Souvenir of School District No. 4, Prairie Gem, Taylor County, Iowa, February 24, 1899.
Pupils [note: they're not listed in alphabetical order]
From online research, hopefully correct: [corrections welcome!]
Teacher Brosie Hanshaw may have been George Ambrose Hanshaw (1878-1952), born 15 March 1878 at Platteville, Iowa, the son of James Smith Hanshaw and wife Elizabeth Ann (Simes or Simms) Hanshaw.
George Ambrose Hanshaw had a younger sister Rebecca Maud Hanshaw. Note that one of the students listed is Maud Hanshaw.
On 24 December 1903 at New Market, Iowa, George Ambrose Hanshaw married Sadie Berniece Peterson (1880-1907), daughter of Peter (or Peto) and Anna (Mangel) Peterson. Sadly, Sadie died as a result of childbirth in 1907. The child, a son, Claude DeVoe Hanshaw, died not long after his birth.
On 20 June 1909 at New Market, Iowa, George Ambrose Hanshaw married Elma Edith Marsell (1884-1924). She was the daughter of John Joseph Marsell and Sarah Jane (Henry) Marsell, born in Vermont and Iowa, respectively.
The director, W. E. McAlpin, shown on the cover, was presumably William Eugene McAlpin. He and wife Amanda (Weaver) McAlpin were the parents of three of the students listed: Nettie McAlpin, Agatha McAlpin and Earl McAlpin.
If you have corrections and/or information to share, please leave a comment for the benefit of other researchers.