Mathematics HL/SL IA

# Guide book

International School of Hellerup

## 1. What is Internal Assessment in IB Mathematics HL/SL Level ?

Internal Assessment (IA) in Maths HL/SL consists of a single internally assessed component (i.e. marked by the teacher) called a mathematical exploration (or just the “Exploration”). The Exploration contributes 20% to your overall IB score for the course.

## 2. What is the Exploration ?

Your Exploration is a written report (6-12 pages) involving a mathematical topic that interests you. You will choose a topic in consultation with the teacher after conducting your own research.

## 3. How is the Exploration assessed ?

Your Exploration will earn a score out of 20 marks based on the following five criteria.

*There is a slight difference in only criterion E for SL and HL. See the link: https://ibpublishing.ibo.org/live-exist/rest/app/tsm.xql?doc=d_5_matsl_tsm_1205_1_e&part=1&chapter=8

A    Communication:  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.

B    Mathematical Presentation:  This criterion assesses to what extent a 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:  This criterion assesses the extent to which a student engages with the exploration and presents it in such a way that they clearly show their own personal approach. Personal engagement may be recognised in different attributes and skills. These include thinking independently and/or creatively, addressing personal interest, presenting mathematical ideas in their own way, using simple language to describe complex ideas and applying unfamiliar mathematics.

D    Reflection:  This criterion assesses how well a student can review, analyse and evaluate the exploration.  Although reflection may be seen in the conclusion to the exploration, a student should also give evidence of reflective thought throughout the exploration. Reflection may be demonstrated by consideration of limitations and/or extensions and relating mathematical ideas to their own previous knowledge.

E    Use of Mathematics:  This criterion assesses to what extent and how well a student uses mathematics in their exploration. The mathematics that is explored in a student's report needs to be at a level appropriate for the IB math course they are taking - either HL or SL.  The chosen topic should involve mathematics either in the syllabus, at a similar level, or beyond the level of the syllabus.  [note: The descriptors for each assessment critieria are the same for HL and SL, except for Criteria E]

The Exploration will earn a numerical score out of a total of 20 possible marks.  The five criteria do not contribute equally to the overall score for your Mathematical Exploration.  For example, criterion E, (Use of Mathematics), is 30% of the overall score whereas criterion B (Mathematical Presentation) and D (Reflection) contribute 15% each.

It is very important that students familiarize themselves with the assessment criteria and refer to them while they are writing their reports (Exploration).

## Some important points to consider:

♦ In your Exploration you need to write about mathematics and not just do mathematics.

♦ Any idea, method, content, etc that is not your own must be cited at the point in the Exploration where it is used. Just listing your sources in a bibliography is not enough and may lead to the IB deciding that malpractice has occurred.

♦ The Exploration is an opportunity for you to learn more about a mathematical topic in which you are genuinely interested. You will be rewarded (personal engagement) for explaining your interest in the topic, and for demonstrating curiosity, creativity & independent thinking.

♦ Your audience is your fellow students – that is, you need to write your Exploration so that your classmates in Maths HL/SL can read and understand it. Thus, it is not necessary to explain in great detail basic mathematics that will be familiar to a student in Math HL/SL.

♦ You will be rewarded (reflection) for expressing what you think about the mathematics you are exploring. You should endeavour to pose your own questions and try to answer them using suitably sufficient level of mathematical ideas and procedures.

♦ You will be required to submit a complete draft of your Exploration – containing an introduction, conclusion and all planned content to sufficiently address all five criteria. You will receive feedback on the draft and then be given an opportunity to revise it to submit a final version.

♦ All of the work you do on your Exploration must be your own work. When finished with your final version you will be required to sign a ‘declaration’ that states, “I confirm that this work is my own and is the final version. I have acknowledged each use of the words or ideas of another person, whether written, oral or visual.”

## Timeline for IA:

 Stages Deadline 1 Brainstorming/ IA Topic draft 14 May 2 IA Topic Final (with research question) 21 May 3 Writing 1st Draft 3 September 4 Getting Feedback 28 September 5 Final Draft 26 October

## Stage 1: Brainstorming/ IA topic draft

• You will be given two weeks to organize a ‘short list’ of topics (3 to 5).
• Click here to open a document in a new window containing 200 ideas for Exploration topics.
• Browse through the list and do some very quick research (perhaps 5 min spent looking at a Wikipedia page) on any topic that catches your interest.
• A quick look at some information about one of the topics may reveal some other topic (not on the list) which interests you.

## Stage 2: Finalizing a topic for your Exploration

• You will need to finalise your potential topic – depending on these three important questions:
• (1) does the topic involve math at a suitable level for an HL Exploration? ;
• (2) is the topic narrow enough so that it can be treated sufficiently in a 6-12 page report? ; and
• (3) does the topic lend itself to demonstrating personal engagement (criterion C)?

That is, can you envision some way that you could apply something of your own – your own viewpoint, your own examples, your own models (conceptual or physical), your own questions & ideas, etc.

## Stage 3: Write a complete draft

Before you start writing your Exploration be sure to carefully read through the details for all five of the assessment criteria. Along with a brief description and achievement level descriptors, there is also helpful Further Guidance notes for each criterion.

A draft is not an abbreviated or incomplete version of your Exploration. It must be complete – including an introduction, a conclusion and a bibliography – with sufficient content to address your stated objective(s) and be in the range of 6 to 12 pages (spacing 1½, font Times New Roman). Your Exploration needs to be:

• logically organized;
• use appropriate mathematical terminology and notation;
•  include explanatory diagrams, graphs, tables, etc;
• contain citations to indicate where a source is used;
• and focuses on the relevant mathematics.

It is important to include your own thoughts, questions, reflections & ideas when possible. Write in the first person, e.g. “I decided that the best method is _____ because I realized that …”

Although the Exploration is an individual assignment and all the work must be your own, you are strongly encouraged to regularly consult with me. Your can be provided verbal guidance and feedback while you are writing your draft.

⇛ Submit a paper and electronic version of your draft to your teacher by the given deadline ⇚

## Stage 4: Teacher feedback

You will get feedback on the draft of your Exploration in two weeks time. Be sure to ask questions about any comments / feedback that you do not completely understand.

## Stage 5: Submit final version of your Exploration

From the time you receive written feedback on your draft you will have 4 weeks to revise your draft and complete the final version of your Exploration. Before submitting your final version complete this student checklist ().

1. Choose a topic in consultation with your teacher that: (i) you’re interested in, (ii) involves math at a level suitable for Math HL, (iii) is narrow enough for 6-12 pages, (iv) has opportunities for personal engagement.

2. Your Exploration must have an aim or objective which involves doing some mathematics. It is important to maintain a focus on the overall aim/objective and a focus on mathematical concepts and methods.

4. Be sure you fully understand the expectations of the five assessment criteria, and refer back to them while you are planning and writing your Exploration.

5. The Exploration is an opportunity to complete a significant assessment item (20% of IB score) while not under the pressure of timed exam conditions. Take advantage of the opportunity by following instructions, meeting deadlines, engaging & reflecting in your own way, and enjoying some math you are interested in.  ---- The End ----