One of the selling points of re-hashed American 1990s high school math programs is that they are "integrated", that is, combine algebra, geometry, statistics, trigonometry just like the European programs do, and the Europeans know better (obligatory nod to Finland follows).

Considering that SE is visited from all over the world, I am interested in validity of this statement. I wonder which countries use integrated math course for HIGH school (not so much interested in middle school, but factoids like starting geometry in 7th grade are appreciated). Also, which countries use courses like algebra and geometry simultaneously in the same grade.

In particular, in Russia algebra starts at 7th grade (elementary and secondary school altogether is 11 years). Geometry also starts at 7th grade simultaneously with algebra. Two subjects are taught in parallel, but the textbooks are separate for each subjects. Physics also starts at 7th grade (there is no "science" subject in Russian schools, there are physics, chemistry, biology, geography, astronomy). All three subjects mentioned above go for five years until the end of school. The last two years of algebra deal with trigonometry and pre-calculus (basics of differential and integral calculus), all mandatory. The last two years of geometry deal with stereometry (3D geometry). Physics do not use any calculus in it, only some trigonometry is used.

I especially would appreciate links to specific programs and textbooks. Searching online is not that easy, considering that I don't know French, German or, say, Malay (meaning that I welcome info from all over the world, not only from Europe).

  • $\begingroup$ Could you provide a link to the curriculum you describe as "re-hashed American 1990s high school math programs", or what you otherwise term as "integrated" programs, in more than one sentence? It hasn't been the 1990's only in some US programs that that previous learning (developmentally) is integrated in further math learning. This can happen sequentially, consecutively, and both, particularly at the secondary school (high school, age 10-18, level). So I think your question needs to be more specific. $\endgroup$
    – amWhy
    Commented Apr 4, 2019 at 21:09
  • $\begingroup$ Perhaps what has happened in America since the 1990s is a statistically significant increase in the percentage of high school math programs using integrated approaches. However, what is actually covered and how it is covered will vary from state to state, city to city, school district to school district, and maybe even sometimes from school to school (in the same school district). For what it's worth, a U.S. high school I taught at for 3 years in the late 1990s has never (before 1990s, during 1990s, from 1990s to now) used such an approach. $\endgroup$ Commented Apr 5, 2019 at 9:15
  • $\begingroup$ The Common Core State Standards only deal with content, so I'm pretty sure that those states which have implemented the standards (not all states have) still have integrated and non-integrated math programs being taught in their school systems. $\endgroup$ Commented Apr 5, 2019 at 18:01
  • $\begingroup$ @DaveLRenfro True, CC supports both AGA and integrated. I was responding to what is covered part, hoping that by the end of HS everything spelled out in CC is covered. $\endgroup$
    – Rusty Core
    Commented Apr 5, 2019 at 19:01
  • $\begingroup$ ... by the end of HS everything spelled out in CC is covered --- I suspect this is an ideal that is not achieved in many places, unfortunately. $\endgroup$ Commented Apr 5, 2019 at 19:38

1 Answer 1


If by high school you mean lukio/gymnasium, the Finnish info is available in Finnish and Sápmi https://www.oph.fi/saadokset_ja_ohjeet/opetussuunnitelmien_ja_tutkintojen_perusteet/lukiokoulutus and in Swedish at https://www.oph.fi/lagar_och_anvisningar/laroplans-_och_examensgrunder/gymnasiet .

The English version does not seem to be free, but does seem to be available, supposing by "high school" you mean upper secondary education: https://www.oph.fi/english/curricula_and_qualifications/general_upper_secondary_education .

In case of link rot, one should search the webpages of Opetushallinto/Utbildningsstyrelsen, the Finnish national agency of education, for more topical links.

If one wishes to read the official document via machine translation, I would recommend starting with the Swedish document as the baseline. Swedish is a larger language and an Indo-European one, so machine translation to other Indo-European languages is likely to be of higher quality, and the document by itself is also easier to understand for someone who knows Indo-European languages. (Use Finnish if machine translating to e.g. Estonian and maybe Hungarian.)

Structure and role of lukio/gymnasium studies

After compulsory education, a child may go to lukio for general studies or to ammattiopisto/yrkeskola to qualify for a profession. Both lukio and ammattiopisto qualify one for higher vocational studies (bachelor level) and lukio also prepares one for university studies (typical default is master level).

In lukio one has to take a certain amount of courses, in addition to which there is the national matriculation examination. Some courses are compulsory. One can take either "short" or "long" mathematics studies, with different compulsory courses. It is possible to change from one to the other during studies.

Books in mathematics for lukio/gymnasium, in Finnish

There are Finnish books in natural science available here: https://www.akateeminen.com/kirjavalikoima/oppikirjat/lukiokirjat/matematiikka . Matematiikka is mathematics, pitkä means long, lyhyt means short.

(Biologia is biology, fysiikka is physics, kemia is chemistry.)

Books in short mathematics: https://tuotteet.sanomapro.fi/tuotteet/lukio/lyhyt-matematiikka.html

Books in long mathematics: https://tuotteet.sanomapro.fi/tuotteet/lukio/pitka-matematiikka.html

Books in both mathematics: https://otava.kauppakv.fi/sivu/lukio-matematiikka/

Mostly books in lukio mathematics: https://www.huuto.net/osasto/kirjat-ja-lehdet/lukion-oppikirjat/matematiikka/285 (this is an Ebay-like site.)

A couple of open textbooks of unknown quality: https://avoinoppikirja.fi/mat-lukio

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    $\begingroup$ I may try to give a summary later, if there is interest, but no time at the moment. $\endgroup$
    – Tommi
    Commented Apr 4, 2019 at 6:35
  • $\begingroup$ Yes, it is very interesting. So far I am reading oph.fi/download/… using Google Translate, and it talks about long and short courses, also "local" courses. I presume that although the syllabus is more or less the same across the country, teachers or even students themselves can choose different topics to be studied either in greater or less detail. $\endgroup$
    – Rusty Core
    Commented Apr 4, 2019 at 16:40
  • $\begingroup$ I also presume that sequencing of the blocks is pre-defined, "A" blocks can be replaced with "B" blocks for deeper study. Also, it seems there is very little to study in geometry section. These requirements are great, it would be better to see actual textbooks. $\endgroup$
    – Rusty Core
    Commented Apr 4, 2019 at 16:52
  • $\begingroup$ This is essentialy a "link-only" answer which offers very little explanation in the form of an answer, other than by copying and pasting internet links into what should be an answer field (answers should seek to be more or less self-contained, and links, which can die, are best used to illustrate what has already been explained. $\endgroup$
    – amWhy
    Commented Apr 4, 2019 at 21:13
  • 1
    $\begingroup$ @RustyCore I'll try to provide a summary in the recent future, since you seem interested. $\endgroup$
    – Tommi
    Commented Apr 5, 2019 at 5:52

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