New IB Math Paper 3 – Math Investigation
By Tracy Man
(ACT, SAT, SSAT, Mathtutor at The Edge Learning Center)
Changes in IB Math
As some of you may already be aware, the IB Diploma Programme (DP) Maths course has undergone some changes effective from the 2019-2020 academic year. The course will now be broken down into two routes: applied vs. pure (please refer to IB Maths: AA or AI by Indrani Banerjee for more information about these changes).
A New Paper 3?
Apart from splitting the Maths course into two routes, there is another change, which will affect the higher-level students, a new Paper 3. If you are now considering between SL and HL Maths, do not let the idea of a third paper stop you off from choosing HL Maths. The IBO states that,
‘Inquiry-based learning is central to mathematics courses in both MYP and the DP, providing students with opportunities to independently and collaboratively investigate, problem solve and communicate their mathematics with an increasing level of sophistication’.
As the current 2019 cohort will be the first group to sit this new exam, there are limited resources for reference; however, according to the IBO Specimen Papers, Paper 3 will a 1 hour paper with 2 questions only and it will be scored out of a possible 55 marks. The questions are long and investigative-styled, which requires students to apply their knowledge to a given problem.
If your school follows the IB curriculum and you are currently studying the Middle Years Programme (MYP), Paper 3 will actually feel very familiar to you. As the third paper is all about investigative Maths and application of mathematical knowledge, it is very similar to Criteria B and D in MYP Maths. However, this does not mean that those of you who did not study MYP will not be able to do Paper 3; as long as you have the required knowledge and you understand the aim of a mathematical investigation, the HL Paper 3 should be attainable.
What is mathematical investigation?
Mathematical investigation is different from problem solving as it is open-ended, and its purpose is the exploration of a mathematical situation and to develop the student’s mathematical habits of mind.
Problem solving has a specific and definite goal – the solution of the problem. Mathematical investigation on the other hand is more open ended where students are expected to consider the problem presented after initial exploration of the mathematical situation. The aim of giving a student the opportunity to explore a mathematical situation, to formulate their own problems, and to discover the solutions is to develop their independent mathematical thinking, as well as to encourage their engagement with mathematical processes such as recording data, searching for patterns, inferring, justifying, explaining generalisations, and etc. These processes allow the student to not only learn mathematics, but to apply their knowledge to everyday situations and to allow them to solve both mathematical and non-mathematical problems.
Allowing students to independently explore a situation, it is expected that the students approach the problem differently, ultimately producing a range of results. The open ended problem may also mean that some students so not fully explore the situation; however, it is essential that the students will experience the following mathematical processes which are the emphasis of mathematical investigation:
- Systematic exploration of the given situation
- Formulating problems and assumptions
- Attempting to provide mathematical justifications for the assumptions.
Links to MYP Assessment Criteria
|Criterion B||Criterion D|
|• Select and apply mathematical problem-solving techniques to discover complex patterns|
• Describe patterns as general rules consistent with findings
• Prove, or verify and justify, general rules.
|• Identify relevant elements of authentic real-life problems
• Select appropriate mathematics when solving authentic real-life problems
• Apply the selected mathematic successfully to reach a solution
• Justify the degree of accuracy of a solution
• Justify whether a solution makes sense in real life
So how is the relevant to Paper 3? Paper 3 is an investigative paper where a problem is presented and you have to consider what mathematical knowledge or strategy should be applied. As the paper consists of 2 questions only (ranging from 25-30 marks each), they will be broken down into multiple parts. Despite being relatively guided, you will have to identify the patterns between each question part and justify the rules you have found. Looking at the MYP criteria, you can see these skills are tested in both Criterion B and Criterion D. Yes, the actual content will be challenging, but the skills tested are only a little harder than MYP. So if you are in MYP now, don’t be put off by the idea of a third paper, it may be worthwhile to consider studying HL Math.
The objective of Criteria B in MYP is to assess a student’s abilities as risk takers, inquirers and critical thinkers and whether they are capable of applying their knowledge to discover patterns in the presented problem. Criterion D, on the other hand, tests whether a student is able to use mathematical knowledge to solve problems in a real-life context. They are expected to use theoretical knowledge in real-world situations, apply appropriate strategies to solve problems, draw valid conclusions and reflect on their results.
What to expect?
It is important that you remember the changes were only made recently. Your school and the IBO will be in the process of ironing out any issues that may pop up in the coming year, so don’t stress. Do the research needed: speak to your school Math teachers to see what is being offered at your school, and read the IBO syllabus on the course.
The Edge also offers IB math common core prep course which includes a paper 3 for students thinking to taking HL math. If you have any questions, don’t hesitate to contact us.
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