The curriculum materials that most of us are familiar with would be those found in texts, workbooks, assessment books and exam papers. These are nationally produced materials that would reflect the goals of the education ministry and would usually be the work of qualified teachers and curriculum experts in the field. As such, they would also be catered for classroom use and national exams. 
Being aimed for the general student, they are affordable, concise and provide the necessary sources of information. These are supplemented by notes and supplementary exercises from teachers. Teachers also play an important role in imparting the knowledge in their own ways to successfully communicate the desired knowledge to the student. Curriculum materials are thus channelled through teachers for knowledge transfer. 
In the new age of information, curriculum materials and teachers are just two of many sources of information. While teachers continue to play an important role, the act of learning and studying has been greatly improved through the use of technology. In the past, one would be rather dependent on teachers and one's more intellectually endowed peers, in trying to study a certain subject should one find difficulty in grasping the concepts. 
However, today, if you have not paid attention in class and have no idea how to do a piece of homework you have many you can refer to online from Google to AIs like ChatGpt, Thus, in terms of the main business of schools- knowledge transfer- its monopoly is much reduced and for those not needing the other services that schools provide- for example, childcare, social network and structure- it has become less and less important for one to have to go to school. 
One can't deny the importance of teachers in providing the human touch to the pursuit of knowledge, but presently, if you aren't able to or would not like to attend an institution of learning for whatever reasons, teachers are available online from different corners of the world whether through online schools or individual tutors on online platforms. There is also, in some countries, the shadow economy of tuition centres. 
Economic reason would expect schools to be more sensitive to their consumers- parents' and students'- needs with the rise in competition. States however are able to monopolise education through legal means such as Compulsory Education and laws with regards to setting up and running schools, directly or indirectly. For example, a law on prohibition of registering local students within a school-going age bracket would deprive alternative private schools from having such students.
Non-residents, not part of the national education agenda, while possibly taxpayers, however are a market for private education. Countries trying to attract foreign investment and labour, may even provide incentives to encourage the set up of private international schools . Companies need labour and labour needs to send their children to schools. 
There may be no motivation for countries to allow alternative institutions to national schools, especially if they refuse to meet the conditions to be part of an oligopoly. How does one skirt around the scenario then? If you do not need to work, you can be that school your child needs. However, just like any private entities, the state can still prevent you from functioning as one or limit your role through legal means as a form of control for it to continue to exist as a monopoly of public education. It will be interesting to look at how parents, as the legal guardians of their children, are seen compared to commercial entities with regards to their rights to educate their children. 

Shortcut for getting improper numbers from mixed numbers


Forty years ago, when I was my youngest daughter’s age, we were taught to multiply the whole number in a mixed number with its denominator and to add the numerator when we want to change it into a mix number. I don’t recall being taught why, but maybe I forgot or was not paying attention in class.
As part of our online class, I decided to introduce this shortcut to my students and ask them to figure out why this formula works. Prior to that students were asked to visually represent a mixed number and an improper fraction. They were not told both these numbers represent the same value or are equal and the very small class of two did not themselves see this relation.

When asked to show how we can use the visuals to show why the formula works, the 2 students were at a loss to show how to.
So, I prompted the students to put together all the halves- they will get the same model as the first one and when they divide the 3 wholes in the visual into two for the mixed number they get the same as the visual for 7/2. We have thus established that they are the same; but still why the sequence in the formula?
To do so we need to look at what 3 1/2 represents. The denominator ‘2’ represents how many parts there are in a whole, so if we have 3 wholes to know how many parts there are we multiply ‘3’ to ‘2’ to get 6, but this only gives us how many parts there are in the ‘wholes’. To get the complete answer we need to add the number of parts that do not make a whole to the product. Hence this process gives us the total number of parts out of the number of parts in one whole.
I’m not quite sure if my explanation made sense to the girls (no worries, they take time) but I think pondering about such simple short cuts such as why you add a zero to a number if you multiply by ten and so forth, firstly gives you that ‘aha!’ moment and on a deeper level, it makes you wonder about what is this order in Mathematics that makes such formulas possible. Hopefully, this can spark their interest in Math. Asking ‘why?’
You also hope that this allows them to access Math at a more conceptual level especially as they move on to more advanced math. Finally, this of course benefits me who wonders why these formulas I learned in school decades ago are the way they are. How would you teach this formula to nine-year-olds?