Teaching History with MathematicsUniversity of Canberra30 March 2016

Alex Thompson

Non-specialists teaching numeracy!

1. “I'm no good at maths, the kids will catch me out and I'll feel like an idiot”• So what if you make a mistake? They (and you) might learn

something• This was every teacher at some point

2. “Kids hate maths, they won't want to do it”• Real applications makes math come alive• It must be math for historical purposes not for its own sake

3. “We are history teachers, it is the job of the maths department to teach maths.”• History is rich in numerical concepts and skills• ACARA, TQI and your schools require you to

Policy Background• Term ‘numeracy’ first appeared in the Crowther Report (Ministry of

Education, 1959) • Subsequent reports have emphasised the importance of numeracy as a

key to social and economic well-being (e.g., DETYA, 2000; Vincent, Stephens, & Steinle, 2005; COAG, 2008)

• Steen (2001) insisted that, for numeracy to be useful to students, it must be learned in multiple contexts and in all school subjects, not just maths

• Idea of developing numeracy across the curriculum was slow to gain ground (Thornton & Hogan, 2004)

• Melbourne Declaration on Educational Goals for Young Australians (MCEETYA, 2008) identifies numeracy as one of seven general capabilities that apply across all discipline content

• Australian National Curriculum includes numeracy in general capacities for all subjects

ACARA, 2016

Key Points on Numeracy from ACARA, 2016

• The curriculum rationale explains that “history is a disciplined process of inquiry into the past”

• the extent to which students are asked to use mathematical information to support the process of inquiry is at the discretion of the teacher

• the numeracy demands depend on the learning opportunities that the teacher creates

ACARA, 2016

Key Points on Numeracy from ACARA, 2016

• developed as it is applied to inquiry

• involves mathematical activity• counting • measuring• calculating • interpreting • working with dates &

calendars• several opportunities• surveys• source work• fieldwork• mapping, using satellite

imagery• modelling• diagrams

Years 7/8 – Focus on Chronology• Explicitly teach• Calendars• BC/AD = BCE/CE, Before Present =

>1950• Centuries• How to make and use timelines• Periodisation

• Make number concepts concrete• Build, model, display, act out

• Reflect on learning using numbers to overcome limited expression

• Keep it fun!• Games, competitions, puzzles, prizes

Using different calendars

Gregorian Julian Islamic Hebrew Chinese

24 July 2015 AD

11 July 2015 AD

7 Shawwal 1436 AH

8 Av 5775 AM

初九 /9Xin Chou Day,

Gui Wei Month, Yi Wei Year

Understand the scale of ‘big history’ using time or a rugby field

Visualising centuries

Timeline game

Why did the samurai replace bows with firearms?

My learning number line

1 2 3 4 5 6 7 8 9 10V. difficult Difficult OK Great

V. Easy

My learning number line – tacking progress over time

1 2 3 4 5 6 7 8 9 10V. difficult Difficult OK Great

V. Easy

My learning number line – how’s someone going with different topics?

1 2 3 4 5 6 7 8 9 10V. difficult Difficult OK Great

V. Easy

My learning number line – how’re group members going?

1 2 3 4 5 6 7 8 9 10V. difficult Difficult OK Great

V. Easy

Years 9/10 – Numbers tell a story• Analyse historical stats to enrich

investigations and test ideas• Check books for tables• Get to know sources of historical

statistics for your topics• Make numbers meaningful• Contextualise prices using value of

labour, price of silver, or Reserve Bank• Relate to their experience – an assembly,

a sold-out grand final etc.• Play to egocentrism to elicit engagement

and opinions• Build into class and assessments

Historical stats: Why did Japan go to war in the 1930s?

Historical stats: Was post-WWI soldier settlement a good policy?

Making stats concrete: Why did WWI cripple the British economy?

• Each round for this .303 Vickers’ machine gun cost ~$1

• Average rate of fire ~400 rounds per minute• = 24 000 rounds per hour• Therefore, to keep one machine gun firing for 1

hour cost $24 000 • = half a salary or a year’s schooling

Historical stats: Why was slave trading so enduring?

Cooking: Did the Allies win WWII because they were better fed?

Published Survey: Attitudes to ANZUS Treaty

Student Survey: Attitudes to Migration

Q1 The Australian government should do more to limit migrationQ2 Migrants have made positive contributions to AustraliaQ3 High migration makes it harder for people in Australia to get a jobQ4 Migrants are more likely to be criminals than mainstream AustraliansQ5 People with disabilities should not be allowed to migrate to Australia

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q100

2

4

6

8

10

12

14

16

18

AgreeDisagreeUnsure

Q6 Migrants need to learn English before they come to AustraliaQ7 The Australian government should consider terrorism risks when making migration policyQ8 The Australian government has got its migration policy about rightQ9 Australia should select migrants based on their capacity to ‘fit in‘Q10 I identify as someone with migrant heritage

Years 11/12 – Numbers aid investigation• Can now analyse historical stats at a deep

level• Consider significance, confidence

intervals etc.• Assess accuracy, reliability, bias etc.

• Use statistical tools when needed for investigation• Normal distributions• Similarity coefficients• χ² test

• Teach cliometrics (quantitative history) as a legitimate historiographical approach

Historical stats: Who voted for the Nazis and why?

Is Matthew’s gospel the most popular because it is the most ascetic?

Numbers in history: How many Persians fought at Thermopylae?

Until they reached Thermopylae, Xerxes armament was free from misfortune. The king’s sea forces amounted to 517,610 men. The number of foot soldiers was 1,700,000; that of the horsemen 80,000; to which must be added Arabs who rode on camels and the Libyans who fought in chariots, whom I reckon at 20,000. The whole number, therefore, of the land and sea forces added together amounts to 2,317,610 fighting men brought by Xerxes, the son of Darius, as far as Thermopylae. Source: From the book The Histories, written by Herodotus in the 450s-420s BCE.

Xerxes decided to make war upon Greece . . . having collected a Persian army, 800,000 men and 1,000 triremes set out against Greece. His general Artapanus, with 10,000 men, fought an engagement with Leonidas, the Spartan general, at Thermopylae. The Persian host was cut to pieces, while only two or three of the Spartans were slain. Source: From Ctesias of Cnidus’s book Persica written in 398 BCE. This excerpt was included in a book by the scholar Photius in the 9th century.

Although it is true that Herodotus . . . had access to all the records available, it is impossible to accept the figures that he gives for the size of the Persian army and of the fleet. . . .General Sir Frederick Maurice, who had the opportunity of covering the area of the march of the Great King not long after the First World War, came up with the conclusion that the total of the Persian army was about 210,000. Unlike most desk-bound scholars he [Maurice] had the opportunity to travel the whole area, and had excellent military and logistical knowledge of the terrain. He based his conclusion particularly on his observation of the water supplies available. . . . It seems that there is no possibility of the army of Xerxes having exceeded 250,000 men.Even this number . . . would have been sufficient to exhaust the water resources at a number of places along their route. Source: Ernle Bradford, The Year of Thermopylae, 1980, p. 34.

No aspect of the Thermopylae campaign has given rise to greater controversy than the size and composition of the army led by Xerxes into Greece. . . .. . . Herodotus puts the strength of Xerxes’ army at around two million men and says that they drank the rivers dry as they advanced. . . . As usual, Herodotus does not tell us where he got this information from, but it does bear all the hallmarks of being an official document. . . . Whatever the source of information given by Herodotus, it is quite clear that the list is not an accurate record of the army Xerxes led into Greece. It would have been physically impossible to march that many men along the roads available to them and keep them supplied.We know that Xerxes sent an advance guard of laborers and engineers forward to prepare the route for his invasion. . . . While it is not recorded exactly what these men did, it is clear that they were undertaking construction work that would aid the army. If streams were dammed to create reservoirs of water, Xerxes would have been able to move an army considerably larger than the 210,000 men that General Maurice [see Bradford] thought the land could support. Even so, it is unlikely that the increase could have been more than around 50%, say a total of 300,000 to 350,000. Source: Rupert Matthews, The Battle of Thermopylae: A Campaign in Context, 2006, p. 10-15.

Historical dating: Reconstructing Manaetho’s Kings List

Josephus Africanus Eusbius (Armenian)

King Reign King Reign King Reign

1. Tethmosis 25/4 Amos — Amoses 25

2. Chebron 13 Chebros 13 Chebron 13

3. Amenophis 20/7 Amenophthis 24 Amophis 21

4. Amessis 21/9 Amensis 22 — —

5. Mephres 12/9 Misaphres 13 Memphres 12

6. Mephramuthosis 25/10 Misphragmuthosis 26 Mispharmuthosis 26

7. Thmosis 9/8 Tuthmosis 9 Tuthmosis 9

8. Amenophis 30/10 Amenophis 31 Amenophis 31

9. Orus 36/5 Orus 37 Orus 28

10. Acencheres 12/1 Acherres 32 Achencheres 16

11. Rathotis 9 Rathos 6 — —12. Acencheres I 12/5 Chebris 12 Acherres 8

13. Acencheres II 12/3 Acherres 12 Cherres 15

14. Harmais 4/1 Armesis 5 Armais 5

15. Ramesses 1/4 Ramesses 1 — —

16. Harmesses Miamen 66/2 — — Ramesses also called Aegyptus

68

17. Amenophis 19/6 Amenophath 19 Amenophis 40

18. Sethos 59 Sethos 51 Sethos 5519. Rampses 66 Rapsaces 61 Rampses 66

Revised Order Corresponding King Josephus Reign High Year Mark

(1) Tethmosis Ahmose 25/4 22

(3) Amenophis Amenhotep I 20/7 21

(2) Chebron Thutmose I 13?? 4 or 9

(5) Mephres Thutmose II 12/9 (8) 14 or 18 (4)

(4) Amessis Hatshepsut/Thutmose III 21/ 9 22 (5)

(6) Mephramuthosis Thutmose III + part of Thutmose II 25/10 54 (6)

(7) Thmosis Thutmose III 9/ 8

(8) Amenophis Amenhotep II 30/10 23

(10) Acencheres Thutmose IV 12/1 8

(9) Orus Amenhotep III 36/5 37

(17) AmenophisAkhenaten

+ Smenkhkare19

17

3

(11) Rathotis Tutankhamen 9 9

(14) Harmais Aye 4/1 4

(12) Acencheres I Horemheb 12/5

27(13) Acencheres II Horemheb 12/3

(15) Ramesses Horemheb/Ramesses I 1/4

(16) Harmesses-Miamun Ramesses I 66/2 1-2

(18) Sethos Sethos I 59 11

(19) Rampses Ramesses II 66 66

Radiocarbon dating

Similarity coefficients: What sort of site is Anemospillia?

Amenospilia site reconstruction (Sarakellis & Sarakellis, 1981)

An exercise: How would you teach…

Origin of Migrants to Australia 1946-2010

• The waves of post-World War II migration to Australia, including the influence of significant world events (ACDSEH144)

THANKYOU

References

Australian Curriculum, Assessment and Reporting Authority (ACARA). (2016). The Australian curriculum. History. Retrieved from http://www.australiancurriculum.edu.au/History/Curriculum/F-10Council of Australian Governments (2008). National numeracy review report. Retrieved from http://www.coag.gov.au/reports/index.cfm#numeracyDepartment of Education, Training and Youth Affairs (2000). Numeracy, a priority for all: Challenges for Australian schools. Canberra: Commonwealth Government of Australia. Goos, M., & Dole, S. (2012). Auditing the Numeracy Demands of the Australian Curriculum. In J. Dindyal, L. P. Cheng & S. F. Ng (Eds.), Mathematics education: Expanding horizons (Proceedings of the 35th annual conference of the Mathematics Education Research Group of Australasia). Singapore: MERGA. Ministry of Education (1959). 15 to 18: A report of the Central Advisory Council for Education. London: HMSO. Steen, L. (2001). The case for quantitative literacy. In L. Steen (Ed.), Mathematics and democracy: The case for quantitative literacy (pp. 1-22). Princeton, NJ: National Council on Education and the Disciplines. Ministerial Council on Education, Employment, Training and Youth Affairs (MCEETYA). (2008). Melbourne Declaration on educational goals for young Australians. Retrieved from http://www.curriculum.edu.au/verve/_resources/National_Declaration_on_the_Educational_Goals_for_Y oung_Australians.pdfPhillips, I. (2002). History and Mathematics or History with Mathematics: does it add up?. Teaching History, (107), 35-40.Thornton, S., & Hogan, J. (2004). Orientations to numeracy teachers’ confidence and disposition to use mathematics across the curriculum. In M. Johnson Hoines & A. Berit Fugelstad (Eds.), Proceedings of the 28th conference of the International Group for the Psychology of Mathematics Education (Vol. 4, pp. 313- 320). Bergen: PME. Vincent, J., Stephens, M., & Steinle, V. (2005). Numeracy research and development initiative 2001-2004 – An overview of numeracy projects. Canberra: Commonwealth of Australia. Retrieved from http://www.dest.gov.au/NR/rdonlyres/C75E96C0-45F9-4495-AF58- DD187874F70D/8470/numeracyoverview_20012004.pdf