Mathematics IA: Exploration

This Mathematics IA exploration leaves lot of room for creativity due to open-endedness. Also  students have opportunity to combine his/her personal interests with mathematics. It should be introduced at the beginning of the course. As a course progresses teachers are expected to highlight areas within the syllabus which leads to exploration topics. 

A student is better prepared to inquire these open ended problems when they are encouraged to do small explorations, to mark sample explorations, to write smooth mathematical writing and they are given required help in terms of appropriate technology and guidance for exploration.

An applied stimulus may lead to modelling tasks and a mathematics stimulus may lead to investigations. Here I am not expecting students to find new mathematical discoveries. Rather, I am looking forward to see a student engages himself/herself to explore, to reflect and  to communicate using mathematics learnt in the classroom and beyond. 

A probable sequence of events towards final work could be
 introduction to the task>research and seek information> students decide the topic and focus> work on explorations> first draft>teacher gives feedback> students finalise after feedback.  It is  very important to store all the sources from which ideas are drawn in order to cite them as expected. 

All candidates must be aware that this task may turn out to be difficult to develop a topic that is not at a suitable level of mathematics. It is therefore recommended to pick topic wisely, so that good marks can be obtained, is doable within the given time frame,  can be reported in approximately 6–12 pages.

[Notes taken from the Helsinki IA workshop
Jarmo Hurri]

Introduction to Functions(real valued) - Points noted(Pathways School Noida, India)

Today as we started talking about one of the most important concepts of mathematics, namely  functions, many different questions were asked. what is a function? What does it mean to evaluate a function? what is the essence of learning functions? or do we have any application in day to day life?

A function is a relation. It is a rule, an association between two sets called domain and range. Elements from domain are plugged into the function and in return function produces elements of range.  One example of a function from economics, the cost functions which was formed as a combination of  fixed cost and  variable cost helped students to understand areas of application( also dependent and independent variables). Few more examples came out in the process, parking charge is related parking time, weight is related to age etc.

Students have found that there are several ways by which a function be represented. They are graphical, formula, order pair,  tabular and mapping. Next question that arise from here, are these forms of the same function represent a function same way? (TOK). After questions and counter questions, it was established that order pair, tabular and mapping can represent only finite number of points out of whole domain and range of a function but  formula and graph represent a function in a better way. Formula being the strongest of all of them.

To find domain and range we need to make sure that we can not  have zero in the denominator, can not have negative sign inside a square root and logarithm of a negative number is undefined.
Thank you all my grade 11 MATH  HL students, Keep enriching yourself.