4
The International Baccalaureate Programme

Given the differences in their origins and goals, it is not surprising that the International Baccalaureate (IB) and Advanced Placement (AP) programs differ significantly. This chapter presents a detailed review of the IB program; a similar review of the AP program is provided in Chapter 3. The first section gives an overview of the IB program; the sections that follow address in turn IB curriculum, instruction, assessment, and professional development.

OVERVIEW

The International Baccalaureate Organisation (IBO), a nonprofit educational foundation headquartered in Geneva, Switzerland, was founded in the 1960s with the mission of fostering in member schools international understanding and responsible world citizenship, as well as intellectual rigor and high academic achievement (IBO, 1997a). The IB Diploma Programme consists of a comprehensive precollege curriculum for highly motivated students in the last 2 years of high school that allows students to fulfill the requirements of various educational systems and aims to incorporate the best elements of many different national models (IBO, 1997a). Each of the IB courses in mathematics and the experimental sciences incorporates a formative internal assessment component and culminates in an internationally administered external examination. Students who complete the program and receive qualifying scores on the examinations are awarded the IB Diploma.1

1  

Although the IBO does not represent its courses as replacements for college courses, some college and university policies allow for granting credit or placement. A database listing these institutions and describing their policies can be accessed at the IBO Web site at http://www.ibo.org/ibo/index.cfm/en/ibo/services/universities (November 28, 2001).



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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 4 The International Baccalaureate Programme Given the differences in their origins and goals, it is not surprising that the International Baccalaureate (IB) and Advanced Placement (AP) programs differ significantly. This chapter presents a detailed review of the IB program; a similar review of the AP program is provided in Chapter 3. The first section gives an overview of the IB program; the sections that follow address in turn IB curriculum, instruction, assessment, and professional development. OVERVIEW The International Baccalaureate Organisation (IBO), a nonprofit educational foundation headquartered in Geneva, Switzerland, was founded in the 1960s with the mission of fostering in member schools international understanding and responsible world citizenship, as well as intellectual rigor and high academic achievement (IBO, 1997a). The IB Diploma Programme consists of a comprehensive precollege curriculum for highly motivated students in the last 2 years of high school that allows students to fulfill the requirements of various educational systems and aims to incorporate the best elements of many different national models (IBO, 1997a). Each of the IB courses in mathematics and the experimental sciences incorporates a formative internal assessment component and culminates in an internationally administered external examination. Students who complete the program and receive qualifying scores on the examinations are awarded the IB Diploma.1 1   Although the IBO does not represent its courses as replacements for college courses, some college and university policies allow for granting credit or placement. A database listing these institutions and describing their policies can be accessed at the IBO Web site at http://www.ibo.org/ibo/index.cfm/en/ibo/services/universities (November 28, 2001).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools The requirements for the IB Diploma are designed to engage students in an integrated program of studies as they complete courses and examinations in one subject from each of six different subject groups.2 Students study some subjects in depth by selecting at least three but no more than four courses at the Higher Level (HL) and explore others more broadly at the Standard Level (SL). This approach represents a deliberate compromise between the early specialization preferred in some national systems and the breadth found in others (IBO, 1998b, p. 2, 2001a, 2001b, 2001c, p. 1). HL courses are 2-year courses. SL courses may be completed in 1 year if scheduling allows for the required number of hours, although many IB schools offer 2-year SL courses.3 In contrast to the AP program, which aims to provide discrete college-level courses for students in high school, the IB courses are part of an integrated program designed to prepare students for college. The IB mathematics program offers a selection of mathematics courses designed to meet the varying needs, interests, and abilities of college-bound high school students. The IB Mathematical Methods SL course is designed to provide a sound mathematical background for students who expect to study subjects at the university level that have a significant mathematical content. The IB Mathematics HL and Further Mathematics SL courses offer more rigorous preparation. Another fundamental difference between the AP and IB mathematics programs is that the IB mathematics courses are not calculus courses; rather, they focus on many advanced mathematics topics that may include calculus.4 Similarly, students are offered both HL and SL courses in each of the experimental sciences; this accommodates students with a strong interest in science while also providing sound preparation in science for those who wish to focus on other subjects. Three additional requirements are designed to give IB Diploma candidates the opportunity to pursue their own interests while at the same time developing a broad understanding of the bases of knowledge in both the humanities and the sciences. Theory of Knowledge is a 2-year course of study unique to IB and mandatory for every diploma candidate. “It challenges students and their teachers to reflect critically on diverse ways of knowing and areas of knowledge, and to consider the role which knowledge plays in a global society. It encourages students to become aware of 2   Language (a student’s first language and a study of world literature), a second modern language, the social sciences, the experimental sciences, mathematics, and the arts and electives. 3   For IB courses, 240 hours of teaching is recommended for HL courses and 150 hours for SL courses. 4   For a detailed discussion of the content of these courses, including their calculus component, and an analysis of how they fit into typical U.S. high school mathematics programs, see the report of the mathematics panel, available at http://www.nap.edu/catalog/10129.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools themselves as thinkers …” (IBO, 2000b, p. 3). The curriculum for the course centers on a series of questions, including those designed to help students understand the nature of knowledge in mathematics and the sciences.5 IB Diploma candidates must also satisfy the Extended Essay requirement by undertaking original research and writing an essay of some 4000 words. This requirement offers students the opportunity to investigate a topic of special interest and acquaints them with the independent research and writing skills expected at the university level. It allows them to deepen their study by investigating a topic that was introduced in one of their higher-level courses or to add breadth to their program by studying a subject not included in their diploma courses. A third requirement—the Creativity, Action, and Service requirement (CAS)—encourages students to become involved in extracurricular activities. A student who satisfies the Theory of Knowledge, Extended Essay, and CAS requirements and achieves a cumulative score of at least 24 points on the six examinations (each of which is graded on a scale from 1 to 7) is awarded the IB Diploma. An IB Certificate is awarded to students who take any number of individual IB courses and the subsequent examinations, but do not fulfill all of the requirements for the diploma. During the past three decades, an increasing number of U.S. high schools have joined IB schools worldwide in offering the Diploma Programme. In May 2000, 18,511 students from 255 U.S. public and private schools took 50,745 IB examinations. Approximately two-thirds of those students were candidates for the IB Diploma,6 and one-third were certificate candidates (May 2000 Summary). Although these students represent less than 2 percent of U.S. high schools, their increasing numbers indicate that the IB program is experiencing a period of rapid growth in this country. The number of IB examinations administered in the United States has increased by an average 16 percent annually every year since 1994. The number of schools applying to International Baccalaureate of North America (IBNA) has tripled over the 5   The central questions examined include the following: How do I or how do we know that a given assertion is true, or a given judgment is well grounded? How is knowledge gained? What role does personal experience play? Do we construct reality, or do we recognize it? How is a mathematical proof different from, or similar to, justifications accepted in other areas of knowledge? Has technology, for example computers and electronic calculators, influenced the knowledge claims made in mathematics? Is the scientific method a product of western culture or is it universal? To what extent can science be understood through the study of just one discipline, for example physics? Are the models and theories created by scientists accurate descriptions of the natural world, or are they primarily useful interpretations for prediction, explanation, and control of the natural world? (IBO, 2000b, pp. 3–4) 6   According to Paul Campbell, director for programs, International Baccalaureate of North America (IBNA) (personal communication), approximately 70 percent of diploma candidates earn the IB Diploma.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools past several years and has been stable recently at 50 to 60 applications per year.7 A high school must offer all the components of the diploma program and be authorized by the IBO to use IB curriculum and assessment materials, register candidates for the IB examinations, and qualify them for the IB Diploma. U.S. schools that are interested in joining the IBO complete a self-study and submit a formal application to IBNA. Receipt of the application is followed by an on-site visit by representatives from IBNA that focuses on evaluating faculty commitment and qualifications; physical facilities, including the library and science laboratories; and commitment at the school level. The process of becoming an IB school can take 2 years or more as IBNA evaluates the ability of both the school and the school district to commit resources to providing the administrative structure, faculty, and facilities needed to support the offering of the IB Diploma Programme. IBNA maintains a relationship with member schools that includes monitoring test registration and administration.8 Every 5 years, each IB school conducts a self-evaluation and submits a school review to IBNA. IB CURRICULUM IB mathematics and science courses are designed to be components of an integrated program, and this objective is reflected in the curriculum materials. The IB program guides for courses in each discipline, including mathematics and the experimental sciences, present common aims and objectives. A discussion of the program model, a description of the examination, and detailed information and guidance for teachers about meeting the internal assessment requirements are common to all of the subject guides for experimental science. The guides also provide a topic outline and a detailed syllabus for each course. Teachers use the guides as the basis for determining the structure of their curriculum. Thus like the curriculum for AP courses, the curriculum for IB courses, as it is designed and implemented, can vary from school to school in sequence and emphasis. However, the specificity of the IB syllabus and the requirements for the IB internal assessment lead to less variability in the content of the curriculum and the nature of the laboratory and other practical experiences provided to students than is the case in the corresponding AP courses. The extent to which the IBO specifies curriculum for IB courses is described in detail in the discussion that follows. 7   Paul Campbell, director of programs, IBNA (personal communication). 8   Schools are not able to maintain membership in the IBO without registering students in IB courses for the examinations and ensuring the security of the examinations.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Development of IB Courses The IB course development process is guided by the IBO’s vision of a rigorous, comprehensive, and balanced college preparatory curriculum. A curriculum review committee with international membership is responsible for articulating, implementing, and maintaining the vision in each subject area. The International Baccalaureate Curriculum and Assessment Centre (IBCA) in Cardiff, Wales, has primary responsibility for curriculum development. IBCA staff representatives, most of whom are former IB teachers, work with teachers representing IB schools from around the world on the curriculum review committees. The committees for all subjects in a discipline convene jointly at IBCA because changes in the mathematics or experimental sciences programs impact all of the subjects in that discipline. The role of the curriculum review committees encompasses identifying topics to be included, as well as reviewing the assessment structure and writing the assessment statements for each topic. The mathematics curriculum review committees are also responsible for specifying presumed knowledge and skills for each IB mathematics course. An important distinguishing feature of IB curriculum review is the systematic involvement of classroom teachers in a “consultative process” (IBO, 1999d). The recent revision of the IB Experimental Sciences curriculum illustrates the process well. The process began with a review of responses to questionnaires sent to each IB biology, chemistry, and physics teacher. Teachers were asked about the instructional time spent on each topic in the syllabus and on laboratory work for each topic, as well as about the technology resources available to them. The biology, chemistry, and physics curriculum committees then made revisions to the diploma guides for each subject. Revised versions of the guides were posted on a password-protected Web site for further teacher review and comment before being published. Content of IB Courses The IB Diploma Programme Guide for each subject includes a detailed topic outline. It provides IB teachers with some guidance in identifying fundamental concepts by grouping “essential principles of the subject” in material designated as the core.9 The core topics are common to both the SL and HL courses in a subject, with additional topics being specified for the latter. 9   In the experimental sciences, 80 hours of instruction is recommended for core material in SL courses, with an additional 55 hours for HL courses. In mathematics courses, 105 hours is recommended for SL and 195 hours for HL courses.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools The guides also provide outlines for optional topics.10 Teachers of each IB experimental science subject at an IB school must collaboratively select two options to include in their curriculum. Options are generally selected on the basis of teachers’ backgrounds and areas of expertise, as well as available local resources. The options for IB mathematics courses allow for studying a topic in more depth. Teachers select one option, and the selection made can determine the nature of the course, resulting in very different experiences for students. In the United States, for example, the Mathematics Methods SL option Further Calculus is often selected over the other two options—Statistical Methods and Further Geometry—to provide students with a course that is comparable to the AP Calculus AB course. The experimental science courses offer options that allow in-depth study of a topic, such as the physics options Astrophysics and Relativity. Many, like the physics option Biomedical Physics, focus on interdisciplinary topics. Schools are also allowed to submit an option of their own design for approval. That some schools have taken advantage of this opportunity is indicated by the addition of Medicine and Drugs, previously a local option, to the most recent revision of the IB program guide for chemistry. The IB program guides provide considerable information about what students are expected to know by specifying assessment statements, expressed in terms of learning outcomes, for each topic in the experimental science courses. The guides also give estimated teaching hours for each topic, but do not recommend a sequence for the presentation of topics. To illustrate the considerably greater detail provided in the IB guides than in the AP course descriptions, the treatment of ionic bonds in IB chemistry can be contrasted with the AP topic outline for Chemical Bonding included in Chapter 3, this volume. The latter outline simply lists “ionic” as one of the binding forces that might appear on the AP chemistry examination. AP chemistry teachers must infer the desired depth of treatment of the topic by reviewing old examination questions. In contrast, the Programme Guide for IB Chemistry (IBO, 2001b, p. 51) gives the following six assessment statements for the same topic: Topic 4: Bonding 4.1 Ionic Bond (2 hours) 4.1.1 Describe the ionic bond as the result of electron transfer leading to attraction between oppositely charged ions. 4.1.2 Determine which ions will be formed when metals in groups 1, 2, and 3 lose electrons. 10   Mathematics courses include one 35-hour option. Experimental science courses include two options—15 hours each in SL courses and 22 hours each in HL courses.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools 4.1.3 Determine which ions will be formed when elements in groups 6 and 7 gain electrons. 4.1.4 State that transition metals can form more than one ion. Restrict examples to simple ions e.g., Fe2+ and Fe3+. 4.1.5 Predict whether a compound of two elements would be mainly ionic or mainly covalent from the position of the elements in the periodic table, or from their electronegativity values. 4.1.6 Deduce the formula and state the name of an ionic compound formed from a group 1, 2, or 3 metal and a group 5, 6, or 7 non-metal. The assessment statements for experimental science use 26 action verbs to indicate expectations for each topic. Some of these verbs are highlighted in bold in the preceding example (“describe,” “determine,” “state,” “predict,” and “deduce”). The guides define each verb and associate it consistently throughout the syllabus and on the IB examinations with one of three content objectives: Demonstrate an understanding. Apply and use. Construct, analyze, and evaluate. Use of the action verbs conveys important information to teachers about the expectations for depth and breadth of content. Teachers and students are expected to be familiar with the definitions of these verbs. They must be aware that, for example, “predict” and “deduce” are associated with the third objective (construct, analyze, and evaluate) and require deeper understanding than “state,” which is associated with the first objective (demonstrate an understanding) and requires only memorization. Laboratory Requirement for IB Experimental Sciences Courses The IB program has more to say about laboratory experimentation than does the AP program, as the score for a student’s laboratory work (assessed internally by the teacher and moderated externally by the IBO) makes up 24 percent of a student’s final examination score. The program guides do not recommend any specific laboratory exercises, but provide general guidance for the design of a laboratory program. The Vade Mecum: Procedures Manual for IB Coordinators and Teachers specifies that the laboratory activities in IB Experimental Sciences courses must include hands-on investigations in the

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools TABLE 4-1 Summary of Eight Assessment Criteria for IB Experimental Sciences and Two or Three Aspects of Each Criterion Assessment Criteria Aspects Planning (a) Defining the problem or research question; formulating a hypothesis or prediction; selecting variables. Planning (b) Selecting appropriate apparatus or materials; designing a method for the control of variables; designing a method for the collection of sufficient relevant data. Data collection Collecting and recording raw data; organizing and presenting raw data. Data processing and presentation Processing raw data; presenting processed data. Conclusion and evaluation Drawing conclusions; evaluating procedure(s) and results; improving the investigation. Manipulative skills Carrying out techniques safely; following a variety of instructions. Personal skills (a) Working within a team; recognizing the contributions of others; exchanging and integrating ideas. Personal skills (b) Approaching scientific investigations with self-motivation and perseverance; working in an ethical manner; paying attention to environmental impact.   SOURCES: Adapted from IBO (2001a, 2001b, 2001c). laboratory or in the field, as well as problem-solving activities involving data analysis (IBO, 2000d, p. 4). At least 25 percent of the teaching program (not including time spent writing up the experiments) must be devoted to the Practical Scheme of Work (PSOW, described in greater detail below).11 Teachers are provided extensive detail about the criteria for the internal assessment of laboratory work, as they must offer opportunities for their students that match the relevant assessment criteria. Specific criteria for the internal assessment guide science teachers in setting the stage for students to design and carry out their own experiments. The IB internal assessment for the experimental sciences uses eight assessment criteria to evaluate the work of both HL and SL candidates (Table 4-1). These are described in the guide for each of the IB experimental sciences courses. For a particular criterion, a student’s laboratory work is judged to see whether the requirements for different aspects of the criterion have been fulfilled completely, partially, or not at all. For example, forming a hypothesis is one of the three aspects of the planning (a) criterion. The following example (Table 4-2) is given in the guide for each of the IB experimental sciences courses. 11   At least 60 hours for HL students and 40 hours for SL students (IBO, 2000d, p. 3), which includes 10–15 hours that candidates must spend on their Group 4 project (IBO, 2000c, p. 3).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools TABLE 4-2 Example of Expectations of Students to Meet the Requirements of One Aspect of the Planning (a) Criterion Formulating a Hypothesis or Prediction Complete Partial Not at all Relates the hypothesis or prediction directly to the research question and explains it, quantitatively where appropriate. States the hypothesis or prediction but does not explain it. Does not state a hypothesis or prediction.   SOURCES: Adapted from IBO (2001a, 2001b, 2001c). The guides also provide a discussion of the criteria to guide teachers. “It is generally not appropriate to assess planning (a) for most experiments or investigations found in standard textbooks, unless the experiments are modified. It is essential that students be given an open-ended problem to investigate” (IBO, 2001a, 2001b, 2001c, p. 24). A separate publication, Teacher Support Material: Experimental Sciences—Internal Assessment (IBO, 1999e), provides teachers with exemplars of student laboratory reports that fulfill all aspects of the criteria completely, as well as examples of those that do not. Teachers of the various experimental science subjects in an IB school must jointly submit to the IBO a PSOW, a summary of all the investigative activities their students carry out. Each PSOW must include at least a few complex investigations that make greater demands on the students than those posed by simple experiments. It must also include the date and a brief description of each investigation and an estimate of the time spent. The PSOW is accompanied by a copy of the instructions given to students for each activity. A script of any verbal instructions offered also must be included. These materials are used in moderating the internal assessment grades to ensure, for example, that if students are offered credit for planning, the teacher has not given them procedures. “The main criticism made by moderators was that the investigations were too directed with no real freedom for the candidates to develop the investigation for themselves” (IBO, 1998a). The PSOW also must include an interdisciplinary project involving all of the IB science students at a school in identifying and investigating an issue of local interest. The project requirements emphasize sharing of concepts and theories from across the disciplines, as well as the processes involved in scientific investigation, rather than products. The PSOW is evaluated yearly, and teachers receive feedback and suggestions for improvement. More detail about the scoring and moderation of the internal assessment and about the feedback the IBO provides to schools on their laboratory programs is provided later in this chapter.

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools IB INSTRUCTION There is variation from classroom to classroom in what is actually taught in an IB course, how much of the topic outline is covered, how much time is devoted to different topics, and what instructional strategies are used. However, the detail provided in the IB guides regarding expected student outcomes directs teachers toward the use of specific instructional strategies. Teachers are told that internal assessment tasks should be built into classroom teaching whenever possible. Internal assessments should form part of the learning experience of the students and should not be seen as an addition to the teaching schedule (IBO, 1999b). IB Programme Guides and Teaching Notes IB mathematics programme guides provide general guidance on instruction, but also offer specific suggestions about instructional strategies. The objectives for students given in the mathematics program guides include the following: Organize and present data in graphic, tabular, and/or diagrammatic form. Formulate a mathematical argument, and communicate it clearly. Recognize patterns and structures in a variety of situations. Use appropriate technological devices as mathematical tools. Teaching notes for each topic in the syllabus for each mathematics course provide suggestions for teachers, while stating that “it is not mandatory that these suggestions be followed” (IBO, 1998b, p. 9). The following are examples of alternative strategies presented in the teaching notes for the Mathematical Methods SL guide: “an informal investigative/experimental approach to statistical inference is envisaged” (IBO, 1997b, p. 21), and “problems might be best solved with the aid of a Venn diagram or tree diagram, without the explicit use of these formulae” (IBO, 1997b, p. 18). The teaching notes also include suggestions for linking content to help students see connections, such as linking the study of the second derivative in the Further Calculus option to the study of exponents and logarithms in the core content (IBO, 1997b, p. 23). The experimental sciences guides do not address instruction directly, other than to indicate consistently that there is no single best approach to teaching IB courses and that teachers should provide a variety of ways of acquiring information that can be accepted or rejected by each student, allowing different routes through the material (IBO, 2001a, 2001b, 2001c, p. 11). The IB program guide for chemistry tells chemistry teachers, for ex-

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools ample, that the “chemistry course includes the essential principles of the subject but also, through selection of options, allows teachers some flexibility to tailor the course to meet the needs of their students” (IBO, 2001b, p. 35). References to instruction also appear in annual subject reports, such as the following example from the 1999 IB chemistry subject report (IBO, 2000a): The main areas of weakness involved applications of principles to specific situations. This process is always a challenge to students. Students need to be exposed repeatedly to the application of basic concepts to new situations. This can be done through examples used in the classroom, by homework assignments which provide a variety of appropriate situations requiring skills beyond recall of information, and by tests and examinations which use questions similar to those used in the IB examination. (p. 401) As indicated in the discussion of curriculum, the use of action verbs in the experimental science assessment statements informs teachers about the depth of treatment required. Teachers then make decisions about the best way to prepare their students for the required outcomes. For example, “describe the ionic bond as the result of electron transfer leading to attraction between oppositely charged ions” (IBO, 2001b, p. 51) means students must be able to recall the definition of ionic bond. Teachers then make individual instructional decisions about the most effective ways to help their students learn this information. At a level requiring deeper understanding, the ability to “predict molecular polarity based on bond polarity and molecular shape” (IBO, 2001b, p. 52) is an outcome that cannot be achieved by memorizing a breadth of detail, but only by building the necessary understanding during a variety of practical experiences with molecular shapes, bond character, and electronegativities. Teachers must decide how best to accomplish this and are guided by the assessment statement to set up a variety of situations in which students can build understanding and experience. Messages About Instruction Conveyed by IB Examinations In specifying aspects of a subject to be assessed, the IB internal assessment criteria require that teachers structure the classroom and laboratory environment so that students have the opportunity to acquire and develop the skills to be evaluated. IB mathematics teachers are encouraged to integrate the internal assessment assignments for the mathematics portfolio into their teaching. Related teaching and learning strategies discussed in the Mathematical Methods SL guide (IBO, 1997b, p. 51) include the following:

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools Candidates need to be provided with the opportunities to experiment, explore, make conjectures and ask questions. Ideally, the atmosphere in the classroom should be one of enquiry. Small groups could work through some relatively simple assignments in order to learn skills associated with portfolio activities. Students may be unaware of certain strategies associated with experimentation, or “playing,” which are an important part of investigative work, particularly if they have only experienced more formal modes of working. Similarly, IB experimental science teachers are given guidance in providing a variety of practical experiences for their students. Sample laboratory investigations are offered and analyzed in the IB Teacher Support Material: Experimental Sciences—Internal Assessment (IBO, 1999e). The program guides provide direction for preparing students for experimentation without specifying laboratory activities. For example, “the teacher might present the aim of an investigation generally in the form ‘investigate the factors that affect X.’ Students should be able to realize that certain factors will influence X and clearly … identify a focused research question” (IBO, 1999e, p. 4). The criteria for personal skills (a) require that a teacher assess a student’s work within a team, defined as follows: “Teams, whose members collaborate, can be formed with a wide variety of people. The views of all team members are respected and actively sought” (IBO, 1998a). Teachers must therefore provide opportunities for students to learn how to work effectively in teams. Teachers are encouraged to use the online curriculum center to share ideas about possible investigations and add resources to the relevant sections of the online subject guides. IB ASSESSMENT Assessment in IB mathematics and science courses has two components—external and internal. The external assessment consists of a written examination that is administered internationally over a period of 2 days in May of each year (in November for split-session schools). The examination tests knowledge of both the core and optional topics. The internal assessment component comprises the teacher’s formative assessment of students’ practical work (laboratory investigations in science courses and portfolios in mathematics courses) judged against established assessment criteria. This component is conducted by teachers within the school environment and is moderated externally by the IBO. In the experimental sciences, the external and internal assessments make up 76 percent and 24 percent of the final examination mark, respectively. IB teachers submit internal assessment marks and a predicted final examination grade for each of their students. The latter is the teacher’s prediction of the grade the candidate will achieve in the

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools subject, based on all the evidence of a candidate’s work and the teacher’s knowledge of IB standards (IBO, 2000d, p. F14). The IB assessments are designed to gauge the educational achievement of candidates against the range of objectives specified for each subject. The structure of each written external examination paper “allows candidates to demonstrate their achievement in terms of content knowledge, depth of understanding and use of specific higher level cognitive skills, as described by the subject objectives.”12 The internal assessment component addresses skills that cannot be demonstrated satisfactorily within the context of a written examination. As stated in the guides, the purpose of the internal assessment for the IB mathematics portfolio is to “provide candidates with opportunities to be rewarded for mathematics carried out under ordinary conditions, that is, without the time limitations and stress associated with written examinations” (IBO, 1998b, p. 47). The requirements for the internal assessment in the experimental sciences are focused on the candidates’ skills in laboratory investigation, including planning; data collection and processing; evaluation of procedures and results; manipulative skills; and personal skills, including working with a team (IBO, 2001a, 2001b, 2001c, pp. 20–22). How IB Assessments Are Developed Examinations for each IB course are written by chief examiners and deputies and are overseen and approved by the examination board at IBCA. Teams of experienced senior examiners prepare the examinations for each administration in a process that is coordinated and overseen by IBO academic staff. Separate examinations are developed for SL and HL courses in a subject area. Single senior examiners normally write individual examination questions, which are directly linked throughout the examination development process to the assessment statements and the objectives to be measured as outlined in the program guides for each subject. “The questions are not field tested, partly because it is difficult to find a suitable trial group of candidates without the possibility of compromising security. New questions are written for each examination session—they are not banked.” Moreover, “for each session, the senior examining team aims to prepare a different form of the examination which is of the same standard of demand as in previous sessions. In practice it is very difficult to achieve a high level of precision.”13 The IBO also does not calculate the internal reliability of the examina- 12   George Pook, assessment director, IBCA (personal communication, May 31, 2001). 13   George Pook, assessment director, IBCA (personal communication, May 31, 2001).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools tions, as it is not one of the assumptions of IB assessment that all the items in each written examination paper will assess the same trait. Thus, high correlation of a candidate’s performance on different parts of the assessment is not expected. Like the College Board, the IBO does not make use of systematic validity research regarding the cognitive characteristics of its examinations. As part of the curriculum development and review process in each subject, the IB curriculum committees specify and describe the internal assessment criteria. The examiners in each subject meet to develop common understandings about how to assess each of the criteria. The IBO communicates the assessment details to classroom teachers and moderators in each subject through program materials and workshops. The assessment structure for each subject is reviewed periodically as part of an overall curriculum review. Proposals for revisions to the assessments are developed by the curriculum review committees through a process similar to that described for curriculum review. The proposals are then reviewed by the Diploma Review Committee, which consists of chief examiners representing each subject group and senior academic staff from the IBO. After each examination session, candidates’ responses are scrutinized closely to determine whether they are in line with expectations for each question. Additionally, all IB teachers are asked to complete feedback forms following the examinations, answering questions about both the emphases of the examination and the content and form of individual questions. Much attention is paid to teachers’ comments about the suitability of examination papers in achieving the intended objectives. Information gained in this manner is fed into the examination development process for future sessions. How IB Assessments Are Scored The IB grading system is criterion referenced. Each student’s performance is measured against seven grade descriptors, given in the form of levels of performance that candidates should be able to demonstrate. The different levels of performance are closely related to the course objectives and are clearly specified for mathematics and the experimental sciences. The descriptors are equally applicable to both HL and SL examinations. As an example, grade descriptors 7, 4, and 1 for the experimental sciences follow (IBO, 1999c): Grade 7 Excellent performance Displays comprehensive knowledge of factual information in the syllabus and a thorough command of concepts and principles. Selects and applies relevant information in a wide variety of contexts. Analyzes and evaluates

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools data thoroughly. Constructs detailed explanations of complex phenomena and makes appropriate predictions. Solves most quantitative and/or qualitative problems proficiently. Communicates logically and concisely using appropriate terminology and conventions. Shows insight or originality. Demonstrates personal skills, perseverance and responsibility in a wide variety of investigative activities in a very consistent manner. Works very well within a team, and approaches investigations in an ethical manner, paying full attention to environmental impact. Displays competence in a wide range of investigative techniques, paying considerable attention to safety, and is fully capable of working independently. Grade 4 Satisfactory performance Displays reasonable knowledge of factual information in the syllabus, though possibly with some gaps. Shows adequate comprehension of most concepts and principles but with limited ability to apply them. Demonstrates some analysis or evaluation of quantitative and qualitative data. Solves basic or routine problems but shows limited ability to deal with new or difficult situations. Communicates adequately but responses may lack clarity and include some repetitive or irrelevant material. Demonstrates personal skills, perseverance and responsibility in some investigative activities, although displays some inconsistency. Works within a team and generally approaches investigations in an ethical manner, with some attention to environmental impact. Displays competence in a range of investigative techniques, paying some attention to safety, although requiring some close supervision. Grade 1 Very poor performance Recalls fragments of factual information and shows very little understanding of any concepts or principles. Rarely demonstrates personal skills, perseverance or responsibility in investigative activities. Does not work within a team. Rarely approaches investigations in an ethical manner, or shows awareness of the environmental impact. Displays little competence in investigative techniques, generally pays no attention to safety, and requires constant supervision (IBO, 1999c). The senior evaluating team uses these descriptors when determining the examination marks, which reflect the combined raw scores for the written examinations and the internal assessments. Examiners look to assign candidates the grade that matches their performance most comprehensively by determining the various grade boundaries for the raw scores the candidates achieve. Each time the examinations are administered and marked, the senior examiners meet to decide what marks equate to the same level of performance as in previous sessions. The process begins by using the grade boundaries suggested by examiners on the basis of their reading of student responses on the written examination. Individual examiners mark students’ responses on the examinations

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools using a set of assessment criteria or mark schemes, which are accompanied by notes about the range of content that might be expected. Scripts with raw scores just below or above the proposed boundaries are reread carefully and evaluated with reference to the criteria described above. Inter-examiner reliability is ensured by a system of moderation in which each examiner sends a sample of his or her marking to a more senior examiner for checking. If the senior examiner’s remarking of the sample indicates a slight disparity in standards, a statistical adjustment based on linear regression is made to all of the assistant examiner’s marks. If there is substantial disagreement or inconsistency, all of the assistant examiner’s work is remarked. Analysis of these moderation samples indicates that in the vast majority of cases, different examiners’ marks are within 5 percent of each other, and that in very few cases is the difference more than 10 percent.14 Schools submit marks for internal assessment to IBCA by a given deadline in April of each year. A moderation process is also used to ensure reliability and an equivalent standard among schools for the internal assessment marks in both mathematics and the experimental sciences. Each school must submit for moderation five marked sets of candidates’ work in each subject, selected to represent the full range of quality of work submitted by students in that subject. If the moderators’ remarking of the students’ work samples indicates a disparity in standards, a statistical adjustment is made to all the internal assessment marks of the teacher involved, and a moderator who is an experienced IB teacher remarks the work. In mathematics, for example, each moderator reviews about 50 portfolios. Each then sends a sample of five sets of student work to a senior moderator, who repeats the grading and sends samples of that work to a principal moderator in each subject. The senior moderator also sends a report to the IBO for inclusion in the chief examiner’s report. How Examination Results Are Reported IBCA communicates examination results directly to the secondary schools. The schools, in turn, are responsible for ensuring that the results are communicated to candidates. IBNA communicates the results to colleges and universities. The results include scores on each examination taken, as well as marks for the Theory of Knowledge course and the Extended Essay and cumulative scores for diploma candidates. A profile of candidates’ grades is available to schools for each examination session. The profile is only for candidates whose examinations are entered by that school and includes predicted grades; examination grades, including marks for each paper; and 14   George Pook, assessment director, IBCA (personal communication, May 31, 2001).

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools internal assessment grades, indicating any adjustments made. All sections of the examination papers are made available to teachers for use in their classrooms 24 hours after the testing date. The IBO publishes yearly detailed reports for each subject that include mark bands for each score, general comments on the application of mark schemes to free-response problems, and comments on the strengths and weaknesses of the candidates in the treatment of individual questions. The subject reports also describe areas of the program and examination that appeared to be difficult for candidates, as well as areas in which candidates appeared to be especially well prepared. Recommendations are offered for teachers regarding assistance and guidance that should be provided for future candidates. Examples from the May 2000 chemistry subject report include the following: “Overall, it appeared that the weaker candidates … did not fully understand the concept of intermolecular forces and typically described covalent bond strengths as affecting boiling points. This is something that teachers might place greater emphasis on in class” (IBO, 2000c, p. 5). The subject report also includes a detailed discussion of the internal assessment and recommendations directed at improving the laboratory program. For example, the May 2000 report states: “Overall most schools presented a suitable Practical Scheme of Work, although some schools presented programs that were significantly deficient, either in the total experimental hours completed or in the degree of syllabus coverage …. The depth and breadth of the experiments was generally found to be good. New teachers are clearly considering the depth of the syllabus when designing experiments, at times with limited resources. These efforts are recognized and applauded” (IBO, 2000c, pp. 17–18). The biggest problem continues to be in providing students with opportunities to demonstrate the internal assessment planning (a) and planning (b) criteria: “These skills cannot be properly assessed if teachers provide students with the purpose, hypothesis and/or procedures for experiments. Some teachers consistently gave far too much direction in their instructions (purpose, method, data table, sample calculations etc.). Candidates have been deprived of the opportunity to design realistic methods for the control of variables. Teachers must use open-ended questions in order to facilitate the assessment of Planning (a) and Planning (b)” (IBO, 1999a, p. 414). Yearly detailed narrative reports are made available to individual schools, for a fee, on the performance of their students as a group for each subject examined. The reports include comments on students’ general examination techniques, along with suggestions for improvement, comments on overall performance in each section of the examination, analysis and evaluation of candidates’ performance on individual questions, and recommendations and guidance for future candidates. Examiners write these reports at the time of

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools marking and then add statistical data and a description of the mark schemes (IBO, 2000d, p. B1). The reports are substantial (7–10 pages) and include the following detailed information: Comments on the candidates’ approach to answering the questions on each test paper, with suggestions for improvement. Quantitative information on the numbers of candidates answering particular questions. Comments on the overall performance of candidates in relation to all portions of each examination paper. An analysis and evaluation of candidates’ performance on individual questions in relation to the marking scheme. Recommendations and guidance for future candidates. Each school can also receive a Moderation Report on the Internal Assessment that provides information on the differences between the teachers’ marks for their students and the marking by the moderator for the internally assessed samples of work. This information lets teachers know whether they are applying the standards correctly (i.e., the average mark awarded by the teacher is within 10 percent of the average mark awarded by the moderator) and consistently (i.e., the correlation between teacher and moderator marks is 0.85 or greater). Also provided are written comments from the moderators on feedback forms for each subject (International Baccalaureate Form 4/IAF, Internal Assessment Feedback Form: Group 4). These comments are provided in the form of responses to questions about clerical/procedural details, as well as the students’ experimental work, including the following: Were the investigations/projects appropriate for the assessment of particular criteria? Was the practical program of the correct duration? Was the syllabus coverage (core, additional high level, and options) appropriate? Was the practical scheme of work of appropriate complexity? IB PROFESSIONAL DEVELOPMENT What Is Known About the Preparation and Credentials of IB Teachers Because the credentials of prospective IB teachers are submitted as part of a school’s application for membership in the IBO, initial staffing decisions and teaching assignments for IB courses are made as part of a comprehensive school plan. IB teaching assignments may be given to experienced or

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools novice teachers. The IBO has established neither teacher qualifications nor standards for faculties, although the application process does ensure that, at least initially, prospective IB teachers attend an IB workshop (see the next subsection). The IBO also does not certify teachers and is not involved in monitoring staffing changes after a school has become an IB school. Consequently, there is not much more information available about the qualifications of IB teachers than exists for AP teachers. Professional Development Experiences of IB Teachers One prerequisite for a school’s obtaining permission to offer the IB program is that every teacher who will teach IB courses must attend a 3- to 5-day workshop offered by IBNA. Teachers new to an already authorized school also must attend an IB workshop, preferably before they begin to teach IB courses. In addition, the IBNA regional office is responsible for conducting weeklong professional development workshops for IB teachers and administrators during the summer, as well as 3- to 5-day workshops during the school year. IBNA has also facilitated the establishment of regional organizations for IB schools. These organizations are supported by IBNA in holding conferences and workshops several times each year. Schools and/or school districts budget resources annually to support attendance by teachers and administrators at these sessions, which are held both nationally and regionally. Experienced IB teachers typically work with representatives from IBNA to prepare materials for and plan and conduct the sessions. Both the conferences and workshops focus on providing guidance and resources for the implementation of IB programs and development of course curricula. Workshops focus on general topics unique to IB, including the following: Restructuring of the school schedule and course registration to accommodate IB course requirements. Internal assessment. Restructuring of the ninth- and tenth-grade curriculum to prepare students for IB courses. Characteristics of IB students. Use of international examples and illustrations in the curriculum. Experimental science workshops focus on designing laboratory experiences that will enable students to meet specific internal assessment criteria. The most recent focus has been on the planning criteria, as the IB examiners have found that the practical work done in most classrooms does not afford students opportunities to practice the skills needed in planning their own

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Learning and Understanding: Improving Advanced Study of Mathematics and Science in U.S. High Schools experiments. In most mathematics workshops, time is spent on preparing teachers to teach an unfamiliar and expanded mathematics curriculum, including vectors and matrices; probability and statistics; and the optional topics—statistics, abstract algebra, and further geometry. A dialogue exists between IB teachers and the IBO that is not a feature of the AP program. Every teacher completes feedback forms following each examination, answering questions about both the emphases of the examination and the content and form of individual test items. The results are summarized by IBCA and provided both to teachers and to the development committees, driving changes in curriculum and instruction the following year, as well as in the assessment instrument itself. After the examinations have been graded, each teacher receives a subject report (general comments about all of the student responses worldwide on the examination) and a school report (specific comments about their students’ performance on the written examination and internal assessment, as well as comments and suggestions about the practical program in each discipline at the school). The comments provided to the schools and teachers serve as the impetus for corresponding changes in the instructional program aimed at improving students’ test scores. Additionally, the IBO maintains an online curriculum site so IB teachers can receive the most current information about the curriculum.