Sometimes I look up Chinese words on my phone, usually on Wiktionary. Any foreign-enough characters (including all 汉字, i.e. Chinese characters) show up in my phone's web browser as mutually-identical blank boxes (tofu). If I want to see the actual form of the 汉字 — I usually do — I must find images, rather than text.

Wiktionary only gives images for a select few common complex 汉字, plus most radicals (simple 汉字, of which all others are combinations). Thus I can infer the form of the original 汉字 I seek by looking up each of its component radicals and combining them myself, sans any glances at their combined form from outside sources. This seems avoidably tedious, even inane, but I usually know the 汉字 I learn this way very well afterward, much better than more obvious methods. It works equally well for Japanese's 漢字 (kanji).

For example, let's learn the character for "hē" ("to drink"). Wiktionary links to its component radicals ("composition"), the first of which is "kǒu" ("mouth"), for which there's an image, showing that radical to be 口. The second is "hé" ("what?"), which in turn consists of "yuē" ("to say"), a radical — 曰 — and a variant of "gài" ("beggar"). That form of "gài" consists of a radical, 勹, and another variant form made of 𠃊 and 人. The full character "hē" is some arrangement of 口 + (曰 + (勹 + (𠃊 + 人))). To arrange these radicals correctly takes a bit of guessing. Wiktionary orders the composition in pairs, either left-right or top-bottom. In this case, 口 is on the left, 曰 at the top-right, and 勹 surrounds 𠃊 + 人 at the bottom-right.

This helps so much with memorising characters sith it forces attention to proper details into the learning process. More obvious ways to learn 汉字, by showing the complete characters, let you mentally model them in whatever way tempts you. Seeing only the radicals forces your understanding of 汉字 to correspond to their true structure.

Depending on how you apply the method, it may also force active recall, which aids memory encoding even further. My phone shows one page at a time, slowly and linearly. If I write out the radicals as I look them up, the method works a bit less well. If I accumulate the radicals in my working memory, and combine them at the end, all in my head, the method works even better.

If you find a 汉字 (or 漢字) you want to memorise:

  1. Use a browser with a limited character set, so as to show all 汉字 as identical in text.
  2. Look up the target 汉字 on Wiktionary.
  3. If Wiktionary gives an image of the 汉字, and it is simple, memorise that image, and stop.
  4. Otherwise, to the "Han character" section and look for "composition".
  5. "Composition" should offer a pair (or triplet) of links to other 汉字.
  6. Mentally keep track of the tree-structured breakdown of the 汉字, and recursively follow those links, as starting from step 2.

Once you know all the radicals and their arrangement, visualise (or draw out) the full character. That should be easy, and will likely remain easy for a while afterward.

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To be honest, as a Chinese person, your method of learning Chinese characters seems more reasonable and effective. When I taught children how to learn Chinese characters, I simply bought a Chinese character book. Each page of the book had several large characters, and there was a picture next to each character to indicate its meaning. By continuously reading aloud to the children and letting them understand the meaning through the pictures, eventually, the children were able to recognize these characters. My method can be effective, I believe it is largely due to the language environment that the children have.