I&#x27;ll give an example based on my international experience. I studied Chinese in my undergraduate major, among other languages I studied as elective subjects, and while in university I learned the International Phonetic Alphabet (IPA)[1] in linguistics classes. Few Americans know IPA. When I began studying in Taiwan after graduation, I observed that all students in Taiwan in those days learned IPA in seventh grade, in their junior high English classes, and young people with just a secondary education could reliably read aloud English texts written in IPA--a skill that amazed many of my fellow foreign students from English-speaking countries. Today, as Taiwan has moved that skill down to the primary school curriculum, most United States reading teachers have never, ever learned IPA, which is helpful for explaining the vagaries of English spelling.<p>Similarly, in primary mathematics instruction, it is well known how do instruction well with multiple representations of mathematical concepts for pupils,[2] and generally it is very well known that teachers of mathematics need to have &quot;profound understanding of fundamental mathematics (PUFM)&quot;[3] and pedagogical content knowledge, but few teachers in the United States gain that from their professional training in teacher education courses.[4] I try to do my part to help teachers already in the classroom by participating in online discussions with other teachers (I myself am a math teacher in private practice) to guide them to helpful resources for learning more mathematics. Simply put, the author of the original article submitted here is correct. The United States could and should do better in teacher education to help teachers do their job as well as they desire to do it.<p>[1] <a href="https:&#x2F;&#x2F;www.internationalphoneticassociation.org&#x2F;content&#x2F;ipa-chart" rel="nofollow">https:&#x2F;&#x2F;www.internationalphoneticassociation.org&#x2F;content&#x2F;ipa...</a><p><a href="http:&#x2F;&#x2F;www.internationalphoneticalphabet.org&#x2F;ipa-sounds&#x2F;ipa-chart-with-sounds&#x2F;" rel="nofollow">http:&#x2F;&#x2F;www.internationalphoneticalphabet.org&#x2F;ipa-sounds&#x2F;ipa-...</a><p>[2] <a href="http:&#x2F;&#x2F;singaporemathsource.com&#x2F;making-math-masters-a-brief-overview-of-singapore-math&#x2F;" rel="nofollow">http:&#x2F;&#x2F;singaporemathsource.com&#x2F;making-math-masters-a-brief-o...</a><p><a href="http:&#x2F;&#x2F;www.thedailyriff.com&#x2F;2010&#x2F;11&#x2F;singapore-math-demystified-part-3-the-famous-bar-models.php" rel="nofollow">http:&#x2F;&#x2F;www.thedailyriff.com&#x2F;2010&#x2F;11&#x2F;singapore-math-demystifi...</a><p>[3] <a href="http:&#x2F;&#x2F;www.amazon.com&#x2F;Knowing-Teaching-Elementary-Mathematics-Understanding&#x2F;dp&#x2F;0415873843" rel="nofollow">http:&#x2F;&#x2F;www.amazon.com&#x2F;Knowing-Teaching-Elementary-Mathematic...</a><p><a href="http:&#x2F;&#x2F;condor.depaul.edu&#x2F;sepp&#x2F;mat660&#x2F;Askey.pdf" rel="nofollow">http:&#x2F;&#x2F;condor.depaul.edu&#x2F;sepp&#x2F;mat660&#x2F;Askey.pdf</a><p><a href="http:&#x2F;&#x2F;www.ams.org&#x2F;notices&#x2F;199908&#x2F;rev-howe.pdf" rel="nofollow">http:&#x2F;&#x2F;www.ams.org&#x2F;notices&#x2F;199908&#x2F;rev-howe.pdf</a><p>[4] <a href="https:&#x2F;&#x2F;www.tc.columbia.edu&#x2F;news.htm?articleId=5974" rel="nofollow">https:&#x2F;&#x2F;www.tc.columbia.edu&#x2F;news.htm?articleId=5974</a><p><a href="http:&#x2F;&#x2F;www.maa.org&#x2F;programs&#x2F;faculty-and-departments&#x2F;curriculum-department-guidelines-recommendations&#x2F;teaching-and-learning&#x2F;preservice-teachers-conceptions" rel="nofollow">http:&#x2F;&#x2F;www.maa.org&#x2F;programs&#x2F;faculty-and-departments&#x2F;curricul...</a><p><a href="https:&#x2F;&#x2F;math.berkeley.edu&#x2F;~wu&#x2F;" rel="nofollow">https:&#x2F;&#x2F;math.berkeley.edu&#x2F;~wu&#x2F;</a>