= Solution
Write $R$ for the current growing chain. <Propene> first binds at the available site of $[\mathrm{Cp_2ZrR}]^+$, giving a coordinated <alkene> adjacent to the <metal>-bound chain. In the <Cossee-Arlman mechanism>, the chain migrates to the substituted <alkene> <carbon> while the terminal <carbon> forms the new Zr–C bond:
$$
[\mathrm{Cp_2Zr{-}R}]^++\mathrm{CH_2{=}CHMe}
\rightleftharpoons[\mathrm{Cp_2Zr(R)(\eta^2\! -CH_2{=}CHMe)}]^+
\longrightarrow[\mathrm{Cp_2Zr{-}CH_2{-}CH(Me){-}R}]^+.
$$
The <electron-pair arrows> for insertion take the old Zr–R bond toward the substituted <alkene> <carbon> and the <alkene> <pi bond> toward the new Zr–terminal-<carbon> bond. A four-center arrangement permits both bonds to change in one <migratory insertion>; Zr remains Zr(IV). The product again has an accessible site, so coordination and insertion can repeat.
\b[Predominant 1,2 insertion leaves a primary Zr–CH$_2$ chain end and generates head-to-tail <polypropylene>.] It avoids the more crowded alternative secondary Zr–CH(Me) end and unfavorable methyl contacts with the <cyclopentadienyl ligands> in the insertion geometry. This explains <regioselectivity>. An unbridged, unsubstituted zirconocene does not by itself establish a fixed <tacticity>; the schematic alignment of methyl groups in a <polymer> drawing is not evidence for an isotactic product.
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