1. Declining the Definite Article and Several Types of Nouns.
a. The Alphabet and Pronunciation. Special attention was required for the umlauted vowels; I explained that the umlaut represented an e following the vowel, and originally was written as an e superscript. I also pointed out ways in which some of the letters were homophones, and which letters (all of them homophones) belonged primarily to foreign words, which appear often in scientific writing such as Haeckel's. I also highlighted the letters that were visually difficult to distinguish in Fraktur, or in the case of capital J and capital I, indistinguishable. I explained why J and I were the same. We used PDF pages 34-36 in Lange's grammar.
b. Introduction to gender, case, and number. All Aryan languages, including English, at one time had a case system. A few other language-families like Semitic and Uro-Altaic also have a case system. In a simplified summary of the German case system, the nominative form of an article or noun is used as the subject of a verb, the accusative is for the direct object, the genitive is translated with the word of, and the dative with to/for. Why do nouns in German have gender? Probably because prehistoric man didn't distinguish between animate and inanimate. How interesting too, that females are not considered to have feminine gender until they marry (die Frau, feminine, compared to das Fraeulein, neuter).
b. The Definite Article (PDF page 37 in the grammar, to be memorized). One should learn all the possibilities for each form. It would have been easy to establish a different form for each gender-case-number designation but for some reason the German language recycles only six forms (der, die, des, dem, den, die) for 16 different designations. Certainly there is a potential for confusion there. You have to be thoroughly familiar with that.
c. Paradigms of various types of noun (to be memorized). This covered most of the material on PDF pages 47-48, with only Herr and Herzen excluded.
d. Nominative forms of the personal pronoun and the present indicative conjugation of Sein.
The student agreed to memorize the declensions of der Tisch, das Bein, die Hand, die Mutter, die Tochter, das Maedchen, der Geist, das Dorf, das Lied, der Mast, der Schmerz, das Auge, der Graf, der Affe, and die Frau, and the definite article. I told him to be able to name the possible gender, case, and number identifications for each form with or without an accompanying definite article. He also agreed to memorize the present, active, indicative conjugation of sein. It seems enough to keep somebody studying for a week. I promised to introduce some similarly declined nouns from Haeckel's vocabulary in the next session.