PGCE textbooks

1. USING TEXTBOOKS TO ENHANCE
THE TEACHING OF MATHEMATICS
Christian Bokhove
Disclaimer: I have drawn from different sources in these slides and have
attempted to adequately reference everything.
If you feel I have missed something, please let me know.

2. Who am I
• Dr Christian Bokhove
• From 1998-2012 teacher maths, computer science, head of ICT
secondary school Netherlands
• National projects Maths & ICT at Freudenthal Instituut, Utrecht
University
• PhD ‘Use of ICT for acquiring, practicing and
assessing algebraic expertise’ with
Prof. Van Maanen and Prof. Drijvers
• Associate Professor at University of
Southampton
• Mathematics education
• Technology use
• Large-scale assessment (PISA/TIMSS)
• Research methods

3. This session
• Quite a broad brief
• So I had to make judgements of what might be worthwhile
• Please let me know if you want to know more about a certain
aspect
• Give you some information on mathematics textbooks
• Background
• What they can do
• Research into textbooks
• Examples of textbooks
• Where might textbooks go?

4. POLICY BACKGROUND

5. England does not use them
• Throughout the years England has
internationally scored relatively low
on textbook use. Textbooks a
supplement rather than primary
source.
• This holds for both year 4 and year
8, but there seems to be more
textbook use in secondary school
year 8 than primary school year 4.
• Over time the relative position of
England in this respect has gone
done from roughly number 5 to
number 1. In other words, England
is the country that seems to use
textbooks least of all participating
countries in TIMSS 2011.

6. .
Figure 1: bar chart of textbook use in year 8 of TIMSS 2011 data

7. http://www.telegraph.co.uk/education/educationnews/10489675/Reintroduce-traditional-textbooks-in-schools-minister-says.html

8. https://www.gov.uk/government/speeches/elizabeth-truss-speaks-to-education-publishers-about-curriculum-reform

9. Role inspection
It has been suggested that OFSTED holds particular views
on textbook use in that it opposes an ‘over-reliance’ on
textbooks, claiming that “in over a third of classes there
was an over-reliance upon a particular published scheme”
and that this “usually led to pupils spending prolonged
periods of time in which they worked at a slow pace, often
on repetitive, undemanding exercises, which did little to
advance their skills or understanding of number, much less
their interest and enthusiasm for mathematics” (OFSTED,
1993, p. 16).

10. (Bokhove & Jones, 2014)

11. Ofqual
The Office of Qualifications and Examinations Regulation
(a non-ministerial government department that regulates
qualifications, exams and tests in England, Ofqual) found
that the evidence about the impact of increased use of
endorsed textbooks on school standards is mixed.
“Overall, the evidence collected suggests there are pros
and cons with current endorsement processes. The
relationship between curriculum and resources has
changed over time in a climate of increasing use of exam
results for accountability, resulting in a very formulaic
approach to textbook.”

12. Ofqual conclude that there are some current practices
which have too much impact on the predictability of exams.
These include:
• ‘the use of questions, contexts and case studies in
examination papers which are very similar to those in
textbooks.
• The style and construction of questions in the exam being
replicated in the textbooks so students become familiar
with these worked examples in textbooks illustrating how
particular styles of questions should be answered to gain
maximum marks.’

13. Coming from a country with a near-100% percentage
of mathematics textbook usage (I can’t remember
one school that didn’t have one) and one exam
board, I understand why this situation arose, but see
a key role for textbooks. This is not a political thing,
rather an argued position.

14. School Mathematics Project
• From the 1960s to the 1990s, the School Mathematics
Project (SMP) was an iconic project in English
mathematics education (Thwaites, 2012; Wikipedia,
2017).
• Originated at the University of Southampton and created
a ground-breaking textbook series that was used in the
majority of mathematics classrooms in England
throughout the 1970s and 1980s
• Combined expertise of both the Mathematics and
Education departments in the University of Southampton,
collaborating fruitfully with numerous schools and
teachers nationally.

15. “High quality textbooks support both teachers and pupils –
they free teachers up to concentrate on refining pedagogy
and developing engaging, effective learning.” (p. 4)
http://www.cambridgeassessment.org.uk/news/new-research-shows-why-textbooks-count-tim-oates/
(Oates, 2014)

16. Features
• Underpinning by well‐grounded learning theory and theory
regarding subject‐specific content
• Clear delineation of content – a precise focus on key
concepts and knowledge
• Coherent learning progressions within the subject
• Stimulation and support of learner reflection
• Varied application of concepts and principles – ‘expansive
application’
• Control of surface and structural features of texts to
ensure consistency with underpinning learning theory’.
(Oates, 2014)

17. “Schmidt’s concept of ‘curriculum coherence’ relates to (i)
material in curriculum frameworks, textbooks etc being in
an appropriate age-related sequence; and (ii) that all
elements in a system should ‘line up’, so that contradictions
are not set up in the different elements, and professionals
are not subject to contradictory incentives and targets
(Schmidt & Prawat 2006).”

18. TIMSS curriculum framework

19. Task: discussion
• What do you know about mathematics textbooks?
• Have you used them during your school time?
• What do you think can be + and – of textbooks?
6 mins

20. TEXTBOOK RESEARCH

21. Fan et al. (2013) again take a broad perspective and
summarise research into mathematics textbook use over
the last 60 years. This research covers various aspects of
textbook use, including its impact on outcomes. It includes
findings from 111 research articles which it categorises by
date and by type of research. The classification of the
research it uses is:
• Role of textbooks (29% of the literature)
• Textbook analysis and comparison (34% of the literature)
• Textbook use (25% of the literature)
• Other areas (12% of the literature, which includes
research into e‐textbooks and the relationship between
textbook use and outcomes).

22. But….
‘the research evidence for a positive
correlation between textbooks and students’
learning outcome is weak and inconclusive.’
(Fan et al., 2013, p. 643)

23. The OECD concludes:
‘The bottom line: Higher performing school
systems allocate resources more equitably
among socio‐economically advantaged and
disadvantaged schools. Supporting
disadvantaged schools does not necessarily
mean providing them with more resources,
but rather with high‐quality human and
material resources.’ (OECD, 2014, p. 4)

24. Askew et al. (2010) conclude that ‘England’s
textbooks are more routine and involve less
variation in the construction of examples
than those of many high attaining countries.
Well‐constructed textbooks not only support
teachers but also provide support for pupils
to work independently out of class’.
(Askew et al., 2010)

25. TEXTBOOKS AS
CULTURAL PRODUCT

26. Different media
The word textbook (a blending of text and book)
did not appear until about 1830 (Stray, 1994, p.
1), with text being a word from the 14th century
that had the meaning “thing woven” (from the
Online Etymology Dictionary at
http://www.etymonline.com).

27. Clay tablets with mathematical content from
ancient Mesopotamia were used as school
texts (Høyrup, 2002, p. 8), as was the Nine
Chapters on the Mathematical Art (Shen,
Crossley, & Lun, 1999), which “served as a
textbook not only in China but also in
neighbouring countries and regions until
western science was introduced into the Far
East around 1600 AD” (p. 1).

28. What messages do textbooks convey?
I draw from a keynote given by Frederick Leung in 2014 at
our mathematics textbook conference.
• Mathematics textbooks are supposed to be conveying
mathematics knowledge or messages
• At the same time, textbooks are socio-cultural products
• They tend to convey the values of the dominant culture,
and there may be a lot of politics involved in the
production and adoption of textbooks
• When talking about values, are mathematics textbooks
exempted from these cultural and political influences?

29. Mathematics textbooks
Mathematics is sometimes conceived of as absolute truth,
with minimum human interference, but
• Mathematics applications are often contrived, meant to
illustrate the mathematics rather than genuine application
of mathematics to different socio-cultural contexts in the
real world
• So a mathematics textbook in say England should look
very similar to a mathematics textbook in Thailand or
Botswana
• But is this the case?

30. Textbooks as socio-cultural product
• “From a socio-cultural perspective the mathematics
textbooks can be regarded as an artifact in the broad
sense of the term. It is historically developed, culturally
formed, produced for certain ends and used with
particular intentions.”(Rezat, 2006)
• Textbooks are “ideological tools to promote a certain
belief system and legitimize an established political and
social order” (Apple, 1992)
• The Dutch’s promotion of middle class values in the first
half of the 20th Century (Beckers, 2000).

31. An example study by Leung (2014)

32. Messages about maths (HK, 1972)
(Leung, 2014)

33. Message about maths learning (Beijing, 1972)
(Leung, 2014)

34. Political messages (Beijing, 1972)
(Leung, 2014)

35. An application item in Beijing 1972 (p.79)
“Before the Liberation, a capitalist owner of a cotton factory
exploited his workers. The workers produced wealth worth
$a everyday, but the capitalist only took 5% (of the profit) to
pay for the workers’ wages. Write down the algebraic
expressions for the wages that the capitalist paid the
workers per day, and the amount of money that he
exploited the workers everyday”
(Leung, 2014)

36. (Leung, 2014)

37. Love & Pimm (1996)
A textbook:
• Is a message from the professional community to
students about what they should learn
• Represents the ideas of the author about how the content
should be taught
• Textbooks are linear and demand “linear textual flow of
reading”
• Textbooks are closed -- have been created in the past
• Special structure expositions, examples and exercises
• Its authoritative image has been the dominant aspect of
the classroom culture

38. Task: different perspectives
1. Modern English textbook, Pearson
2. First SMP series, 1965
3. Swedish textbook, 1989
4. Exam revision book
5. SMP interact, 2006
6. Japanese textbook, Math-1, 2011, English translation, Junior
High School, grade 7 (12 yr olds)
Have a look at each textbook.
Layout, text features, content (as much as you can, Swedish
perhaps tricky), what are the messages, what do you notice?
(Of course it will be hard to evaluate the progression in a
textbook, based on a few pages)
20 mins

39. And?
Based on these books….
Is a cylinder a prism?

40. INTEGRATION OF
TECHNOLOGY

41. Technology use: mixed results
• OECD report
• Ma overview
http://www.keepeek.com/Digital-Asset-Management/oecd/education/students-computers-and-
learning_9789264239555-en#.V8wy2jV5-aU

42. https://www.nber.org/papers/w23744
“experimental evidence suggests that giving a child a
computer may have limited impacts on learning
outcomes, but generally improves computer proficiency
and other cognitive outcomes.”

43. “From our review, computer-assisted learning and
behavioral interventions emerge as two areas that show
considerable promise. Especially when equipped with a
feature of personalization, computer-assisted learning
can be quite effective in helping students learn,
particularly with math.”
For example:
“a fairly low-intensity online program that provides students
with immediate feedback on math homework was found to
have an effect size of 0.18 standard deviations”

44. International Conference on Mathematics Textbook
Research and Development 2014.
Strand on e-Textbooks and technology.
From Prof. Yerushalmy’s talk

45. Examples
• Apple iBooks
• Great looks
• Limited interaction
• Limited student
management
options

46. MC-squared project
• Design and develop a new genre of authorable e-book,
which we call 'the c-book' (c for creative)
• Creative Mathematical Thinking (CMT)
• Initiate a ‘Community of Interest’ (CoI) (Fischer, 2001)
• A community of interest consists of several stakeholders from
various ‘Communities of Practice’ (Wenger, 1998).
• England, Spain, Greece, France
• Within these teachers who co-design and use resources for
teaching, can contribute to their own professional development
(e.g., Jaworski, 2006).
• Social Creativity, Boundary objects
• UK CoI: learning analytics

48. More than sum of the parts
• Different types of applications integrated
• Interaction: the books give feedback
• Interoperability: works on all platforms
• Storing results:
what students do
is stored
• Standards: you
can share the
books
• Authorability: you
can change parts
of the book

49. THE FUTURE OF
MATHEMATICS TEXTBOOKS
IN ENGLAND?

50. • Mathematics textbooks
• International elements
• Digital layer
Towards a School Mathematics Project 2.0

51. Brief history of SMP
• From the 1960s to the 1990s, the School Mathematics
Project (SMP) was an iconic project in English
mathematics education (Thwaites, 2012; Wikipedia,
2017).
• Originated at the University of Southampton and created
a ground-breaking textbook series that was used in the
majority of mathematics classrooms in England
throughout the 1970s and 1980s
• Combined expertise of both the Mathematics and
Education departments in the University of Southampton,
collaborating fruitfully with numerous schools and
teachers nationally.

52. “But it hasn’t always been so. In the 1960s and
1970s, English mathematics textbooks produced
by initiatives such as the School Mathematics
Project were widely recognised as amongst the
very best in the world. The development of these
textbooks involved extended collaborations
between educational researchers and teachers
together with a rigorous and iterative process of
design, trailing and feedback.“
Professor Jeremy Hodgen

53. Decline
• Changes to how exam boards were organised meant a
decline in its popularity.
• Textbooks not always used widely. Why not (contrast with
my experience in the Netherlands).
• ..but now

54. ..but now
• Return of the SMP archives and copyright to the university
• Renewed interest of schools and government into high
quality textbooks (Department for Education, 2015),
• Opportunities for digital books (e.g. Bokhove & Drijvers,
2012; Bokhove, 2017)
Can we revive these quality resources and transform SMP
into an SMP 2.0 ?

55. Mapping and digitising the SMP archive.
Registerathttp://www.smp2.co.uk

56. Mathematics Textbook Archive

57. Concluding message
• Good textbooks can help in teaching a coherent, high
quality curriculum.
• It can ensure that teachers are roughly ‘on the same
page’.
• However, there is plenty of scope for own professionality.
• You will probably not encounter many schools that use
them, but perhaps you can see their affordances.
• A cylinder is not a prism ;-)

58. Wrap-up
• Any questions?
• C.Bokhove@soton.ac.uk
• Twitter: @cbokhove
• Interested in this topic or any of these projects? Let me
know.
• Consider staying in contact regarding SMP 2.0
• Love old mathematics textbooks? Follow @mathsjem on
Twitter.

59. Selected references
• Askew, M., Hodgen, J., Hossain, S., & Bretscher, N. (2010). Values and Variables: Mathematics Education in High Performing
Countries. London: Nuffield Foundation [online]. Retrieved from
http://www.nuffieldfoundation.org/sites/default/files/Values_and_Variables_Nuffield_Foundation_v__web_FINAL.pdf
• Beckers, D. (2000). My little arithmeticians! Pedagogic ideals in Dutch mathematics textbooks, 1790-1850. Paedagogica
Historica: International Journal of the History of Education, 36, 978–1001.
• Bokhove, C., & Jones, K. (2014). Mathematics textbook use in England: mining Ofsted reports for views on textbooks. In
Proceedings of the International Conference on Mathematics Textbook Research and Development (ICMT-2014). University of
Southampton. pp. 159-166. https://eprints.soton.ac.uk/367607/
• Fan, L., Zhu, Y., & Miao, Z. (2013).‘Textbook research in mathematics education: development status and directions, ZDM, 45(5),
633–646.
• Hoyles C., Morgan C., & Woodhouse, G. (1999). Rethinking the maths curriculum. Falmer Press.
• Høyrup, J. (2002). Lengths – widths- surfaces. A portrait of Old Babylonian algebra and its kin. New York/Berlin/Heidelberg.
• Kangshen, S., Crossley, J. N., & Lun, A. W-C. (1999). The Nine Chapters on the Mathematical Art Companion and Commentary.
Oxford UK: Oxford University Press.
• Leung, F.K.S. (2014). Messages Conveyed in Textbooks: A Study of Mathematics Textbooks during the Cultural Revolution in
China. Retrieved from http://blog.soton.ac.uk/icmtrd2014/files/2014/10/Leung_ICMT2014.pdf
• Mullis I., Martin M., Foy P., & Arora A. (2013). TIMSS 2011 International results in mathematics. Boston College.
• Nisbet I. (2013). Is there a place for China’s wise laoshi? TES 14 06 13.
• Oates, T. (2014). Why Textbooks Count: a Policy Paper. Cambridge: Cambridge Assessment [online]. Retrieved from
http://www.cambridgeassessment.org.uk/news/new-research-shows-why-textbooks-count-tim-oates/
• OECD (2014). How is equity in resource allocation related to student performance? PISA in focus. Retrieved from
https://www.oecd.org/pisa/pisaproducts/pisainfocus/pisa-in-focus-n44-(eng)-final.pdf
• Ofqual (2012). Textbooks: Risks and Opportunities. Retrieved from https://dera.ioe.ac.uk/15933/1/2012-11-07-textbooks-
risksand-opportunities-action-plan.pdf
• Ofsted (1993). The teaching and learning of number in primary schools: National curriculum mathematics attainment target.
London: HMSO.
• Schmidt W., & Prawat R. (2006) Curriculum coherence and national control of education: Issue or non-issue? Journal of
Curriculum Studies, 38(6), 641-658.
• Stary, C. (1994). Paradigms regained: Towards a historical sociology of the textbook. Journal of Curriculum Studies, 26(1), 1-29.