Hi, I'd say you are, PETTER>MATHIAS Sr>JOHN C.
I have everything in storage and have nothing on hand but a slight TEACH chart on this computer ----- all this chart has is your JOHN C TEACH b1798, so sorry.
it has his siblings were Mathias Jr 1801 and Catherine 1793-1880 (Fulton Co IL), Daniel --no dates-- , and Jacob 1785-1857 ( Franklin Co IL) and my own Peter 1790-1873 (Fulton Co IL).
for their father it has Mathia Sr, son of Petter Teach (Dietz) immigrant on the Bilender Thistle 1738 to PA.
sure hope this helps, there are a lot of TEACH genealogists putting messages here and on familytreemaker genforum who can help too.