I was reading a CNN article this morning that features the below image:

Photo Protests over integrating schools is not new. In 1965 members of a parents’ association picketed outside the Board of Education in Brooklyn, New York, against a proposal to integrate public schools.

I’m curious about the sign on the far left: “6-3-3, 5-3,4, 2-2-2, ?-?-?”

My first instinct is that these were ratios of races of students, but that seems improbable to me as segregation was (as far as I know) enforced in terms of “white” and “colored,” which would only account for two numbers. I did a cursory Google search but found nothing.

What do these numbers mean? What event in the history of integrating American schools are they referencing?

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    I genuinely thought this question was about the history of mathematical notation.
    – Lucian
    Commented Aug 1, 2020 at 18:20
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    It's not even clear that the photo depicts people protesting integration.
    – Spencer
    Commented Aug 1, 2020 at 21:18
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    Jerome Hall, A 2-2-2 Plan for College-Law Education.
    – Lucian
    Commented Aug 2, 2020 at 0:14
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    @JMS "Antidifferentiation" is a mathematical term in calculus, and the opposite of a Differential is an Integral, and the process of finding an Integral is Integration - and the "dy/dx" operator is sometimes called "the differentiation sign" - so reading "anti-integration sign" and "numbers" meant that my first-thought of seeing this question title in the sidebar was this was about someone confused about calculus notation - also I'm British, not American (despite living here), so local connotations aren't obvious to me.
    – Dai
    Commented Aug 2, 2020 at 1:57
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    @Dai: I didn't think of that interpretation until I saw you describe it, and now it's the only one I think of when I see this title :D
    – gktscrk
    Commented Aug 6, 2020 at 13:21

4 Answers 4


Short and "to the point" answer: Those numbers are just identifiers for various school district organization plans. The digits refer to the number of years a student spends in each "section" of a schooling system. The general notation is A-B-C, where "A" is the number of years in primary school (elementary school), "B" is the number of years spent in middle/junior high school, and "C" is the number of years spent in secondary (high) school. 6-3-3 and 5-3-4 were both fairly common at the time, but recent (proposed) policy changes in the Brooklyn school systems led to confusion and even outrage in the area. More details on the specific meanings of the numbers are included below.

That sign is simply mocking the changes, as a "2-2-2" system doesn't exist (and is in fact completely nonsensical) and "?-?-?" is seemingly a way of asking "What's next? How much longer are we going to mess with the system, treating our children like pawns in some game of political chess?". The numbers almost certainly aren't referring to dates or court cases.

Detailed answer (the most important details are bolded): It's important to note that this is the source of the image. The photo was taken on April 14, 1965 and submitted to the Associated Press image library in 2011. The submission notes for the photo read as follows:

"Pickets from the Parents and Taxpayers Association march outside the city Board of Education building in Brooklyn, New York, April 14, 1965. The demonstration was held to protest a report submitted to the board by school superintendent Calvin E. Gross. The report was called a "blueprint for further action toward quality integrated education." Two groups picketed the building opposing the report, the other was headed by the Congress of Racial Equality."

If we're hoping to learn more about the specific protest featured in that photo, then this description tells us some pretty useful information. Apparently this crowd was protesting against the ideas of a man called Calvin E. Gross. Gross, according to his obituary featured in the New York Times, was the superintendent of schools in New York city around the time that this photo was taken (particularly, in early 1965). Apparently, he was asked to resign after a storm of criticisms and controveries due to the report he released, referenced in the blockquote.

I'm not entirely clear on what exactly this report was, but we can learn a lot about what Calvin Gross was proposing from other information at the time. According to yet another NY Times archive I found, this time dating to mid-late 1964, Gross was fairly vocal about his plans for the integration of segregated schools. On top of unspecified "proposed steps", he also intended to immediately pair up "four sets of elementary schools", create five additional "Educational Complexes", and change up the year sequence of the school districts, namely adding one year to high school (presumably so that the year systems of various segregated schools matched up, in order to ensure a smooth integration). Gross was planning to spend around $4.3 million on all of this. As you can imagine, the vagueness of some of these announcements (as well as the cost) naturally irritated many people who would be affected by the changes.

Let's set that aside for a moment and go back to those numbers themselves. Since the image description describes the protest in relation to education troubles, the meaning of the numbers in this case must be whatever relates them to the education system. This paper reveals what the numbering system means, and details the history of their relevance to school programs in the United States.

Personally, I went to school in a 4-5-3 plan, but it seems that the 5-3-4 plan is most common nowadays in the United States. Notice that the sum of the three numbers is always 12, since it represents the twelve years of primary through secondary school that students take.

Pre-1960's schools systems often didn't even have middle school or junior high, leading to more of an "A-C" system. Sometimes the notation is extended to include A-B-C-D, where "D" refers to the number of years typically spent in college or university for a particular area (i.e. 4). The notation can be extended even further as X-A-B-C, where "X" refers to Kindergarten, preschool, or whatever it is chosen to represent in a particular instance.

Despite these special cases, the more general A-B-C notation is most commonly used (...not that any of this knowledge is "common" to begin with. I had to do some serious sleuthing to learn all of this, and now my entire afternoon is gone!). It's also worth noting that there is no such thing as a "2-2-2" system. Those numbers don't even add up to 12!

Anyways, the 6-3-3 system of learning (6 years of primary school, 3 years of middle school, 3 years of high school) was starting to become pretty common in the New York City area during the 1960's (I live in New York and it's actually still not uncommon), but it wasn't exactly something people were used to. So when Calvin E. Gross suggested adding a new year to high school, implying a sudden shift to the 5-3-4 plan that was just starting at the time, I imagine that annoyed quite a few people!

One of the common criticisms of Calvin Gross' proposed system that I described above comes down to the fact that he was proposing a lot of sudden changes to the education system that many were uneasy about, something that always gives rise to outrage from the public.

It's pretty clear from the photo that this is what the protest was about. The "DON'T MAKE PAWNS OF OUR CHILDREN" and "HASTY IMPLEMENTATION" signs make it obvious that the people are protesting sudden and uncomfortable changes, which is consistent with all of the evidence described above.

I believe the sign on the left was trying to emphasize the supposed ridiculousness of the changes that were supposed to have taken place. In a "We recently had to adapt to the 6-3-3 system, and now we might already need to switch to the 5-3-4 system all in the name of racial integration???" sort of way. The "2-2-2" part of the sign was just mocking the numbering notation entirely in a "What are we going to switch to next?" manner, and the "?-?-?" part is clearly a continuation of the point: "What comes next? Where does it stop?"

I completely disagree with the comments saying that the numbers refer to dates or Supreme Court decisions. X-Y-Z is an extremely unusual notation for representing dates, and one that I've never seen before, not even in the early 1900's. That interpretation also doesn't add up with all of the evidence and points I've presented that are directly supported by the original description of the image.

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    So 5-3-4 was a thing at that time? I grew up thinking what is typical was 6-2-4 and that I and my classmates lived in a somewhat unusual jurisdiction that followed 6-3-3. Only many years later did I hear that some have adopted 5-3-4 and call the "3" part "middle school". (In particular, the district in which I went to school now uses that schedule, if I'm not mistaken.) Commented Aug 2, 2020 at 18:38
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    @MichaelHardy I grew up in a district that was 6-3-3 and was one of the last in the state. It converted to 5-3-4 a few years ago. We called B in the first configuration "junior high," and in the second, "middle school." Never heard of a 6-2-4 (seems like a waste to build a whole school for two grades?). On the other hand it seems like a pretty lame thing to protest Commented Aug 2, 2020 at 19:44
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    @Barmar Thanks. I actually originally had it say TL;DR, but I ended up adding a bit more to the short answer in an edit, and now the "short" answer is pretty lengthy on its own!
    – K.T.B.
    Commented Aug 2, 2020 at 22:11
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    @AzorAhai--hehim - I grew up in a 6-2-4 jurisdiction (in Massachusetts) - imagine my surprise when I learned that middle school wasn't always just 7th and 8th grades!
    – Vikki
    Commented Aug 3, 2020 at 2:00
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    I grew up in a 6-2-4 jurisdiction and maybe because it was the midwest I always thought that the three grade "middle school" was weird. But with regards to having a whole school for only two grades, that's not odd for two reasons, one having to do with the development of kids that age (at least two me, 6th grade seemed like being a kid and 9th like being a young adult, leaving 7th and 8th for that awkward in between time), and the other due to how we had a bunch of elementary schools that fed into only a couple of junior highs, so even with only two grades it was quite a large building!
    – Andy
    Commented Aug 3, 2020 at 19:22

Question: What do the numbers on this 1960s anti-integration sign mean?

short answer:
The numbers 6-3-3 and 5-4-3, adding up to 12 are references to school system organizational plans. Americans attend 12 years of public school stacked in Elementary, Middle, and High school. Public schools are decentralized and their organization reflects local county and state interests rather than a federal mandated unified organization. The numbers reflect how many years one spends in each elementary, middle school, and highschool which were of interest during the Civil Rights Era as they pertained to busing and school integration.

The 2-2-2 number and the ?-?-? highlight (perhaps a fear) that integration of schools is occuring at an earlier age. School integration began in middle school. The series on the poster asks the question, how young do proponents of integration want to go?.. 6-3-3, Seventh Grade? 5,3,4, Sixth Grade, 2-2-2, Third Graders? ?-?-?, Younger?

detailed answer:

From the refferenced article which contained the photo
Protests over integrating schools is not new. In 1965 members of a parents' association picketed outside the Board of Education in Brooklyn, New York, against a proposal to integrate public schools.

6-3-3, 5-3-4 6-2-4, and 6-6, are organizational plans for school grades. They are being mentioned in segregation marches because school integration typically did not apply to elementary school children. Thus the sign is complaining about integration occuring earlier and earlier by mentioning the fictitious 2-2-2 (third graders) and ?-?-? plans. "?-?-?" where will it end.

all these plans saw various advantages in different groupings and the numbers could be interpreted thusly.

#1- #2 - #3
#1 - The last elementary grade.
#2 - The number of years the integration student would attend a transitional middle school
#3 - The number of years the integration student would attend an integrated high school

(. Note Kindergarden did not become standard in US public schools until the mid 1970's so it's not included in the numbers ).

The 6-3-3 (Grades K-6, 7-9. 10-12). plan inferred that integration would begin after the sixth grade, students would go to a 3 year transitional middle school before attending a 3 year high school program.

The 5-3-4 (Grades k-5, 6-8, 9-12) program can be interpreted as Integration will begin after the 5th grade giving students 3 years of middle school and 4 years of high school in integrated school system. An advantage of this proposal was to limit disruption to sports and extra curiculaler activities as well as scholastic programs which could begin in 9th grade high school.

The sign in question displays the 2-2-2 and ?-?-? programs which didn't exist, suggesting integrators will eventually want to integrate second graders and "where will it all end?".

The leadership advantages given to sixth graders in a 6-3-3, 6-2-4, or 6-6 organization could be given to fifth graders in the 5-3-4 plan
The 5-3-4 plan would facilitate a flexibility in grouping children for instructional purposes and would afford an opportunity for a broader curriculum offering in the high school than does the 6-3-3 plan. The restraint of organizing part of a school to meet high school graduation requirements (Carnegie units) required in grade 9 of the 6-3-3 pattern would be removed. College admission and state high school graduation requirements are based upon the assumption of a 9-12 program.

Articles about school desegregation cases which reference school organizational numbers in the pictured sign.


The Segregation of Topeka's Public School System, 1879-1951
The board of education established a 6-3-3 system or six years in elementary school, three years in junior high school and three years in high school for the city's white students. Black students were assigned to school under an 8-1-3 plan, attending elementary school through grade eight and then attending only grade nine in a junior high school before entering high school.


Brown v. Board of Education of Topeka, Part 2
When Topeka adopted the junior high system, it implemented a different educational curriculum for seventh and eighth grade students based on race. White students were provided with a 6-3-3 system, consisting of six years of elementary or grade school, three years of junior high school, and three years of senior high school. Black children were under an 8-1-3 plan.


1965 - Educational Implications of De Facto Segregation
Related to this plan is a proposed change in the typical 6-3-3 school organization. Some of the motivation for this proposal comes from doubts that have been expressed concerning the values of the urban junior high school.

  • @JMS Everything you included into post after comments came up adds to the confusion your own speculation elicits. Please cut this down via edits. // While the initial approach seems plausible, '2-2-2' eludes me, entirely. Can you find a contemporary source that tackles the pic? (That I'd accept much more readily…) Commented Aug 1, 2020 at 23:17
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    by your argument shouldn't the third line be 2-2-8 ?
    – Jasen
    Commented Aug 2, 2020 at 5:45
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    @Jansen if the woman's argument was strengthened by accuracy then absolutely. She wasn't relying upon accuracy to strengthen her argument. I rather think repetition of 2s was to instill fear. Just as her repetition of ? tried to instill uncertainty and doubt.
    – user27618
    Commented Aug 2, 2020 at 10:53
  • When was the term "middle school" introduced? I attended "elementary school" which was K–6, then "junior high school" which was 7–9, although we knew very well that in most of the country it was 7–8, and "high school", which was 10–12 (but in most places 9–12). I never heard of anything called "middle school" until much later. Commented Aug 2, 2020 at 18:42
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    @MichaelHardy Yes in the early 70's I attended a school with middle school in the name and we called it Junior High. It's been 50 years but that's my recollection.
    – user27618
    Commented Aug 2, 2020 at 20:19

The overall meaning of the sign is not certain, but it is probably not a direct reference to racial integration. What is clear is that "6-3-3" is a common term for the structure of 6 levels of elementary education, followed by 3 levels of junior high and 3 levels of senior high. I see no other possible way to interpret this.

It is very likely that the 5-3-4 system was either recently implemented or at least being discussed in New York City by 1965, replacing the 3 years of junior high with three years of middle school. One article from 1966 shows that nearby New Rochelle, NY made this change around that time, and another from the same year says that all junior high schools were expected to be replaced by middle schools in New York State by 1972.

Based on this I would further guess that the "2-2-2" and "?-?-?" may have been intended to imply that the educational system was on a slippery slope of lowering standards.

EDIT: Here is an article from 1964 directly mentioning that phasing out the 6-3-3 model as an explicit part of NY state's integration plan. And according to a history published by a teacher's union (p. 7) in 1965:

State Education Commissioner James Allen Jr. sought to promote integration by having four years of elementary, four years of middle and four years of high school (instead of the existing 6-3-3 system). New York City Superintendent Calvin Gross suggested busing 40,000 students, while “pairing” black and white schools in outerborough “border” areas, with racially mixed classes attending both schools during their elementary years; he started by pairing eight schools and 5,600 students.

Upset, a group of white parents spawned an organization called Parents and Taxpayers (PAT), which soon claimed 300,000 members in 100 chapters. Through boycotts and demonstrations, PAT raised enough of a ruckus to induce both Senator Kenneth Keating and Robert F. Kennedy, who would defeat Keating for re-election, to denounce PAT’s chief concern, long-distance busing (which was not part of either Allen’s or Gross’ plans).

Counting or not counting kindergarten may explain the discrepancy between the "5-4-4" on the sign and the "4-4-4" Allen proposed.


The sign refers to the fact that the integration fight intersected with another big debate at the time: the minimum amount of compulsory schooling.

Today's rules are more stringent, but at the time, the debate for the minimum compulsory schooling was between eight years and nine years. The term 6-3-3 referred to the "old" formula of six years of primary school, three years of "junior high" and three years of "senior high." Not all children were expected to complete "senior" high school, and "junior high" (nine years of schooling) was the logical drop out point for those students.

The formula of 5-3-4 refers to a plan of five years of elementary school, three years of "middle" school, and four years of senior high school. A plan of this sort made it easier to administer integration by limiting it to the first eight years of school, and "exempting" the new "senior" high schools, since the majority of children (at the time) didn't attend, or at least finish them anyway.This was particularly true of blacks, who were more likely than whites to complete only eight years of schooling.

But the 5-3-4 plan was anathema to most white parents, especially poor ones, not only because of integration, but because it appeared to "roll back" the compulsory years of schooling from nine to eight years, the last thing that most such parents would want.

A hypothetical hybrid plan might have been 6-2-4, but that was also unsatisfactory; it hardly makes sense to have a school for only two years. The term "2-2-2" was a take-off on this, and would have denoted "two years of elementary school, two years of middle school, and two years of high school." That is, if you are going to "roll back" the period of compulsory education from nine years to eight, why not go all the way back to six, to make integration even easier. This is a debate technique called "reductio ad absurdum"

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