – Did have an impact on your confidence in teaching Biology? – And the maths component in particular? (engagement, confidence, liking, valuing) • Did you feel the whole process has had an impact on students? – Engagement with maths? Confidence in maths? Liking maths? – Valuing maths?
  9. 9. Example of data collection modified Fennema-Sherman Attitude Scales
  10. 10. Tentative findings: process • Usefulness of the Community of Interest • Knowledge acquisition • Improved confidence in teaching the maths in A level biology • Better understanding of the processes involved in the calculations
  11. 11. Tentative findings: product/day • Valued content exponentials/logarithms • More confident statistics but worthwhile to compare and discuss pedagogy • On confidence: – They think they can learn maths – They think it's important and worthwhile – They need maths for their work – But it's hard! – So need support.
  12. 12. Challenges • Getting teachers away from school for CPD – Design phase twilight – Day was free – After A-level exams • Data collection • Culture clash – Research v Practice – Maths v Science
  13. 13. Taster from the CPD day
  14. 14. Powers and exponential
  15. 15. Slide exam curriculum From (i) A.0 - arithmetic and numerical computation A.0.5 Use calculators to find and use power, exponential and logarithmic functions Candidates may be tested on their ability to: estimate the number of bacteria grown over a certain length of time From (ii) A.2 – algebra A.2.5 Use logarithms in relation to quantities that range over several orders of magnitude Candidates may be tested on their ability to: use a logarithmic scale in the context of microbiology, e.g. growth rate of a microorganism such as yeast
  16. 16. Powers of 10 Movie on youtube ThereisanewerversioncalledCosmicVoyage,narratedby MorganFreeman.It,however,doesnothavethestandard notationincluded.
  17. 17. 17 ACTIVITY Exponentials Take an A4 sheet of paper. How many times can you fold it in half?
  18. 18. MYTHBUSTERS Movie on youtube
  19. 19. 19 How many layers do you produce? HANDOUT Number of folds (x) Number of layers (y) Mult Power Heig ht (cm) 0 1 0.01 1 2 2 2 2*2 3 2*2*2 4 2*2*2*2 24 5 Table of results H
  20. 20. 20 Plot your values on graph paper: - 3 - 2 - 1 1 2 3 4 5 6 7 8 - 100 100 200 300 x y - 3 - 2 - 1 1 2 3 4 5 6 7 8 - 100 100 200 300 x y
  21. 21. 21 Exponential growth Imagine you contracted a virus (such as SARS) where you infected the first five people that you met, and they each infected the first five people that they met and so on…. There are 186,701 people living in Southampton. How many interactions would it take until everyone was infected?
  22. 22. 22 How many infections? Number of interactions (x) Number of infected people (y) 0 1 1 5 2 25 3 4 5 Table of results
  23. 23. 23 General form: y=bt where b is the base and x is the power (or exponent)
  24. 24. 24 The exponential graph - 2 2 4 6 8 - 200 200 400 x y ACTIVITY: Use Desmos or Geogebra online to graph
  25. 25. 25 How many layers do you produce? Number of folds (x) Number of layers (y) Heig ht (cm) 0 1 0.01 1 2 2 2 2*2 3 2*2*2 4 2*2*2*2 24 5 Table of results y=2x
  26. 26. 26 Common features of y=bx all curves pass through (0,1) exponential growth (and decay) takes place very rapidly b > 0 b 0 b 1 b > 1 has a positive gradient (PLOT THIS!) 0 < b < 1 has a negative gradient (PLOT THIS!)   https://www.desmos.com/calculator/auubsaje fh
  27. 27. Number of interactions (x) Number of people with the disease (y) 0 1 1 5 2 25 3 125 4 625 5 3,125 6 15,625 7 78,125 8 390,625
  28. 28. Statistics
  29. 29. Slide exam curriculum From (i) A.1 - handling data A.1.9 Select and use a statistical test Candidates may be tested on their ability to select and use: • the Chi squared test to test the significance of the difference between observed and expected results • the Students t-test • the correlation coefficient A.1.11 Identify uncertainties in measurements and use simple techniques to determine uncertainty when data are combined Candidates may be tested on their ability to: • calculate percentage error where there are uncertainties in measurement
  30. 30. Statistical tests • Type of data collected – Measurements – Frequencies • What are you looking for? – Associations – Differences (Source: TES site)
  31. 31. (Source: TES site)
  32. 32. Conclusion • CPD day designed by Community of Interest for Biology teachers • Improvement maths confidence • Now writing up the study • Questions? • Thank you for your attention. http://is.gd/maths4bio

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