while the changes in the _percentage of classes taught by teachers with higher education_ were concentrated to the very lower percentiles of the distribution, for _higher education in the field_ indicator the changes spread also to higher order percentiles. So schools seem to be converging to universalization of teachers training at the tertiary level, excepting for field training of Portuguese teachers. Table 5 – Percentage of Classes Taught by Teachers with Higher Education

||||||<br>|Percentile<br>|<br>|||||
|---|---|---|---|---|---|---|---|---|---|---|---|
||p5|p10|p15|p20|p30|p40|p50|p60|p70|p80|p90|
|_Math classes h_|_igher_|||||||||||
|2009|50.0%|73.3%|87.5%|100%|100%|100%|100%|100%|100%|100%|100%|
|2015|66.7%|81.0%|90.9%|100%|100%|100%|100%|100%|100%|100%|100%|
|_Portuguese cl_|_asses higher_|||||||||||
|2009|63.6%|82.4%|94.0%|100%|100%|100%|100%|100%|100%|100%|100%|
|2015|76.9%|90.3%|100%|100%|100%|100%|100%|100%|100%|100%|100%|
|_Math classes h_|_igher in the_|_field_||||||||||
|2009|0.0%|16.0%|31.3%|41.7%|60.0%|72.7%|83.3%|95.3%|100%|100%|100%|
|2015|14.3%|33.3%|45.7%|55.0%|66.7%|76.9%|85.7%|95.2%|100%|100%|100%|
|_Portuguese cl_|_asses higher_|_in the fi_|_eld_|||||||||
|2009|20.0%|42.9%|59.4%|69.2%|83.3%|94.4%|100%|100%|100%|100%|100%|
|2015|25.0%|44.4%|56.3%|64.3%|76.9%|86.7%|95.7%|100%|100%|100%|100%|

It would be more interesting to see how many schools increased the indicator and to what degree this happened. Tables 6 and 7 show the transition of the schools between percentile strata shown in Table 5, based on the percentile intervals in 2009. The blue cells show how many schools managed to raise the indicators in the period and the red cells show how many schools faced a decrease in indicators.

Table 6 – Number of schools by _Percentage of Classes Taught by Teachers with Higher_ _<u>Education</u>_ – Transition between percentile strata, 2009 and 2015.

|_Math c_|_lasses_<br>|<br>(87.5%, 100%]|<br>(73.3%, 87.5%]|<br>2015<br>(50.0%, 73.3%]|<br>(0%, 50.0%]|Total|
|---|---|---|---|---|---|---|
||(87.5%, 100%]|<br>**8,545**|**508**|**370**|**162**|9,585|
||(73.3%, 87.5%]|<br>**454**|65|36|27|582|
|2009|(50.0%, 73.3%]|<br>**414**|55|45|24|538|
||[0%, 50.0%]|**386**|62|72|75|595|
||Total|9,799|690|523|288|11,300|
|_Portug_|_uese classes_|||2015|||
|||(94.0%, 100%]|(82.4%, 94.0%]|(63.6%, 82.4%]|(0%, 63.6%]|Total|
||(94.0%, 100%]|<br>**8,265**|**400**|**350**|**185**|9,200|
||(82.4%, 94.0%]|<br>**441**|55|28|17|541|
|2009|(63.6%, 82.4%]|<br>**424**|48|41|22|535|
||[0%, 63.6%]|**397**|55|58|41|551|
||Total|9,527|558|477|265|10,827|

_Note._ Strata were constructed based on 5th, 10th, and 15th percentiles. Blue (red) color indicates schools that moved the indicator to a superior (inferior) stratus between years 2009 and 2015.

Table 7 – Number of schools by _Percentage of Classes Taught by Teachers with Higher Education in_ _<u>the Field</u>_ – Transition between percentile strata, 2009 and 2015.

|_Math c_|_lasses_|<br>(72.7%, 100%]|<br>(60.0%, 72.7%]|<br>2015<br>(41.7%, 60.0%]|<br>(16.0%, 41.7%]|<br>(0%, 16.0%]|Total|
|---|---|---|---|---|---|---|---|
||(72.7%, 100%]|<br>**4,986**|**674**|**576**|**322**|**179**|6,737|
||(60.0%, 72.7%]|<br>**630**|163|155|82|40|1,070|
|2009|(41.7%, 60.0%]|<br>**684**|185|209|105|53|1,236|
||(16.0%, 41.7%]|<br>**519**|144|196|179|95|1,133|
||[0%, 16.0%]|**445**|106|171|173|229|1,124|
||Total|7,264|1,272|1,307|861|596|11,300|
|_Portug_|_uese classes_|||2015||||
|||(94.4%,100%]|(83.3%, 94.4%]|(69.2%, 83.3%]|(42.9%, 69.2%]|(0%, 42.9%]|Total|
||(94.4%,100%]|<br>**3,812**|**743**|**790**|**702**|**444**|6,491|
|2009|(83.3%, 94.4%]|<br>**474**|168|185|149|78|1,054|
||(69.2%, 83.3%]|<br>**477**|148|197|179|114|1,115|

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