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）

References 0

	付婉迪. (2021). 中美数学高考试卷比较及对我国高中数学教学管理的启示. 上海: 上海师范大学教育硕士专业学位论文.
	国务院办公厅. (2019). 关于新时代推进普通高中育人方式改革的指导意见. 取自: http://www.gov.cn/zhengce/content/2019-06/19/content_5401568.htm
	胡耀华. (2009). 信息技术环境下的数学评价——图形计算器在国外大学入学数学考试中的使用情况及启示. 现代教育技术, 19 (5), 37- 40. doi: 10.3969/j.issn.1009-8097.2009.05.009
	教育部. (2020). 普通高中数学课程标准 (2017年版2020年修订). 北京: 人民教育出版社.
	教育部. (2021). 教育部关于做好2021年普通高校招生工作的通知. 取自: http://www.moe.gov.cn/srcsite/A15/moe_776/s3258/202102/t20210208_513027.html
	李作滨. (2019). 2018 年13 套高考数学试卷审思: 基于核心素养的视角. 教育测量与评价, (4), 51- 57; 64.
	廖运章, 卢建川. (2015). 2014英国国家数学课程述评. 课程•教材•教法, 35 (4), 116- 120.
	林风. (2012). 基于图形计算器开展数学实验的实践与思考. 中国电化教育, (2), 105- 108. doi: 10.3969/j.issn.1006-9860.2012.02.020
	林磊. (2001). 用图形计算器解2001年上海市高考试题. 数学教学, (5), 24- 26+33.
	林米儿. (2006). 关于现代教育技术在数学教育中应用的探索——由图形计算器解数学高考题引起的若干思考. 现代教育技术, 16 (2), 38- 41. doi: 10.3969/j.issn.1009-8097.2006.02.009
	刘娟娟. (2016). 计算器在美国小学数学教学中的使用及启示. 课程•教材•教法, 36 (11), 123- 127.
	刘琴. (2010). 中外数学考试中计算器使用的比较研究. 上海师范大学学报 (基础教育版), 39 (4), 44- 49.
	马峰. (2021). 国际文凭数学课程改革的特点分析及其启示. 比较教育学报, (3), 150- 163. doi: 10.3969/j.issn.2096-7810.2021.03.011
	任子朝, 陈昂. (2016). SAT数学考试改革研究——兼议对我国高考改革的启示. 中国考试, (6), 20- 24. doi: 10.3969/j.issn.1005-8427.2016.06.005
	上海市教育考试院. (2021). 2022 年普通高等学校招生全国统一考试（上海卷）考试手册（语文、数学、外语）. 上海: 上海教育出版社.
	沈建刚. (2015). 借助图形计算器平台, 用实验法求解解析几何高考题. 中小学数学(高中版), (12), 62- 64.
	数学教学. (2000). 函数型计算器今年进入上海高考. 数学教学, (2), 19.
	数学教学. (2001a). 2001年上海市普通高等学校春季招生考试数学试卷. 数学教学, (1), 33- 36.
	数学教学. (2001b). 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). 数学教学, (4), 37- 41.
	孙元清, 徐淀芳, 张福生, 赵才欣. (2016). 上海课程改革25年 (1988—2013). 上海: 上海教育出版社.
	王焕霞. (2015). 高中物理学业水平考试与课程标准的一致性研究. 课程•教材•教法, 35 (8), 60- 66.
	汪文. (2001). 素质教育在上海. 中国青年报, 2001-01-10
	虞涛. (2008). 上海高考使用计算器8年的回顾与思考. 数学教学, (4), 1- 5.
	虞涛. (2017). 与时俱新的高考数学上海卷应用问题. 数学教学, (6), 49- 53.
	张京京. (2020). 2010-2019年上海高考数学发展趋势研究. 上海: 上海师范大学教育硕士专业学位论文.
	张沿沿, 顾建军, 徐维炯, 陆叶丰. (2018). 对我国8省市区义务教育阶段学生技术素养的调查与研究. 华东师范大学学报 (教育科学版), 36 (6), 29- 41.
	张阳开, 梁策力, 陈朝东. (2014). 高考数学使用计算器的争鸣及思考. 数学教育学报, 23 (4), 88- 91.
	张玉环, 周侠. (2020). 综合难度视角下中法高考数学试题的比较研究——基于2015—2019 年中国和法国高考数学试卷. 数学教育学报, 29 (3), 43- 50.
	Brown, R. G. (2005). The impact of the introduction of the graphics calculator on system wide ‘high stakes’ end of secondary school mathematics examinations. Doctoral dissertation, Swinburne University of Technology.
	Brown, R. G. (2010). Does the introduction of the graphics calculator into system-wide examinations lead to change in the types of mathematical skills tested? Educational Studies in Mathematics, 73(2), 181−203.
	Browne, R. & Ellis, W. (1997). Type, purpose and validity of assessment. In J. Berry, M. Kronfellner, B. Kutzler, & J. Monaghan (Eds.) The State of Computer Algebra in Mathematics Education (pp. 63−70). Bromley: Chartwell-Bratt.
	College Board. (2021). SAT Math Test. Retrieved from https://collegereadiness.collegeboard.org/sat/inside-the-test/math
	Department of Basic Education, Republic of South Africa. (2020). Mathematics P2 for National Senior Certificate. Retrieved from https://wcedonline.westerncape.gov.za/documents/ExamPapers%26Memos/NSC-Exams-2020-Nov/non-languages/Mathematics/Mathematics%20P2%20Nov%202020%20Eng.pdf
	Eunoia Junior College. (2020). JC 2 Preliminary Examination 2020, General Certificate of Education Advanced Level, Higher 1. Retrieved from https://www.sgtestpaper.com/gce/test_papers/jc2_math_h1_2020/JC2_Maths_H1_2020_EJC.pdf
	IBO. (2021). Mathematics: Applications and Interpretation Guide: First Assessment 2021. Retrieved from https://resources.ibo.org/data/mathematics-applications-and-interpretation-guide_3573b93d-5f69-4c19-8e30-c135da72b01c/mathematics-applications-andinterpretation-guide-en_5659ecbf-2f8b-4873-8075-c931f676e101.pdf
	Makonye, J. P. & Fakude, J. (2016). A study of errors and misconceptions in the learning of addition and subtraction of directed numbers in grade 8. SAGE Open, 6 (4), 1- 10.
	NSW Education Standards Authority. (2020). Higher School Certification Examination Mathematics Standard 2. Retrieved from https://educationstandards.nsw.edu.au/wps/wcm/connect/bbfe0d35-4e7e-4276-b7f7-d663194714a0/2020-hsc-mathematics-standard-2.pdf?MOD=AJPERES&CACHEID=ROOTWORKSPACE-bbfe0d35-4e7e-4276-b7f7-d663194714a0-no2PDZc
	OECD. (2018). PISA 2018. Retrieved from https://www.oecd.org/pisa/aboutpisa/pisa-2018-participants.htm
	Ruthven, K. (2022). Ergonomic, epistemological and existential challenges of integrating digital tools into school mathematics. Asian Journal for Mathematics Education, 1 (1), 1- 12. doi: 10.1177/27527263221077314
	Senk, S. L., Beckmann, C. E. & Thompson, D. R. (1997). Assessment and grading in high school mathematics classrooms. Journal for Research in Mathematics Education, 28 (2), 187- 215. doi: 10.2307/749761
	The World Bank. (2021). 2018 GDP Per Capita (current US$). Retrieved from https://data.worldbank.org/indicator/NY.GDP.PCAP.CD?end=2021&name_desc=false&start=1960&view=map&year=2018

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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