Math Exploration
HL Math Exploration Notes and Rubric.pdfHL Math Exploration Rubric
As a reminder, the rubric criteria are [Communication / Mathematical Presentation / Personal Engagement / Reflection / Use of Mathematics]
Sample HL Explorations:
Pretty good HL example (functions, physics, derivatives): Optimal Way to Throw to a Dog [HL Rubric: 4 / 3 / 3 / 2 / 5 / Total: 17]
Exploration is clear, concise, and very well written. Mathematics present is comprehensive and well represented and good understanding is developed throughout. Diagrams and charts enhance readability. A consistent sense of evaluation and personal engagement is present throughout the actual writing and was present throughout the creative process of working on the Exploration. Mathematics is commensurate with the course and shows good understanding, but perhaps lacks a final concluding piece of working to incorporate all the disparate mathematical ideas. See annotations on uploaded Exploration for specific rationale for criteria marks.Average HL example (physics, integrals): Moment of Inertia [HL Rubric: 3 / 3 / 1 / 2 / 4 / Total: 13]
Exploration reads well and includes sophisticated, but descriptive, mathematics. Only superficial personal engagement is displayed in the writing. Good reflection is present in the conclusion of the Exploration. Mathematics looks good and is accompanied by definitions of terms and constants. See annotations on uploaded Exploration for specific rationale for criteria marks.Poor HL example (geometry, functions): Area of a Fractal [HL Rubric: 1 / 1 / 2 / 0 / 1 / Total: 5]
Mathematics is descriptive and does not delve into any depth. Exploration reads logically, but it lacks direction. See annotations on uploaded Exploration for specific rationale for criteria marks.Sample SL Explorations:
The rubric for HL is the same as for SL except Criterion E: Use of Mathematics. The HL rubric is stricter and demands more correctness, sophistication, and rigor. To estimate the HL score for these papers, subtract 1-2 points from the Criterion E score for the low-scoring papers and subtract 2-3 points from the Criterion E score for the high-scoring papers.
Pretty good SL example (derivatives and optimization): Optimal Shape of a Pizza Box [SL Rubric: 4 / 3 / 3 / 2 / 5 / Total: 17]
Exploration is clear, concise, well-organized, complete, driven by creative, candidate-generated examples. Candidates uses word processing and GDC technologies to full effect. Candidate reflects throughout Exploration on meaning of his working. Mathematics is relevant, commensurate to the course, correct, and good understanding is shown. See annotations on uploaded Exploration for specific rationale for criteria marks.Pretty good SL example (statistics, regression): Nation's Happiness vs. Concern for Climate [SL Rubric: 4 / 3 / 2 / 3 / 5 / Total: 17]
Exploration is coherent, well-organized, and complete. Candidate writes in a way to very clearly show the reader the thinking processes at play and to show the Exploration's logical development and mathematical aim. Mathematical presentation is appropriate throughout and multiple forms of mathematical presentation are used. Candidate shows good evidence of personal engagement in the mathematical ideas at the heart of the Exploration through the report and shows consistent evidence of meaningful and substantial reflection all all times. Mathematics used is correct and shows good understanding of mathematical ideas at work. Please see annotations on the uploaded Exploration for more specific rationale for the criteria marks.Pretty good SL example (trigonometry, functions): Musical Dissidence and Consonance [SL Rubric: 4 / 2 / 3 / 1 / 5 / Total: 15]
Exploration is coherent, well-organized, and complete. Candidate writes in a way to elucidate thinking and bring the reader along for the journey in a precise and concise way. Mathematics used is relevant to the topic at hand, shows good understanding of trigonometric function graphs, and is certainly commensurate with the level of the course. Math is presented clearly and most charts and diagrams serve to further add meaning the the Exploration. Candidate makes effective use of online graphing technology. Candidate shows significant personal engagement in the choice of the topic and in the sustained creativity throughout the Exploration, showing investment in the process and the work. Reflection on mathematical processes and the process of writing the Exploration is superficial. Please see annotations on the uploaded Exploration for more specific rationale for the criteria marks.Average SL example (statistics, regression): Rising Sea Levels [SL Rubric: 3 / 3 / 2 / 2 / 4 / Total: 14]
Exploration reads well and is a coherent body of work. Presentation is accurate and varied and good. Personal engagement and reflection are present throughout Exploration and extend beyond a superficial level, but are neither abundant nor critical. Mathematics presented is relevant and commensurate with the course, but lacks true depth of understanding. See annotations on uploaded Exploration for more specific rationale for criteria marks.Slightly below average SL example (vectors): Vectors in Football [SL Rubric: 2 / 2 / 1 / 0 / 3 / Total: 8]
Exploration has some organization and some coherence, but lacks depth. Mathematics is relevant and commensurate with level of course, but lacks rigor and sophistication and notation and presentation suffers from small inconsistencies. Candidate demonstrates superficial personal engagement and offers no critical reflection of mathematics or Exploration as a whole. See annotations on uploaded Exploration for more specific rationale for criteria marks.Slightly below average SL example (statistics, regression): Number of Starbucks vs. Economic Standing [SL Rubric: 2 / 1 / 1 / 1 / 3 / Total: 8]
Exploration show some organization and some coherence, but is not complete and lacks detail and rigor. Candidate does demonstrate in superficial personal engagement and superficial reflection. Mathematics used is limited in nature, though correct and appropriate for the stated aim. Though commensurate with the level of the course, only a limited understanding is demonstrated, with several missed opportunities to show deeper understandings. Please see annotations on the uploaded Exploration for more specific rationale for the criteria marks.Poor SL example (physics, functions): Vehicle Stopping Distance [SL Rubric: 1 / 1 /1 / 0 / 1 / Total: 4]
Exploration is organized, but lacks coherence, and does not read as a complete work of math. Interesting facts are given but very little mathematical working is provided. The mathematics used is relevant to the stated aim and topic, but is not commensurate with the level of the course and does not show any sophistication of understanding. Only superficial personal engagement is present in the description of the motivation for the Exploration. No reflection is present. Please see annotations on the uploaded Exploration for more specific rationale for the criteria marks.Here are all the website notes from our days working on the Exploration, in reverse chronological order:
Almost-Complete Draft Due - please upload to ManageBac and almost-complete draft that Mr. Lao will read and give comments on to help you improve by 10 PM on Thursday, December 19th.
Tuesday, 11/26 - we swapped drafts and did peer review. Here are the slides from class. Here is the personal graphic organizer and peer review template we used to organize our thoughts. Here again is the rubric for the Math Exploration.
Wednesday, 11/27 - we acted on the feedback our peers gave us and also planned out our time for December. Here are the slides from class. Here is the calendar and graphic organizer we used to plan out our time.
Peer Draft Submission - please have something printed out in class on Tuesday, 11/26 so that we can swap with each other and get feedback.
Thursday, 11/7 - we read more sample Math Explorations. Here are the slides from class. Please see the "Math Exploration" section of this website for sample explorations.
Wednesday, 11/6 - we reminded ourselves about the rubric for the Math Exploration and we reviewed our topic submissions to see if we were approved on this public spreadsheet. Here are the slides from class. Please see the "Math Exploration" section of this website for sample explorations and the spreadsheet of topic submissions.
Topic Submission - please submit your topic idea + brief list of math + back up topic at the following link by 10 PM on Saturday, 11/2:
Tuesday, 9/10 - we received general feedback on our mind maps and looked at the rubric for the Math Exploration for Math HL. Here are the slides from class. Here also is a list of past questions generated by TBLS students for their Math Explorations. Your next mind map, of your choice, is due on Wednesday, 9/18. You will have one mind map of your choice due every Wednesday for the next few weeks.
Monday, 9/9 - we made and looked at "math-to-topic" mind maps that might help us generate topics for our Explorations. Here are the slides from class. Your HW is to create one "math-to-topic" mind map for a stimulus word of your choosing, due tomorrow, to be collected.
Friday, 9/6 - We are starting the process of writing our Internal Assessments in IB Math HL, called the Math Exploration.
We made and looked at "topic-to-math" mind maps that might help us generate topics for our Explorations. Here are the slides from class.
Your HW is to create one "topic-to-math" mind map for a topic of your choosing, due Monday, to be collected. The idea is not to get a definitive topic out of this exercise (but you might!) but instead to practice making mind maps to help you start thinking more critically about what kind of topic you'd like to write about and also to see the world in a mathematical light.