Introduction
Purpose and Scope of the IB Mathematics Comparability Study
This report summarizes two independently written reports created as a part of the IB Mathematics Comparability Study. The purpose of the IB Mathematics Comparability Study is “to review and compare a selection of well-esta...
The summary is based on full reports by Adriana Alcántara and UK NARIC.
Adriana Alcántara, Ph.D. UK NARIC
International Education The National Recognition Information Centre,
Consultant United Kingdom
, Introduction
Purpose and Scope of the IB Mathematics Comparability Study
This report summarizes two independently written reports created as a part of the IB Mathematics
Comparability Study. The purpose of the IB Mathematics Comparability Study is “to review and compare a
selection of well-established mathematics qualifications offered in a range of high-performing education
systems around the world whose primary function is to prepare senior secondary students for higher
education”.1 In this study, IB’s four Diploma Program mathematics courses – Mathematical Studies SL,
Mathematics SL, Mathematics HL and Further Mathematics HL – are compared with five mathematics
qualifications chosen on the basis of their market share, the extent of their university recognition,
geographical spread and their performance on PISA tests (where relevant):2
1) Alberta Diploma (Canada): Alberta Math 30-1, Alberta Math 30-2, Alberta 31
2) Advanced Placement (AP) (US and Canada, growing overseas market): AP Calculus AB, AP Calculus BC
3) GCE A Levels (England and overseas market): A Level Mathematics and A Level Further Mathematics
4) Singapore-Cambridge GCE A Levels (SIPCAL) (Singapore): Singapore H1 Math, Singapore H2 Math,
Singapore Math H3
5) Gāokăo (China): Gāokăo
This study is composed of two distinct components: the Curriculum Comparison, which involves a compilation,
analysis and comparison of the attributes of these qualifications, and the Assessment Comparison, which
involves a comparative analysis of the assessment objectives, assessment methods, and marking guidelines.
Dr. Adriana Alcántara performed the curriculum analysis and the National Recognition Information Centre in
the United Kingdom (UK NARIC) conducted the assessment comparison. It is important to note the term
“curriculum” is used when referring to the content of the qualifications analyzed. Often studies of this nature
use the term “standards”. Standards are generally considered the benchmark for judging student progress.
Standards outline what students are expected to know at each level. Curriculum is generally understood to be
more comprehensive. Curriculum usually refers to the collection of teaching materials used to facilitate
student learning so that each student can reach or exceed the standards.
Theoretical framework
This work extends on two previous alignment projects involving the IB DP. In 2014 Dr. Faas explored the
extent the IB DP aligns with national standards in selected regions in Germany and Switzerland3. Additionally,
Dr. Conley performed an alignment study between the IB DP and the Knowledge and Skills for University
Success (KSUS). Faas’ research compares the DP written curriculum to selected German and Swiss regional
curriculums with regard to content, cognitive demand and philosophical underpinnings. The findings suggest
that while there is a high level of content alignment between the DP and Swiss and the DP and German
curriculums in the natural sciences (biology and mathematics), there is less alignment in the social sciences
1
IB Mathematics Comparability Study Project Plan, 29/01/2015.
2
The focus of this study is on the qualifications themselves, not on the national or state systems that sustain them (in the relevant
cases).
3
Faas, D, & Friesenhahn, I. (2014a). Curriculum Alignment between the IB DP and national systems: Germany. Bethesda, MD, USA.
International Baccalaureate Organization; Faas, D, & Friesenhahn, I. (2014b). Curriculum Alignment between the IB DP and national
systems: Switzerland. Bethesda, MD, USA. International Baccalaureate Organization.
1
,and humanities (history and Spanish). The DP also appears to offer greater flexibility than the Swiss and
German curriculums, allowing students to pursue their academic interests.
In 2009 Conley and Ward4 analyzed the alignment of the IB DP standards and the Knowledge and Skills for
University Success (KSUS) and found IB standards to be highly aligned with the KSUS standards. The study also
confirmed complete alignment between the IB Diploma’s mathematical studies and the KSUS’ algebra,
trigonometry and statistics standards.
Methodology
There are numerous methodologies for investigating curriculum comparisons5. Researchers often rely on
methods like the Webb Model6 or the Achieve Model7 which convene a panel of judges to score intended
curriculum using qualitative and quantitative indicators. This can be difficult to apply to the international
comparisons required by this study because consistent information is not available for all the courses
examined in this research. It is difficult to gather exactly the same categories of data, in the same degree of
detail, from a wide range of international educational qualifications, due to language barriers, different rules
about the public accessibility and confidentiality of data, or simply different approaches to laying out
curricular requirements. Therefore, it is not feasible to establish the uniform scoring categories required by
the Webb Model or Achieve Model. To encourage an objective analysis two independent researchers were
commissioned to carry out the curriculum and assessment comparisons. Similar to the Webb Model and the
Achieve Model, both researchers utilized the intended curriculum in their analyses. The curriculum
comparison was performed by Dr. Adriana Alcántara. Data was gathered mainly from primary sources,
consisting of the most recent guidance documents and course specifications or guides provided by the
administering authorities of each qualification (available on their official websites). Secondary sources were
also used to enrich the data, namely existing international studies that have compared various mathematics
qualifications. One particularly useful source for this report is Ofqual’s 2012 International Comparisons in
Senior Secondary Assessment (hereafter referred to as ICOSSA), which provides a methodological model in
some ways, and contains a large amount of detailed data on several of the qualifications included in this study.
With regard to concerns over objectivity, the curriculum research highlights similarities and differences
between other qualifications and IB qualifications in its analysis and conclusions, but IB qualifications were not
used as a benchmark against which to compare the others. In order to establish an external framework for
determining certain equivalencies between the qualifications, the textbooks and course outlines used by top
global universities in science and engineering were referred to for defining objective categories of
mathematics content.
The assessment comparison was carried out by UK NARIC. Again, because each qualification being compared
had different details available it was difficult to quantitatively score the qualifications. Therefore, a qualitative
comparison approach was utilized. To arrive at a point at which reliable comparisons could be drawn between
the international awards; it was important to thoroughly explore each qualification and its mathematics
4
Conley, D., Ward, T. (2009). International Baccalaureate Standards Development and Alignment Project. Educational Policy
Improvement Center, Eugene, Oregon.
5
Bloom, B.S., Madaus, G.F., & Hastings, J.T. (1981). Evaluation to Improve Learning, New York: McGraw-Hill.; Webb, N.L. (1999).
Alignment of Science and Mathematics Standards and Assessments in Four States, Washington: Council of Chief State School
Officers.; Faas, 2014
6
Webb, 1999
7
developed by Achieve, Inc. in 2000 (http://www.achieve.org/)
2
, programme(s) in isolation, building up comprehensive and objective profiles. The awarding bodies or
government websites were reviewed and any publically available documentation was collected. Using this
information, or sources provided through the awarding bodies or governments, additional websites providing
information pertaining to the international qualifications were reviewed with any relevant information
collated. Where documentation was lacking, which was the case for most of the awards, an overall web
search was completed for any remaining websites containing information related to the international
qualifications. The main documents searched for included:
Examination papers and mark schemes
Student or teacher handbooks/guides
Grade distribution data.
The comparative analysis involved comparing each of the IB DP Mathematics courses with the international
counterparts considering factual information gathered, with the aim of highlighting similarities and
differences. Some aspects of the comparative analysis were, by their very nature, more subjective. It is
important however to highlight that UK NARIC, both in its capacity as a national agency and as a credential
evaluation organisation rather than awarding body, undertook a fully independent and objective analysis.
Curriculum: Overview of Mathematics Similarities and Differences
Comprehensive individual profiles for each qualification are available in the full report. Similarities and
differences in 1) structure 2) content, 3) cognitive demand, 4) philosophical underpinnings and 5) university
recognition for the qualifications are discussed below.
In general, it is clear that the mathematics courses seek to provide a solid preparation for further study in
higher education. Specifically, three courses (the IB DP Further Mathematics HL, A Level Further Mathematics
and the Singapore Math H3) are intended for those who have a strong aptitude and enthusiasm for
mathematics.
Structure
Three of the six qualifications analyzed are baccalaureate-style qualifications (the Alberta Diploma, Singapore-
Cambridge A Level Curriculum, and the International Baccalaureate Diploma), whose purpose is to provide
students with a holistic education that covers a variety of subjects from different areas. The Chinese Gāokăo is
a comprehensive examination that defines the content of the Senior Secondary curriculum; thus, it also
requires students to follow a certain fixed combination of subjects. Advanced Placement and A Levels, in
contrast, provide stand-alone qualifications in a variety of subjects that can be taken independently of each
other. AP courses are currently offered in 34 subjects; they are stand-alone courses, which can be taken in
any number or order, and are not part of any structured Diploma. Nonetheless, it is important to note that a
certain number or combination of AP courses are sometimes incorporated by individual schools or school
districts into a specific set of requirements for completing an academic track. The College Board itself has also
created an AP “Capstone Diploma”, launched at some participating schools in 2014, which is awarded to
students who obtain scores of 3 or higher on four AP courses and who also take two new courses, AP Seminar
(focusing on analyzing and evaluating information and making sound arguments) and AP Research (producing
and defending a scholarly academic thesis).8 This Diploma appears to be an attempt to emulate the
8
The College Board (2015). Advances in AP. Retrieved from https://advancesinap.collegeboard.org/ap-capstone.
3
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