This is a repost from four years ago. It contains important insights on how teachers of Mathematics affect learning outcomes in Mathematics. It goes without saying that teaching mathematics requires more than just knowing how to do mathematics. If knowing how to do math is all that it takes then I can easily teach my son who is in second grade math. Teachers of mathematics in basic education are not only trained in doing math but also in teaching math. It is therefore reasonable to expect that learning outcomes in math depend on the quality of training teachers of mathematics have received.
The following are some of the exhibits provided by
The Teacher Education Study in Mathematics (TEDSM) in 2008 of the International Association for the Evaluation of Educational Achievement (IEA). This is an interesting study because it includes both the Philippines and the United States. It also includes countries that perform very well in international standardized exams in math like Singapore and Taipei. The first one is a qualitative description of the amount of control over higher education institutions responsible for the training of math teachers. With this criterion, the Philippines as well as the United States belong to the group where there is "weak control". The highperforming countries, on the other hand, belong to the "strong control" set.
The next exhibit groups the countries according to how attractive the teaching profession is perceived. In this grouping, once again, Taipei and Singapore belong to the "highly attractive" group while teaching in the Philippines is deemed "low" in atractiveness:
In the next ranking, the selection requirements of the teaching schools are evaluated. Here, students who do well in international math exams are taught by teachers that met specific requirements just to be enrolled in the teaching schools.
Another aspect TEDSM considered is the level of mathematics students in teaching schools have received prior to enrollment. Here, the Philippines together with Chile and Thailand are the only countries that do not have any specific math requirement. A high school diploma will do.
The quality of teaching schools is maintained by accreditation. This process requires a regular assessment of the programs. Here, one can see a significant difference between the US and the Philippines. Although both countries are characterized by "weak control" over schools, the US has external evaluation and accreditation. This accreditation is provided by professional agencies and these agencies or organizations have the power to say that a particular teaching school is poor and not worth attending.
The Philippines ranks in the middle at least in one criterion. The Philippines does require a licensure examination in order to teach in a public school.
Of course, there are other factors that come into play in basic education. The following exhibit highlights some of these factors. In this list, it can be seen that the Philippines demands quite a bit on its basic education system. It is tied with Botswana in terms of the percentage of the population requiring basic education. Unfortunately, while the needs are high, the expenditure (expressed as percent of GDP) is among the lowest for the Philippines. The Philippines has so many students to teach yet it spends the lowest. The bulk of the education budget of any country is the salary of the teachers. Thus, with the relatively low funding of education in the Philippines, it simply follows that teachers in the Philippines are poorly paid. In this list, it should be no surprise that the Philippines has the lowest graduation rate at the end of basic education. It also has the highest number of pupils per teacher. These factors are important. Otherwise, one may completely blame the failure of education on the quality of teaching instruction. These other factors are expected to make basic education in the Philippines much more challenging that in the other countries in this list.
The quality of the training of math teachers depends as well on the expertise of their trainers. It is also useful to look at the qualifications of the teachers of teachers. Only half of the educators of math teachers in the Philippines have math as their "main specialty".
Although subject knowledge is not sufficient for being an effective teacher. One may reasonably think that it helps to know the subject matter one is trying to teach. TEDSM therefore administered a test to the math teachers to assess their subject matter knowledge. The teachers from the Philippines are near the bottom of this list:

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Lastly, it is also informative to check the bias of teachers in math. It is known that mathematical ability is something students can improve. Effort counts, yet some people believe that being able to do math is an inborn talent or gift. This belief apparently correlates with poor performance of students. Botswana, Georgia, Malaysia, Thailand and the Philippines have a significant fraction of their math teachers subscribing to this wrong belief.

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It is true that teacher quality is not the only factor that determines learning outcomes. But it is one factor....