Should Calculators Be Allowed to Use in College Entrance Examinations in Mathematics: An International Comparison of 30 Countries and Regions’ Calculator Use Policies and Practices in College Entrance Examinations

doi:10.16382/j.cnki.1000-5560.2023.04.007

Abstract

Abstract:

Whether calculators should be introduced to College Entrance Examinations in Mathematics (CEE-M) in China is a long-standing controversial topic. This study examined calculator use policies and practices in CEE-M in 30 relatively economically developed countries and regions, and compared their delivery modes (single, mixed), types of calculators allowed and roles of calculators in exam questions and solutions; representative questions in selected sample exams were also used for case analysis. The study found that most CEE-M allowed students to use calculators, with mainly the single delivery mode using scientific calculators, and introducing calculators into the CEE-M can provide a new opportunity to enhance the real-life context, openness, and flexibility of questions in mathematics examinations. According to the results, the study concluded that there is a need to fully realize the value of introducing calculators in CEE-M, carry out more research in designing exam questions allowing calculators to promote examination reform and innovation, and establish a long-term plan for introducing calculators into mathematics classrooms and examinations.

Key words: college entrance examinations in mathematics, education examination policy, calculator use, ICT, international and comparative education

Shuhui Li, Shang Li, Lianghuo Fan. Should Calculators Be Allowed to Use in College Entrance Examinations in Mathematics: An International Comparison of 30 Countries and Regions’ Calculator Use Policies and Practices in College Entrance Examinations[J]. Journal of East China Normal University(Educational Sciences), 2023, 41(4): 83-92.

Figures/Tables 4

国家、地区	考试及数据年份	计算器种类	模式
美国	Scholastic Assessment Test (SAT) Math Test, 2021	科学/图形（含CAS）	混合
美国	American College Test (ACT) Math, 2021	科学/图形（不含CAS）	单一
加拿大¹	Uniform Examination for Secondary IV Mathematics, 2021	科学/图形（不含CAS）	单一
加拿大¹	Alberta Diploma Examinations - Mathematics, 2021	科学/图形（不含CAS）	单一
德国	Abitur Mathematik, 2021 (英文：The German Abitur)	科学²	单一
英国³	General Certificate of Education Advanced Level (GCE A-Level) Mathematics & Further Mathematics, 2021	科学/图形（不含CAS）	混合
法国	Baccalauréat en mathématiques, 2019 (英文：The French Baccalaureate)	科学/图形（不含CAS）	单一
意大利	Esame di Stato conclusivo del secondo ciclo di istruzione - Matematica, 2020 (英文：The Upper Secondary School Leaving Exam (State Exam) in Italy)	科学/图形（不含CAS）	单一
西班牙	Evaluación de Bachillerato para el Acceso a la Universidad - Matemáticas II, 2021 (英文：The Spanish Baccalaureate)	科学²	单一
荷兰	VWO wiskunde (A, B, C), 2022 (英文：VMO)	科学/图形（不含CAS）	单一
丹麦	Vejledende enkeltopgaver stx Mat A & stx Mat B, 2020 (英文：The Higher General Examination Programme (stx) Exam in Denmark)	科学/图形（含CAS）等⁴	混合
芬兰	Ylioppilastutkinto - Matematiikka, 2021 (英文：The Finnish Matriculation Examination)	科学/图形（含CAS）等⁴	混合
澳大利亚⁵	NSW Higher School Certificate Examination - Mathematics Standard 1 & 2, 2022	科学	单一
南非	National Senior Certificate Examination of South Africa - Mathematics P1&P2, 2020	科学	单一
阿联酋	????? ???????? ??????? 2021 (英文：The Emirates Standard Test)	科学⁶	单一
新加坡	Singapore-Cambridge GCE A-Level Mathematics, 2021	科学/图形（不含CAS）⁷	单一
以色列	????? ????? (Levels 3-5), 2021 (英文：The Israeli Matriculation Exams (Bagrut))	科学/图形（不含CAS）	单一
中国上海⁸	普通高等学校招生全国统一考试上海数学试卷, 2021	科学	单一
中国香港	香港中学文凭考试数学必修部分, 2021	科学	单一
马来西亚	Sijil Pelajaran Malaysia Mathematics, 2021	科学	单一
IB	Mathematics: Analysis and Approaches; Applications and Interpretation, 2021	图形（不含CAS）	混合

来源	样题节选/解答
2020年南非样卷第2题图表（Department of Basic Education, Republic of South Africa，2020）
2001年上海市普通高等学校春季招生考试数学试卷第12题（数学教学，2001a）	12. 甲、乙两人于同一天分别携款1万元到银行储蓄。甲存五年期定期储蓄，年利率为2.88%。乙存一年期定期储蓄，年利率为2.25%，并在每年到期时将本息续存一年期定期储蓄。按规定每次计息时，储户须交纳利息的20%作为利息税。若存满五年后两人同时从银行取出存款，则甲与乙所得本息之和的差为_元。(假定利率五年内保持不变。结果精确到1分)
2020年新加坡A-level样卷第5题（v）解答（Eunoia Junior College，2020）
2001年全国普通高等学校招生统一考试上海数学试卷（理工农医类）第16题（数学教学，2001b）
2020年澳大利亚HSC Mathematics Standard 2样卷第36题节选（NSW Education Standards Authority，2020）	36. 雄性蟋蟀会发出唧唧渣渣的声音。一位科学家想要探索温度（以摄氏度为单位）与15秒内蟋蟀鸣叫次数之间的关系。科学家每天收集一次数据，连续收集了20天。基于这20天的数据，科学家提供了以下信息。 ? 下图是一个显示温度数据的box-plot统计图。 ? 平均温度（the mean temperature）比中间温度（the median tempreature）低0.525°C。 ? 科学家在20天中总共收集了684次蟋蟀鸣叫。科学家用最小二乘法线性回归直线对收集的数据进行拟合。x表示温度（以摄氏度为单位）， $ y $ 表示15秒内蟋蟀鸣叫的次数。线性回归直线的方程是 $y=-$ 10.6063+bx，其中b是回归直线的斜率。请计算19摄氏度时每15秒间隔内预期的蟋蟀鸣叫的次数。（精确到整数）
2020年新加坡A-level样卷第6题解答（Eunoia Junior College，2020）

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大洲	人均GDP上位圈的国家及地区¹
亚洲	中国大陆（上海、上海以外地区）²、日本、韩国、印度尼西亚、沙特阿拉伯、泰国、阿联酋、新加坡、以色列、中国香港、马来西亚、中国澳门、中国台湾³
北美洲	美国、加拿大
南美洲	巴西、哥伦比亚
欧洲	德国、英国、法国、意大利、俄罗斯、西班牙、土耳其、荷兰、丹麦、芬兰
大洋洲	澳大利亚
非洲	南非

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