IB programme

Math SL Assessment component

External Assessment (3h)

Paper1(1h 30m) Section A Section B 90 marks

40%

Paper1(1h 30m) Section A Section B 90 marks

40%

Internal Assessment

Mathematical Exploration

20 marks 20%

Math HL Assessment component

External Assessment

(5h)

Paper 1(2h) Section A Section B 120 marks

30%

Paper 2(2h) Section A Section B 120 marks

30%

Paper 3 (1h)

60 marks 20%

Internal Assessment

Mathematical Exploration

20 marks 20%

Math Exploration

• The internally assessed component in these courses is a mathematical exploration.

• This is a short report (6-12 pages) written by the student based on a topic chosen by him or her, and it should focus on the mathematics of that particular area.

• The emphasis is on mathematical communication (including formulae, diagrams, graphs and so on), with accompanying commentary, good mathematical writing and thoughtful reflection.

• A student should develop his or her own focus, with the teacher providing feedback via, for example, discussion and interview. This will allow all students to develop an area of interest for them, without a time constraint as in an examination, and will allow all to experience a feeling of success.

Skills and strategies required by students

Skills and strategies required by students

Skills and strategies required by students

Skills and strategies required by students

Skills and strategies required by students

Skills and strategies required by students

Use of technology

The exploration may offer opportunities for this objective to be achieved, although this is not a requirement for the exploration. For external assessment, the use of technology is limited to the graphic display calculator, but for the exploration there are no such limitations. It is reasonable, but not essential, to expect that the students, when producing their explorations, will utilize technology in one or more ways.

A possible time frame for the exploration

• Choosing a focus/topic: 2 weeks • Draft exploration: 3 weeks • Teacher to review and comment on drafts:

4 – 8 weeks • Final writing: 2 weeks

Deadlines for TED IB Students in 2012-2013

• Choosing a focus/topic: December 2012 • First draft: April 2013

STIMULI

• space • orbits

• Biology • chemistry• physics

• business • economics • population • communication

Games codes the internet algorithms

• Health • Food • Water • Psychology • viruses

Mind map

• One way of choosing a topic is to start with a general area of interest and create a mind map. This can lead to some interesting ideas on applications of mathematics to explore.

• The mind map below shows how the broad Geography can lead to suggestions for explorations into such diverse topics as the spread of disease, earthquakes or global warming.

Internal Assessment Criteria

• The exploration is internally assessed by the teacher and externally moderated by the IB using assessment criteria that relate to the objectives for mathematics SL and HL. Each exploration is assessed against the following five criteria. The final mark for each exploration is the sum of the scores for each criterion. The maximum possible final mark is 20. Students will not receive a grade for mathematics SL and HL if they have not submitted an exploration.

• A Communication (4 marks): This criterion assesses the organisation and coherence of the exploration. A well-organised exploration has an introduction, a rationale (which includes a brief explanation of why the topic was chosen), describes the aim of the exploration and has a conclusion. A coherent exploration is logically developed and easy to follow.

• B Mathematical Presentation (3 marks): This criterion assesses to what extent the student is able to:

• Use appropriate mathematical language (notation, symbols & terminology) • Define key terms, where necessary • Use multiple forms of mathematical representation such as formulae, diagrams, tables, charts, graphs and models

• C Personal Engagement (4 marks): This criterion assesses the extent to which the student engages with the exploration and makes it their own. These include thinking independently and/or creatively, addressing personal interest and presenting mathematical ideas in their own way.

• D Reflection (3 marks): This criterion assesses how the student reviews, analyses and evaluates the exploration. Although reflection may be seen in the conclusion to the exploration, it may also be found throughout the exploration. Reflection may be demonstrated by consideration of limitations and/or extensions and relating mathematical ideas to your own previous knowledge.

• E Use of Mathematics (6 marks): This criterion assesses to what extent students use mathematics in the exploration. The mathematics explored should either be part of the syllabus, or at a similar level or beyond. It should not be completely based on mathematics listed in the prior learning. If the level of mathematics is not commensurate with the course, a maximum of two marks can be awarded for this criterion. A piece of mathematics can be regarded as correct even if there are a few minor errors so long as they do not cause a disruption to the flow of mathematics or lead to an incorrect or inaccurate result.

Frequently Asked Questions

Frequently Asked Questions

• What is the difference between a mathematical exploration and an extended essay in mathematics?

• The criteria are completely different. It is intended that the exploration is to be a much less extensive piece of work than a mathematics extended essay. The intention is for students to “explore” an idea rather than have to do the formal research demanded in an extended essay.

Frequently Asked Questions

• How long should it be? • It is difficult to be prescriptive about mathematical

writing. However, the Mathematics SL guide and the Mathematics HL guide state that 6–12 pages should be appropriate. A common failing of mathematical writing is excessive repetition, and this should be avoided, as such explorations will be penalized for lack of conciseness. However, it is recognized that some explorations will require the use of several diagrams, which may extend them beyond the page limit.

Frequently Asked Questions

• Can students in the same school/class use the same title for the exploration?

• Yes, but the explorations must be different, based on the avenues followed by each student. As noted above, the title should give an idea of what the exploration is about. Group work is not allowed.

Frequently Asked Questions

• Can students in the same school/class use the same stimulus?

• Yes, this is permissible. However, the stimuli are intended to be broad themes around which a variety of foci could develop. It is therefore expected that, even if students use the same stimuli, the resulting explorations will be very different.

Frequently Asked Questions

• Can SL and HL students use the same stimulus?

• Yes, there is no reason to restrict any stimulus to a particular level, although the assessment of criterion E will be different.

Frequently Asked Questions

• How much help can a teacher give the student in finding a topic/focus for their exploration?

• The role of the teacher here is to provide advice to the student on choosing the topic, and there is no set limit to the amount of help a teacher can give in this respect. However, if the student has little or no input into the decision about which focus to choose, then it is unlikely that he or she will be able to explore the ideas successfully in order to generate a good exploration.

Frequently Asked Questions

• How much help can the teacher give to the student with the mathematical content of the exploration?

• If a student needs help with the revision of a particular topic because they are having some problems using this in their exploration, then it is permissible (indeed, this is good practice) for the teacher to give this help. However, this must be done in such a way that is not directly connected with the exploration.

Frequently Asked Questions

• When is a good time in the course to introduce the exploration?

• It is a good idea to mention it as early as possible, so that students are aware of the requirements, and to make reference to it during the early part of the course. Certain topics may lend themselves more easily to exploration work, and teachers should try to make suggestions about this when appropriate. Ideally, the work on the exploration should start before the end of the first year.

Frequently Asked Questions

• Can the students use mathematics other than that they have done in class?

• Yes, but this must be clearly explained and referenced, and teacher comments should clarify this.

• Can students use mathematics that is outside the syllabus?

• Yes, as long as the mathematics used is relevant. However, this is not necessary to obtain full marks.

Frequently Asked Questions

• What is the difference between criterion A (communication) and criterion B (mathematical presentation)?

• Communication is focusing on the overall organization and coherence of the exploration, whereas mathematical presentation focuses on the appropriateness of the mathematics. An exploration that is logically set out in terms of its overall structure could score well in criterion A despite using inappropriate mathematics. Conversely, an exploration that uses appropriate diagrams and technology to develop the ideas could score well in criterion B but poorly in criterion A because it lacked a clear aim or conclusion, for example.

Frequently Asked Questions

• Does the exploration have to be word processed or handwritten?

• It can be in either form as long as it is clearly legible

Frequently Asked Questions

• What is personal engagement? • The exploration is intended to be an opportunity

for students to use mathematics to develop an area of interest to them rather than merely to solve a problem set by someone else. Criterion C (personal engagement) will be looking at how well the student is able to demonstrate that he or she has “made the exploration their own” and expressed ideas in an individual way.

Frequently Asked Questions

• What is the difference between precise and correct?

• As outlined in criterion E (use of mathematics), “precise” mathematics requires absolute accuracy with appropriate use of notation. “Correct” mathematics may contain the occasional error as long as it does not seriously interfere with the flow of the work or give rise to conclusions or answers that are clearly wrong.

Frequently Asked Questions

• Can you recommend a target date for completion of the exploration?

• This will, of course, vary from school to school depending upon several factors, not to mention other deadlines set within the Diploma Programme (for example, guided coursework, extended essays, laboratory reports). Teachers should also allow themselves plenty of time for the assessment process. The IB’s deadline for samples of student work for moderation is in April for a May examination session or in October for a November examination session. Therefore, it is not unreasonable for teachers to collect final explorations six to eight weeks prior to this deadline.

Exploration Examples for SL and HL

• Mathematical Exploration: Minesweeper

Criterion  A  B  C  D  E (SL) 

E (HL) 

Total (SL) 

Total (HL) 

Achievement level awarded  2  1  1  1  0  0  5  5 Maximum possible achievement level 

4  3  4  3  6  6  20  20 

Criterion A: Communication A2—There is an introduction, but no aim or rationale, although the aim is implied on the last page. The exploration has some coherence and organization. There is no explanation of the statements on page 3.

Criterion B: Mathematical presentation B1—The student uses minimal mathematical terminology, and some of it is incorrect.

Criterion C: Personal engagement C1—There is limited evidence: student creates examples; unfamiliar maths is quoted, but not explained.

Criterion D: Reflection D1—Only superficial reflection is shown.

SL Criterion E: Use of mathematics E0—There is no use of mathematics.

HL Criterion E: Use of mathematics E0—There is no use of mathematics.

• A Communication (4 marks): This criterion assesses the organisation and coherence of the exploration. A well-organised exploration has an introduction, a rationale (which includes a brief explanation of why the topic was chosen), describes the aim of the exploration and has a conclusion. A coherent exploration is logically developed and easy to follow.

Criterion  A  B  C  D  E (SL) 

E (HL) 

Total (SL) 

Total (HL) 

Achievement level awarded  2  1  1  1  0  0  5  5 Maximum possible achievement level  4  3  4  3  6  6  20  20 

A2—There is an introduction, but no aim or rationale, although the aim is implied on the last page.

• B Mathematical Presentation (3 marks): This criterion assesses to what extent the student is able to:

• Use appropriate mathematical language (notation, symbols & terminology) • Define key terms, where necessary • Use multiple forms of mathematical representation such as formulae, diagrams, tables, charts, graphs and models

Criterion  A  B  C  D  E (SL) 

E (HL) 

Total (SL) 

Total (HL) 

Achievement level awarded  2  1  1  1  0  0  5  5 Maximum possible achievement level  4  3  4  3  6  6  20  20 

B1—The student uses minimal mathematical terminology, and some of it is incorrect

• C Personal Engagement (4 marks): This criterion assesses the extent to which the student engages with the exploration and makes it their own. These include thinking independently and/or creatively, addressing personal interest and presenting mathematical ideas in their own way.

Criterion  A  B  C  D  E (SL) 

E (HL) 

Total (SL) 

Total (HL) 

Achievement level awarded  2  1  1  1  0  0  5  5 Maximum possible achievement level  4  3  4  3  6  6  20  20 

C1—There is limited evidence: student creates examples; unfamiliar maths is quoted, but not explained.

• D Reflection (3 marks): This criterion assesses how the student reviews, analyses and evaluates the exploration. Although reflection may be seen in the conclusion to the exploration, it may also be found throughout the exploration. Reflection may be demonstrated by consideration of limitations and/or extensions and relating mathematical ideas to your own previous knowledge.

Criterion  A  B  C  D  E (SL) 

E (HL) 

Total (SL) 

Total (HL) 

Achievement level awarded  2  1  1  1  0  0  5  5 Maximum possible achievement level  4  3  4  3  6  6  20  20 

D1—Only superficial reflection is shown.

• E Use of Mathematics (6 marks): This criterion assesses to what extent students use mathematics in the exploration. The mathematics explored should either be part of the syllabus, or at a similar level or beyond. It should not be completely based on mathematics listed in the prior learning. If the level of mathematics is not commensurate with the course, a maximum of two marks can be awarded for this criterion. A piece of mathematics can be regarded as correct even if there are a few minor errors so long as they do not cause a disruption to the flow of mathematics or lead to an incorrect or inaccurate result.

Criterion  A  B  C  D  E (SL) 

E (HL) 

Total (SL) 

Total (HL) 

Achievement level awarded  2  1  1  1  0  0  5  5 Maximum possible achievement level  4  3  4  3  6  6  20  20 

E0—There is no use of mathematics.(SL) E0—There is no use of mathematics.(HL)

• The Polar Area Diagrams of Florence Nightingale

Criterion  A  B  C  D  E (SL) 

E (HL) 

Total (SL) 

Total (HL) 

Achievement level awarded  4  3  4  3  6  3  20  17 

Maximum possible achievement level  4  3  4  3  6  6  20  20 

Criterion A: Communication A4—The exploration is concise and easy to follow. A couple of typing errors does not detract from the flow.

Criterion B: Mathematical presentation B3—Multiple forms are well used.

Criterion C: Personal engagement C4—The work is highly original, and the student used historical idea to create her own similar situation. She is clearly engaged in the work.

Criterion D: Reflection D3—There is critical reflection, where the student tries to resolve contradictions discovered.

SL Criterion E: Use of mathematics E6—Areas of sectors using radians and descriptive statistics are commensurate with the mathematics SL course, and are done well enough at achieve level 6.

HL Criterion E: Use of mathematics E3—While areas of sector using radians and descriptive statistics are commensurate with the mathematics HL course, the mathematics is not sophisticated enough for a level 4, even though is it rigorous.

http://library.tedankara.k12.tr/ IB Kaynakları Mathematic New IB Curriculum Workshop Materials / Tim Garry Student Samples of Math Exploration