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snowflake
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How to make adjustments in language exposure using mathematics

We are family of five with three children 3, 6 and 7 years old. We live in Finland and use OPOL in such a way that I speak my native language Swedish and my husband his native language English with the children. We speak English with each other. The children attend daycare and school in Swedish and the oldest child attends a Finnish&German after school program four times per week. The children watch TV mostly in Finnish, but also in German and English and occasionally Spanish. During the summer, the oldest attends a one week summer camp for Finnish speakers learning Spanish. The oldest also takes part in two hours of English for native speakers instruction per week arranged by the school and will start one weekly one hour lesson in Finnish in school in the fall. German and Spanish can be studied in school when the children get older. So we are trying to teach our children five different languages but to varying degree.

I like maths so I have been trying to calculate how much the children will learn during one year and compare it with the expected progress on https://en.wikipedia.org/wiki/Common_European_Framework_of_Reference_for_Languages#Relationship_with_duration_of_learning_process For illustration I will use the amount of hours my oldest child spends learning the different languages during the calendar year 2018.

Finnish
After school program 350 hours
Watching TV 300 hours
Community/playing with mostly bilingual friends 50 hours
Hobbies 30 hours
Finnish class in school 20 hours
Summer activities 20 hours
Total 770 hours

German
After school program 200 hours
TV 100 hours
Total 300 hours

Spanish
Summer class 20 hours
TV 20 hours

I then divide these numbers with two because most activities are somewhat conducted in multiple languages and most are also not focused language study. The resulting hours are

Finnish
385 hours
German
150 hours
Spanish
20 hours

Comparing with the duration of learning process table and considering the starting knowledge of the child at the start of the year, the results for my child should be an increase in knowledge level approximately like this

Finnish
From upper beginner A2 to upper intermediate B2
German
From no knowledge to about mid beginner level between A1 and A2
Spanish
From knowing a few words to knowing a few more words but no increase in language level

Being halfway through the year I then check how the midway progress is going to see if my predictions are accurate and this far the predictions seem quite accurate. I have of course not officially tested my children, but having studied multiple languages myself up to C1 or C2 level, I can make an educated guess about their knowledge for their age group. I then take it further to estimate what level the child will reach after another year if following the same pattern.

At the end of 2019 my oldest child is estimated to have reached the following language levels in the chosen languages

Finnish
Lower advanced C1
German
Between upper beginner A2 and lower intermediate B1
Spanish
Will still not have reached a full language level, not even lower beginner

If we then extrapolate this until my child reaches the age of 18, assuming no change in the amount of time spent on each language, the language levels obtained will be as follows

Finnish
Near native beyond upper advanced C2
German
Upper advanced C2
Spanish
Maybe upper beginner A2, but progress slowed down by infrequent exposure

Taking into account that the child will age out of the after school program in about one to two years, but adding some extra school lessons and especially more community exposure in Finnish, the results can be adjusted to

Finnish
Near native beyond upper advanced C2
German
Upper intermediate B2
Spanish
Upper beginner A2, possibly lower intermediate B1 depending on amount of time studying the language in school

So based on my calculations, some adjustments need to be made. It seems like the exposure to Finnish will be sufficient to surpass upper advanced level C2 by a lot. Therefore, the exposure to Finnish can be somewhat decreased after the child reaches at least a B2 level, enough for interactions in the environment to be quite easy. At the same time, exposure to the other two languages can be increased. Already at this point it would be beneficial to consider the end goal with the language. Is upper intermediate level B2 in both German and Spanish more desired than lower advanced C1 in German and Upper beginner A2 in Spanish? In our case, both languages are equally important so exposure to Spanish should be increased, for example by watching more TV in Spanish and less in Finnish, or online lessons.

Of course, the older the child gets the more autonomous it will get and start making decisions by themselves. This is about giving them a head start so that it will be easier for them to master a language should they later decide that they want to do so. These calculations are also useful for giving accurate and realistic predictions about how much your child will actually learn of a language with the exposure you give them. Is the weekly Spanish course really enough to make my child fluent? Will watching 20 minutes of French TV per day make my child able to communicate with people while on vacation in France? You will of course have to expose your child to a language through many different sources and human interaction is essential, but the amount of time spent with the language in general is also an important factor.

Does anybody else use mathematics to make decisions about which language your child should watch movies in or use a similar system in any way?
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