R.Nazim Khan School of Mathematics and Statistics The ... · “ From elementary school through high school, Chinese students are not allowed to use calculators.” “Students reported

FYi July 2017: Should calculators be allowed in university mathematics units? R.Nazim Khan – 1

Should calculators be allowed in university mathematics units?

R.Nazim Khan

School of Mathematics and Statistics

The University of Western Australia

Sixth FYi Maths WorkshopJuly 2017

History of calculating machines


Time Advancement2000 BC Abacus by Egyptians and Sumerians

1620–1630 Slide rules based on Napier’s logarithms. Used in calculations for theApollo 11 moon landing! (Hidden Figures!)

1630–1948 Mechanical devices1961 First electronic desktop calculator–vacuum tubes

1962–64 Transistor based desk top calculators, costing the same as family car1965 First and-held calculators1965 Bulgaria’s ELKA 6521, first hand-held to include√

1969 First battery-powered hand-held calculator1971 First micro-processor based hand-held calculator1980 First hand held computer, QWERTY keyboard, ran Basic1985 First graphics calculator2003 First graphics calculator with touch functionality2010 First colour graphics calculator

Some examples


1820 Thomas de ColmarFrench-patented four function

Arithmometer

1887 Dorr. E. Felt US-patented keydriven Comptometer

1946 ENIAC (Electronic NumericalIntegrator And Computer)

1972 HP-35 scientific almostpocket-sized with trigonometric andalgebraic functions $395

Traditional academic wisdom


■ Should calculators be allowed in mathematics?




■ In primary school?




■ In primary school? Which type?





■ In high school?





■ In high school? Which type?






■ In university?






■ In university? Which type?

Some opinions


■ “. . . many of us teaching at first year try to train the students tobe lessdependent on their CAS calculator from year 12 - as we have found theyactually don’t understand the maths as well as when they do it ”by hand”.For example, many commencing students cannot provide even a roughsketch of a sine curve without their calculator.”

Some opinions


■ “. . . many of us teaching at first year try to train the students tobe lessdependent on their CAS calculator from year 12 - as we have found theyactually don’t understand the maths as well as when they do it ”by hand”.For example, many commencing students cannot provide even a roughsketch of a sine curve without their calculator.”

■ “My personal view is that calculators cripple the brain and discouragethinking and reasoning and thus should be abandoned.”

Some opinions


■ “. . . when I realised that so many students didn’t have any ability with evenfundamental arithmetic or times-tables, and showed very little willingness toput the effort in to learn them. Students straight from school were also quitedistraught at losing access to their calculators, because unfortunately, the(state) school systememphasises the “use of technology” in the classroom.This means that many students, even good students, equate mathematicswith calculators.”

Some opinions


1. “Lack of student facility with basic skills led to allowing calculators.”

2. “Students don’t understand the maths as well if they don’t do it by hand.”

Summary of Universities survey


■ 27 Universities responded to questionnaire

■ 9 do not allow calculators in any Mathematics unit

■ 8 allow ANY calculator

■ 18 allow approved Scientific calculator (1 allows programmable calculatorand text retrieval devices).

It seems that many universities do not have a policy on calculators, and it is leftto the unit co-ordinator to decide.

This Research


■ To investigate the effect of allowing calculators on student performance in alow-level mathematics unit.

■ To investigate the attitude of university teaching staff on calculators inmathematics in university and school mathematics.

■ To investigate the attitude of school teachers on calculatorsin mathematicsin primary and high school.

First Study


■ MATH1720 is taken by students who do not have Mathematics Methods.

■ It covers numbers, algebra, quadratic, exp and log functions,graphs, briefintroduction to calculus (one week).

■ Calculators were not allowed in this unit prior to semester 2 2016.

■ We trialled a scientific calculator in the unit as below.

S1 S22016 No Calculator Calculator

2017 Calculator No Calculator

Data exploration


Results up till now for 2016.

2015 S2 2016 S1 2016 S2Exam Overall Exam Overall Exam Overall

Minimum 0 8 0 3 1 0LQ 50 51 49 50 42 50Median 70 62 68 65 63 66Mean 67 65 66 65 61 64UQ 92 87 86 84 80 81Maximum 100 100 100 100 100 99SD 26 22 24 23 24 22

Data exploration


No Yes

010

2030

4050

60

Calculator

Exam

mar

k

Data exploration


No Yes

020

4060

8010

0

Calculator

Ove

rall

Data Modelling


Linear model. Variables are:

■ Exam or Overall: response(%)■ Age■ Type: Ausr, Int, PR, NZ■ Sex■ Course■ Repeat: whether repeating unit■ HSMaths: maths unit taken in high school■ HSmark: mark in HS maths unit■ TER: Tertiary exam rank

Results


■ Older students (26 and above) performed better.

■ A higher TER gave a higher exam mark.

■ A higher mark in HSMaths gave a higher final mark.

■ No difference in performance between males and females.

Results


■ Older students (26 and above) performed better.

■ A higher TER gave a higher exam mark.

■ A higher mark in HSMaths gave a higher final mark.

■ No difference in performance between males and females.

■ Calculator had NO difference in average performance.

Further data exploration


1 2 3 4 5 6 7 8 9 10

Caculator: NoCalculator: Yes

Exam mark

Decile

Perc

ent o

f cla

ss

05

1015

2025

Further data exploration


1 2 3 4 5 6 7 8 9 10

Caculator: NoCalculator: Yes

Overall mark

Decile

Perc

ent o

f cla

ss

05

1015

2025

30

Conclusions


■ After adjusting for other variables,NO difference in average performancewith and without calculator.

■ BUT

Conclusions



■ BUT top students do not perform as well with calculator.

■ There may be some difference as HS mathematics curriculum for 2015 and2016 cohort was different.

Conclusions



■ BUT top students do not perform as well with calculator.

■ There may be some difference as HS mathematics curriculum for 2015 and2016 cohort was different.

Further trials this year in each semester.

Further studies


■ Survey of academics on attitude to use of calculators in schoolmathematics.

■ Survey of school teachers on attitude to use of calculators in schoolmathematics.

■ Comparison between Australia and other countries, particularly India, China,Singapore and selected European countries.

Preliminary Results


No YesBasic Scientific Graphing CAS

Primary 33 6 0 1 1High School 7 0 27 3 4University 8 0 22 5 6

For TEE/WACE exams, scientific calculators were first allowed in 1980,Graphics in 1996 and CAS in 2009.

In England:


Primary maths

http://www.telegraph.co.uk/education/educationnews/10734641/Calculators-banned-in-tough-new-primary-school-exams.html

In India:


Central Board of Secondary Education

http://www.thehindu.com/todays-paper/tp-features/tp-educationplus/use-of-calculator-not-allowed-in-cbse-exams/article2863785.ece

Singapore


No CAS

http://www.seab.gov.sg/content/calculator/GuidelinesCalculators.pdf

And finally: China!


Comparison of US and China“ From elementary school through high school, Chinese students are not allowedto use calculators.”

http://www.internationalnewsroom.com/cn-us-education/

And finally: China!


Comparison of US and China“ From elementary school through high school, Chinese students are not allowedto use calculators.”

“Students reported they did not use calculators until senior high school. Juniorhigh school students displayed well-developed algebraic techniques. Themechanics of mathematics, learned in primary school, are applied in secondaryschool. In contrast, time in English secondary schools has to be spent developingnumerical and algebraic techniques; insufficient time is given to applying theseskills to real life contexts.” —Report on research into maths andscience teachingin the Shanghai region Research by National Leaders of Education and SubjectSpecialists in Shanghai and Ningbo, China 11-18 January 2013

http://www.internationalnewsroom.com/cn-us-education/

Mathematics Olympiad Rankings


Country Top RankingChina 19

Soviet Union/Russia 16Hungary 6

USA 5Romania 5

Moscow University Entrance Examination


https://brilliant.org/problems/moscow-state-university-entrance-exam-question-2/

https://brilliant.org/problems/moscow-state-university-entrance-exam-question-2/

Russian Primary Mathematics—sans calculator!


■ Write a three digit number twice without any space, so you get a six digitnumber. This number is divisible by 7. Why?

■ Is there a number that has more than one digit and equals the product of itsdigits?

Another opinion


For W. Stephen Wilson, a math and education professor at Johns HopkinsUniversity, using a calculator is akin to relying on a crutch when one doesnt havea bad leg. “I have not yet encountered a mathematics concept that requiredtechnology to either teach it or assess it. The concepts and skills we teach are sofundamental that technology is not needed to either elucidate them or enhancethem. There might be teachers who can figure out a way to enhance learningwith the use of technology, but its absolutely unnecessary,”’ Wilson wrote in thejournal Education Studies in Mathematics.

https://www.theatlantic.com/education/archive/2016/12/the-conundrum-of-calculators-in-the-classroom/493961/

https://www.theatlantic.com/education/archive/2016/12/the-conundrum-of-calculators-in-the-classroom/493961/

What do you think?


Please complete my survey:

http://uwa.qualtrics.com/SE/?SID=SV_bqO5tRNIt3wQog5

http://uwa.qualtrics.com/SE/?SID=SV_bqO5tRNIt3wQog5

Reference


1. Kastberg, S. and Leatham, K. (2005). Research on graphing calculators atthe secondary level: Implications for mathematics teacher education.Contemporary Issues in Technology and TeacherEducation, 5(1), 25–37 .

2. Kissane, B., NG, W. L. and Springer, G. T. (2015) Graphics calculators andthe school mathematics curriculum: Perspectives and issues from threecountries.Proceedings of the 20th Asian Technology Conference inMathematics, Leshan, China.

3. Sheets, C. L. (2007) Calculators in the Classroom: Help or Hindrance?Action Research Projects. Paper 33.http://digitalcommons.unl.edu/mathmidactionresearch/33

4. Report on research into maths and science teaching in the Shanghai region.Research by National Leaders of Education and Subject Specialists inShanghai and Ningbo, China 11–18 January 2013.

http://digitalcommons.unl.edu/mathmidactionresearch/33

Documents

R.Nazim Khan School of Mathematics and Statistics The ... · “ From elementary school through high school, Chinese students are not allowed to use calculators.” “Students reported