Each child is called out of class to spend around 20 minutes with one of the Rotary Readers.
They bring a pile of books with them, and can choose which one to read. Usually the children will read one book then, if they want, the reader will read another book to them.
The pupils clearly enjoy the one-on-one interaction with an adult. I went into one class to ask the teacher for the list of students who would be reading that day, and the entire class suddenly sprang to attention, every single child sitting upright with arms folded, willing the teacher to pick him or her.
Some of the children are extremely focused on their reading - one 8-year-old girl who read to me didn't hesitate over words like "irresistible" and "unfortunately" - while others were more easily distracted.
That included the young boy who plopped down next to me, thumping his book on my knee and declaring, "I can't read, you'll have to read to me." (He ended up reading me two books.)
The Wanganui East School Rotary Readers is a small but dedicated group that spends every Tuesday morning at the school. In all there are nearly 80 Rotary Readers in 13 Wanganui schools.
The co-ordinator of the Wanganui East Rotary Readers, Ann Petherick, said every child had the chance to read with the Rotary Readers, but the focus was on those who would benefit most from it.
"Some children don't ever have the opportunity to read to an adult at home," she said.
She said the programme was about building relationships with the children, and helped to give them confidence in their reading.
Mrs Petherick said the programme was started by Rotary because it was felt that many children didn't have male role models in their lives. The programme's early volunteers were men, but now women are involved as well. Not all of them are Rotary members - anyone can be a volunteer.
Mrs Petherick has been a volunteer for four years, and she loves it.
"It's so satisfying to see how the kids progress over time."